Index: .hgtags =================================================================== --- .hgtags (revision 3697) +++ .hgtags (revision 3472) @@ -84,3 +84,2 @@ 25adb2b4a6d4a2266a3ffad26fff59d2adef5d7e sage-2.2 36198dd0dfa2d81d3b1ed7a15d5323b566c92667 sage-2.2-rc1 -383ce31836f8af9625436c803e7649797dfce9dd 2.4.1.3 Index: MANIFEST.in =================================================================== --- MANIFEST.in (revision 3698) +++ MANIFEST.in (revision 3115) @@ -1,2 +1,2 @@ -recursive-include * *.c *.h *.pyx *.pyxe *.pxd *.pxi *.cc *.txt *.tex *.i *.d 00* +recursive-include * *.c *.h *.pyx *.pyxe *.pxd *.pxi *.cc *.txt *.tex *.i 00* include install sage-push spkg-dist spkg-install MANIFEST.in README.txt .hgignore .hg .hg/* bundle export mercurial-howto.txt pull test_changed Index: sage/algebras/free_algebra.py =================================================================== --- sage/algebras/free_algebra.py (revision 4007) +++ sage/algebras/free_algebra.py (revision 1860) @@ -13,26 +13,4 @@ sage: G.base_ring() Free Algebra on 3 generators (x, y, z) over Integer Ring - -TESTS: - sage: F = FreeAlgebra(GF(5),3,'x') - sage: F == loads(dumps(F)) - True - - sage: F. = FreeAlgebra(GF(5),3) - sage: F == loads(dumps(F)) - True - - sage: F = FreeAlgebra(GF(5),3, ['xx', 'zba', 'Y']) - sage: F == loads(dumps(F)) - True - - sage: F = FreeAlgebra(GF(5),3, 'abc') - sage: F == loads(dumps(F)) - True - - sage: F = FreeAlgebra(FreeAlgebra(ZZ,1,'a'), 2, 'x') - sage: F == loads(dumps(F)) - True - """ @@ -220,5 +198,5 @@ if P is self: return x - if not (P is self.base_ring()): + if not (P == self.base_ring()): return FreeAlgebraElement(self, x) # ok, not a free algebra element (or should not be viewed as one). @@ -226,5 +204,5 @@ R = self.base_ring() # coercion from free monoid - if isinstance(x, FreeMonoidElement) and x.parent() is F: + if isinstance(x, FreeMonoidElement) and x.parent() == F: return FreeAlgebraElement(self,{x:R(1)}) # coercion via base ring @@ -290,5 +268,5 @@ # monoid - if R is self.__monoid: + if R == self.__monoid: return self(x) Index: sage/algebras/free_algebra_element.py =================================================================== --- sage/algebras/free_algebra_element.py (revision 4007) +++ sage/algebras/free_algebra_element.py (revision 1859) @@ -3,9 +3,4 @@ AUTHOR: David Kohel, 2005-09 - -TESTS: - sage: R. = FreeAlgebra(QQ,2) - sage: x == loads(dumps(x)) - True """ @@ -49,5 +44,5 @@ self.__monomial_coefficients = { x:R(1) } elif True: - self.__monomial_coefficients = dict([ (A.monoid()(e1),R(e2)) for e1,e2 in x.items()]) + self.__monomial_coefficients = x else: raise TypeError, "Argument x (= %s) is of the wrong type."%x Index: sage/algebras/free_algebra_quotient.py =================================================================== --- sage/algebras/free_algebra_quotient.py (revision 4006) +++ sage/algebras/free_algebra_quotient.py (revision 1840) @@ -1,19 +1,4 @@ """ Free algebra quotients - -TESTS: - sage: n = 2 - sage: A = FreeAlgebra(QQ,n,'x') - sage: F = A.monoid() - sage: i, j = F.gens() - sage: mons = [ F(1), i, j, i*j ] - sage: r = len(mons) - sage: M = MatrixSpace(QQ,r) - sage: mats = [M([0,1,0,0, -1,0,0,0, 0,0,0,-1, 0,0,1,0]), M([0,0,1,0, 0,0,0,1, -1,0,0,0, 0,-1,0,0]) ] - sage: H2. = A.quotient(mons,mats) - sage: H2 == loads(dumps(H2)) - True - sage: i == loads(dumps(i)) - True """ @@ -104,13 +89,4 @@ ParentWithGens.__init__(self, R, names, normalize=False) - def __eq__(self,right): - return type(self) == type(right) and \ - self.ngens() == right.ngens() and \ - self.rank() == right.rank() and \ - self.module() == right.module() and \ - self.matrix_action() == right.matrix_action() and \ - self.monomial_basis() == right.monomial_basis() - - def __call__(self, x): if isinstance(x, FreeAlgebraQuotientElement) and x.parent() is self: @@ -163,10 +139,4 @@ return self.__dim - def matrix_action(self): - return self.__matrix_action - - def monomial_basis(self): - return self.__monomial_basis - def rank(self): """ Index: sage/algebras/free_algebra_quotient_element.py =================================================================== --- sage/algebras/free_algebra_quotient_element.py (revision 4008) +++ sage/algebras/free_algebra_quotient_element.py (revision 1855) @@ -46,11 +46,6 @@ if isinstance(x, FreeAlgebraQuotientElement) and x.parent() is A: return x - AlgebraElement.__init__(self, A) Q = self.parent() - - if isinstance(x, FreeAlgebraQuotientElement) and x.parent() == Q: - self.__vector = Q.module()(x.vector()) - return if isinstance(x, (int, long, Integer)): self.__vector = Q.module().gen(0) * x @@ -109,10 +104,7 @@ else: return x - + def vector(self): return self.__vector - - def __cmp__(self, right): - return cmp(self.vector(),right.vector()) def __neg__(self): Index: sage/algebras/quaternion_algebra.py =================================================================== --- sage/algebras/quaternion_algebra.py (revision 4013) +++ sage/algebras/quaternion_algebra.py (revision 4068) @@ -3,13 +3,4 @@ AUTHOR: David Kohel, 2005-09 - -TESTS: - sage: A = QuaternionAlgebra(QQ, -1,-1, names=list('ijk')) - sage: A == loads(dumps(A)) - True - sage: i, j, k = A.gens() - sage: i == loads(dumps(i)) - True - """ @@ -40,5 +31,5 @@ from sage.algebras.algebra_element import AlgebraElement from sage.algebras.free_algebra_quotient_element import FreeAlgebraQuotientElement -from sage.algebras.quaternion_algebra_element import QuaternionAlgebraElement, QuaternionAlgebraElement_fast +from sage.algebras.quaternion_algebra_element import QuaternionAlgebraElement import weakref @@ -120,5 +111,5 @@ _cache = {} -def QuaternionAlgebra(K, a, b, names, denom=1): +def QuaternionAlgebra(K, a, b, names=['i','j','k'], denom=1): """ Return the quaternion algebra over $K$ generated by $i$, $j$, and $k$ @@ -150,4 +141,16 @@ raise ValueError, "Base ring K (= %s) must be a field."%K + if K(2) == 0: + raise ValueError, "Base ring K (= %s) must be a field of characteristic different from 2."%K + + try: + a = K(a) + except TypeError: + raise ValueError, "Arguments a = %s and b = %s must coerce into K (= %s)."%(a,b,K) + try: + b = K(b) + except TypeError: + raise ValueError, "Arguments a = %s and b = %s must coerce into K (= %s)."%(a,b,K) + if a == 0 or b == 0: raise ValueError, "Arguments a = %s and b = %s must be nonzero."%(a,b) @@ -168,7 +171,7 @@ if K is RationalField(): prms = ramified_primes(a,b) - H = QuaternionAlgebra_generic(K, prms) + H = QuaternionAlgebra_generic(K, [2,0,0,0], prms) else: - H = QuaternionAlgebra_generic(K) + H = QuaternionAlgebra_generic(K, [2,0,0,0]) A = FreeAlgebra(K,3, names=names) F = A.monoid() @@ -231,5 +234,5 @@ vki = V([ -t13, t3, 0, t1 ]) - vik vjk = V([ -t23, 0, t3, t2 ]) - vkj - H = QuaternionAlgebra_generic(K) + H = QuaternionAlgebra_generic(K, [2,t1,t2,t3]) A = FreeAlgebra(K,3, names=names) F = A.monoid() @@ -254,5 +257,5 @@ return QuaternionAlgebraWithInnerProduct(K,norms,traces,names=names) -def QuaternionAlgebraWithDiscriminants(D1, D2, T, names, M=2): +def QuaternionAlgebraWithDiscriminants(D1, D2, T, names=['i','j','k'], M=2): r""" Return the quaternion algebra over the rationals generated by $i$, @@ -315,8 +318,9 @@ mj = MQ([0,0,1,0, 0,0,0,1, -n2,0,t2,0, 0,-n2,0,t2]) # N.B. mk = mi*mj - mk = MQ([0,0,0,1, 0,0,-n1,t1, -n2*t1,n2,t1*t2-t12,0, -n1*n2,0,0,t1*t2-t12]) + t3 = t1*t2-t12 + mk = MQ([0,0,0,1, 0,0,-n1,t1, -n2*t1,n2,t3,0, -n1*n2,0,0,t3]) mats = [ mi, mj, mk ] prms = ramified_primes_from_discs(D1,D2,T) - H = QuaternionAlgebra_generic(QQ, prms) + H = QuaternionAlgebra_generic(QQ, [2,t1,t2,t3], prms) A = FreeAlgebra(QQ,3, names=names) F = A.monoid() @@ -327,21 +331,17 @@ class QuaternionAlgebra_generic(FreeAlgebraQuotient): - def __init__(self, K, ramified_primes=None): - """ - """ - self.__vector_space = VectorSpace(K,4) + def __init__(self, K, basis_traces = None, ramified_primes=None): + """ + """ if ramified_primes != None: - self.__ramified_primes = ramified_primes + self._ramified_primes = ramified_primes + if basis_traces != None: + self._basis_traces = basis_traces def __call__(self, x): - if hasattr(self, 'discriminants'): - if isinstance(x, QuaternionAlgebraElement_fast) and x.parent() is self: - return x - return QuaternionAlgebraElement_fast(self,x) - else: - if isinstance(x, QuaternionAlgebraElement) and x.parent() is self: - return x - return QuaternionAlgebraElement(self,x) - + if isinstance(x, QuaternionAlgebraElement) and x.parent() is self: + return x + return QuaternionAlgebraElement(self,x) + def __repr__(self): return "Quaternion algebra with generators %s over %s"%( @@ -366,21 +366,22 @@ def gram_matrix(self): - V = self.__vector_space - if not V._FreeModule_generic__inner_product_is_dot_product: - return V.inner_product_matrix() - K = self.base_ring() - M = MatrixSpace(K,4)(0) - B = self.basis() - for i in range(4): - x = B[i] - M[i,i] = 2*(x.reduced_norm()) - for j in range(i+1,4): - y = B[j] - c = (x * y.conjugate()).reduced_trace() - M[i,j] = c - M[j,i] = c - # TODO: Make it so one can correctly set these things. - V._FreeModule_generic__inner_product_is_dot_product = False - V._FreeModule_generic__inner_product_matrix = M + """ + The Gram matrix of the inner product determined by the norm. + """ + try: + M = self.__vector_space.inner_product_matrix() + except: + K = self.base_ring() + M = MatrixSpace(K,4)(0) + B = self.basis() + for i in range(4): + x = B[i] + M[i,i] = 2*(x.reduced_norm()) + for j in range(i+1,4): + y = B[j] + c = (x * y.conjugate()).reduced_trace() + M[i,j] = c + M[j,i] = c + self.__vector_space = VectorSpace(K,4,inner_product_matrix = M) return M @@ -397,10 +398,7 @@ return False - def _set_ramified_primes(self, prms): - self.__ramified_primes = prms - def ramified_primes(self): try: - return self.__ramified_primes + return self._ramified_primes except: raise AttributeError, "Ramified primes have not been computed." @@ -411,21 +409,9 @@ def vector_space(self): - V = self.__vector_space try: - _ = V._FreeModule_generic__inner_product_matrix + V = self.__vector_space except: - V._FreeModule_generic__inner_product_matrix = self.gram_matrix() - return self.__vector_space - - -def QuaternionAlgebra_fast(K, a, b, names="ijk"): - H = QuaternionAlgebra(K, a, b, names) - H.discriminants = (a,b) - return H - -class QuaternionAlgebra_faster(QuaternionAlgebra_generic): - - def __call__(self, x): - if isinstance(x, QuaternionAlgebraElement_fast) and x.parent() is self: - return x - return QuaternionAlgebraElement_fast(self,x) + M = self.gram_matrix() # induces construction of V + V = self.__vector_space + return V + Index: sage/algebras/quaternion_algebra_element.py =================================================================== --- sage/algebras/quaternion_algebra_element.py (revision 3727) +++ sage/algebras/quaternion_algebra_element.py (revision 1859) @@ -37,5 +37,5 @@ def conjugate(self): - return self.parent()(self.reduced_trace()) - self + return self.parent()(self.reduced_trace()) - self def reduced_trace(self): @@ -96,36 +96,2 @@ minimal_polynomial = minpoly - - -class QuaternionAlgebraElement_fast(QuaternionAlgebraElement): - - def __init__(self, H, x): - FreeAlgebraQuotientElement.__init__(self, H, x) - if isinstance(x, list): - self._list = list(self.vector()) - else: - self._list = x - - def _add_(self, other): - return QuaternionAlgebraElement_fast(self.parent(), [self._list[i] + other._list[i] for i in range(4)]) - - def _sub_(self, other): - return QuaternionAlgebraElement_fast(self.parent(), [self._list[i] - other._list[i] for i in range(4)]) - - def _neg_(self, other): - return QuaternionAlgebraElement_fast(self.parent(), [-r for r in self._list]) - - def _mul_(self, other): - d1, d2 = self.parent().discriminants - a = self._list - b = other._list - return QuaternionAlgebraElement_fast(self.parent(), - [a[0]*b[0] + d1*a[1]*b[1] + d2*a[2]*b[2] - d1*d2*a[3]*b[3], - a[0]*b[1] + a[1]*b[0] + d2*a[3]*b[1] - d2*a[2]*b[3], - a[0]*b[2] + a[2]*b[0] + d1*a[1]*b[3] - d1*a[3]*b[1], - a[0]*b[3] + a[3]*b[0] + a[1]*b[2] - a[2]*b[1]]) - - def conjugate(self): - return QuaternionAlgebraElement_fast(self.parent(), [self._list[0], -self._list[1], -self._list[2], -self._list[3]]) - - Index: sage/all.py =================================================================== --- sage/all.py (revision 4016) +++ sage/all.py (revision 3634) @@ -30,11 +30,17 @@ import os, sys -if not os.environ.has_key('SAGE_ROOT'): - raise RuntimeError, "To use the SAGE libraries, set the environment variable SAGE_ROOT to the SAGE build directory and LD_LIBRARY_PATH to $SAGE_ROOT/local/lib" - if sys.version_info[:2] < (2, 5): print >>sys.stderr, "SAGE requires Python 2.5 or newer" sys.exit(1) +try: + _l = '%s/local/lib'%os.environ['SAGE_ROOT'] + if os.environ.has_key('LD_LIBRARY_PATH'): + if not _l in os.environ['LD_LIBRARY_PATH']: + raise KeyError + del _l +except KeyError, msg: + raise RuntimeError, "To use the SAGE libraries, set the environment variable SAGE_ROOT to the SAGE build directory and LD_LIBRARY_PATH to $SAGE_ROOT/local/lib" + ################################################################### @@ -71,5 +77,5 @@ from sage.interfaces.all import * from sage.functions.all import * -from sage.calculus.all import * +#from sage.calculus.all import * from sage.server.all import * from sage.dsage.all import * @@ -114,4 +120,5 @@ # very useful 2-letter shortcuts CC = ComplexField() +I = CC.gen(0) QQ = RationalField() RR = RealField() # default real field @@ -135,5 +142,5 @@ oo = infinity -#x = PolynomialRing(QQ,'x').gen() +x = PolynomialRing(QQ,'x').gen() # grab signal handling back from PARI or other C libraries Index: sage/calculus/all.py =================================================================== --- sage/calculus/all.py (revision 4063) +++ sage/calculus/all.py (revision 2327) @@ -1,78 +1,7 @@ -from equations import SymbolicEquation, forget, assume, assumptions, solve - -from calculus import (SymbolicExpressionRing, - is_SymbolicExpressionRing, - is_SymbolicExpression, - CallableSymbolicExpressionRing, - is_CallableSymbolicExpressionRing, - is_CallableSymbolicExpression, - SR, - sin, cos, sec, tan, log, erf, sqrt, asin, acos, atan, - tanh, sinh, cosh, coth, sech, csch, ln, - ceil, floor, - abs_symbolic, exp, - is_SymbolicExpression, - is_SymbolicExpressionRing) +from calculus import (SER, + var, + sin, cos, sec, + x, y, z, w, t) -from functional import (diff, derivative, - laplace, inverse_laplace, - expand, - integrate, limit, lim, - taylor, simplify) - -from var import (var, function) - -from predefined import (a, - b, - c, - d, - f, - g, - h, - i, - j, - k, - l, - m, - n, - o, - p, - q, - r, - s, - t, - u, - v, - w, - x, - y, - z, - A, - B, - C, - D, - E, - F, - G, - H, - J, - K, - L, - M, - N, - P, - Q, - R, - S, - T, - U, - V, - W, - X, - Y, - Z) - -def symbolic_expression(x): - return SR(x) - +from functional import diff Index: sage/calculus/calculus.py =================================================================== --- sage/calculus/calculus.py (revision 4065) +++ sage/calculus/calculus.py (revision 2630) @@ -1,186 +1,9 @@ -r""" -Symbolic Computation. - -AUTHORS: - Bobby Moretti and William Stein: 2006--2007 - -The \sage calculus module is loosely based on the \sage Enhahcement Proposal -found at: http://www.sagemath.org:9001/CalculusSEP. - -EXAMPLES: - - The basic units of the calculus package are symbolic expressions - which are elements of the symbolic expression ring (SR). There are - many subclasses of SymbolicExpression. The most basic of these is - the formal indeterminate class, SymbolicVariable. To create a - SymbolicVariable object in \sage, use the var() method, whose - argument is the text of that variable. Note that \sage is - intelligent about {\latex}ing variable names. - - sage: x1 = var('x1'); x1 - x1 - sage: latex(x1) - \mbox{x}_{1} - sage: theta = var('theta'); theta - theta - sage: latex(theta) - \theta - - \sage predefines upper and lowercase letters as global - indeterminates. Thus the following works: - sage: x^2 - x^2 - sage: type(x) - - - More complicated expressions in SAGE can be built up using - ordinary arithmetic. The following are valid, and follow the rules - of Python arithmetic: (The '=' operator represents assignment, and - not equality) - sage: f = x + y + z/(2*sin(y*z/55)) - sage: g = f^f; g - (z/(2*sin(y*z/55)) + y + x)^(z/(2*sin(y*z/55)) + y + x) - - Differentiation and integration are available, but behind the - scenes through maxima: - - sage: f = sin(x)/cos(2*y) - sage: f.derivative(y) - 2*sin(x)*sin(2*y)/(cos(2*y)^2) - sage: g = f.integral(x); g - -cos(x)/(cos(2*y)) - - Note that these methods require an explicit variable name. If none - is given, \sage will try to find one for you. - sage: f = sin(x); f.derivative() - cos(x) - - However when this is ambiguous, \sage will raise an exception: - sage: f = sin(x+y); f.derivative() - Traceback (most recent call last): - ... - ValueError: must supply an explicit variable for an expression containing more than one variable - - Substitution works similarly. We can substitute with a python dict: - sage: f = sin(x*y - z) - sage: f({x: t, y: z}) - sin(t*z - z) - - Also we can substitute with keywords: - sage: f = sin(x*y - z) - sage: f(x = t, y = z) - sin(t*z - z) - - If there is no ambiguity of variable names, we don't have to specify them: - sage: f = sin(x) - sage: f(y) - sin(y) - sage: f(pi) - 0 - - However if there is ambiguity, we must explicitly state what - variables we're substituting for: - - sage: f = sin(2*pi*x/y) - sage: f(4) - sin(8*pi/y) - - We can also make CallableSymbolicExpressions, which is a SymbolicExpression - that are functions of variables in a fixed order. Each - SymbolicExpression has a function() method used to create a - CallableSymbolicExpression. - - sage: u = log((2-x)/(y+5)) - sage: f = u.function(x, y); f - (x, y) |--> log((2 - x)/(y + 5)) - - There is an easier way of creating a CallableSymbolicExpression, which - relies on the \sage preparser. - - sage: f(x,y) = log(x)*cos(y); f - (x, y) |--> log(x)*cos(y) - - Then we have fixed an order of variables and there is no ambiguity - substituting or evaluating: - - sage: f(x,y) = log((2-x)/(y+5)) - sage: f(7,t) - log(-5/(t + 5)) - - Some further examples: - - sage: f = 5*sin(x) - sage: f - 5*sin(x) - sage: f(2) - 5*sin(2) - sage: f(pi) - 0 - sage: float(f(pi)) # random low order bits - 6.1232339957367663e-16 - -COERCION EXAMPLES: - -We coerce various symbolic expressions into the complex numbers: - - sage: CC(I) - 1.00000000000000*I - sage: CC(2*I) - 2.00000000000000*I - sage: ComplexField(200)(2*I) - 2.0000000000000000000000000000000000000000000000000000000000*I - sage: ComplexField(200)(sin(I)) - 1.1752011936438014568823818505956008151557179813340958702296*I - sage: f = sin(I) + cos(I/2); f - I*sinh(1) + cosh(1/2) - sage: CC(f) - 1.12762596520638 + 1.17520119364380*I - sage: ComplexField(200)(f) - 1.1276259652063807852262251614026720125478471180986674836290 + 1.1752011936438014568823818505956008151557179813340958702296*I - sage: ComplexField(100)(f) - 1.1276259652063807852262251614 + 1.1752011936438014568823818506*I - -We illustrate construction of an inverse sum where each denominator -has a new variable name: - sage: f = sum(1/var('n%s'%i)^i for i in range(10)) - sage: print f - 1 1 1 1 1 1 1 1 1 - --- + --- + --- + --- + --- + --- + --- + --- + -- + 1 - 9 8 7 6 5 4 3 2 n1 - n9 n8 n7 n6 n5 n4 n3 n2 - -Note that after calling var, the variables are immediately available for use: - sage: (n1 + n2)^5 - (n2 + n1)^5 - -We can, of course, substitute: - sage: print f(n9=9,n7=n6) - 1 1 1 1 1 1 1 1 387420490 - --- + --- + --- + --- + --- + --- + --- + -- + --------- - 8 6 7 5 4 3 2 n1 387420489 - n8 n6 n6 n5 n4 n3 n2 - -TESTS: -We test pickling: - sage: f = -sqrt(pi)*(x^3 + sin(x/cos(y))) - sage: bool(loads(dumps(f)) == f) - True - -Substitution: - sage: f = x - sage: f(x=5) - 5 - -""" - -import weakref +"""nodoctest""" from sage.rings.all import (CommutativeRing, RealField, is_Polynomial, - is_MPolynomial, is_MPolynomialRing, is_RealNumber, is_ComplexNumber, RR, - Integer, Rational, CC, - PolynomialRing) - -from sage.structure.element import RingElement, is_Element + Integer, Rational, CC) +#import sage.rings.rational +from sage.structure.element import RingElement from sage.structure.parent_base import ParentWithBase @@ -194,62 +17,12 @@ from sage.misc.sage_eval import sage_eval -from sage.calculus.equations import SymbolicEquation -from sage.rings.real_mpfr import RealNumber -from sage.rings.complex_number import ComplexNumber -from sage.rings.real_double import RealDoubleElement -from sage.rings.complex_double import ComplexDoubleElement -from sage.rings.real_mpfi import RealIntervalFieldElement -from sage.rings.infinity import InfinityElement - -from sage.libs.pari.gen import pari, gen as PariGen - -from sage.rings.complex_double import ComplexDoubleElement - -import sage.functions.constants - -import math - -is_simplified = False - -infixops = {operator.add: '+', - operator.sub: '-', - operator.mul: '*', - operator.div: '/', - operator.pow: '^'} - - -def is_SymbolicExpression(x): - """ - EXAMPLES: - sage: is_SymbolicExpression(sin(x)) - True - sage: is_SymbolicExpression(2/3) - False - sage: is_SymbolicExpression(sqrt(2)) - True - """ - return isinstance(x, SymbolicExpression) - -def is_SymbolicExpressionRing(x): - """ - EXAMPLES: - sage: is_SymbolicExpressionRing(QQ) - False - sage: is_SymbolicExpressionRing(SR) - True - """ - return isinstance(x, SymbolicExpressionRing_class) - - +from sage.functions.constants import Constant +import sage.functions.constants as c + +# There will only ever be one instance of this class class SymbolicExpressionRing_class(CommutativeRing): - """ - The ring of all formal symbolic expressions. - - EXAMPLES: - sage: SR - Symbolic Ring - sage: type(SR) - - """ + ''' + A Ring of formal expressions. + ''' def __init__(self): self._default_precision = 53 # default precision bits @@ -257,32 +30,8 @@ def __call__(self, x): - """ - Coerce x into the symbolic expression ring SR. - - EXAMPLES: - sage: a = SR(-3/4); a - -3/4 - sage: type(a) - - sage: a.parent() - Symbolic Ring - - If a is already in the symblic expression ring, coercing returns - a itself (not a copy): - sage: SR(a) is a - True - - A Python complex number: - sage: SR(complex(2,-3)) - 2.00000000000000 - 3.00000000000000*I - """ - if is_Element(x) and x.parent() is self: - return x - elif hasattr(x, '_symbolic_'): - return x._symbolic_(self) return self._coerce_impl(x) def _coerce_impl(self, x): - if isinstance(x, CallableSymbolicExpression): + if isinstance(x, CallableFunction): return x._expr elif isinstance(x, SymbolicExpression): @@ -290,33 +39,16 @@ elif isinstance(x, MaximaElement): return symbolic_expression_from_maxima_element(x) - elif is_Polynomial(x) or is_MPolynomial(x): + elif is_Polynomial(x): return SymbolicPolynomial(x) - elif isinstance(x, (RealNumber, - RealDoubleElement, - RealIntervalFieldElement, - float, - sage.functions.constants.Constant, - Integer, - int, - Rational, - PariGen, - ComplexNumber, - ComplexDoubleElement, - InfinityElement - )): - return SymbolicConstant(x) - elif isinstance(x, complex): - return evaled_symbolic_expression_from_maxima_string('%s+%%i*%s'%(x.real,x.imag)) + elif isinstance(x, Integer): + return Constant_object(x) else: - raise TypeError, 'cannot coerce %s into a SymbolicExpression.'%x - - def _repr_(self): - return 'Symbolic Ring' - - def _latex_(self): - return 'SymbolicExpressionRing' - - def var(self, x): - return var(x) + return Symbolic_object(x) + + def _repr_(self): + return "Ring of Symbolic Expressions" + + def _latex_(self): + return "SymbolicExpressionRing" def characteristic(self): @@ -329,381 +61,88 @@ return True - def is_exact(self): - return False - -# Define the unique symbolic expression ring. -SR = SymbolicExpressionRing_class() - -# The factory function that returns the unique SR. -def SymbolicExpressionRing(): - """ - Return the symbolic expression ring. - - EXAMPLES: - sage: SymbolicExpressionRing() - Symbolic Ring - sage: SymbolicExpressionRing() is SR - True - """ - return SR +# ... and here it is: +SymbolicExpressionRing = SymbolicExpressionRing_class() +SER = SymbolicExpressionRing +# conversions is the dict of the form system:command class SymbolicExpression(RingElement): """ A Symbolic Expression. - - EXAMPLES: - """ - def __init__(self): - RingElement.__init__(self, SR) - if is_simplified: - self._simp = self - - def __nonzero__(self): - # Best to error on side of being nonzero in most cases. - return not bool(self == SR.zero_element()) - - def __str__(self): - """ - Printing an object explicitly gives ASCII art: - - EXAMPLES: - sage: f = y^2/(y+1)^3 + x/(x-1)^3 - sage: f - y^2/(y + 1)^3 + x/(x - 1)^3 - sage: print f - 2 - y x - -------- + -------- - 3 3 - (y + 1) (x - 1) - - """ - return self.display2d(onscreen=False) - - def display2d(self, onscreen=True): - """ - Display self using ASCII art. - - INPUT: - onscreen -- string (optional, default True) If True, - displays; if False, returns string. - - EXAMPLES: - We display a fraction: - sage: f = (x^3+y)/(x+3*y^2+1); f - (y + x^3)/(3*y^2 + x + 1) - sage: print f - 3 - y + x - ------------ - 2 - 3 y + x + 1 - - Use onscreen=False to get the 2d string: - sage: f.display2d(onscreen=False) - '\t\t\t\t\t 3\r\n\t\t\t\t y + x\r\n \t\t\t ------------\r\n\t\t\t\t 2\r\n\t\t\t\t 3 y + x + 1' - - ASCII art is really helps for the following integral: - sage: f = integral(sin(x^2)); f - sqrt(pi)*((sqrt(2)*I + sqrt(2))*erf((sqrt(2)*I + sqrt(2))*x/2) + (sqrt(2)*I - sqrt(2))*erf((sqrt(2)*I - sqrt(2))*x/2))/8 - sage: print f - (sqrt(2) I + sqrt(2)) x - sqrt( pi) ((sqrt(2) I + sqrt(2)) erf(------------------------) - 2 - (sqrt(2) I - sqrt(2)) x - + (sqrt(2) I - sqrt(2)) erf(------------------------))/8 - 2 - """ - s = self._maxima_().display2d(onscreen=False) - s = s.replace('%pi',' pi').replace('%i',' I').replace('%e', ' e') - if onscreen: - print s - else: - return s - - def is_simplified(self): - return hasattr(self, '_simp') and self._simp is self - - def _declare_simplified(self): - self._simp = self - - def hash(self): - return hash(self._repr_(simplify=False)) - - def plot(self, *args, **kwds): - from sage.plot.plot import plot - - # see if the user passed a variable in. - if kwds.has_key('param'): - param = kwds['param'] - else: - param = None - for i in range(len(args)): - if isinstance(args[i], SymbolicVariable): - param = args[i] - args = args[:i] + args[i+1:] - break - - F = self.simplify() - if isinstance(F, Symbolic_object): - if hasattr(F._obj, '__call__'): - f = lambda x: F._obj(x) - else: - y = float(F._obj) - f = lambda x: y - - elif param is None: - if isinstance(self, CallableSymbolicExpression): - A = self.arguments() - if len(A) == 0: - raise ValueError, "function has no input arguments" - else: - param = A[0] - f = lambda x: self(x) - else: - A = self.variables() - if len(A) == 0: - y = float(self) - f = lambda x: y - else: - param = A[0] - f = self.function(param) - else: - f = self.function(param) - return plot(f, *args, **kwds) - - def __lt__(self, right): - return SymbolicEquation(self, SR(right), operator.lt) - - def __le__(self, right): - return SymbolicEquation(self, SR(right), operator.le) - - def __eq__(self, right): - return SymbolicEquation(self, SR(right), operator.eq) - - def __ne__(self, right): - return SymbolicEquation(self, SR(right), operator.ne) - - def __ge__(self, right): - return SymbolicEquation(self, SR(right), operator.ge) - - def __gt__(self, right): - return SymbolicEquation(self, SR(right), operator.gt) + def __init__(self, conversions={}): + RingElement.__init__(self, SymbolicExpressionRing) + + def _maxima_(self, maxima=maxima): + try: + return self.__maxima + except AttributeError: + m = maxima(self._maxima_init_()) + self.__maxima = m + return m + + def _neg_(self): + return SymbolicArithmetic([self], operator.neg) def __cmp__(self, right): - """ - Compares self and right. - - This is by definition the comparison of the underlying Maxima - objects. - - EXAMPLES: - These two are equal: - sage: cmp(e+e, e*2) - 0 - """ return cmp(maxima(self), maxima(right)) - - def _neg_(self): - """ - Return the formal negative of self. - - EXAMPLES: - sage: -a - -a - sage: -(x+y) - -y - x - """ - return SymbolicArithmetic([self], operator.neg) - - ################################################################## - # Coercions to interfaces - ################################################################## - # The maxima one is special: - def _maxima_init_(self): - return self._repr_(simplify=False) - - - # The others all go through _sys_init_, which is defined below, - # and does all interfaces in a unified manner. - - def _axiom_init_(self): - return self._sys_init_('axiom') - - def _gp_init_(self): - return self._sys_init_('pari') # yes, gp goes through pari - - def _maple_init_(self): - return self._sys_init_('maple') - - def _magma_init_(self): - return '"%s"'%self.str() - - def _kash_init_(self): - return self._sys_init_('kash') - - def _macaulay2_init_(self): - return self._sys_init_('macaulay2') - - def _mathematica_init_(self): - return self._sys_init_('mathematica') - - def _octave_init_(self): - return self._sys_init_('octave') - - def _pari_init_(self): - return self._sys_init_('pari') - - def _sys_init_(self, system): - return repr(self) - - ################################################################## - # These systems have no symbolic or numerical capabilities at all, - # really, so we always just coerce to a string - ################################################################## - def _gap_init_(self): - """ - Conversion of symbolic object to GAP always results in a GAP string. - - EXAMPLES: - sage: gap(e+pi^2 + x^3) - "x^3 + pi^2 + e" - """ - return '"%s"'%repr(self) - - def _singular_init_(self): - """ - Conversion of symbolic object to Singular always results in a Singular string. - - EXAMPLES: - sage: singular(e+pi^2 + x^3) - x^3 + pi^2 + e - """ - return '"%s"'%repr(self) - - ################################################################## - # Non-canonical coercions to compiled built-in rings and fields - ################################################################## - def __int__(self): - """ - EXAMPLES: - sage: int(sin(2)*100) - 90 - """ - try: - return int(repr(self)) - except (ValueError, TypeError): - return int(float(self)) - - def __long__(self): - """ - EXAMPLES: - sage: long(sin(2)*100) - 90L - """ - return long(int(self)) - - - def _mpfr_(self, field): - raise TypeError - - def _complex_mpfr_field_(self, field): - raise TypeError - - def _complex_double_(self, C): - raise TypeError - - def _real_double_(self, R): - raise TypeError - - def _rational_(self): - return Rational(repr(self)) - - def __abs__(self): - return abs_symbolic(self) - - def _integer_(self): - """ - EXAMPLES: - - """ - return Integer(repr(self)) - + def _add_(self, right): - """ - EXAMPLES: - sage: x + y - y + x - sage: x._add_(y) - y + x - """ - return SymbolicArithmetic([self, right], operator.add) + # if we are adding a negation, instead subtract the operand of negation + #if isinstance(right, SymbolicArithmetic): + # if right._operator is operator.neg: + # return SymbolicArithmetic([self, right._operands[0]], operator.sub) + #elif isinstance(right, Symbolic_object) and right < 0: + # return SymbolicArithmetic([self, SER(abs(right._obj))], operator.sub) + #else: + return SymbolicArithmetic([self, right], operator.add) def _sub_(self, right): - """ - EXAMPLES: - sage: x - y - x - y - """ return SymbolicArithmetic([self, right], operator.sub) def _mul_(self, right): - """ - EXAMPLES: - sage: x * y - x*y - """ + # do some simplification... pull out negatives from the operands and put it + # in front of this multiplication + #if isinstance(self, SymbolicArithmetic) and isinstance(right, SymbolicArithmetic): + # if self._operator is operator.neg and right._operator is operator.neg: + # s_unneg = self._operands[0] + # r_unneg = right._operands[0] + # return SymbolicArithmetic([s_unneg, r_unneg], operator.mul) + #if isinstance(self, SymbolicArithmetic): + # if self._operator is operator.neg and (not isinstance(right, SymbolicArithmetic) \ + # or not (right._operator is operator.neg)): + # s_unneg = self._operands[0] + # return -SymbolicArithmetic([s_unneg, right], operator.mul) + #if isinstance(right, SymbolicArithmetic): + # if not isinstance(self, SymbolicArithmetic) or (not (self._operator is operator.neg)) \ + # and right._operator is operator.neg: + # r_unneg = right._operands[0] + # return -SymbolicArithmetic([self, r_unneg], operator.mul) + return SymbolicArithmetic([self, right], operator.mul) def _div_(self, right): - """ - EXAMPLES: - sage: x / y - x/y - """ + # do some simplification... pull out negatives from the operands and put it + # in front of this division + #if isinstance(self, SymbolicArithmetic) and isinstance(right, SymbolicArithmetic): + # if self._operator is operator.neg and right._operator is operator.neg: + # s_unneg = self._operands[0] + # r_unneg = right._operands[0] + # return SymbolicArithmetic([s_unneg, r_unneg], operator.div) + #elif isinstance(self, SymbolicArithmetic): + # if self._operator is operator.neg and (not isinstance(right, SymbolicArithmetic) \ + # or not (right._operator is operator.neg)): + # s_unneg = self._operands[0] + # return -SymbolicArithmetic([s_unneg, right], operator.div) + #elif isinstance(right, SymbolicArithmetic): + # if not isinstance(self, SymbolicArithmetic) or (not (self._operator is operator.neg)) \ + # and right._operator is operator.neg: + # r_unneg = right._operands[0] + # return -SymbolicArithmetic([self, r_unneg], operator.div) + return SymbolicArithmetic([self, right], operator.div) def __pow__(self, right): - """ - EXAMPLES: - sage: x^(n+1) - x^(n + 1) - """ right = self.parent()(right) return SymbolicArithmetic([self, right], operator.pow) - - def variables(self, vars=tuple([])): - """ - Return sorted list of variables that occur in the simplified - form of self. - - OUTPUT: - a Python set - - EXAMPLES: - sage: f = x^(n+1) + sin(pi/19); f - x^(n + 1) + sin(pi/19) - sage: f.variables() - (n, x) - - sage: a = e^x - sage: a.variables() - (x,) - """ - return vars - - def _first_variable(self): - try: - return self.__first_variable - except AttributeError: - pass - v = self.variables() - if len(v) == 0: - ans = var('x') - else: - ans = v[0] - self.__first_variable = ans - return ans def _has_op(self, operator): @@ -747,166 +186,11 @@ - def __call__(self, dict=None, **kwds): - return self.substitute(dict, **kwds) - - def power_series(self, base_ring): - """ - Return algebraic power series associated to this symbolic - expression, which must be a polynomial in one variable, with - coefficients coercible to the base ring. - - The power series is truncated one more than the degree. - - EXAMPLES: - sage: var('theta') - theta - sage: f = theta^3 + (1/3)*theta - 17/3 - sage: g = f.power_series(QQ); g - -17/3 + 1/3*theta + theta^3 + O(theta^4) - sage: g^3 - -4913/27 + 289/9*theta - 17/9*theta^2 + 2602/27*theta^3 + O(theta^4) - sage: g.parent() - Power Series Ring in theta over Rational Field - """ - v = self.variables() - if len(v) != 1: - raise ValueError, "self must be a polynomial in one variable but it is in the variables %s"%tuple([v]) - f = self.polynomial(base_ring) - from sage.rings.all import PowerSeriesRing - R = PowerSeriesRing(base_ring, names=f.parent().variable_names()) - return R(f, f.degree()+1) - - def polynomial(self, base_ring): - r""" - Return self as an algebraic polynomial over the given base ring, if - possible. - - The point of this function is that it converts purely symbolic - polynomials into optimized algebraic polynomials over a given - base ring. - - WARNING: This is different from \code{self.poly(x)} which is used - to rewrite self as a polynomial in x. - - INPUT: - base_ring -- a ring - - EXAMPLES: - sage: f = x^2 -2/3*x + 1 - sage: f.polynomial(QQ) - x^2 - 2/3*x + 1 - sage: f.polynomial(GF(19)) - x^2 + 12*x + 1 - - sage: f = x^2*e + x + pi/e - sage: f.polynomial(RDF) - 2.71828182846*x^2 + 1.0*x + 1.15572734979 - sage: g = f.polynomial(RR); g - 2.71828182845905*x^2 + 1.00000000000000*x + 1.15572734979092 - sage: g.parent() - Univariate Polynomial Ring in x over Real Field with 53 bits of precision - sage: f.polynomial(RealField(100)) - 2.7182818284590452353602874714*x^2 + 1.0000000000000000000000000000*x + 1.1557273497909217179100931833 - sage: f.polynomial(CDF) - 2.71828182846*x^2 + 1.0*x + 1.15572734979 - sage: f.polynomial(CC) - 2.71828182845905*x^2 + 1.00000000000000*x + 1.15572734979092 - - We coerce a multivariate polynomial with complex symbolic coefficients: - sage: f = pi^3*x - y^2*e - I; f - -1*e*y^2 + pi^3*x - I - sage: f.polynomial(CDF) - -1.0*I + (-2.71828182846)*y^2 + 31.0062766803*x - sage: f.polynomial(CC) - -1.00000000000000*I + (-2.71828182845905)*y^2 + 31.0062766802998*x - sage: f.polynomial(ComplexField(70)) - -1.0000000000000000000*I + (-2.7182818284590452354)*y^2 + 31.006276680299820175*x - - Another polynomial: - sage: f = sum((e*I)^n*x^n for n in range(5)); f - e^4*x^4 - e^3*I*x^3 - e^2*x^2 + e*I*x + 1 - sage: f.polynomial(CDF) - 54.5981500331*x^4 + (-20.0855369232*I)*x^3 + (-7.38905609893)*x^2 + 2.71828182846*I*x + 1.0 - sage: f.polynomial(CC) - 54.5981500331442*x^4 + (-20.0855369231877*I)*x^3 + (-7.38905609893065)*x^2 + 2.71828182845905*I*x + 1.00000000000000 - - A multivariate polynomial over a finite field: - sage: f = (3*x^5 - 5*y^5)^7; f - (3*x^5 - 5*y^5)^7 - sage: g = f.polynomial(GF(7)); g - 2*y^35 + 3*x^35 - sage: parent(g) - Polynomial Ring in x, y over Finite Field of size 7 - """ - vars = self.variables() - if len(vars) == 0: - vars = ['x'] - R = PolynomialRing(base_ring, names=vars) - G = R.gens() - V = R.variable_names() - return self.substitute_over_ring( - dict([(var(V[i]),G[i]) for i in range(len(G))]), ring=R) - - def _polynomial_(self, R): - """ - Coerce this symbolic expression to a polynomial in R. - - EXAMPLES: - sage: R = QQ[x,y,z] - sage: R(x^2 + y) - y + x^2 - sage: R = QQ[w] - sage: R(w^3 + w + 1) - w^3 + w + 1 - sage: R = GF(7)[z] - sage: R(z^3 + 10*z) - z^3 + 3*z - - NOTE: If the base ring of the polynomial ring is the symbolic - ring, then a constant polynomial is always returned. - sage: R = SR[x] - sage: a = R(sqrt(2) + x^3 + y) - sage: a - y + x^3 + sqrt(2) - sage: type(a) - - sage: a.degree() - 0 - - We coerce to a double precision complex polynomial ring: - sage: f = e*x^3 + pi*y^3 + sqrt(2) + I; f - pi*y^3 + e*x^3 + I + sqrt(2) - sage: R = CDF[x,y] - sage: R(f) - 1.41421356237 + 1.0*I + 3.14159265359*y^3 + 2.71828182846*x^3 - - We coerce to a higher-precision polynomial ring - sage: R = ComplexField(100)[x,y] - sage: R(f) - 1.4142135623730950066967437806 + 1.0000000000000000000000000000*I + 3.1415926535897932384626433833*y^3 + 2.7182818284590452353602874714*x^3 - - """ - vars = self.variables() - B = R.base_ring() - if B == SR: - if is_MPolynomialRing(R): - return R({tuple([0]*R.ngens()):self}) - else: - return R([self]) - G = R.gens() - sub = [] - for v in vars: - r = repr(v) - for g in G: - if repr(g) == r: - sub.append((v,g)) - if len(sub) == 0: - return R(B(self)) - return self.substitute_over_ring(dict(sub), ring=R) + def __call__(self, **kwds): + return self.substitute(**kwds) def function(self, *args): """ - Return a CallableSymbolicExpression, fixing a variable order - to be the order of args. + Return a CallableFunction, fixing a variable order to be the order of + args. EXAMPLES: @@ -914,37 +198,11 @@ sage: g = u.function(x,y) sage: g(x,y) - x*cos(y) + sin(x) + sin(x) + x*cos(y) sage: g(t,z) - t*cos(z) + sin(t) - sage: g(x^2, x^y) - x^2*cos(x^y) + sin(x^2) - - sage: f = (x^2 + sin(a*w)).function(a,x,w); f - (a, x, w) |--> x^2 + sin(a*w) - sage: f(1,2,3) - sin(3) + 4 - - Using the function method we can obtain the above function f, - but viewed as a function of different variables: - sage: h = f.function(w,a); h - (w, a) |--> x^2 + sin(a*w) - - This notation also works: - sage: h(w,a) = f - sage: h - (w, a) |--> x^2 + sin(a*w) - - You can even make a symbolic expression $f$ into a function by - writing \code{f(x,y) = f}: - sage: f = x^n + y^n; f - y^n + x^n - sage: f(x,y) = f - sage: f - (x, y) |--> y^n + x^n - sage: f(2,3) - 3^n + 2^n - """ - R = CallableSymbolicExpressionRing(args) - return R(self) + sin(t) + t*cos(z) + sage: g(x^2, log(y)) + sin(x^2) + x^2*cos(log(y)) + """ + return CallableFunction(self, args) @@ -967,24 +225,11 @@ # check each time s = "" - # see if we can implicitly supply a variable name - try: - a = args[0] - except IndexError: - # if there were NO arguments, try assuming - a = 1 - if a is None or isinstance(a, (int, long, Integer)): - vars = self.variables() - if len(vars) == 1: - s = "%s, %s" % (vars[0], a) - else: - raise ValueError, "must supply an explicit variable for an " +\ - "expression containing more than one variable" for i in range(len(args)): if isinstance(args[i], SymbolicVariable): - s = s + '%s, ' %repr(args[i]) + s = s + '%s, ' %str(args[i]) # check to see if this is followed by an integer try: if isinstance(args[i+1], (int, long, Integer)): - s = s + '%s, ' %repr(args[i+1]) + s = s + '%s, ' %str(args[i+1]) else: s = s + '1, ' @@ -1008,582 +253,19 @@ f = self.parent()(t) return f - - differentiate = derivative - diff = derivative ################################################################### - # Taylor series - ################################################################### - def taylor(self, v, a, n): - """ - Expands self in a truncated Taylor or Laurent series in the - variable v around the point a, containing terms through $(x - a)^n$. - - INPUT: - v -- variable - a -- number - n -- integer - + # integral + ################################################################### + def integral(self, v): + """ EXAMPLES: - sage: taylor(a*log(z), z, 2, 3) - log(2)*a + a*(z - 2)/2 - (a*(z - 2)^2/8) + a*(z - 2)^3/24 - sage: taylor(sqrt (sin(x) + a*x + 1), x, 0, 3) - 1 + (a + 1)*x/2 - ((a^2 + 2*a + 1)*x^2/8) + (3*a^3 + 9*a^2 + 9*a - 1)*x^3/48 - sage: taylor (sqrt (x + 1), x, 0, 5) - 1 + x/2 - (x^2/8) + x^3/16 - (5*x^4/128) + 7*x^5/256 - sage: taylor (1/log (x + 1), x, 0, 3) - 1/x + 1/2 - (x/12) + x^2/24 - (19*x^3/720) - sage: taylor (cos(x) - sec(x), x, 0, 5) - -x^2 - (x^4/6) - sage: taylor ((cos(x) - sec(x))^3, x, 0, 9) - -x^6 - (x^8/2) - sage: taylor (1/(cos(x) - sec(x))^3, x, 0, 5) - -1/x^6 + 1/(2*x^4) + 11/(120*x^2) - 347/15120 - (6767*x^2/604800) - (15377*x^4/7983360) - """ - v = var(v) - l = self._maxima_().taylor(v, SR(a), Integer(n)) - return self.parent()(l) - - ################################################################### - # limits - ################################################################### - def limit(self, dir=None, **argv): - """ - Return the limit as the variable v approaches a from the - given direction. - - \begin{verbatim} - expr.limit(x = a) - expr.limit(x = a, dir='above') - \end{verbatim} - - INPUT: - dir -- (default: None); dir may have the value `plus' (or 'above') - for a limit from above, `minus' (or 'below') for a limit from - below, or may be omitted (implying a two-sided - limit is to be computed). - **argv -- 1 named parameter - - NOTE: Output it may also use `und' (undefined), `ind' - (indefinite but bounded), and `infinity' (complex infinity). - - EXAMPLES: - sage: f = (1+1/x)^x - sage: f.limit(x = oo) - e - sage: f.limit(x = 5) - 7776/3125 - sage: f.limit(x = 1.2) - 2.069615754672029 - sage: f.limit(x = I) - e^(I*log(1 - I)) - sage: f(1.2) - 2.069615754672029 - sage: f(I) - (1 - I)^I - sage: CDF(f(I)) - 2.06287223508 + 0.74500706218*I - sage: CDF(f.limit(x = I)) - 2.06287223508 + 0.74500706218*I - - More examples: - sage: limit(x*log(x), x = 0, dir='above') - 0 - sage: lim((x+1)^(1/x),x = 0) - e - sage: lim(e^x/x, x = oo) - +Infinity - sage: lim(e^x/x, x = -oo) - 0 - sage: lim(-e^x/x, x = oo) - -Infinity - - The following means "indefinite but bounded": - sage: lim(sin(1/x), x = 0) - ind - """ - if len(argv) != 1: - raise ValueError, "call the limit function like this, e.g. limit(expr, x=2)." - else: - k = argv.keys()[0] - v = var(k, create=False) - a = argv[k] - if dir is None: - l = self._maxima_().limit(v, a) - elif dir == 'plus' or dir == 'above': - l = self._maxima_().limit(v, a, 'plus') - elif dir == 'minus' or dir == 'below': - l = self._maxima_().limit(v, a, 'minus') - else: - raise ValueError, "dir must be one of 'plus' or 'minus'" - return self.parent()(l) - - ################################################################### - # Laplace transform - ################################################################### - def laplace(self, t, s): - r""" - Attempts to compute and return the Laplace transform of self - with respect to the variable t and transform parameter s. If - Laplace cannot find a solution, a formal function is returned. - - The function that is returned maybe be viewed as a function of s. - - DEFINITION: - The Laplace transform of a function $f(t)$, defined for all - real numbers $t \geq 0$, is the function $F(s)$ defined by - $$ - F(s) = \int_{0}^{\infty} e^{-st} f(t) dt. - $$ - - EXAMPLES: - We compute a few Laplace transforms: - sage: sin(x).laplace(x, s) - 1/(s^2 + 1) - sage: (z + exp(x)).laplace(x, s) - z/s + 1/(s - 1) - - We do a formal calculation: - sage: f = function('f', x) - sage: g = f.diff(x); g - diff(f(x), x, 1) - sage: g.laplace(x, s) - s*laplace(f(x), x, s) - f(0) - - """ - return self.parent()(self._maxima_().laplace(var(t), var(s))) - - def inverse_laplace(self, t, s): - r""" - Attempts to compute the inverse Laplace transform of self with - respect to the variable t and transform parameter s. If - Laplace cannot find a solution, a formal function is returned. - - The function that is returned maybe be viewed as a function of s. - - - DEFINITION: - The inverse Laplace transform of a function $F(s)$, - is the function $f(t)$ defined by - $$ - F(s) = \frac{1}{2\pi i} \int_{\gamma-i\infty}^{\gamma + i\infty} e^{st} F(s) dt, - $$ - where $\gamma$ is chosen so that the contour path of - integration is in the region of convergence of $F(s)$. - - EXAMPLES: - sage: f = (1/(w^2+10)).inverse_laplace(w, m); f - sin(sqrt(10)*m)/sqrt(10) - sage: laplace(f, m, w) - 1/(w^2 + 10) - """ - return self.parent()(self._maxima_().ilt(var(t), var(s))) - - - ################################################################### - # a default variable, for convenience. - ################################################################### - def default_variable(self): - vars = self.variables() - if len(vars) < 1: - return var('x') - else: - return vars[0] - - ################################################################### - # integration - ################################################################### - def integral(self, v=None, a=None, b=None): - """ - Returns the indefinite integral with respect to the variable - $v$, ignoring the constant of integration. Or, if endpoints - $a$ and $b$ are specified, returns the definite integral over - the interval $[a, b]$. - - If \code{self} has only one variable, then it returns the - integral with respect to that variable. - - INPUT: - v -- (optional) a variable or variable name - a -- (optional) lower endpoint of definite integral - b -- (optional) upper endpoint of definite integral - - - EXAMPLES: - sage: h = sin(x)/(cos(x))^2 + sage: h = sin(x)/cos(x) sage: h.integral(x) - 1/cos(x) - - sage: f = x^2/(x+1)^3 - sage: f.integral() - log(x + 1) + (4*x + 3)/(2*x^2 + 4*x + 2) - - sage: f = x*cos(x^2) - sage: f.integral(x, 0, sqrt(pi)) - 0 - sage: f.integral(a=-pi, b=pi) - 0 - - Constraints are sometimes needed: - sage: integral(x^n,x) - Traceback (most recent call last): - ... - TypeError: Computation failed since Maxima requested additional constraints (use assume): - Is n+1 zero or nonzero? - sage: assume(n > 0) - sage: integral(x^n,x) - x^(n + 1)/(n + 1) - sage: forget() - - NOTE: Above, putting assume(n == -1) does not yield the right behavior. - Directly in maxima, doing - - The examples in the Maxima documentation: - sage: integral(sin(x)^3) - cos(x)^3/3 - cos(x) - sage: integral(x/sqrt(b^2-x^2)) - x*log(2*sqrt(b^2 - x^2) + 2*b) - sage: integral(x/sqrt(b^2-x^2), x) - -sqrt(b^2 - x^2) - sage: integral(cos(x)^2 * exp(x), x, 0, pi) - 3*e^pi/5 - 3/5 - sage: integral(x^2 * exp(-x^2), x, -oo, oo) - sqrt(pi)/2 - - We integrate the same function in both Mathematica and SAGE (via Maxima): - sage: f = sin(x^2) + y^z - sage: g = mathematica(f) # optional -- requires mathematica - sage: print g # optional - z 2 - y + Sin[x ] - sage: print g.Integrate(x) # optional - z Pi 2 - x y + Sqrt[--] FresnelS[Sqrt[--] x] - 2 Pi - sage: print f.integral(x) - z (sqrt(2) I + sqrt(2)) x - x y + sqrt( pi) ((sqrt(2) I + sqrt(2)) erf(------------------------) - 2 - (sqrt(2) I - sqrt(2)) x - + (sqrt(2) I - sqrt(2)) erf(------------------------))/8 - 2 - - We integrate the above function in maple now: - sage: g = maple(f); g # optional -- requires maple - sin(x^2)+y^z - sage: g.integrate(x) # optional -- requires maple - 1/2*2^(1/2)*Pi^(1/2)*FresnelS(2^(1/2)/Pi^(1/2)*x)+y^z*x - - We next integrate a function with no closed form integral. Notice that - the answer comes back as an expression that contains an integral itself. - sage: A = integral(1/ ((x-4) * (x^3+2*x+1)), x); A - log(x - 4)/73 - (integrate((x^2 + 4*x + 18)/(x^3 + 2*x + 1), x)/73) - sage: print A - / 2 - [ x + 4 x + 18 - I ------------- dx - ] 3 - log(x - 4) / x + 2 x + 1 - ---------- - ------------------ - 73 73 - """ - - if v is None: - v = self.default_variable() - + """ if not isinstance(v, SymbolicVariable): - v = var(repr(v)) - #raise TypeError, 'must integrate with respect to a variable' - if (a is None and (not b is None)) or (b is None and (not a is None)): - raise TypeError, 'only one endpoint given' - if a is None: - return self.parent()(self._maxima_().integrate(v)) - else: - return self.parent()(self._maxima_().integrate(v, a, b)) - - integrate = integral - - def nintegral(self, x, a, b, - desired_relative_error='1e-8', - maximum_num_subintervals=200): - r""" - Return a numerical approximation to the integral of self from - a to b. - - INPUT: - x -- variable to integrate with respect to - a -- lower endpoint of integration - b -- upper endpoint of integration - desired_relative_error -- (default: '1e-8') the desired - relative error - maximum_num_subintervals -- (default: 200) maxima number - of subintervals - - OUTPUT: - -- float: approximation to the integral - -- float: estimated absolute error of the approximation - -- the number of integrand evaluations - -- an error code: - 0 -- no problems were encountered - 1 -- too many subintervals were done - 2 -- excessive roundoff error - 3 -- extremely bad integrand behavior - 4 -- failed to converge - 5 -- integral is probably divergent or slowly convergent - 6 -- the input is invalid - - ALIAS: - nintegrate is the same as nintegral - - REMARK: - There is also a function \code{numerical_integral} that implements - numerical integration using the GSL C library. It is potentially - much faster and applies to arbitrary user defined functions. - - EXAMPLES: - sage: exp(-sqrt(x)).nintegral(x, 0, 1) - (0.52848223531423055, 4.1633141378838452e-11, 231, 0) - - We can also use the \code{numerical_integral} function, which calls - the GSL C library. - sage: numerical_integral(exp(-sqrt(x)), 0, 1) - (0.52848223225314706, 6.8392846084921134e-07) - """ - v = self._maxima_().quad_qags(var(x), - a, b, desired_relative_error, - maximum_num_subintervals) - return float(v[0]), float(v[1]), Integer(v[2]), Integer(v[3]) - - nintegrate = nintegral - - - ################################################################### - # Manipulating epxressions - ################################################################### - def coeff(self, x, n=1): - """ - Returns the coefficient of $x^n$ in self. - - INPUT: - x -- variable, function, expression, etc. - n -- integer, default 1. - - Sometimes it may be necessary to expand or factor first, since - this is not done automatically. - - EXAMPLES: - sage: f = (a*sqrt(2))*x^2 + sin(y)*x^(1/2) + z^z - sage: f.coeff(sin(y)) - sqrt(x) - sage: f.coeff(x^2) - sqrt(2)*a - sage: f.coeff(x^(1/2)) - sin(y) - sage: f.coeff(1) - 0 - sage: f.coeff(x, 0) - z^z - """ - return self.parent()(self._maxima_().coeff(x, n)) - - def coeffs(self, x=None): - """ - Coefficients of self as a polynomial in x. - - INPUT: - x -- optional variable - OUTPUT: - list of pairs [expr, n], where expr is a symbolic expression and n is a power. - - EXAMPLES: - sage: p = x^3 - (x-3)*(x^2+x) + 1 - sage: p.coeffs() - [[1, 0], [3, 1], [2, 2]] - sage: p = expand((x-a*sqrt(2))^2 + x + 1); p - x^2 - 2*sqrt(2)*a*x + x + 2*a^2 + 1 - sage: p.coeffs(a) - [[x^2 + x + 1, 0], [-2*sqrt(2)*x, 1], [2, 2]] - sage: p.coeffs(x) - [[2*a^2 + 1, 0], [1 - 2*sqrt(2)*a, 1], [1, 2]] - - A polynomial with wacky exponents: - sage: p = (17/3*a)*x^(3/2) + x*y + 1/x + x^x - sage: p.coeffs(x) - [[1, -1], [x^x, 0], [y, 1], [17*a/3, 3/2]] - """ - f = self._maxima_() - P = f.parent() - P._eval_line('load(coeflist)') - if x is None: - x = self.default_variable() - x = var(x) - G = f.coeffs(x) - S = symbolic_expression_from_maxima_string(repr(G)) - return S[1:] - - def poly(self, x=None): - r""" - Express self as a polynomial in x. Is self is not a polynomial - in x, then some coefficients may be functions of x. - - WARNING: This is different from \code{self.polynomial()} which - returns a SAGE polynomial over a given base ring. - - EXAMPLES: - sage: p = expand((x-a*sqrt(2))^2 + x + 1); p - x^2 - 2*sqrt(2)*a*x + x + 2*a^2 + 1 - sage: p.poly(a) - (x^2 + x + 1)*1 + -2*sqrt(2)*x*a + 2*a^2 - sage: bool(expand(p.poly(a)) == p) - True - sage: p.poly(x) - (2*a^2 + 1)*1 + (1 - 2*sqrt(2)*a)*x + 1*x^2 - """ - f = self._maxima_() - P = f.parent() - P._eval_line('load(coeflist)') - if x is None: - x = self.default_variable() - x = var(x) - G = f.coeffs(x) - ans = None - for i in range(1, len(G)): - Z = G[i] - coeff = SR(Z[0]) - n = SR(Z[1]) - if repr(coeff) != '0': - if repr(n) == '0': - xpow = SR(1) - elif repr(n) == '1': - xpow = x - else: - xpow = x**n - if ans is None: - ans = coeff*xpow - else: - ans += coeff*xpow - ans._declare_simplified() - return ans - - def combine(self): - """ - Simplifies self by combining all terms with the same - denominator into a single term. - - EXAMPLES: - sage: f = x*(x-1)/(x^2 - 7) + y^2/(x^2-7) + 1/(x+1) + b/a + c/a - sage: print f - 2 - y (x - 1) x 1 c b - ------ + --------- + ----- + - + - - 2 2 x + 1 a a - x - 7 x - 7 - sage: print f.combine() - 2 - y + (x - 1) x 1 c + b - -------------- + ----- + ----- - 2 x + 1 a - x - 7 - """ - return self.parent()(self._maxima_().combine()) - - def numerator(self): - """ - EXAMPLES: - sage: f = x*(x-a)/((x^2 - y)*(x-a)) - sage: print f - x - ------ - 2 - x - y - sage: f.numerator() - x - sage: f.denominator() - x^2 - y - """ - return self.parent()(self._maxima_().num()) - - def denominator(self): - """ - EXAMPLES: - sage: f = (sqrt(x) + sqrt(y) + sqrt(z))/(x^10 - y^10 - sqrt(var('theta'))) - sage: print f - sqrt(z) + sqrt(y) + sqrt(x) - --------------------------- - 10 10 - - y + x - sqrt(theta) - sage: f.denominator() - -y^10 + x^10 - sqrt(theta) - """ - return self.parent()(self._maxima_().denom()) - - ################################################################### - # solve - ################################################################### - def roots(self, x=None): - r""" - Returns the roots of self, with multiplicities. - - INPUT: - x -- variable to view the function in terms of - (use default variable if not given) - OUTPUT: - list of pairs (root, multiplicity) - - If there are infinitely many roots, e.g., a function - like sin(x), only one is returned. - - EXAMPLES: - A simple example: - sage: ((x^2-1)^2).roots() - [(-1, 2), (1, 2)] - - A complicated example. - sage: f = expand((x^2 - 1)^3*(x^2 + 1)*(x-a)); f - x^9 - a*x^8 - 2*x^7 + 2*a*x^6 + 2*x^3 - 2*a*x^2 - x + a - - The default variable is a, since it is the first in alphabetical order: - sage: f.roots() - [(x, 1)] - - As a polynomial in a, x is indeed a root: - sage: f.poly(a) - (x^9 - 2*x^7 + 2*x^3 - x)*1 + (-x^8 + 2*x^6 - 2*x^2 + 1)*a - sage: f(a=x) - 0 - - The roots in terms of x are what we expect: - sage: f.roots(x) - [(a, 1), (-1*I, 1), (I, 1), (1, 3), (-1, 3)] - - Only one root of $\sin(x) = 0$ is given: - sage: f = sin(x) - sage: f.roots(x) - [(0, 1)] - - We derive the roots of a general quadratic polynomial: - sage: (a*x^2 + b*x + c).roots(x) - [((-sqrt(b^2 - 4*a*c) - b)/(2*a), 1), ((sqrt(b^2 - 4*a*c) - b)/(2*a), 1)] - """ - if x is None: - x = self.default_variable() - S, mul = self.solve(x, multiplicities=True) - return [(S[i].rhs(), mul[i]) for i in range(len(mul))] - - def solve(self, x, multiplicities=False): - r""" - Solve the equation \code{self == 0} for the variable x. - - INPUT: - x -- variable to solve for - multiplicities -- bool (default: False); if True, return corresponding multiplicities. - - EXAMPLES: - sage: (z^5 - 1).solve(z) - [z == e^(2*I*pi/5), z == e^(4*I*pi/5), z == e^(-(4*I*pi/5)), z == e^(-(2*I*pi/5)), z == 1] - """ - x = var(x) - return (self == 0).solve(x, multiplicities=multiplicities) + raise TypeError, "second argument to diff must be a variable" + return self.parent()(self._maxima_().integrate(v)) + ################################################################### @@ -1591,20 +273,13 @@ ################################################################### def simplify(self): - try: - return self._simp - except AttributeError: - S = evaled_symbolic_expression_from_maxima_string(self._maxima_init_()) - S._simp = S - self._simp = S - return S + return self.parent()(self._maxima_()) def simplify_trig(self): r""" - First expands using trig_expand, then employs the identities - $\sin(x)^2 + \cos(x)^2 = 1$ and $\cosh(x)^2 - \sin(x)^2 = 1$ - to simplify expressions containing tan, sec, etc., to sin, - cos, sinh, cosh. - - ALIAS: trig_simplify and simplify_trig are the same + Employs the identities $\sin(x)^2 + \cos(x)^2 = 1$ and + $\cosh(x)^2 - \sin(x)^2 = 1$ to simplify expressions + containing tan, sec, etc., to sin, cos, sinh, cosh. + + trig_simplify() and simplify_trig() are the same method. EXAMPLES: @@ -1615,78 +290,9 @@ sage: f.simplify_trig() 1 - """ - # much better to expand first, since it often doesn't work - # right otherwise! - return self.parent()(self._maxima_().trigexpand().trigsimp()) + + """ + return self.parent()(self._maxima_().trigsimp()) trig_simplify = simplify_trig - - def simplify_rational(self): - """ - Simplify by expanding repeatedly rational expressions. - - ALIAS: rational_simplify and simplify_rational are the same - - EXAMPLES: - sage: f = sin(x/(x^2 + x)) - sage: f - sin(x/(x^2 + x)) - sage: f.simplify_rational() - sin(1/(x + 1)) - - sage: f = ((x - 1)^(3/2) - (x + 1)*sqrt(x - 1))/sqrt((x - 1)*(x + 1)) - sage: print f - 3/2 - (x - 1) - sqrt(x - 1) (x + 1) - -------------------------------- - sqrt((x - 1) (x + 1)) - sage: print f.simplify_rational() - 2 sqrt(x - 1) - - ------------- - 2 - sqrt(x - 1) - """ - return self.parent()(self._maxima_().fullratsimp()) - - rational_simplify = simplify_rational - - ################################################################### - # factor - ################################################################### - def factor(self, dontfactor=[]): - """ - Factors self, containing any number of variables or functions, - into factors irreducible over the integers. - - INPUT: - self -- a symbolic expression - dontfactor -- list (default: []), a list of variables with - respect to which factoring is not to occur. - Factoring also will not take place with - respect to any variables which are less - important (using the variable ordering - assumed for CRE form) than those on the - `dontfactor' list. - - EXAMPLES: - sage: (x^3-y^3).factor() - (-(y - x))*(y^2 + x*y + x^2) - sage: factor(-8*y - 4*x + z^2*(2*y + x)) - (2*y + x)*(z - 2)*(z + 2) - sage: f = -1 - 2*x - x^2 + y^2 + 2*x*y^2 + x^2*y^2 - sage: F = factor(f/(36*(1 + 2*y + y^2)), dontfactor=[x]) - sage: print F - 2 - (x + 2 x + 1) (y - 1) - ---------------------- - 36 (y + 1) - """ - if len(dontfactor) > 0: - m = self._maxima_() - name = m.name() - cmd = 'block([dontfactor:%s],factor(%s))'%(dontfactor, name) - return evaled_symbolic_expression_from_maxima_string(cmd) - else: - return self.parent()(self._maxima_().factor()) ################################################################### @@ -1707,5 +313,5 @@ cos(2*x)*cos(y) - sin(2*x)*sin(y) - ALIAS: trig_expand and expand_trig are the same + ALIAS: trig_expand """ return self.parent()(self._maxima_().trigexpand()) @@ -1714,217 +320,144 @@ + ################################################################### # substitute ################################################################### - def substitute(self, in_dict=None, **kwds): + def substitute(self, dict=None, **kwds): """ Takes the symbolic variables given as dict keys or as keywords and replaces them with the symbolic expressions given as dict values or as - keyword values. Also run when you call a SymbolicExpression. - - INPUT: - in_dict -- (optional) dictionary of inputs - **kwds -- named parameters - + keyword values. Also run when you call a SymbolicExpression. + EXAMPLES: sage: u = (x^3 - 3*y + 4*t) sage: u.substitute(x=y, y=t) - y^3 + t + y^3 - 3*t + 4*t sage: f = sin(x)^2 + 32*x^(y/2) - sage: f(x=2, y = 10) - sin(2)^2 + 1024 + sage: f.substitute(x=2, y = 10) + sin(2)^2 + 32*2^(10/2) sage: f(x=pi, y=t) - 32*pi^(t/2) - - sage: f = 2*x^2 - sin(x) - sage: f(pi) - 2*pi^2 + sin(pi)^2 + 32*pi^(t/2) + + sage: f(x=pi, y=t).simplify() + AUTHORS: -- Bobby Moretti: Initial version """ - X = self.simplify() - kwds = self.__parse_in_dict(in_dict, kwds) - kwds = self.__varify_kwds(kwds) - return X._recursive_sub(kwds) - - def subs(self, *args, **kwds): - return self.substitute(*args, **kwds) + if dict is not None: + for k, v in dict.iteritems(): + kwds[str(k)] = v + # find the keys from the keywords + return self._recursive_sub(kwds) def _recursive_sub(self, kwds): - raise NotImplementedError, "implement _recursive_sub for type '%s'!"%(type(self)) - - def _recursive_sub_over_ring(self, kwds, ring): - raise NotImplementedError, "implement _recursive_sub_over_ring for type '%s'!"%(type(self)) - - def __parse_in_dict(self, in_dict, kwds): - if in_dict is None: - return kwds - - if not isinstance(in_dict, dict): - if len(kwds) > 0: - raise ValueError, "you must not both give the variable and specify it explicitly when doing a substitution." - in_dict = SR(in_dict) - vars = self.variables() - #if len(vars) > 1: - # raise ValueError, "you must specify the variable when doing a substitution, e.g., f(x=5)" - if len(vars) == 0: - return {} + # if we have operands, call ourself on each operand + try: + ops = self._operands + except AttributeError: + pass + if isinstance(self, SymbolicVariable): + s = str(self) + if s in kwds: + return kwds[s] else: - return {vars[0]: in_dict} - - # merge dictionaries - kwds.update(in_dict) - return kwds - - def __varify_kwds(self, kwds): - return dict([(var(k),w) for k,w in kwds.iteritems()]) - - def substitute_over_ring(self, in_dict=None, ring=None, **kwds): - X = self.simplify() - kwds = self.__parse_in_dict(in_dict, kwds) - kwds = self.__varify_kwds(kwds) - if ring is None: - return X._recursive_sub(kwds) + return self + elif isinstance(self, SymbolicConstant): + return self + elif isinstance(self, SymbolicArithmetic): + new_ops = [op._recursive_sub(kwds) for op in ops] + return SymbolicArithmetic([new_ops[0], new_ops[1]], self._operator) + elif isinstance(self, SymbolicComposition): + return SymbolicComposition(ops[0], ops[1]._recursive_sub(kwds)) + +class PrimitiveFunction(SymbolicExpression): + def __init__(self): + pass + + def __call__(self, x): + # if we're calling with a symbolic expression, do function composition + if isinstance(x, SymbolicExpression) and not isinstance(x, Constant): + return SymbolicComposition(self, x) + + # if x is a polynomial object, first turn it into a function and + # compose self with x + elif is_Polynomial(x): + return Function_composition(self, SymbolicPolynomial(x)) + + # if we can't figure out what x is, return a symbolic version of x + elif isinstance(x, (Integer, Rational, + int, long, float, complex)): + return self(Constant_object(x)) + else: - return X._recursive_sub_over_ring(kwds, ring) - - - ################################################################### - # Real and imaginary parts - ################################################################### - def real(self): - """ - Return the real part of self. - - EXAMPLES: - sage: a = log(3+4*I) - sage: print a - log(4 I + 3) - sage: print a.real() - log(5) - sage: print a.imag() - 4 - atan(-) - 3 - - Now make a and b symbolic and compute the general real part: - sage: restore('a,b') - sage: f = log(a + b*I) - sage: f.real() - log(b^2 + a^2)/2 - """ - return self.parent()(self._maxima_().real()) - - def imag(self): - """ - Return the imaginary part of self. - - EXAMPLES: - sage: sqrt(-2).imag() - sqrt(2) - - We simplify Ln(Exp(z)) to z for -Pi %s" % (self._varlist[0], self._expr._repr_()) + else: + vars = ", ".join(map(str, self._varlist)) + return "(%s) |--> %s" % (vars, self._expr._repr_()) + + def _latex_(self): + if len(self._varlist) == 1: + return "%s \\ {\mapsto}\\ %s" % (self._varlist[0], + self._expr._latex_()) + else: + vars = ", ".join(map(latex, self._varlist)) + # the weird TeX is to workaround an apparent JsMath bug + return "\left(%s \\right)\\ {\\mapsto}\\ %s" % (vars, self._expr._latex_()) + + def derivative(self, dt): + return CallableFunction(self._expr.derivative(dt), self._varlist) + + def integral(self, dx): + return CallableFunction(self._expr.integral(dx), self._varlist) + + def substitute(self, dict=None, **kwds): + return CallableFunction(self._expr.substitute(dict, kwds), self._varlist) + + def simplify(self): + return CallableFunction(self._expr.simplify(), self._varlist) + + def trig_simplify(self): + return CallableFunction(self._expr.trig_simplify(), self._varlist) + + #TODO: Arithmetic, expand, trig_expand, etc... class Symbolic_object(SymbolicExpression): - r""" - A class representing a symbolic expression in terms of a SageObject (not - necessarily a 'constant'). - """ + r''' + A class representing a symbolic expression in terms of a SageObject. + ''' + def __init__(self, obj): SymbolicExpression.__init__(self) @@ -1932,56 +465,51 @@ def obj(self): - """ - EXAMPLES: - """ return self._obj - def __float__(self): - """ - EXAMPLES: - """ - return float(self._obj) - - def __complex__(self): - """ - EXAMPLES: - """ - return complex(self._obj) - - def _mpfr_(self, field): - """ - EXAMPLES: - """ - return field(self._obj) - - def _complex_mpfr_field_(self, C): - """ - EXAMPLES: - """ - return C(self._obj) - - def _complex_double_(self, C): - """ - EXAMPLES: - """ - return C(self._obj) - - def _real_double_(self, R): - """ - EXAMPLES: - """ - return R(self._obj) - - def _repr_(self, simplify=True): - """ - EXAMPLES: - """ - return repr(self._obj) - - def _latex_(self): - """ - EXAMPLES: - """ + def _repr_(self): + return str(self._obj) + + def _latex_(self): return latex(self._obj) + + def __pow__(self, right): + if isinstance(right, Symbolic_object): + try: + return Symbolic_object(self._obj + right._obj) + except TypeError: + pass + return SymbolicExpression.__pow__(self, right) + + def _add_(self, right): + if isinstance(right, Symbolic_object): + try: + return Symbolic_object(self._obj + right._obj) + except TypeError: + pass + return SymbolicExpression._add_(self, right) + + def _sub_(self, right): + if isinstance(right, Symbolic_object): + try: + return Symbolic_object(self._obj - right._obj) + except TypeError: + pass + return SymbolicExpression._sub_(self, right) + + def _mul_(self, right): + if isinstance(right, Symbolic_object): + try: + return Symbolic_object(self._obj * right._obj) + except TypeError: + pass + return SymbolicExpression._mul_(self, right) + + def _div_(self, right): + if isinstance(right, Symbolic_object): + try: + return Symbolic_object(self._obj / right._obj) + except TypeError: + pass + return SymbolicExpression._div_(self, right) def str(self, bits=None): @@ -1992,144 +520,28 @@ return str(R(self._obj)) - def _maxima_init_(self): - return maxima_init(self._obj) - - def _sys_init_(self, system): - return sys_init(self._obj, system) - -def maxima_init(x): - try: - return x._maxima_init_() - except AttributeError: - return repr(x) - -def sys_init(x, system): - try: - return x.__getattribute__('_%s_init_'%system)() - except AttributeError: - try: - return x._system_init_(system) + def _maxima_(self, maxima=maxima): + try: + return self.__maxima except AttributeError: - return repr(x) - -class SymbolicConstant(Symbolic_object): - def __init__(self, x): - Symbolic_object.__init__(self, x) - - def _is_atomic(self): - try: - return self._atomic - except AttributeError: - if isinstance(self, Rational): - self._atomic = False - else: - self._atomic = True - return self._atomic - - def _recursive_sub(self, kwds): - """ - EXAMPLES: - sage: a = SR(5/6) - sage: type(a) - - sage: a(x=3) - 5/6 - """ - return self - - def _recursive_sub_over_ring(self, kwds, ring): - return ring(self) - - + m = maxima(self._obj) + self.__maxima = m + return m class SymbolicPolynomial(Symbolic_object): - """ - An element of a polynomial ring as a formal symbolic expression. - - EXAMPLES: - A single variate polynomial: - sage: R. = QQ[] - sage: f = SR(x^3 + x) - sage: f(y=7) - x^3 + x - sage: f(x=5) - 130 - sage: f.integral(x) - x^4/4 + x^2/2 - sage: f(x=y) - y^3 + y - - A multivariate polynomial: - - sage: R. = ZZ[] - sage: f = SR(x^3 + x + y + theta^2); f - theta^2 + y + x + x^3 - sage: f(x=y, theta=y) - y^3 + y^2 + 2*y - sage: f(x=5) - y + theta^2 + 130 - - The polynomial must be over a field of characteristic 0. - sage: R. = GF(7)[] - sage: f = SR(w^3 + 1) - Traceback (most recent call last): - ... - TypeError: polynomial must be over a field of characteristic 0. - """ - # for now we do nothing except pass the info on to the superconstructor. It's + "An element of a polynomial ring as a formal symbolic expression." + + # for now we do nothing except pass the info on to the supercontructor. It's # not clear to me why we need anything else in this class -Bobby def __init__(self, p): - if p.parent().base_ring().characteristic() != 0: - raise TypeError, "polynomial must be over a field of characteristic 0." - Symbolic_object.__init__(self, p) - - def _recursive_sub(self, kwds): - return self._recursive_sub_over_ring(kwds, ring) - - def _recursive_sub_over_ring(self, kwds, ring): - f = self._obj - if is_Polynomial(f): - # Single variable case - v = f.parent().variable_name() - if kwds.has_key(v): - return ring(f(kwds[v])) - else: - if not ring is SR: - return ring(self) - else: - # Multivariable case - t = [] - for g in f.parent().gens(): - s = repr(g) - if kwds.has_key(s): - t.append(kwds[s]) - else: - t.append(g) - return ring(f(*t)) - - def polynomial(self, base_ring): - """ - Return self as a polynomial over the given base ring, if possible. - - INPUT: - base_ring -- a ring - - EXAMPLES: - sage: R. = QQ[] - sage: f = SR(x^2 -2/3*x + 1) - sage: f.polynomial(QQ) - x^2 - 2/3*x + 1 - sage: f.polynomial(GF(19)) - x^2 + 12*x + 1 - """ - f = self._obj - if base_ring is f.base_ring(): - return f - return f.change_ring(base_ring) - -################################################################## - - -zero_constant = SymbolicConstant(Integer(0)) + Symbolic_object.__init__(self, p) + +class SymbolicConstant(SymbolicExpression): + def __call__(self, x): + return self + +class Constant_object(SymbolicConstant, Symbolic_object): + pass + +zero_constant = Constant_object(Integer(0)) class SymbolicOperation(SymbolicExpression): @@ -2139,42 +551,33 @@ def __init__(self, operands): SymbolicExpression.__init__(self) - self._operands = operands # don't even make a copy -- ok, since immutable. - - def variables(self, vars=tuple([])): - """ - Return sorted list of variables that occur in the simplified - form of self. The ordering is alphabetic. - - EXAMPLES: - sage: f = (x - x) + y^2 - z/z + (w^2-1)/(w+1); f - y^2 + (w^2 - 1)/(w + 1) - 1 - sage: f.variables() - (w, y) - - sage: (x + y + z + a + b + c).variables() - (a, b, c, x, y, z) - - sage: (x^2 + x).variables() - (x,) - """ - if not self.is_simplified(): - return self.simplify().variables(vars) - - try: - return self.__variables + self._operands = [SER(op) for op in operands] + +class SymbolicComposition(SymbolicOperation): + r''' + Represents the symbolic composition of $f \circ g$. + ''' + def __init__(self, f, g): + SymbolicOperation.__init__(self, [f,g]) + + def _is_atomic(self): + return True + + def _repr_(self): + ops = self._operands + return "%s(%s)"% (ops[0]._repr_(), ops[1]._repr_()) + + def _latex_(self): + ops = self._operands + return r"%s \left( %s \right)"% (latex(ops[0]), latex(ops[1])) + + def _maxima_(self, maxima=maxima): + try: + return self.__maxima except AttributeError: - pass - if vars is None: - vars = [] - else: - vars = list(vars) - vars = list(set(sum([list(op.variables()) for op in self._operands], []))) - vars.sort(var_cmp) - vars = tuple(vars) - self.__variables = vars - return vars - -def var_cmp(x,y): - return cmp(str(x), str(y)) + ops = self._operands + m = ops[0]._maxima_(maxima)(ops[1]._maxima_(maxima)) + self.__maxima = m + return m + symbols = {operator.add:' + ', operator.sub:' - ', operator.mul:'*', @@ -2183,176 +586,82 @@ class SymbolicArithmetic(SymbolicOperation): - r""" + r''' Represents the result of an arithemtic operation on $f$ and $g$. - """ + ''' + def __init__(self, operands, op): SymbolicOperation.__init__(self, operands) + + if op is operator.add: + self._atomic = False + elif op is operator.sub: + self._atomic = False + elif op is operator.mul: + self._atomic = True + elif op is operator.div: + self._atomic = False + elif op is operator.pow: + self._atomic = True + elif op is operator.neg: + self._atomic = False + self._operator = op - def _recursive_sub(self, kwds): - """ - EXAMPLES: - sage: f = (x - x) + y^2 - z/z + (w^2-1)/(w+1); f - y^2 + (w^2 - 1)/(w + 1) - 1 - sage: f(y=10) - (w^2 - 1)/(w + 1) + 99 - sage: f(w=1,y=10) - 99 - sage: f(y=w,w=y) - (y^2 - 1)/(y + 1) + w^2 - 1 - - sage: f = y^5 - sqrt(2) - sage: f(10) - 100000 - sqrt(2) - """ - ops = self._operands - new_ops = [SR(op._recursive_sub(kwds)) for op in ops] - return self._operator(*new_ops) - - def _recursive_sub_over_ring(self, kwds, ring): - ops = self._operands - if self._operator == operator.pow: - new_ops = [ops[0]._recursive_sub_over_ring(kwds, ring=ring), Integer(ops[1])] - else: - new_ops = [op._recursive_sub_over_ring(kwds, ring=ring) for op in ops] - return ring(self._operator(*new_ops)) - - def __float__(self): - fops = [float(op) for op in self._operands] - return self._operator(*fops) - - def __complex__(self): - fops = [complex(op) for op in self._operands] - return self._operator(*fops) - - def _mpfr_(self, field): - if not self.is_simplified(): - return self.simplify()._mpfr_(field) - rops = [op._mpfr_(field) for op in self._operands] - return self._operator(*rops) - - def _complex_mpfr_field_(self, field): - if not self.is_simplified(): - return self.simplify()._complex_mpfr_field_(field) - rops = [op._complex_mpfr_field_(field) for op in self._operands] - return self._operator(*rops) - - def _complex_double_(self, field): - if not self.is_simplified(): - return self.simplify()._complex_double_(field) - rops = [op._complex_double_(field) for op in self._operands] - return self._operator(*rops) - - def _real_double_(self, field): - if not self.is_simplified(): - return self.simplify()._real_double_(field) - rops = [op._real_double_(field) for op in self._operands] - return self._operator(*rops) - def _is_atomic(self): - try: - return self._atomic - except AttributeError: - op = self._operator - # todo: optimize with a dictionary - if op is operator.add: - self._atomic = False - elif op is operator.sub: - self._atomic = False - elif op is operator.mul: - self._atomic = True - elif op is operator.div: - self._atomic = False - elif op is operator.pow: - self._atomic = True - elif op is operator.neg: - self._atomic = False - return self._atomic - - def _repr_(self, simplify=True): - """ - TESTS: - sage: a = (1-1/r)^(-1); a - 1/(1 - (1/r)) - sage: a.derivative(r) - -1/((1 - (1/r))^2*r^2) - - sage: reset('a,b') - sage: s = 0*(1/a) + -b*(1/a)*(1 + -1*0*(1/a))*(1/(a*b + -1*b*(1/a))) - sage: s - -b/(a*(a*b - (b/a))) - sage: s(a=2,b=3) - -1/3 - sage: -3/(2*(2*3-(3/2))) - -1/3 - """ - if simplify: - if hasattr(self, '_simp'): - return self._simp._repr_(simplify=False) - else: - return self.simplify()._repr_(simplify=False) + return self._atomic + + def _repr_(self): ops = self._operands op = self._operator - - ############### - # some bugs here in parenthesis -- exposed by above doctest - ############### - - s = [o._repr_(simplify=False) for o in ops] - + + s = [str(o) for o in ops] # for the left operand, we need to surround it in parens when the # operator is mul/div/pow, and when the left operand contains an # operation of lower precedence - if op in [operator.mul, operator.div]: + if op in [operator.mul, operator.div, operator.pow]: if ops[0]._has_op(operator.add) or ops[0]._has_op(operator.sub): if not ops[0]._is_atomic(): s[0] = '(%s)' % s[0] - else: - try: - if isinstance(ops[0]._obj, Rational): - s[0] = '(%s)' % s[0] - except AttributeError: - pass - try: - if isinstance(ops[1]._obj, Rational): - s[1] = '(%s)' % s[1] - except AttributeError: - pass - - # for the right operand, we need to surround it in parens when - # the operation is mul/div/sub, and when the right operand - # contains a + or -. - if op in [operator.mul, operator.sub]: + # for the right operand, we need to surround it in parens when the + # operation is mul/div/sub and the, and when the right operand contains + # a + or -. + if op in [operator.mul, operator.div, operator.sub]: + if ops[1]._has_op(operator.add) or ops[1]._has_op(operator.sub): # avoid drawing parens if s1 an atomic operation if not ops[1]._is_atomic(): s[1] = '(%s)' % s[1] - - elif op is operator.div: - if not ops[1]._is_atomic() or ops[1]._has_op(operator.mul): + # if we have a compound expression on the right, then we need parens on + # the right... but in TeX, this is expressed by font size and position + elif op is operator.pow: + if ops[1]._has_op(operator.add) or \ + ops[1]._has_op(operator.sub) or \ + ops[1]._has_op(operator.mul) or \ + ops[1]._has_op(operator.div) or \ + ops[1]._has_op(operator.pow): s[1] = '(%s)' % s[1] - - elif op is operator.pow: - if not ops[0]._is_atomic(): - s[0] = '(%s)'% s[0] - if not ops[1]._is_atomic() or ('/' in s[1] or '*' in s[1]): - s[1] = '(%s)'% s[1] - if op is operator.neg: - if ops[0]._is_atomic(): - return '-%s' % s[0] - else: - return '-(%s)'%s[0] + return '-%s' % s[0] else: return '%s%s%s' % (s[0], symbols[op], s[1]) def _latex_(self): - # if we are not simplified, return the latex of a simplified version - if not self.is_simplified(): - return self.simplify()._latex_() op = self._operator ops = self._operands - s = [x._latex_() for x in self._operands] + ops_tex = [x._latex_() for x in self._operands] + + s = [o._latex_() for o in ops] + + # follow a very similar logic to _repr_, but we don't parenthesize + # exponents + if op in [operator.mul, operator.div, operator.pow]: + if ops[0]._has_op(operator.add) or ops[0]._has_op(operator.sub): + if not ops[0]._is_atomic(): + s[0] = '\\left( %s \\right)' % s[0] + if op in [operator.mul, operator.div, operator.sub]: + if ops[1]._has_op(operator.add) or ops[1]._has_op(operator.sub): + if not ops[1]._is_atomic(): + s[1] = '\\left( %s \\right)' % s[1] if op is operator.add: @@ -2361,35 +670,24 @@ return '%s - %s' % (s[0], s[1]) elif op is operator.mul: - if ops[0]._has_op(operator.add) or ops[0]._has_op(operator.sub): - s[0] = r'\left( %s \right)' %s[0] return '{%s \\cdot %s}' % (s[0], s[1]) elif op is operator.div: return '\\frac{%s}{%s}' % (s[0], s[1]) elif op is operator.pow: - if ops[0]._has_op(operator.add) or ops[0]._has_op(operator.sub) \ - or ops[0]._has_op(operator.mul) or ops[0]._has_op(operator.div) \ - or ops[0]._has_op(operator.pow): - s[0] = r'\left( %s \right)' % s[0] return '{%s}^{%s} ' % (s[0], s[1]) elif op is operator.neg: return '-%s' % s[0] - def _maxima_init_(self): - ops = self._operands - if self._operator is operator.neg: - return '-(%s)' % ops[0]._maxima_init_() - else: - return '(%s) %s (%s)' % (ops[0]._maxima_init_(), - infixops[self._operator], - ops[1]._maxima_init_()) - - def _sys_init_(self, system): - ops = self._operands - if self._operator is operator.neg: - return '-(%s)' % sys_init(ops[0], system) - else: - return '(%s) %s (%s)' % (sys_init(ops[0], system), - infixops[self._operator], - sys_init(ops[1], system)) + def _maxima_(self, maxima=maxima): + try: + return self.__maxima + except AttributeError: + ops = self._operands + if self._operator is operator.neg: + m = self._operator(ops[0]._maxima_(maxima)) + else: + m = self._operator(ops[0]._maxima_(maxima), + ops[1]._maxima_(maxima)) + self.__maxima = m + return m import re @@ -2402,34 +700,8 @@ raise ValueError, "variable name must be nonempty" - def _recursive_sub(self, kwds): - # do the replacement if needed - if kwds.has_key(self): - return kwds[self] - else: - return self - - def _recursive_sub_over_ring(self, kwds, ring): - if kwds.has_key(self): - return ring(kwds[self]) - else: - return ring(self) - - def variables(self, vars=tuple([])): - """ - Return sorted list of variables that occur in the simplified - form of self. - """ - return (self, ) - - def __cmp__(self, right): - if isinstance(right, SymbolicVariable): - return cmp(self._repr_(), right._repr_()) - else: - return SymbolicExpression.__cmp__(self, right) - - def _repr_(self, simplify=True): - return self._name - - def __str__(self): + def __call__(self, x): + raise AttributeError, "A symbolic variable is not callable." + + def _repr_(self): return self._name @@ -2451,9 +723,11 @@ return a - def _maxima_init_(self): - return self._name - - def _sys_init_(self, system): - return self._name + def _maxima_(self, maxima=maxima): + try: + return self.__maxima + except AttributeError: + m = maxima(self._name) + self.__maxima = m + return m common_varnames = ['alpha', @@ -2498,1614 +772,105 @@ _vars = {} -def var(s, create=True): - r""" - Create a symbolic variable with the name \emph{s}. - - EXAMPLES: - sage: var('xx') - xx - """ - if isinstance(s, SymbolicVariable): - return s - s = str(s) - if ',' in s: - return tuple([var(x.strip()) for x in s.split(',')]) - elif ' ' in s: - return tuple([var(x.strip()) for x in s.split()]) +def var(s): + r''' Create a symbolic variable with the name \emph{s}''' try: - X = _vars[s]() - if not X is None: - return X + return _vars[s] except KeyError: - if not create: - raise ValueError, "the variable '%s' has not been defined"%var - pass - v = SymbolicVariable(s) - _vars[s] = weakref.ref(v) - _syms[s] = v - return v - - -######################################################################################### -# Callable functions -######################################################################################### -def is_CallableSymbolicExpressionRing(x): - """ - EXAMPLES: - sage: is_CallableSymbolicExpressionRing(QQ) - False - sage: is_CallableSymbolicExpressionRing(CallableSymbolicExpressionRing((x,y,z))) - True - """ - return isinstance(x, CallableSymbolicExpressionRing_class) - -class CallableSymbolicExpressionRing_class(CommutativeRing): - def __init__(self, args): - self._default_precision = 53 # default precision bits - self._args = args - ParentWithBase.__init__(self, RR) - - def __call__(self, x): - """ - - TESTS: - sage: f(x) = x+1; g(y) = y+1 - sage: f.parent()(g) - x |--> y + 1 - sage: g.parent()(f) - y |--> x + 1 - sage: f(x) = x+2*y; g(y) = y+3*x - sage: f.parent()(g) - x |--> y + 3*x - sage: g.parent()(f) - y |--> 2*y + x - """ - return self._coerce_impl(x) - - def _coerce_impl(self, x): - if isinstance(x, SymbolicExpression): - if isinstance(x, CallableSymbolicExpression): - x = x._expr - return CallableSymbolicExpression(self, x) - return self._coerce_try(x, [SR]) - - def _repr_(self): - return "Callable function ring with arguments %s"%(self._args,) - - def args(self): - return self._args - - def arguments(self): - return self.args() - - def zero_element(self): - try: - return self.__zero_element - except AttributeError: - z = CallableSymbolicExpression(SR.zero_element(), self._args) - self.__zero_element = z - return z - - def _an_element_impl(self): - return self.zero_element() - - -_cfr_cache = {} -def CallableSymbolicExpressionRing(args, check=True): - if check: - if len(args) == 1 and isinstance(args[0], (list, tuple)): - args = args[0] - for arg in args: - if not isinstance(arg, SymbolicVariable): - raise TypeError, "Must construct a function with a tuple (or list) of" \ - +" SymbolicVariables." - args = tuple(args) - if _cfr_cache.has_key(args): - R = _cfr_cache[args]() - if not R is None: - return R - R = CallableSymbolicExpressionRing_class(args) - _cfr_cache[args] = weakref.ref(R) - return R - -def is_CallableSymbolicExpression(x): - """ - Returns true if x is a callable symbolic expression. - - EXAMPLES: - sage: f(x,y) = a + 2*x + 3*y + z - sage: is_CallableSymbolicExpression(f) - True - sage: is_CallableSymbolicExpression(a+2*x) - False - sage: def foo(n): return n^2 - ... - sage: is_CallableSymbolicExpression(foo) - False - """ - return isinstance(x, CallableSymbolicExpression) - -class CallableSymbolicExpression(SymbolicExpression): - r""" - A callable symbolic expression that knows the ordered list of - variables on which it depends. - - EXAMPLES: - sage: f(x,y) = a + 2*x + 3*y + z - sage: f - (x, y) |--> z + 3*y + 2*x + a - sage: f(1,2) - z + a + 8 - """ - def __init__(self, parent, expr): - RingElement.__init__(self, parent) - self._expr = expr - - def variables(self): - """ - EXAMPLES: - sage: g(x) = sin(x) + a - sage: g.variables() - (a, x) - sage: g.args() - (x,) - sage: g(y,x,z) = sin(x) + a - a - sage: g - (y, x, z) |--> sin(x) - sage: g.args() - (y, x, z) - """ - return self._expr.variables() - - def expression(self): - """ - Return the underlying symbolic expression (i.e., forget the - extra map structure). - """ - return self._expr - - def args(self): - return self.parent().args() - - def _maxima_init_(self): - return self._expr._maxima_init_() - - def __float__(self): - return float(self._expr) - - def __complex__(self): - return complex(self._expr) - - def _mpfr_(self, field): - """ - Coerce to a multiprecision real number. - - EXAMPLES: - sage: RealField(100)(SR(10)) - 10.000000000000000000000000000 - """ - return (self._expr)._mpfr_(field) - - def _complex_mpfr_field_(self, field): - return field(self._expr) - - def _complex_double_(self, C): - return C(self._expr) - - def _real_double_(self, R): - return R(self._expr) - - # TODO: should len(args) == len(vars)? - def __call__(self, *args): - vars = self.args() - dct = dict( (vars[i], args[i]) for i in range(len(args)) ) - return self._expr.substitute(dct) - - def _repr_(self, simplify=True): - args = self.args() - if len(args) == 1: - return "%s |--> %s" % (args[0], self._expr._repr_(simplify=simplify)) - else: - args = ", ".join(map(str, args)) - return "(%s) |--> %s" % (args, self._expr._repr_(simplify=simplify)) - - def _latex_(self): - args = self.args() - if len(args) == 1: - return "%s \\ {\mapsto}\\ %s" % (args[0], - self._expr._latex_()) - else: - vars = ", ".join(map(latex, args)) - # the weird TeX is to workaround an apparent JsMath bug - return "\\left(%s \\right)\\ {\\mapsto}\\ %s" % (args, self._expr._latex_()) - - def _neg_(self): - return CallableSymbolicExpression(self.parent(), -self._expr) - - def __add__(self, right): - """ - EXAMPLES: - sage: f(x,n,y) = x^n + y^m; g(x,n,m,z) = x^n +z^m - sage: f + g - (x, n, m, y, z) |--> z^m + y^m + 2*x^n - sage: g + f - (x, n, m, y, z) |--> z^m + y^m + 2*x^n - """ - if isinstance(right, CallableSymbolicExpression): - if self.parent() is right.parent(): - return self._add_(right) - else: - args = self._unify_args(right) - R = CallableSymbolicExpressionRing(args) - return R(self) + R(right) - else: - return RingElement.__add__(self, right) - - def _add_(self, right): - return CallableSymbolicExpression(self.parent(), self._expr + right._expr) - - def __sub__(self, right): - """ - EXAMPLES: - sage: f(x,n,y) = x^n + y^m; g(x,n,m,z) = x^n +z^m - sage: f - g - (x, n, m, y, z) |--> y^m - z^m - sage: g - f - (x, n, m, y, z) |--> z^m - y^m - """ - if isinstance(right, CallableSymbolicExpression): - if self.parent() is right.parent(): - return self._sub_(right) - else: - args = self._unify_args(right) - R = CallableSymbolicExpressionRing(args) - return R(self) - R(right) - else: - return RingElement.__sub__(self, right) - - def _sub_(self, right): - return CallableSymbolicExpression(self.parent(), self._expr - right._expr) - - def __mul__(self, right): - """ - EXAMPLES: - sage: f(x) = x+2*y; g(y) = y+3*x - sage: f*(2/3) - x |--> 2*(2*y + x)/3 - sage: f*g - (x, y) |--> (y + 3*x)*(2*y + x) - sage: (2/3)*f - x |--> 2*(2*y + x)/3 - - sage: f(x,y,z,a,b) = x+y+z-a-b; f - (x, y, z, a, b) |--> z + y + x - b - a - sage: f * (b*c) - (x, y, z, a, b) |--> b*c*(z + y + x - b - a) - sage: g(x,y,w,t) = x*y*w*t - sage: f*g - (x, y, a, b, t, w, z) |--> t*w*x*y*(z + y + x - b - a) - sage: (f*g)(2,3) - 6*t*w*(z - b - a + 5) - - sage: f(x,n,y) = x^n + y^m; g(x,n,m,z) = x^n +z^m - sage: f * g - (x, n, m, y, z) |--> (y^m + x^n)*(z^m + x^n) - sage: g * f - (x, n, m, y, z) |--> (y^m + x^n)*(z^m + x^n) - """ - if isinstance(right, CallableSymbolicExpression): - if self.parent() is right.parent(): - return self._mul_(right) - else: - args = self._unify_args(right) - R = CallableSymbolicExpressionRing(args) - return R(self)*R(right) - else: - return RingElement.__mul__(self, right) - - def _mul_(self, right): - return CallableSymbolicExpression(self.parent(), self._expr * right._expr) - - def __div__(self, right): - """ - EXAMPLES: - - sage: f(x,n,y) = x^n + y^m; g(x,n,m,z) = x^n +z^m - sage: f / g - (x, n, m, y, z) |--> (y^m + x^n)/(z^m + x^n) - sage: g / f - (x, n, m, y, z) |--> (z^m + x^n)/(y^m + x^n) - """ - if isinstance(right, CallableSymbolicExpression): - if self.parent() is right.parent(): - return self._div_(right) - else: - args = self._unify_args(right) - R = CallableSymbolicExpressionRing(args) - return R(self) / R(right) - else: - return RingElement.__div__(self, right) - - def _div_(self, right): - return CallableSymbolicExpression(self.parent(), self._expr / right._expr) - - def __pow__(self, right): - return CallableSymbolicExpression(self.parent(), self._expr ** right) - - def _unify_args(self, x): - r""" - Takes the variable list from another CallableSymbolicExpression object and - compares it with the current CallableSymbolicExpression object's variable list, - combining them according to the following rules: - - Let \code{a} be \code{self}'s variable list, let \code{b} be - \code{y}'s variable list. - - \begin{enumerate} - - \item If \code{a == b}, then the variable lists are identical, - so return that variable list. - - \item If \code{a} $\neq$ \code{b}, then check if the first $n$ - items in \code{a} are the first $n$ items in \code{b}, - or vice-versa. If so, return a list with these $n$ - items, followed by the remaining items in \code{a} and - \code{b} sorted together in alphabetical order. - - \end{enumerate} - - Note: When used for arithmetic between CallableSymbolicExpressions, - these rules ensure that the set of CallableSymbolicExpressions will have - certain properties. In particular, it ensures that the set is - a \emph{commutative} ring, i.e., the order of the input - variables is the same no matter in which order arithmetic is - done. - - INPUT: - x -- A CallableSymbolicExpression - - OUTPUT: - A tuple of variables. - - EXAMPLES: - sage: f(x, y, z) = sin(x+y+z) - sage: f - (x, y, z) |--> sin(z + y + x) - sage: g(x, y) = y + 2*x - sage: g - (x, y) |--> y + 2*x - sage: f._unify_args(g) - (x, y, z) - sage: g._unify_args(f) - (x, y, z) - - sage: f(x, y, z) = sin(x+y+z) - sage: g(w, t) = cos(w - t) - sage: g - (w, t) |--> cos(w - t) - sage: f._unify_args(g) - (t, w, x, y, z) - - sage: f(x, y, t) = y*(x^2-t) - sage: f - (x, y, t) |--> (x^2 - t)*y - sage: g(x, y, w) = x + y - cos(w) - sage: f._unify_args(g) - (x, y, t, w) - sage: g._unify_args(f) - (x, y, t, w) - sage: f*g - (x, y, t, w) |--> (x^2 - t)*y*(y + x - cos(w)) - - sage: f(x,y, t) = x+y - sage: g(x, y, w) = w + t - sage: f._unify_args(g) - (x, y, t, w) - sage: g._unify_args(f) - (x, y, t, w) - sage: f + g - (x, y, t, w) |--> y + x + w + t - - AUTHORS: - -- Bobby Moretti, thanks to William Stein for the rules - - """ - a = self.args() - b = x.args() - - # Rule #1 - if [str(x) for x in a] == [str(x) for x in b]: - return a - - # Rule #2 - new_list = [] - done = False - i = 0 - while not done and i < min(len(a), len(b)): - if var_cmp(a[i], b[i]) == 0: - new_list.append(a[i]) - i += 1 - else: - done = True - - temp = set([]) - # Sorting remaining variables. - for j in range(i, len(a)): - if not a[j] in temp: - temp.add(a[j]) - - for j in range(i, len(b)): - if not b[j] in temp: - temp.add(b[j]) - - temp = list(temp) - temp.sort(var_cmp) - new_list.extend(temp) - return tuple(new_list) - - -######################################################################################### -# End callable functions -######################################################################################### - -class SymbolicComposition(SymbolicOperation): - r""" - Represents the symbolic composition of $f \circ g$. - """ - def __init__(self, f, g): - """ - INPUT: - f, g -- both must be in the symbolic expression ring. - """ - SymbolicOperation.__init__(self, [f,g]) - - def _recursive_sub(self, kwds): - ops = self._operands - return ops[0](ops[1]._recursive_sub(kwds)) - - def _recursive_sub_over_ring(self, kwds, ring): - ops = self._operands - return ring(ops[0](ops[1]._recursive_sub_over_ring(kwds, ring=ring))) + v = SymbolicVariable(s) + _vars[s] = v + return v + +_syms = {} + +t = var('t') +x = var('x') +y = var('y') +z = var('z') +w = var('w') + +class Function_sin(PrimitiveFunction): + ''' + The sine function + ''' + def _repr_(self): + return "sin" + + def _latex_(self): + return "\\sin" def _is_atomic(self): return True - def _repr_(self, simplify=True): - if simplify: - if hasattr(self, '_simp'): - return self._simp._repr_(simplify=False) - else: - return self.simplify()._repr_(simplify=False) - ops = self._operands - return "%s(%s)"% (ops[0]._repr_(simplify=False), ops[1]._repr_(simplify=False)) - - def _latex_(self): - if not self.is_simplified(): - return self.simplify()._latex_() - ops = self._operands - # certain functions (such as \sqrt) need braces in LaTeX - if (ops[0]).tex_needs_braces(): - return r"%s{ %s }" % ( (ops[0])._latex_(), (ops[1])._latex_()) - # ... while others (such as \cos) don't - return r"%s \left( %s \right)"%((ops[0])._latex_(),(ops[1])._latex_()) - - def _maxima_init_(self): - ops = self._operands - return '%s(%s)' % (ops[0]._maxima_init_(), ops[1]._maxima_init_()) - - def _sys_init_(self, system): - ops = self._operands - return '%s(%s)' % (sys_init(ops[0],system), sys_init(ops[1],system)) - - def _mathematica_init_(self): - system = 'mathematica' - ops = self._operands - return '%s[%s]' % (sys_init(ops[0],system).capitalize(), sys_init(ops[1],system)) - - def __float__(self): - f = self._operands[0] - g = self._operands[1] - return float(f._approx_(float(g))) - - def __complex__(self): - f = self._operands[0] - g = self._operands[1] - return complex(f._approx_(float(g))) - - def _mpfr_(self, field): - """ - Coerce to a multiprecision real number. - - EXAMPLES: - sage: RealField(100)(sin(2)+cos(2)) - 0.49315059027853930839845163641 - - sage: RR(sin(pi)) - 0.000000000000000 - - sage: type(RR(sqrt(163)*pi)) - - - sage: RR(coth(pi)) - 1.00374187319732 - sage: RealField(100)(coth(pi)) - 1.0037418731973212882015526912 - sage: RealField(200)(acos(1/10)) - 1.4706289056333368228857985121870581235299087274579233690964 - """ - if not self.is_simplified(): - return self.simplify()._mpfr_(field) - f = self._operands[0] - g = self._operands[1] - x = f(g._mpfr_(field)) - if isinstance(x, SymbolicExpression): - if field.prec() <= 53: - return field(float(x)) - else: - raise TypeError, "precision loss" - else: - return x - - - def _complex_mpfr_field_(self, field): - """ - Coerce to a multiprecision complex number. - - EXAMPLES: - sage: ComplexField(100)(sin(2)+cos(2)+I) - 0.49315059027853930839845163641 + 1.0000000000000000000000000000*I - - """ - if not self.is_simplified(): - return self.simplify()._complex_mpfr_field_(field) - f = self._operands[0] - g = self._operands[1] - x = f(g._complex_mpfr_field_(field)) - if isinstance(x, SymbolicExpression): - if field.prec() <= 53: - return field(complex(x)) - else: - raise TypeError, "precision loss" - else: - return x - - def _complex_double_(self, field): - """ - Coerce to a complex double. - - EXAMPLES: - sage: CDF(sin(2)+cos(2)+I) - 0.493150590279 + 1.0*I - sage: CDF(coth(pi)) - 1.0037418732 - """ - if not self.is_simplified(): - return self.simplify()._complex_double_(field) - f = self._operands[0] - g = self._operands[1] - z = f(g._complex_double_(field)) - if isinstance(z, SymbolicExpression): - return field(complex(z)) - return z - - def _real_double_(self, field): - """ - Coerce to a real double. - - EXAMPLES: - sage: RDF(sin(2)+cos(2)) - 0.493150590279 - """ - if not self.is_simplified(): - return self.simplify()._real_double_(field) - f = self._operands[0] - g = self._operands[1] - z = f(g._real_double_(field)) - if isinstance(z, SymbolicExpression): - return field(float(z)) - return z - -class PrimitiveFunction(SymbolicExpression): - def __init__(self, needs_braces=False): - self._tex_needs_braces = needs_braces - - def plot(self, *args, **kwds): - f = self(var('x')) - return SymbolicExpression.plot(f, *args, **kwds) +sin = Function_sin() +_syms['sin'] = sin + +class Function_cos(PrimitiveFunction): + ''' + The cosine function + ''' + def _repr_(self): + return "cos" + + def _latex_(self): + return "\\cos" def _is_atomic(self): return True - - def tex_needs_braces(self): - return self._tex_needs_braces - - def __call__(self, x, *args): - if isinstance(x, float): - return self._approx_(x) - try: - return getattr(x, self._repr_())(*args) - except AttributeError: - return SymbolicComposition(self, SR(x)) - - def _approx_(self, x): # must *always* be called with a float x as input. - s = '%s(%s), numer'%(self._repr_(), float(x)) - return float(maxima.eval(s)) - -_syms = {} - -class Function_erf(PrimitiveFunction): - r""" - The error function, defined as $\text{erf}(x) = - \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt$. - """ - - def _repr_(self, simplify=True): - return "erf" - - def _latex_(self): - return "\\text{erf}" - - def _approx_(self, x): - return float(1 - pari(float(x)).erfc()) - -erf = Function_erf() -_syms['erf'] = erf - -class Function_abs(PrimitiveFunction): - """ - The absolute value function. - - EXAMPLES: - sage: abs(x) - abs(x) - sage: abs(x^2 + y^2) - y^2 + x^2 - sage: abs(-2) - 2 - sage: sqrt(x^2) - abs(x) - sage: abs(sqrt(x)) - sqrt(x) - """ - def _repr_(self, simplify=True): - return "abs" - - def _latex_(self): - return "\\abs" - - def _approx_(self, x): - return float(x.__abs__()) - - def __call__(self, x): # special case - return SymbolicComposition(self, SR(x)) - -abs_symbolic = Function_abs() -_syms['abs'] = abs_symbolic - - - -class Function_ceil(PrimitiveFunction): - """ - The ceiling function. - - EXAMPLES: - sage: a = ceil(2/5 + x) - sage: a - ceil(x + 2/5) - sage: a(4) - 5 - sage: a(4.0) - 5 - sage: ZZ(a(3)) - 4 - sage: a = ceil(x^3 + x + 5/2) - sage: a - ceil(x^3 + x + 1/2) + 2 - sage: a(x=2) - 13 - - sage: ceil(5.4) - 6 - sage: type(ceil(5.4)) - - """ - def _repr_(self, simplify=True): - return "ceil" - - def _latex_(self): - return "\\text{ceil}" - - def _maxima_init_(self): - return "ceiling" - - _approx_ = math.ceil - - def __call__(self, x): - try: - return x.ceil() - except AttributeError: - if isinstance(x, float): - return math.ceil(x) - return SymbolicComposition(self, SR(x)) - -ceil = Function_ceil() -_syms['ceiling'] = ceil # spelled ceiling in maxima - - -class Function_floor(PrimitiveFunction): - """ - The floor function. - - EXAMPLES: - sage: floor(5.4) - 5 - sage: type(floor(5.4)) - - sage: a = floor(5.4 + x); a - floor(x + 0.4000000000000004) + 5 - sage: a(2) - 7 - """ - def _repr_(self, simplify=True): - return "floor" - - def _latex_(self): - return "\\text{floor}" - - def _maxima_init_(self): - return "floor" - - _approx_ = math.floor - - def __call__(self, x): - try: - return x.floor() - except AttributeError: - if isinstance(x, float): - return math.floor(x) - return SymbolicComposition(self, SR(x)) - -floor = Function_floor() -_syms['floor'] = floor # spelled ceiling in maxima - - -class Function_sin(PrimitiveFunction): - """ - The sine function - """ - def _repr_(self, simplify=True): - return "sin" - - def _latex_(self): - return "\\sin" - - _approx_ = math.sin - - def __call__(self, x): - try: - return x.sin() - except AttributeError: - if isinstance(x, float): - return math.sin(x) - return SymbolicComposition(self, SR(x)) - -sin = Function_sin() -_syms['sin'] = sin - -class Function_cos(PrimitiveFunction): - """ - The cosine function - """ - def _repr_(self, simplify=True): - return "cos" - - def _latex_(self): - return "\\cos" - - _approx_ = math.cos - - def __call__(self, x): - try: - return x.cos() - except AttributeError: - if isinstance(x, float): - return math.cos(x) - return SymbolicComposition(self, SR(x)) - - cos = Function_cos() _syms['cos'] = cos class Function_sec(PrimitiveFunction): - """ + ''' The secant function - - EXAMPLES: - sage: sec(pi/4) - sqrt(2) - sage: RR(sec(pi/4)) - 1.41421356237310 - sage: sec(1/2) - sec(1/2) - sage: sec(0.5) - 1.139493927324549 - """ - def _repr_(self, simplify=True): + ''' + def _repr_(self): return "sec" def _latex_(self): return "\\sec" - - def _approx_(self, x): - return 1/math.cos(x) sec = Function_sec() _syms['sec'] = sec -class Function_tan(PrimitiveFunction): - """ - The tangent function - - EXAMPLES: - sage: tan(pi) - 0 - sage: tan(3.1415) - -0.0000926535900581913 - sage: tan(3.1415/4) - 0.999953674278156 - sage: tan(pi/4) - 1 - sage: tan(1/2) - tan(1/2) - sage: RR(tan(1/2)) - 0.546302489843790 - """ - def _repr_(self, simplify=True): - return "tan" - - def _latex_(self): - return "\\tan" - - def _approx_(self, x): - return math.tan(x) - -tan = Function_tan() -_syms['tan'] = tan - -def atan2(y, x): - return atan(y/x) - -_syms['atan2'] = atan2 - -class Function_asin(PrimitiveFunction): - """ - The arcsine function - - EXAMPLES: - sage: asin(0.5) - 0.523598775598299 - sage: asin(1/2) - pi/6 - sage: asin(1 + I*1.0) - 1.061275061905036*I + 0.6662394324925153 - """ - def _repr_(self, simplify=True): - return "asin" - - def _latex_(self): - return "\\sin^{-1}" - - def _approx_(self, x): - return math.asin(x) - -asin = Function_asin() -_syms['asin'] = asin - -class Function_acos(PrimitiveFunction): - """ - The arccosine function - - EXAMPLES: - sage: acos(0.5) - 1.04719755119660 - sage: acos(1/2) - pi/3 - sage: acos(1 + I*1.0) - 0.9045568943023813 - 1.061275061905036*I - """ - def _repr_(self, simplify=True): - return "acos" - - def _latex_(self): - return "\\cos^{-1}" - - def _approx_(self, x): - return math.acos(x) - -acos = Function_acos() -_syms['acos'] = acos - - -class Function_atan(PrimitiveFunction): - """ - The arctangent function. - - EXAMPLES: - sage: atan(1/2) - atan(1/2) - sage: RDF(atan(1/2)) - 0.463647609001 - sage: atan(1 + I) - atan(I + 1) - """ - def _repr_(self, simplify=True): - return "atan" - - def _latex_(self): - return "\\tan^{-1}" - - def _approx_(self, x): - return math.atan(x) - -atan = Function_atan() -_syms['atan'] = atan - - -####### -# Hyperbolic functions -####### - -#tanh -class Function_tanh(PrimitiveFunction): - """ - The hyperbolic tangent function. - - EXAMPLES: - sage: tanh(pi) - tanh(pi) - sage: tanh(3.1415) - 0.996271386633702 - sage: float(tanh(pi)) # random low-order bits - 0.99627207622074987 - sage: tan(3.1415/4) - 0.999953674278156 - sage: tanh(pi/4) - tanh(pi/4) - sage: RR(tanh(1/2)) - 0.462117157260010 - - sage: CC(tanh(pi + I*e)) - 0.997524731976164 - 0.00279068768100315*I - sage: ComplexField(100)(tanh(pi + I*e)) - 0.99752473197616361034204366446 - 0.0027906876810031453884245163923*I - sage: CDF(tanh(pi + I*e)) - 0.997524731976 - 0.002790687681*I - """ - def _repr_(self, simplify=True): - return "tanh" - - def _latex_(self): - return "\\tanh" - - def _approx_(self, x): - return math.tanh(x) - -tanh = Function_tanh() -_syms['tanh'] = tanh - -#sinh -class Function_sinh(PrimitiveFunction): - """ - The hyperbolic sine function. - - EXAMPLES: - sage: sinh(pi) - sinh(pi) - sage: sinh(3.1415) - 11.5476653707437 - sage: float(sinh(pi)) - 11.548739357257748 - sage: RR(sinh(pi)) - 11.5487393572577 - """ - def _repr_(self, simplify=True): - return "sinh" - - def _latex_(self): - return "\\sinh" - - def _approx_(self, x): - return math.sinh(x) - -sinh = Function_sinh() -_syms['sinh'] = sinh - -#cosh -class Function_cosh(PrimitiveFunction): - """ - The hyperbolic cosine function. - - EXAMPLES: - sage: cosh(pi) - cosh(pi) - sage: cosh(3.1415) - 11.5908832931176 - sage: float(cosh(pi)) - 11.591953275521519 - sage: RR(cosh(1/2)) - 1.12762596520638 - """ - def _repr_(self, simplify=True): - return "cosh" - - def _latex_(self): - return "\\cosh" - - def _approx_(self, x): - return math.cosh(x) - -cosh = Function_cosh() -_syms['cosh'] = cosh - -#coth -class Function_coth(PrimitiveFunction): - """ - The hyperbolic cotangent function. - - EXAMPLES: - sage: coth(pi) - coth(pi) - sage: coth(3.1415) - 1.00374256795520 - sage: float(coth(pi)) - 1.0037418731973213 - sage: RR(coth(pi)) - 1.00374187319732 - """ - def _repr_(self, simplify=True): - return "coth" - - def _latex_(self): - return "\\coth" - - def _approx_(self, x): - return 1/math.tanh(x) - -coth = Function_coth() -_syms['coth'] = coth - -#sech -class Function_sech(PrimitiveFunction): - """ - The hyperbolic secant function. - - EXAMPLES: - sage: sech(pi) - sech(pi) - sage: sech(3.1415) - 0.0862747018248192 - sage: float(sech(pi)) - 0.086266738334054432 - sage: RR(sech(pi)) - 0.0862667383340544 - """ - def _repr_(self, simplify=True): - return "sech" - - def _latex_(self): - return "\\sech" - - def _approx_(self, x): - return 1/math.cosh(x) - -sech = Function_sech() -_syms['sech'] = sech - - -#csch -class Function_csch(PrimitiveFunction): - """ - The hyperbolic cosecant function. - - EXAMPLES: - sage: csch(pi) - csch(pi) - sage: csch(3.1415) - 0.0865975907592133 - sage: float(csch(pi)) - 0.086589537530046945 - sage: RR(csch(pi)) - 0.0865895375300470 - """ - def _repr_(self, simplify=True): - return "csch" - - def _latex_(self): - return "\\csch" - - def _approx_(self, x): - return 1/math.sinh(x) - -csch = Function_csch() -_syms['csch'] = csch - -############# -# log and exp -############# - class Function_log(PrimitiveFunction): - """ - The log funtion. - - EXAMPLES: - sage: log(e^2) - 2 - sage: log(1024, 2) # the following is ugly (for now) - log(1024)/log(2) - sage: log(10, 4) - log(10)/log(4) - - sage: RDF(log(10,2)) - 3.32192809489 - sage: RDF(log(8, 2)) - 3.0 - sage: log(RDF(10)) - 2.30258509299 - sage: log(2.718) - 0.999896315728952 - """ - def __init__(self): - PrimitiveFunction.__init__(self) - - def _repr_(self, simplify=True): + ''' + The log function + ''' + def _repr_(self): return "log" - + def _latex_(self): return "\\log" - _approx_ = math.log - -function_log = Function_log() -ln = function_log - -def log(x, base=None): - if base is None: - try: - return x.log() - except AttributeError: - return function_log(x) - else: - try: - return x.log(base) - except AttributeError: - return function_log(x) / function_log(base) - -class Function_sqrt(PrimitiveFunction): - """ - The square root function. - - EXAMPLES: - sage: sqrt(-1) - I - sage: sqrt(2) - sqrt(2) - sage: sqrt(x^2) - abs(x) - """ - def __init__(self): - PrimitiveFunction.__init__(self, needs_braces=True) - - def _repr_(self, simplify=True): - return "sqrt" - - def _latex_(self): - return "\\sqrt" - - def __call__(self, x): - # if x is an integer or rational, never call the sqrt method - if isinstance(x, float): - return self._approx_(x) - if not isinstance(x, (Integer, Rational)): - try: - return x.sqrt() - except AttributeError: - pass - return SymbolicComposition(self, SR(x)) - - - def _approx_(self, x): - return math.sqrt(x) - -sqrt = Function_sqrt() -_syms['sqrt'] = sqrt - -class Function_exp(PrimitiveFunction): - """ - The square root function. - - EXAMPLES: - sage: exp(-1) - e^-1 - sage: exp(2) - e^2 - sage: exp(x^2 + log(x)) - x*e^x^2 - sage: exp(2.5) - 12.1824939607035 - sage: exp(float(2.5)) - 12.182493960703473 - sage: exp(RDF('2.5')) - 12.1824939607 - """ - def __init__(self): - PrimitiveFunction.__init__(self, needs_braces=True) - - def _repr_(self, simplify=True): - return "exp" - - def _latex_(self): - return "\\exp" - - def __call__(self, x): - # if x is an integer or rational, never call the sqrt method - if isinstance(x, float): - return self._approx_(x) - if not isinstance(x, (Integer, Rational)): - try: - return x.exp() - except AttributeError: - pass - return SymbolicComposition(self, SR(x)) - - - def _approx_(self, x): - return math.exp(x) - -exp = Function_exp() -_syms['exp'] = exp - +log = Function_log() +_syms['log'] = log ####################################################### -# Symbolic functions -####################################################### - -class SymbolicFunction(PrimitiveFunction): - """ - A formal symbolic function. - - EXAMPLES: - sage: f = function('foo') - sage: g = f(x,y,z) - sage: g - foo(x, y, z) - sage: g(x=var('theta')) - foo(theta, y, z) - """ - def __init__(self, name): - PrimitiveFunction.__init__(self, needs_braces=True) - self._name = str(name) - - def _repr_(self, simplify=True): - return self._name - - def _is_atomic(self): - return True - - def _latex_(self): - return "{\\rm %s}"%self._name - - def _maxima_init_(self): - return "'%s"%self._name - - def _approx_(self, x): - raise TypeError - - def __call__(self, *args): - return SymbolicFunctionEvaluation(self, [SR(x) for x in args]) - -class SymbolicFunction_delayed(SymbolicFunction): - def simplify(self): - return self - - def is_simplified(self): - return True - - def _maxima_init_(self): - return "%s"%self._name - - def __call__(self, *args): - return SymbolicFunctionEvaluation_delayed(self, [SR(x) for x in args]) - - - -class SymbolicFunctionEvaluation(SymbolicExpression): - """ - The result of evaluating a formal symbolic function. - - EXAMPLES: - sage: h = function('gfun', x); h - gfun(x) - sage: k = h.integral(x); k - integrate(gfun(x), x) - sage: k(gfun=sin) - -cos(x) - sage: k(gfun=cos) - sin(x) - sage: k.diff(x) - gfun(x) - """ - def __init__(self, f, args): - """ - INPUT: - f -- symbolic function - args -- a tuple or list of symbolic expressions, at which - f is formally evaluated. - """ - SymbolicExpression.__init__(self) - self._f = f - if not isinstance(args, tuple): - args = tuple(args) - self._args = args - - def _is_atomic(self): - return True - - def arguments(self): - return tuple(self._args) - - def _repr_(self, simplify=True): - if simplify: - return self.simplify()._repr_(simplify=False) - else: - return '%s(%s)'%(self._f._name, ', '.join([x._repr_(simplify=simplify) - for x in self._args])) - - def _latex_(self): - return "{\\rm %s}(%s)"%(self._f._name, ', '.join([x._latex_() for - x in self._args])) - - def _maxima_init_(self): - try: - return self.__maxima_init - except AttributeError: - n = self._f._name - if not (n in ['integrate', 'diff']): - n = "'" + n - s = "%s(%s)"%(n, ', '.join([x._maxima_init_() - for x in self._args])) - self.__maxima_init = s - return s - - def _recursive_sub(self, kwds): - """ - EXAMPLES: - sage: f = function('foo',x); f - foo(x) - sage: f(foo=sin) - sin(x) - sage: f(x+y) - foo(y + x) - sage: a = f(pi) - sage: a.substitute(foo = sin) - 0 - sage: a = f(pi/2) - sage: a.substitute(foo = sin) - 1 - sage: b = f(pi/3) + x + y - sage: b - y + x + foo(pi/3) - sage: b(foo = sin) - y + x + sqrt(3)/2 - sage: b(foo = cos) - y + x + 1/2 - sage: b(foo = cos, x=y) - 2*y + 1/2 - """ - function_sub = False - for x in kwds.keys(): - if repr(x) == self._f._name: - g = kwds[x] - function_sub = True - break - if function_sub: - del kwds[x] - - arg = tuple([SR(x._recursive_sub(kwds)) for x in self._args]) - - if function_sub: - return g(*arg) - else: - return self.__class__(self._f, arg) - - def _recursive_sub_over_ring(self, kwds, ring): - raise TypeError, "no way to coerce the formal function to ring." - - def variables(self): - """ - Return the variables appearing in the simplified form of self. - - EXAMPLES: - sage: foo = function('foo') - sage: w = foo(x,y,a,b,z) + t - sage: w - foo(x, y, a, b, z) + t - sage: w.variables() - (a, b, t, x, y, z) - """ - try: - return self.__variables - except AttributeError: - pass - vars = sum([list(op.variables()) for op in self._args], []) - vars.sort(var_cmp) - vars = tuple(vars) - self.__variables = vars - return vars - -class SymbolicFunctionEvaluation_delayed(SymbolicFunctionEvaluation): - def simplify(self): - return self - - def is_simplified(self): - return True - - def __float__(self): - return float(self._maxima_()) - - def __complex__(self): - return complex(self._maxima_()) - - def _real_double_(self, R): - return R(float(self)) - - def _complex_double_(self, C): - return C(float(self)) - - def _mpfr_(self, field): - if field.prec() <= 53: - return field(float(self)) - raise TypeError - - def _complex_mpfr_field_(self, field): - if field.prec() <= 53: - return field(float(self)) - raise TypeError - - def _maxima_init_(self): - try: - return self.__maxima_init - except AttributeError: - n = self._f._name - s = "%s(%s)"%(n, ', '.join([x._maxima_init_() - for x in self._args])) - self.__maxima_init = s - return s - - - -_functions = {} -def function(s, *args): - """ - Create a formal symbolic function with the name \emph{s}. - - EXAMPLES: - sage: f = function('cr', a) - sage: g = f.diff(a).integral(b) - sage: g - diff(cr(a), a, 1)*b - sage: g(cr=cos) - -sin(a)*b - sage: g(cr=sin(x) + cos(x)) - (cos(a) - sin(a))*b - """ - if len(args) > 0: - return function(s)(*args) - if isinstance(s, SymbolicFunction): - return s - s = str(s) - if ',' in s: - return tuple([function(x.strip()) for x in s.split(',')]) - elif ' ' in s: - return tuple([function(x.strip()) for x in s.split()]) - try: - X = _functions[s]() - if not X is None: - return X - except KeyError: - pass - v = SymbolicFunction(s) - _functions[s] = weakref.ref(v) - return v - -####################################################### - - - - -####################################################### - -symtable = {'%pi':'pi', '%e': 'e', '%i':'I', '%gamma':'euler_gamma'} - -from sage.rings.infinity import infinity, minus_infinity - -_syms['inf'] = infinity -_syms['minf'] = minus_infinity - -from sage.misc.multireplace import multiple_replace - -maxima_tick = re.compile("'[a-z|A-Z|0-9|_]*") - -maxima_qp = re.compile("\?\%[a-z|A-Z|0-9|_]*") # e.g., ?%jacobi_cd - -maxima_var = re.compile("\%[a-z|A-Z|0-9|_]*") # e.g., ?%jacobi_cd - -def symbolic_expression_from_maxima_string(x, equals_sub=False, maxima=maxima): +symtable = {'%pi':'_Pi_', '%e': '_E_', '%i':'_I_'} +import sage.functions.constants as c +_syms['_Pi_'] = SER(c.Pi) +_syms['_E_'] = SER(c.E) +_syms['_I_'] = SER(CC.gen(0)) # change when we create a symbolic I. + +def symbolic_expression_from_maxima_string(x): global _syms - - if len(x) == 0: - raise RuntimeError, "invalid symbolic expression -- ''" - maxima.set('_tmp_',x) - - # This is inefficient since it so rarely is needed: - #r = maxima._eval_line('listofvars(_tmp_);')[1:-1] - - s = maxima._eval_line('_tmp_;') - - formal_functions = maxima_tick.findall(s) - if len(formal_functions) > 0: - for X in formal_functions: - _syms[X[1:]] = function(X[1:]) - # You might think there is a potential very subtle bug if 'foo is in a string literal -- - # but string literals should *never* ever be part of a symbolic expression. - s = s.replace("'","") - - delayed_functions = maxima_qp.findall(s) - if len(delayed_functions) > 0: - for X in delayed_functions: - _syms[X[2:]] = SymbolicFunction_delayed(X[2:]) - s = s.replace("?%","") - - s = multiple_replace(symtable, s) - s = s.replace("%","") - - if equals_sub: - s = s.replace('=','==') - - global is_simplified - try: - # use a global flag so all expressions obtained via - # evaluation of maxima code are assumed pre-simplified - is_simplified = True - last_msg = '' - while True: - try: - w = sage_eval(s, _syms) - except NameError, msg: - if msg == last_msg: - raise NameError, msg - msg = str(msg) - last_msg = msg - i = msg.find("'") - j = msg.rfind("'") - nm = msg[i+1:j] - _syms[nm] = var(nm) - else: - break - if isinstance(w, (list, tuple)): - return w - else: - x = SR(w) - return x - except SyntaxError: - raise TypeError, "unable to make sense of Maxima expression '%s' in SAGE"%s - finally: - is_simplified = False + maxima.eval('listdummyvars: false') + maxima.eval('_tmp_: %s'%x) + r = maxima.eval('listofvars(_tmp_)')[1:-1] + if len(r) > 0: + # Now r is a list of all the indeterminate variables that + # appear in the expression x. + v = r.split(',') + for a in v: + _syms[a] = var(a) + s = maxima.eval('_tmp_') + for x, y in symtable.iteritems(): + s = s.replace(x, y) + #print s + #print _syms + return SymbolicExpressionRing(sage_eval(s, _syms)) def symbolic_expression_from_maxima_element(x): return symbolic_expression_from_maxima_string(x.name()) -def evaled_symbolic_expression_from_maxima_string(x): - return symbolic_expression_from_maxima_string(maxima.eval(x)) - - Index: age/calculus/equations.py =================================================================== --- sage/calculus/equations.py (revision 4058) +++ (revision ) @@ -1,374 +1,0 @@ -r""" -Symbolic Equations and Inequalities. - -SAGE can solving symbolic equations and expressing inequalities. -For example, we derive the quadratic formula as follows: - - sage: qe = (a*x^2 + b*x + c == 0) - sage: print qe - 2 - a x + b x + c == 0 - sage: print solve(qe, x) - [ - 2 - - sqrt(b - 4 a c) - b - x == ---------------------- - 2 a, - 2 - sqrt(b - 4 a c) - b - x == -------------------- - 2 a - ] - -AUTHORS: - -- Bobby Moretti: initial version - -- William Stein: second version - -EXAMPLES: - sage: f = x^2 + y^2 == 1 - sage: f.solve(x) - [x == (-sqrt(1 - y^2)), x == sqrt(1 - y^2)] - - sage: f = x^5 + a - sage: solve(f==0,x) - [x == -e^(2*I*pi/5)*a^(1/5), x == -e^(4*I*pi/5)*a^(1/5), x == -e^(-(4*I*pi/5))*a^(1/5), x == -e^(-(2*I*pi/5))*a^(1/5), x == (-a^(1/5))] -""" - -_assumptions = [] - -from sage.structure.sage_object import SageObject -from sage.structure.sequence import Sequence -from sage.interfaces.maxima import maxima -from sage.misc.sage_eval import sage_eval - -import operator - -symbols = {operator.lt:' < ', operator.le:' <= ', operator.eq:' == ', - operator.ne:' != ', - operator.ge:' >= ', operator.gt:' > '} - -maxima_symbols = dict(symbols) -maxima_symbols[operator.eq] = '=' - - -latex_symbols = {operator.lt:' < ', operator.le:' \\leq ', operator.eq:' = ', - operator.ne:' \\neq ', - operator.ge:' \\geq ', operator.gt:' > '} - -comparisons = {operator.lt:set([-1]), operator.le:set([-1,0]), operator.eq:set([0]), - operator.ne:set([-1,1]), operator.ge:set([0,1]), operator.gt:set([1])} - -def var_cmp(x,y): - return cmp(str(x), str(y)) - -def paren(x): - if x._is_atomic(): - return repr(x) - else: - return '(%s)'%repr(x) - -class SymbolicEquation(SageObject): - def __init__(self, left, right, op): - self._left = left - self._right = right - self._op = op - - def __call__(self, *args, **argv): - return self._op(self._left(*args, **argv), self._right(*args,**argv)) - - def __cmp__(self, right): - """ - EXAMPLES: - sage: (x>0) == (x>0) - True - sage: (x>0) == (x>1) - False - sage: (x>0) != (x>1) - True - """ - if not isinstance(right, SymbolicEquation): - return cmp(type(self), type(right)) - c = cmp(self._op, right._op) - if c: return c - i = bool(self._left == right._left) - if not i: return -1 - i = bool(self._right == right._right) - if not i: return 1 - return 0 - - def _repr_(self): - return "%s%s%s" %(paren(self._left), symbols[self._op], paren(self._right)) - - def variables(self): - """ - EXAMPLES: - sage: f = (x+y+w) == (x^2 - y^2 - z^3); f - (y + x + w) == (-z^3 - y^2 + x^2) - sage: f.variables() - [w, x, y, z] - """ - try: - return self.__variables - except AttributeError: - v = list(set(list(self._left.variables()) + list(self._right.variables()))) - v.sort(var_cmp) - self.__variables = v - return v - - def operator(self): - return self._op - - def left(self): - return self._left - lhs = left - left_hand_side = left - - def right(self): - return self._right - rhs = right - right_hand_side = right - - def __str__(self): - """ - EXAMPLES: - sage: f = (x^2 - x == 0) - sage: f - (x^2 - x) == 0 - sage: print f - 2 - x - x == 0 - """ - s = self._maxima_().display2d(onscreen=False) - s = s.replace('%pi','pi').replace('%i',' I').replace('%e', ' e').replace(' = ',' == ') - return s - - def _latex_(self): - return "%s %s %s" %(self._left._latex_(), latex_symbols[self._op], - self._right._latex_()) - - # this is an excellent idea by Robert Bradshaw - #def __nonzero__(self): - # result = self._left.__cmp__(self._right) - # return result in comparisons[self._op] - def __nonzero__(self): - """ - Return True if this equality is definitely true. Return False - if it is false or the algorithm for testing equality is - inconclusive. - """ - m = self._maxima_() - try: - s = m.parent()._eval_line('is (%s)'%m.name()) - except TypeError, msg: - #raise ValueError, "unable to evaluate the predicate '%s'"%repr(self) - return cmp(self._left._maxima_() , self._right._maxima_()) == 0 - return s == 'true' - - def _maxima_init_(self, maxima=maxima, assume=False): - l = self._left._maxima_init_() - r = self._right._maxima_init_() - if assume and self._op == operator.eq: - return 'equal(%s, %s)'%(l, r) - return '(%s)%s(%s)' % (l, maxima_symbols[self._op], r) - - def assume(self): - if not self in _assumptions: - m = self._maxima_init_(assume=True) - maxima.assume(m) - _assumptions.append(self) - - def forget(self): - """ - Forget the given constraint. - """ - m = self._maxima_() - m.parent().forget(m) - try: - _assumptions.remove(self) - except ValueError: - pass - - def solve(self, x=None, multiplicities=False): - """ - Symbolically solve for the given variable. - - WARNING: In many cases, only one solution is computed. - - INPUT: - x -- a SymbolicVariable object (if not given, the first in the expression is used) - multiplicities -- (default: False) if True, also returns the multiplicities - of each solution, in order. - - OUTPUT: - A list of SymbolicEquations with the variable to solve for on the - left hand side. - - EXAMPLES: - sage: S = solve(x^3 - 1 == 0, x) - sage: S - [x == ((sqrt(3)*I - 1)/2), x == ((-sqrt(3)*I - 1)/2), x == 1] - sage: S[0] - x == ((sqrt(3)*I - 1)/2) - sage: S[0].right() - (sqrt(3)*I - 1)/2 - - We illustrate finding multiplicities of solutions: - sage: f = (x-1)^5*(x^2+1) - sage: solve(f == 0, x) - [x == -1*I, x == I, x == 1] - sage: solve(f == 0, x, multiplicities=True) - ([x == -1*I, x == I, x == 1], [1, 1, 5]) - sage: solve(g == 0, x) - [] - """ - if not self._op is operator.eq: - raise ValueError, "solving only implemented for equalities" - if x is None: - v = self.variables() - if len(v) == 0: - if multiplicities: - return [], [] - else: - return [] - x = v[0] - - m = self._maxima_() - P = m.parent() - s = m.solve(x).str() - - X = string_to_list_of_solutions(s) - if multiplicities: - if len(X) == 0: - return X, [] - else: - return X, sage_eval(P.get('multiplicities')) - else: - return X - - - -def assume(*args): - """ - Make the given assumptions. - - INPUT: - *args -- assumptions - - EXAMPLES: - sage: assume(x > 0) - sage: bool(sqrt(x^2) == x) - True - sage: forget() - sage: bool(sqrt(x^2) == x) - False - """ - for x in args: - if isinstance(x, (tuple, list)): - for y in x: - assume(y) - else: - try: - x.assume() - except KeyError: - raise TypeError, "assume not defined for objects of type '%s'"%type(x) - -def forget(*args): - """ - Forget the given assumption, or call with no arguments to forget - all assumptions. - - Here an assumption is some sort of symbolic constraint. - - INPUT: - *args -- assumptions (default: forget all assumptions) - - EXAMPLES: - We define and forget multiple assumptions: - sage: assume(x>0, y>0, z == 1, y>0) - sage: assumptions() - [x > 0, y > 0, z == 1] - sage: forget(x>0, z==1) - sage: assumptions() - [y > 0] - """ - if len(args) == 0: - forget_all() - return - for x in args: - if isinstance(x, (tuple, list)): - for y in x: - assume(y) - else: - try: - x.forget() - except KeyError: - raise TypeError, "forget not defined for objects of type '%s'"%type(x) - -def assumptions(): - """ - List all current symbolic assumptions. - - EXAMPLES: - sage: forget() - sage: assume(x^2+y^2 > 0) - sage: assumptions() - [(y^2 + x^2) > 0] - sage: forget(x^2+y^2 > 0) - sage: assumptions() - [] - sage: assume(x > y) - sage: assume(z > w) - sage: assumptions() - [x > y, z > w] - sage: forget() - sage: assumptions() - [] - """ - return list(_assumptions) - -def forget_all(): - global _assumptions - if len(_assumptions) == 0: - return - maxima._eval_line('forget(facts());') - #maxima._eval_line('forget([%s]);'%(','.join([x._maxima_init_() for x in _assumptions]))) - _assumptions = [] - -def solve(f, *args, **kwds): - """ - Algebraically solve an equation of system of equations for given variables. - - INPUT: - f -- equation or system of equations (given by a list or tuple) - *args -- variables to solve for. - - EXAMPLES: - sage: solve([x+y==6, x-y==4], x, y) - [[x == 5, y == 1]] - sage: solve([x^2+y^2 == 1, y^2 == x^3 + x + 1], x, y) - [[x == ((-sqrt(3)*I - 1)/2), y == ((-sqrt(3 - sqrt(3)*I))/sqrt(2))], - [x == ((-sqrt(3)*I - 1)/2), y == (sqrt(3 - sqrt(3)*I)/sqrt(2))], - [x == ((sqrt(3)*I - 1)/2), y == ((-sqrt(sqrt(3)*I + 3))/sqrt(2))], - [x == ((sqrt(3)*I - 1)/2), y == (sqrt(sqrt(3)*I + 3)/sqrt(2))], - [x == 0, y == -1], - [x == 0, y == 1]] - """ - if isinstance(f, (list, tuple)): - m = maxima(list(f)) - try: - s = m.solve(args) - except: - raise ValueError, "Unable to solve %s for %s"%(f, args) - a = repr(s) - return string_to_list_of_solutions(a) - else: - return f.solve(*args, **kwds) - -import sage.categories.all -objs = sage.categories.all.Objects() - -def string_to_list_of_solutions(s): - from sage.calculus.calculus import symbolic_expression_from_maxima_string - v = symbolic_expression_from_maxima_string(s, equals_sub=True) - return Sequence(v, universe=objs) - Index: sage/calculus/functional.py =================================================================== --- sage/calculus/functional.py (revision 4059) +++ sage/calculus/functional.py (revision 2327) @@ -1,327 +1,10 @@ -""" -Functional notation support for common calculus methods. -""" +from calculus import SER, SymbolicExpression -from calculus import SR, SymbolicExpression, CallableSymbolicExpression +def diff(f, *args): + if not isinstance(f, SymbolicExpression): + f = SER(f) + return f.derivative(*args) -def simplify(f): - """ - Simplify the expression f. - """ - try: - return f.simplify() - except AttributeError: - return f +derivative = diff -def derivative(f, *args, **kwds): - """ - The derivative of f. - - EXAMPLES: - We differentiate a callable symbolic function: - sage: f(x,y) = x*y + sin(x^2) + e^(-x) - sage: f - (x, y) |--> x*y + sin(x^2) + e^(-x) - sage: derivative(f, x) - (x, y) |--> y + 2*x*cos(x^2) - e^(-x) - sage: derivative(f, y) - (x, y) |--> x - - We differentiate a polynomial: - sage: t = polygen(QQ, 't') - sage: f = (1-t)^5; f - -t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1 - sage: derivative(f) - -5*t^4 + 20*t^3 - 30*t^2 + 20*t - 5 - - We differentiate a symbolic expression: - sage: f = exp(sin(a - x^2))/x - sage: diff(f, x) - -2*cos(x^2 - a)*e^(-sin(x^2 - a)) - (e^(-sin(x^2 - a))/x^2) - sage: diff(f, a) - cos(x^2 - a)*e^(-sin(x^2 - a))/x - """ - try: - return f.derivative(*args, **kwds) - except AttributeError: - pass - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.derivative(*args, **kwds) - -diff = derivative -differentiate = derivative - -def integral(f, *args, **kwds): - """ - The integral of f. - - EXAMPLES: - sage: integral(sin(x), x) - -cos(x) - sage: integral(sin(x)^2, x, pi, 123*pi/2) - 121*pi/4 - sage: integral( sin(x), x, 0, pi) - 2 - - We integrate a symbolic function: - sage: f(x,y) = x*y/z + sin(z) - sage: integral(f, z) - (x, y) |--> x*y*log(z) - cos(z) - - sage: assume(b-a>0) - sage: integral( sin(x), x, a, b) - cos(a) - cos(b) - sage: forget() - - sage: print integral(x/(x^3-1), x) - 2 x + 1 - 2 atan(-------) - log(x + x + 1) sqrt(3) log(x - 1) - - --------------- + ------------- + ---------- - 6 sqrt(3) 3 - - sage: print integral( exp(-x^2), x ) - sqrt( pi) erf(x) - ---------------- - 2 - - You can have SAGE calculate multiple integrals. For example, - consider the function $exp(y^2)$ on the region between the lines - $x=y$, $x=1$, and $y=0$. We find the value of the integral on - this region using the command: - sage: area = integral(integral(exp(y^2),x,0,y),y,0,1); area - e/2 - 1/2 - sage: float(area) - 0.85914091422952255 - - We compute the line integral of sin(x) along the arc of the curve - $x=y^4$ from $(1,-1)$ to $(1,1)$: - sage: (x,y) = (t^4,t) - sage: (dx,dy) = (diff(x,t), diff(y,t)) - sage: integral(sin(x)*dx, t,-1, 1) - 0 - sage: restore('x,y') # restore the symbolic variables x and y - - SAGE is unable to do anything with the following integral: - sage: print integral( exp(-x^2)*log(x), x ) - / 2 - [ - x - I e log(x) dx - ] - / - - SAGE does not know how to compute this integral either. - sage: print integral( exp(-x^2)*ln(x), x, 0, oo) - inf - / 2 - [ - x - I e log(x) dx - ] - / - 0 - - This definite integral is easy: - sage: integral( ln(x)/x, x, 1, 2) - log(2)^2/2 - - SAGE can't do this elliptic integral (yet): - sage: integral(1/sqrt(2*t^4 - 3*t^2 - 2), t, 2, 3) - integrate(1/(sqrt(2*t^4 - 3*t^2 - 2)), t, 2, 3) - - A double integral: - sage: integral(integral(x*y^2, x, 0, y), y, -2, 2) - 32/5 - - This illustrates using assumptions: - sage: integral(abs(x), x, 0, 5) - 25/2 - sage: integral(abs(x), x, 0, a) - integrate(abs(x), x, 0, a) - sage: assume(a>0) - sage: integral(abs(x), x, 0, a) - a^2/2 - sage: forget() # forget the assumptions. - - We integrate and differentiate a huge mess: - sage: f = (x^2-1+3*(1+x^2)^(1/3))/(1+x^2)^(2/3)*x/(x^2+2)^2 - sage: g = integral(f, x) - sage: h = f - diff(g, x) - - Numerically h is 0, but the symbolic equality checker - unfortunately can't tell for sure: - sage: print [float(h(i)) for i in range(5)] - [0.0, -1.1102230246251565e-16, -8.3266726846886741e-17, -4.163336342344337e-17, -6.9388939039072284e-17] - sage: bool(h == 0) - False - """ - try: - return f.integral(*args, **kwds) - except AttributeError: - pass - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.integral(*args, **kwds) - -integrate = integral - -def limit(f, dir=None, **argv): - """ - Return the limit as the variable v approaches a from the - given direction. - - \begin{verbatim} - limit(expr, x = a) - limit(expr, x = a, dir='above') - \end{verbatim} - - INPUT: - dir -- (default: None); dir may have the value `plus' (or 'above') - for a limit from above, `minus' (or 'below') for a limit from - below, or may be omitted (implying a two-sided - limit is to be computed). - **argv -- 1 named parameter - - ALIAS: You can also use lim instead of limit. - - EXAMPLES: - sage: limit(sin(x)/x, x=0) - 1 - sage: limit(exp(x), x=oo) - +Infinity - sage: lim(exp(x), x=-oo) - 0 - sage: lim(1/x, x=0) - und - - SAGE does not know how to do this limit (which is 0), - so it returns it unevaluated: - sage: lim(exp(x^2)*(1-erf(x)), x=infinity) - limit(e^x^2 - e^x^2*erf(x), x, +Infinity) - - """ - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.limit(dir=dir, **argv) - -lim = limit - -def taylor(f, v, a, n): - """ - Expands self in a truncated Taylor or Laurent series in the - variable v around the point a, containing terms through $(x - a)^n$. - - INPUT: - v -- variable - a -- number - n -- integer - - EXAMPLES: - sage: taylor (sqrt (1 - k^2*sin(x)^2), x, 0, 6) - 1 - (k^2*x^2/2) - ((3*k^4 - 4*k^2)*x^4/24) - ((45*k^6 - 60*k^4 + 16*k^2)*x^6/720) - sage: taylor ((x + 1)^n, x, 0, 4) - 1 + n*x + (n^2 - n)*x^2/2 + (n^3 - 3*n^2 + 2*n)*x^3/6 + (n^4 - 6*n^3 + 11*n^2 - 6*n)*x^4/24 - - """ - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.taylor(v=v,a=a,n=n) - - -def expand(x, *args, **kwds): - """ - EXAMPLES: - sage: a = (1+I)*(2-sqrt(3)*I); a - (I + 1)*(2 - sqrt(3)*I) - sage: expand(a) - -sqrt(3)*I + 2*I + sqrt(3) + 2 - sage: a = (x-1)*(x^2 - 1); a - (x - 1)*(x^2 - 1) - sage: expand(a) - x^3 - x^2 - x + 1 - - You can also use expand on polynomial, integer, and other - factorizations: - sage: x = polygen(ZZ) - sage: F = factor(x^12 - 1); F - (x - 1) * (x + 1) * (x^2 - x + 1) * (x^2 + 1) * (x^2 + x + 1) * (x^4 - x^2 + 1) - sage: expand(F) - x^12 - 1 - sage: F.expand() - x^12 - 1 - sage: F = factor(2007); F - 3^2 * 223 - sage: expand(F) - 2007 - - Note: If you want to compute the expanded form of a polynomial - arithmetic operation quickly and the coefficients of the polynomial - all lie in some ring, e.g., the integers, it is vastly faster to - create a polynomial ring and do the arithmetic there. - - sage: x = polygen(ZZ) # polynomial over a given base ring. - sage: f = sum(x^n for n in range(5)) - sage: f*f # much faster, even if the degree is huge - x^8 + 2*x^7 + 3*x^6 + 4*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1 - - """ - try: - return x.expand(*args, **kwds) - except AttributeError: - return x - - -def laplace(f, t, s): - r""" - Attempts to compute and return the Laplace transform of self - with respect to the variable t and transform parameter s. If - Laplace cannot find a solution, a delayed function is returned. - - The function that is returned maybe be viewed as a function of s. - - EXAMPLES: - sage: f = exp (2*t + a) * sin(t) * t; f - t*e^(2*t + a)*sin(t) - sage: L = laplace(f, t, s); L - e^a*(2*s - 4)/((s^2 - 4*s + 5)^2) - sage: inverse_laplace(L, s, t) - t*e^(2*t + a)*sin(t) - - Unable to compute solution: - sage: laplace(1/s, s, t) - laplace(1/s, s, t) - """ - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.laplace(t,s) - -def inverse_laplace(f, t, s): - r""" - Attempts to compute and return the inverse Laplace transform of - self with respect to the variable t and transform parameter s. If - Laplace cannot find a solution, a delayed function is returned, which - is called \code{ilt}. - - EXAMPLES: - sage: f = t*cos(t) - sage: L = laplace(f, t, s); L - 2*s^2/(s^2 + 1)^2 - (1/(s^2 + 1)) - sage: inverse_laplace(L, s, t) - t*cos(t) - sage: print inverse_laplace(1/(s^3+1), s, t) - sqrt(3) t sqrt(3) t - sin(---------) cos(---------) - t - t/2 2 2 e - e (-------------- - --------------) + ----- - sqrt(3) 3 3 - - No explicit inverse Laplace transform, so one is returned formally as a function ilt. - sage: inverse_laplace(cos(s), s, t) - ilt(cos(s), s, t) - """ - if not isinstance(f, SymbolicExpression): - f = SR(f) - return f.inverse_laplace(t,s) - - Index: age/calculus/notes.txt =================================================================== --- sage/calculus/notes.txt (revision 4057) +++ (revision ) @@ -1,43 +1,0 @@ -On 4/22/07, Ondrej Certik wrote: -> As to the extensibility - I think it would be quite difficult to -> extend for example Maxima's limits facility (there are some limits -> that Maxima cannot do, but SymPy can), or Maxima's differential -> equations solver module. Either it would have to be done in LISP, or -> rewrite the whole module to python, neither of which I find easy. Or -> is there a better approach? - -I had in mind the following iterative approach: - - (1) Implement the basic limit formulas for products, sums, quotients, etc., - in Python. - (2) This reduces computing limits of symbolic expressions to computing - the limits of the leaves in the tree, i.e., symbolic variables, constants, and - primitive functions (like sinh, exp, log, erf). - (3) Limits of symbolic variables and constants are trivial. - (4) For some special functions one writes an optional method _limit_ - that computes the limit of that special function at a point from a given - direction. The default _limit_ method in the base class computes the - limit using maxima. So for each function for which you want better - speed or a different behavior from maxima, you just fill in the _limit_ method. - -Exactly the steps above would also work for symbolic differentiation. -(Integration is a completely different story.) - -Ondrej doesn't this will work (I totally disagree): - -"I don't think that would work for limits (it should work for -differentiation though) except some simple cases. As an example, let's -take this limit, that Maxima cannot do: - -limit((5**x+3**x)**(1/x), x, infty) - -(if you type this in SymPy, you will get 5, because we use the Gruntz -algorithm, as described here: -http://sympy.googlecode.com/svn/trunk/doc/gruntz.pdf). The only thing -that occurs to me how to fix maxima is to match the expression and -return 5 immediatelly, or implement the whole algorithm from scratch, -but then you will just write the same code as we did for SymPy. - -Integration is quite easy - just match the expression and return a -table integral. The general Risch algorithm is difficult, but I think -Axiom can do it." Index: age/calculus/predefined.py =================================================================== --- sage/calculus/predefined.py (revision 4062) +++ (revision ) @@ -1,53 +1,0 @@ -from calculus import var - -a = var('a') -b = var('b') -c = var('c') -d = var('d') -f = var('f') -g = var('g') -h = var('h') -i = var('i') -j = var('j') -k = var('k') -l = var('l') -m = var('m') -n = var('n') -o = var('o') -p = var('p') -q = var('q') -r = var('r') -s = var('s') -t = var('t') -u = var('u') -v = var('v') -w = var('w') -x = var('x') -y = var('y') -z = var('z') -A = var('A') -B = var('B') -C = var('C') -D = var('D') -E = var('E') -F = var('F') -G = var('G') -H = var('H') -J = var('J') -K = var('K') -L = var('L') -M = var('M') -N = var('N') -O = var('O') -P = var('P') -Q = var('Q') -R = var('R') -S = var('S') -T = var('T') -U = var('U') -V = var('V') -W = var('W') -X = var('X') -Y = var('Y') -Z = var('Z') - Index: age/calculus/tests.py =================================================================== --- sage/calculus/tests.py (revision 4061) +++ (revision ) @@ -1,57 +1,0 @@ -""" -TESTS -Compute the Christoffel symbol. - - sage: var('r theta phi') - (r, theta, phi) - sage: m = matrix(SR, [[(1-1/r),0,0,0],[0,-(1-1/r)^(-1),0,0],[0,0,-r^2,0],[0,0,0,-r^2*(sin(theta))^2]]) - sage: print m - [ 1 - (1/r) 0 0 0] - [ 0 -1/(1 - (1/r)) 0 0] - [ 0 0 -r^2 0] - [ 0 0 0 -r^2*sin(theta)^2] - - sage: def christoffel(i,j,k,vars,g): - ... s = 0 - ... ginv = g^(-1) - ... for l in range(g.nrows()): - ... s = s + (1/2)*ginv[k,l]*(g[j,l].diff(vars[i])+g[i,l].diff(vars[j])-g[i,j].diff(vars[l])) - ... return s - - sage: christoffel(3,3,2, [t,r,theta,phi], m) - -cos(theta)*sin(theta) - sage: X = christoffel(1,1,1,[t,r,theta,phi],m) - sage: print X - 1 - - - 1 - r - ------------- - 1 2 2 - 2 (1 - -) r - r - sage: print X.rational_simplify() - 1 - - ---------- - 2 - 2 r - 2 r - -Some basic things: - - sage: f(x,y) = x^3 + sinh(1/y) - sage: f - (x, y) |--> sinh(1/y) + x^3 - sage: f^3 - (x, y) |--> (sinh(1/y) + x^3)^3 - sage: (f^3).expand() - (x, y) |--> sinh(1/y)^3 + 3*x^3*sinh(1/y)^2 + 3*x^6*sinh(1/y) + x^9 - -A polynomial over a symbolic base ring: - sage: R = SR[x] - sage: f = R([1/sqrt(2), 1/(4*sqrt(2))]) - sage: f - 1/(4*sqrt(2))*x + 1/sqrt(2) - sage: -f - (-1/(4*sqrt(2)))*x + -1/sqrt(2) - sage: (-f).degree() - 1 -""" Index: age/calculus/var.pyx =================================================================== --- sage/calculus/var.pyx (revision 4059) +++ (revision ) @@ -1,111 +1,0 @@ -import calculus - -def var(s): - """ - Create a symbolic variable with the name \emph{s}. - - INPUT: - s -- a string, either a single variable name, - or a space or comma separated list of - variable names. - - NOTE: The new variable is both returned and automatically injected - into the global namespace. If you use var in library code, it is - better to use sage.calculus.calculus.var, since it won't touch the - global namespace. - - EXAMPLES: - We define three variables: - sage: var('xx yy zz') - (xx, yy, zz) - - Then we make an algebraic expression out of them. - sage: f = xx^n + yy^n + zz^n; f - zz^n + yy^n + xx^n - - We can substitute a new variable name for n. - sage: f(n = var('sigma')) - zz^sigma + yy^sigma + xx^sigma - - If you make an important builtin variable into a symbolic variable, - you can get back the original value using restore: - sage: var('QQ RR') - (QQ, RR) - sage: QQ - QQ - sage: restore('QQ') - sage: QQ - Rational Field - - We make two new variables separated by commas: - sage: var('theta, gamma') - (theta, gamma) - sage: theta^2 + gamma^3 - gamma^3 + theta^2 - - The new variables are of type SymbolicVariable, and belong - to the symbolic expression ring: - sage: type(theta) - - sage: parent(theta) - Symbolic Ring - """ - G = globals() # this is the reason the code must be in SageX. - v = calculus.var(s) - if isinstance(v, tuple): - for x in v: - G[repr(x)] = x - else: - G[repr(v)] = v - return v - -def function(s, *args): - """ - Create a formal symbolic function with the name \emph{s}. - - INPUT: - s -- a string, either a single variable name, - or a space or comma separated list of - variable names. - - NOTE: The new function is both returned and automatically injected - into the global namespace. If you use var in library code, it is - better to use sage.calculus.calculus.function, since it won't - touch the global namespace. - - EXAMPLES: - We create a formal function called supersin. - sage: f = function('supersin', x) - sage: f - supersin(x) - - We can immediately use supersin in symbolic expressions: - sage: supersin(y+z) + A^3 - A^3 + supersin(z + y) - - We can define other functions in terms of supersin. - sage: g(x,y) = supersin(x)^2 + sin(y/2) - sage: g - (x, y) |--> sin(y/2) + supersin(x)^2 - sage: g.diff(y) - (x, y) |--> cos(y/2)/2 - sage: g.diff(x) - (x, y) |--> 2*supersin(x)*diff(supersin(x), x, 1) - sage: k = g.diff(x); k - (x, y) |--> 2*supersin(x)*diff(supersin(x), x, 1) - sage: k.substitute(supersin=sin) - 2*sin(x)*diff(supersin(x), x, 1) - """ - if len(args) > 0: - return function(s)(*args) - - G = globals() # this is the reason the code must be in SageX. - v = calculus.function(s) - if isinstance(v, tuple): - for x in v: - G[repr(x)] = x - else: - G[repr(v)] = v - return v - - Index: age/calculus/wester.py =================================================================== --- sage/calculus/wester.py (revision 4058) +++ (revision ) @@ -1,538 +1,0 @@ -""" -These are all the problems at - http://yacas.sourceforge.net/essaysmanual.html - -They come from the 1994 paper "Review of CAS mathematical capabilities", -by Michael Wester, who put forward 123 problems that a reasonable computer -algebra system should be able to solve and tested the then current -versions of various commercial CAS on this list. SAGE can do most of -the problems natively now, i.e., with no explicit calls to maxima or -other systems. - - -sage: factorial(50) -30414093201713378043612608166064768844377641568960512000000000000 -sage: factor(factorial(50)) -2^47 * 3^22 * 5^12 * 7^8 * 11^4 * 13^3 * 17^2 * 19^2 * 23^2 * 29 * 31 * 37 * 41 * 43 * 47 - -sage: # 1/2+...+1/10 = 4861/2520 -sage: sum(1/n for n in range(2,10+1)) == 4861/2520 -True - -sage: # Evaluate e^(Pi*Sqrt(163)) to 50 decimal digits -sage: a = e^(pi*sqrt(163)); a -e^(sqrt(163)*pi) -sage: print RealField(150)(a) -262537412640768743.99999999999925007259719819 - -sage: # Evaluate the Bessel function J[2] numerically at z=1+I. -sage: # NOTE -- we get a different answer than yacas -sage: bessel_J(2.0,1.0+I) -0.874211097673326 - 0.222469792478650*I - -sage: # Obtain period of decimal fraction 1/7=0.(142857). -sage: a = 1/7 -sage: print a -1/7 -sage: print a.period() -6 - -sage: # Continued fraction of 3.1415926535 -sage: a = 3.1415926535 -sage: continued_fraction(a) -[3, 7, 15, 1, 292, 1, 1, 6, 2, 13, 4] - -sage: # (not exactly ok) Sqrt(2*Sqrt(3)+4)=1+Sqrt(3). -sage: # The maxima backend equality checker fails this; maybe it *should*, since -sage: # the equality only holds for one choice of sign. -sage: a = sqrt(2*sqrt(3) + 4); b = 1 + sqrt(3) -sage: print float(a-b) -0.0 -sage: print bool(a == b) -False -sage: # We can, of course, do this in a quadratic field -sage: k. = QuadraticField(3) -sage: asqr = 2*sqrt3 + 4 -sage: b = 1+sqrt3 -sage: asqr == b^2 -True - -sage: # (not exactly ok) Sqrt(14+3*Sqrt(3+2*Sqrt(5-12*Sqrt(3-2*Sqrt(2)))))=3+Sqrt(2). -sage: a = sqrt(14+3*sqrt(3+2*sqrt(5-12*sqrt(3-2*sqrt(2))))) -sage: b = 3+sqrt(2) -sage: print a, b -sqrt(3 sqrt(2 sqrt(5 - 12 sqrt(3 - 2 sqrt(2))) + 3) + 14) sqrt(2) + 3 -sage: print bool(a==b) -False -sage: print float(a-b) -1.7763568394e-15 -sage: # 2*Infinity-3=Infinity. -sage: 2*infinity-3 == infinity -True - -sage: # (YES) Standard deviation of the sample (1, 2, 3, 4, 5). -sage: v = vector(RDF, 5, [1,2,3,4,5]) -sage: v.standard_deviation() -1.5811388300841898 - -sage: # (NO) Hypothesis testing with t-distribution. -sage: # (NO) Hypothesis testing with chi^2 distribution - -sage: # (YES) (x^2-4)/(x^2+4*x+4)=(x-2)/(x+2). -sage: R. = QQ[] -sage: (x^2-4)/(x^2+4*x+4) == (x-2)/(x+2) -True -sage: restore('x') - -sage: # (NO -- Maxima doesn't consider them equal.) -sage: # (Exp(x)-1)/(Exp(x/2)+1)=Exp(x/2)-1. -sage: f = (exp(x)-1)/(exp(x/2)+1) -sage: g = exp(x/2)-1 -sage: f -(e^x - 1)/(e^(x/2) + 1) -sage: g -e^(x/2) - 1 -sage: print f(10.0), g(10.0) -147.4131591025766 147.4131591025766 -sage: print bool(f == g) -False - -sage: # (YES) Expand (1+x)^20, take derivative and factorize. -sage: # first do it is using algebraic polys -sage: R. = QQ[] -sage: f = (1+x)^20 -sage: print f -x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 -sage: print f.factor() -(x + 1)^20 -sage: # next do it symbolically -sage: restore('x') -sage: f = (1+x)^20; f -(x + 1)^20 -sage: g = f.expand(); g -x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 -sage: g.factor() -(x + 1)^20 - - -sage: # (YES) Factorize x^100-1. -sage: factor(x^100-1) -(x - 1)*(x + 1)*(x^2 + 1)*(x^4 - x^3 + x^2 - x + 1)*(x^4 + x^3 + x^2 + x + 1)*(x^8 - x^6 + x^4 - x^2 + 1)*(x^20 - x^15 + x^10 - x^5 + 1)*(x^20 + x^15 + x^10 + x^5 + 1)*(x^40 - x^30 + x^20 - x^10 + 1) -sage: # Also, algebraically -sage: x = polygen(QQ) -sage: factor(x^100 - 1) -(x - 1) * (x + 1) * (x^2 + 1) * (x^4 - x^3 + x^2 - x + 1) * (x^4 + x^3 + x^2 + x + 1) * (x^8 - x^6 + x^4 - x^2 + 1) * (x^20 - x^15 + x^10 - x^5 + 1) * (x^20 + x^15 + x^10 + x^5 + 1) * (x^40 - x^30 + x^20 - x^10 + 1) -sage: restore('x') - - -sage: # (YES) Factorize x^4-3*x^2+1 in the field of rational numbers extended by roots of x^2-x-1. -sage: k.< a> = NumberField(x^2 - x -1) -sage: R.< y> = k[] -sage: f = y^4 - 3*y^2 + 1 -sage: f -y^4 + (-3)*y^2 + 1 -sage: factor(f) -(y + -a) * (y + -a + 1) * (y + a - 1) * (y + a) - -sage: # (YES) Factorize x^4-3*x^2+1 mod 5. -sage: k.< x > = GF(5) [ ] -sage: f = x^4 - 3*x^2 + 1 -sage: f.factor() -(x + 2)^2 * (x + 3)^2 -sage: # Alternatively, from symbol x as follows: -sage: reset('x') -sage: f = x^4 - 3*x^2 + 1 -sage: f.polynomial(GF(5)).factor() -(x + 2)^2 * (x + 3)^2 - -sage: # (YES) Partial fraction decomposition of (x^2+2*x+3)/(x^3+4*x^2+5*x+2) -sage: f = (x^2+2*x+3)/(x^3+4*x^2+5*x+2) -sage: print f - 2 - x + 2 x + 3 - ------------------- - 3 2 - x + 4 x + 5 x + 2 - -sage: print f.partial_fraction() - 3 2 2 - ----- - ----- + -------- - x + 2 x + 1 2 - (x + 1) - - -sage: # (BUG?) Assuming x>=y, y>=z, z>=x, deduce x=z. -sage: # Maxima doesn't agree that x==z is a conclusion... -sage: forget() -sage: restore('x,y,z') -sage: assume(x>=y, y>=z,z>=x) -sage: print bool(x==z) -False - -sage: # (YES) Assuming x>y, y>0, deduce 2*x^2>2*y^2. -sage: forget() -sage: assume(x>y, y>0) -sage: print assumptions() -[x > y, y > 0] -sage: print bool(2*x^2 > 2*y^2) -True -sage: forget() -sage: print assumptions() -[] -sage: # Solve the inequality Abs(x-1)>2. - -sage: # (NO) Maxima doesn't solve inequalities: -sage: eqn = abs(x-1) > 2 -sage: print eqn - abs(x - 1) > 2 - -sage: # (NO) Solve the inequality (x-1)*...*(x-5)<0. -sage: eqn = prod(x-i for i in range(1,5 +1)) < 0 -sage: # but don't know how to solve -sage: print eqn - (x - 5) (x - 4) (x - 3) (x - 2) (x - 1) < 0 - - -sage: # (YES) Cos(3*x)/Cos(x)=Cos(x)^2-3*Sin(x)^2 or similar equivalent combination. -sage: f = cos(3*x)/cos(x) -sage: g = cos(x)^2 - 3*sin(x)^2 -sage: h = f-g -sage: print h.trig_simplify() - 0 - -sage: # (YES) Cos(3*x)/Cos(x)=2*Cos(2*x)-1. -sage: f = cos(3*x)/cos(x) -sage: g = 2*cos(2*x) - 1 -sage: h = f-g -sage: print h.trig_simplify() - 0 -sage: # (NO) Define rewrite rules to match Cos(3*x)/Cos(x)=Cos(x)^2-3*Sin(x)^2. -sage: # SAGE has no notion of "rewrite rules". - - -sage: # (YES) Sqrt(997)-(997^3)^(1/6)=0 -sage: a = sqrt(997) - (997^3)^(1/6) -sage: print a - 0 -sage: print bool(a == 0) -True - -sage: # (NO) Sqrt(99983)-99983^3^(1/6)=0 -sage: # For some reason Maxima decides its not zero because of the factorization. -sage: a = sqrt(99983) - (99983^3)^(1/6) -sage: print a - sqrt(99983) - sqrt(13) sqrt(7691) -sage: print bool(a==0) -False -sage: print float(a) -1.13686837722e-13 -sage: print 13*7691 -99983 - -sage: # (YES) (2^(1/3) + 4^(1/3))^3 - 6*(2^(1/3) + 4^(1/3))-6 = 0 -sage: ## same issue as above -- can only do using number fields -sage: a = (2^(1/3) + 4^(1/3))^3 - 6*(2^(1/3) + 4^(1/3)) - 6 -sage: print a - 1/3 1/3 3 1/3 1/3 - (4 + 2 ) - 6 (4 + 2 ) - 6 -sage: print bool(a==0) -False -sage: print float(a) -3.5527136788e-15 -sage: ## but we can do it using number fields. -sage: reset('x') -sage: k. = NumberField(x^3-2) -sage: a = (b + b^2)^3 - 6*(b + b^2) - 6 -sage: print a -0 - -sage: # (YES) Ln(Tan(x/2+Pi/4))-ArcSinh(Tan(x))=0 -sage: # Yes, in that the thing is clearly not equal to 0! -sage: f = log(tan(x/2 + pi/4)) - asin(tan(x)) -sage: bool(f == 0) -False -sage: [float(f(i/10)) for i in range(1,5)] # random low order bits -[-0.00033670040754082975, -0.0027778004096620235, -0.0098909940914040928, -0.025411145508414501] - -sage: # (YES) Numerically, the expression Ln(Tan(x/2+Pi/4))-ArcSinh(Tan(x))=0 and its derivative at x=0 are zero. -sage: g = f.derivative() -sage: print float(f(0)) --1.11022302463e-16 -sage: print float(g(0)) --1.11022302463e-16 -sage: print g - 2 x pi - sec (- + ---) 2 - 2 4 sec (x) - -------------- - ----------------- - x pi 2 - 2 tan(- + ---) sqrt(1 - tan (x)) - 2 4 - - -sage: # (NO?) Ln((2*Sqrt(r) + 1)/Sqrt(4*r 4*Sqrt(r) 1))=0. -sage: f = log( (2*sqrt(r) + 1) / sqrt(4*r + 4*sqrt(r) + 1)) -sage: print f - 2 sqrt(r) + 1 - log(-------------------------) - sqrt(4 r + 4 sqrt(r) + 1) -sage: print bool(f == 0) -False -sage: print [float(f(i)) for i in [0.1,0.3,0.5]] -[0.0, 0.0, 0.0] - - -sage: # (NO, except numerically) -sage: # (4*r+4*Sqrt(r)+1)^(Sqrt(r)/(2*Sqrt(r)+1))*(2*Sqrt(r)+1)^(2*Sqrt(r)+1)^(-1)-2*Sqrt(r)-1=0, assuming r>0. -sage: assume(r>0) -sage: f = (4*r+4*sqrt(r)+1)^(sqrt(r)/(2*sqrt(r)+1))*(2*sqrt(r)+1)^(2*sqrt(r)+1)^(-1)-2*sqrt(r)-1 -sage: print f - 1 sqrt(r) - ------------- ------------- - 2 sqrt(r) + 1 2 sqrt(r) + 1 - (2 sqrt(r) + 1) (4 r + 4 sqrt(r) + 1) - - 2 sqrt(r) - 1 -sage: print bool(f == 0) -False -sage: print [float(f(i)) for i in [0.1,0.3,0.5]] -[0.0, 0.0, -2.2204460492503131e-16] - - -sage: # (YES) Obtain real and imaginary parts of Ln(3+4*I). -sage: a = log(3+4*I) -sage: print a - log(4 I + 3) -sage: print a.real() - log(5) -sage: print a.imag() - 4 - atan(-) - 3 - -sage: # (YES) Obtain real and imaginary parts of Tan(x+I*y) -sage: a = tan(x + I*y) -sage: print a - tan( I y + x) -sage: print a.real() - sin(2 x) - -------------------- - cosh(2 y) + cos(2 x) -sage: print a.imag() - sinh(2 y) - -------------------- - cosh(2 y) + cos(2 x) - -sage: # (YES) Simplify Ln(Exp(z)) to z for -Pi0, Re(y)>0, deduce x^(1/n)*y^(1/n)-(x*y)^(1/n)=0. -sage: assume(real(x) > 0, real(y) > 0) -sage: f = x^(1/n)*y^(1/n)-(x*y)^(1/n) -sage: print f - 0 -sage: forget() - -sage: # (??) Transform equations, (x==2)/2+(1==1)=>x/2+1==2. -sage: # This doesn't make any sense, in my opinion. Adding equations - -sage: # (SOMEWHAT) Solve Exp(x)=1 and get all solutions. -sage: solve(exp(x) == 1) -[x == 0] - -sage: # (SOMEWHAT) Solve Tan(x)=1 and get all solutions. -sage: solve(tan(x) == 1) -[x == (pi/4)] - -sage: # (YES) Solve a degenerate 3x3 linear system. -sage: # x+y+z==6,2*x+y+2*z==10,x+3*y+z==10 -sage: # First symbolically: -sage: solve([x+y+z==6, 2*x+y+2*z==10, x+3*y+z==10], x,y,z) -[[x == (4 - r1), y == 2, z == r1]] - -sage: # (YES) Invert a 2x2 symbolic matrix. -sage: # [[a,b],[1,a*b]] -sage: # Using multivariate poly ring -- much nicer -sage: R. = QQ[] -sage: m = matrix(2,2,[a,b, 1, a*b]) -sage: zz = m^(-1) -sage: print zz -[ a/(-1 + a^2) (-1)/(-1 + a^2)] -[(-1)/(-1*b + a^2*b) a/(-1*b + a^2*b)] - -sage: # (YES) Compute and factor the determinant of the 4x4 Vandermonde matrix in a, b, c, d. -sage: restore('a,b,c,d') -sage: m = matrix(SR, 4, 4, [[z^i for i in range(4)] for z in [a,b,c,d]]) -sage: print m - [ 1 a a^2 a^3] - [ 1 b b^2 b^3] - [ 1 c c^2 c^3] - [ 1 d d^2 d^3] -sage: d = m.determinant() -sage: print d.factor() - (b - a) (c - a) (c - b) (d - a) (d - b) (d - c) - -sage: # (YES) Compute and factor the determinant of the 4x4 Vandermonde matrix in a, b, c, d. -sage: # Do it instead in a multivariate ring -sage: R. = QQ[] -sage: m = matrix(R, 4, 4, [[z^i for i in range(4)] for z in [a,b,c,d]]) -sage: print m -[ 1 a a^2 a^3] -[ 1 b b^2 b^3] -[ 1 c c^2 c^3] -[ 1 d d^2 d^3] -sage: d = m.determinant() -sage: print d -b*c^2*d^3 - b*c^3*d^2 - b^2*c*d^3 + b^2*c^3*d + b^3*c*d^2 - b^3*c^2*d - a*c^2*d^3 + a*c^3*d^2 + a*b^2*d^3 - a*b^2*c^3 - a*b^3*d^2 + a*b^3*c^2 + a^2*c*d^3 - a^2*c^3*d - a^2*b*d^3 + a^2*b*c^3 + a^2*b^3*d - a^2*b^3*c - a^3*c*d^2 + a^3*c^2*d + a^3*b*d^2 - a^3*b*c^2 - a^3*b^2*d + a^3*b^2*c -sage: print d.factor() -(-1) * (-1*d + c) * (-1*d + b) * (-1*c + b) * (b - a) * (-1*d + a) * (-1*c + a) - -sage: # Find the eigenvalues of a 3x3 integer matrix. -sage: m = matrix(QQ, 3, [5,-3,-7, -2,1,2, 2,-3,-4]) -sage: m.eigenspaces() -[ -(3, [ -(1, 0, -1) -]), -(1, [ -(1, 1, -1) -]), -(-2, [ -(0, 1, 1) -]) -] - -sage: # OK Verify some standard limits found by L'Hopital's rule: -sage: # Verify(Limit(x,Infinity) (1+1/x)^x, Exp(1)); -sage: # Verify(Limit(x,0) (1-Cos(x))/x^2, 1/2); -sage: print limit( (1+1/x)^x, x = oo) -e -sage: print limit( (1-cos(x))/(x^2), x = 1/2) - 1 - 4 - 4 cos(-) - 2 - -sage: # (OK-ish) D(x)Abs(x) -sage: # Verify(D(x) Abs(x), Sign(x)); -sage: diff(abs(x)) -x/abs(x) - -sage: # (NO) (Integrate(x)Abs(x))=Abs(x)*x/2 -sage: integral(abs(x), x) -integrate(abs(x), x) - -sage: # (YES) Compute derivative of Abs(x), piecewise defined. -sage: # Verify(D(x)if(x<0) (-x) else x, -sage: # Simplify(if(x<0) -1 else 1)) -Piecewise defined function with 2 parts, [[(-10, 0), -1], [(0, 10), 1]] -sage: # (NOT really) Integrate Abs(x), piecewise defined. -sage: # Verify(Simplify(Integrate(x) -sage: # if(x<0) (-x) else x), -sage: # Simplify(if(x<0) (-x^2/2) else x^2/2)); -sage: f = piecewise([ [[-10,0], -x], [[0,10], x]]) -sage: f.integral() -100 - -sage: # (YES) Taylor series of 1/Sqrt(1-v^2/c^2) at v=0. -sage: restore('v,c') -sage: taylor(1/sqrt(1-v^2/c^2), v, 0, 7) -1 + v^2/(2*c^2) + 3*v^4/(8*c^4) + 5*v^6/(16*c^6) - -sage: # (OK-ish) (Taylor expansion of Sin(x))/(Taylor expansion of Cos(x)) = (Taylor expansion of Tan(x)). -sage: # TestYacas(Taylor(x,0,5)(Taylor(x,0,5)Sin(x))/ -sage: # (Taylor(x,0,5)Cos(x)), Taylor(x,0,5)Tan(x)); -sage: f = taylor(sin(x), x, 0, 8) -sage: g = taylor(cos(x), x, 0, 8) -sage: h = taylor(tan(x), x, 0, 8) -sage: f = f.power_series(QQ) -sage: g = g.power_series(QQ) -sage: h = h.power_series(QQ) -sage: f - g*h -O(x^8) - -sage: # (YES) Taylor expansion of Ln(x)^a*Exp(-b*x) at x=1. -sage: taylor(log(x)^a * exp(-b*x), x, 1, 3) -(x - 1)^a/e^b - (((x - 1)^a*a + 2*b*(x - 1)^a)*(x - 1)/(2*e^b)) + (3*(x - 1)^a*a^2 + (12*b + 5)*(x - 1)^a*a + 12*b^2*(x - 1)^a)*(x - 1)^2/(24*e^b) - (((x - 1)^a*a^3 + (6*b + 5)*(x - 1)^a*a^2 + (12*b^2 + 10*b + 6)*(x - 1)^a*a + 8*b^3*(x - 1)^a)*(x - 1)^3/(48*e^b)) - -sage: # (YES) Taylor expansion of Ln(Sin(x)/x) at x=0. -sage: taylor(log(sin(x)/x), x, 0, 10) --x^2/6 - (x^4/180) - (x^6/2835) - (x^8/37800) - (x^10/467775) - -sage: # (NO) Compute n-th term of the Taylor series of Ln(Sin(x)/x) at x=0. -sage: # need formal functions - -sage: # (NO) Compute n-th term of the Taylor series of Exp(-x)*Sin(x) at x=0. -sage: # (Sort of, with some work) -sage: # Solve x=Sin(y)+Cos(y) for y as Taylor series in x at x=1. -sage: # TestYacas(InverseTaylor(y,0,4) Sin(y)+Cos(y), -sage: # (y-1)+(y-1)^2/2+2*(y-1)^3/3+(y-1)^4); -sage: # Note that InverseTaylor does not give the series in terms of x but in terms of y which is semantically -sage: # wrong. But other CAS do the same. -sage: f = sin(y) + cos(y) -sage: g = f.taylor(y, 0, 10) -sage: h = g.power_series(QQ) -sage: k = (h - 1).reversion() -sage: print k -y + 1/2*y^2 + 2/3*y^3 + y^4 + 17/10*y^5 + 37/12*y^6 + 41/7*y^7 + 23/2*y^8 + 1667/72*y^9 + 3803/80*y^10 + O(y^11) - -sage: # [OK] Compute Legendre polynomials directly from Rodrigues's formula, P[n]=1/(2^n*n!) *(Deriv(x,n)(x^2-1)^n). -sage: # P(n,x) := Simplify( 1/(2*n)!! * -sage: # Deriv(x,n) (x^2-1)^n ); -sage: # TestYacas(P(4,x), (35*x^4)/8+(-15*x^2)/4+3/8); -sage: def P(n,x): -... return simplify(diff((x^2-1)^n,x,n) / (2^n * factorial(n))) -... -sage: print P(4,x).expand() - 4 2 - 35 x 15 x 3 - ----- - ----- + - - 8 4 8 - -sage: # (YES) Define the polynomial p=Sum(i,1,5,a[i]*x^i). -sage: # symbolically -sage: ps = sum(var('a%s'%i)*x^i for i in range(1,6)) -sage: print 'symbolic\n',ps -symbolic - 5 4 3 2 - a5 x + a4 x + a3 x + a2 x + a1 x -sage: # algebraically -sage: R = PolynomialRing(QQ,5,names='a') -sage: S. = PolynomialRing(R) -sage: p = S(list(R.gens()))*x -sage: print 'algebraic\n',p -algebraic -a4*x^5 + a3*x^4 + a2*x^3 + a1*x^2 + a0*x - -sage: # (YES) Convert the above to Horner's form. -sage: # Verify(Horner(p, x), ((((a[5]*x+a[4])*x -sage: # +a[3])*x+a[2])*x+a[1])*x); -sage: # We use the trick of evaluating the algebraic poly at a symbolic variable: -sage: restore('x') -sage: p(x) -x*(x*(x*(x*(a4*x + a3) + a2) + a1) + a0) - -sage: # (NO) Convert the result of problem 127 to Fortran syntax. -sage: # CForm(Horner(p, x)); - -sage: # (YES) Verify that True And False=False. -sage: (True and False) == False -True - -sage: # (YES) Prove x Or Not x. -sage: for x in [True, False]: -... print x or (not x) -True -True - -sage: # (YES) Prove x Or y Or x And y=>x Or y. -sage: for x in [True, False]: -... for y in [True, False]: -... if x or y or x and y: -... if not (x or y): -... print "failed!" -""" Index: sage/catalogue/catalogue.py =================================================================== --- sage/catalogue/catalogue.py (revision 3983) +++ sage/catalogue/catalogue.py (revision 2320) @@ -120,6 +120,7 @@ elementary = Elementary() function.elementary = elementary -import sage.calculus.all -elementary.sin = sage.calculus.all.sin -elementary.cos = sage.calculus.all.cos -elementary.log = sage.calculus.all.log +import sage.functions.all +elementary.sin = sage.functions.all.sin +elementary.cos = sage.functions.all.cos + + Index: sage/coding/all.py =================================================================== --- sage/coding/all.py (revision 3972) +++ sage/coding/all.py (revision 2132) @@ -24,19 +24,3 @@ from ag_code import ag_code -from code_bounds import (codesize_upper_bound, - dimension_upper_bound, - volume_hamming, - gilbert_lower_bound, - plotkin_upper_bound, - griesmer_upper_bound, - elias_upper_bound, - hamming_upper_bound, - singleton_upper_bound, - gv_info_rate, - entropy, - gv_bound_asymp, - hamming_bound_asymp, - singleton_bound_asymp, - plotkin_bound_asymp, - elias_bound_asymp, - mrrw1_bound_asymp) +from code_bounds import * Index: sage/coding/code_bounds.py =================================================================== --- sage/coding/code_bounds.py (revision 4062) +++ sage/coding/code_bounds.py (revision 3290) @@ -136,5 +136,5 @@ from sage.interfaces.all import gap -from sage.rings.all import QQ, RR, ZZ, RDF +from sage.rings.all import QQ, RR, ZZ from sage.rings.arith import factorial from sage.misc.functional import log, sqrt @@ -373,8 +373,8 @@ EXAMPLES: sage: elias_bound_asymp(1/4,2) - 0.399123963308 + 0.399123963307144 """ r = 1-1/q - return RDF((1-entropy(r-sqrt(r*(r-delta)), q))) + return (1-entropy(r-sqrt(r*(r-delta)), q)) def mrrw1_bound_asymp(delta,q): @@ -385,11 +385,11 @@ EXAMPLES: sage: mrrw1_bound_asymp(1/4,2) - 0.354578902665 - - """ - return RDF(entropy((q-1-delta*(q-2)-2*sqrt((q-1)*delta*(1-delta)))/q,q)) - - - - - + 0.354578902665270 + + """ + return entropy((q-1-delta*(q-2)-2*sqrt((q-1)*delta*(1-delta)))/q,q) + + + + + Index: sage/coding/linear_code.py =================================================================== --- sage/coding/linear_code.py (revision 4063) +++ sage/coding/linear_code.py (revision 2779) @@ -142,11 +142,4 @@ added LinearCode_from_vectorspace, extended_code, zeta_function -- Nick Alexander (2006-12-10): factor GUAVA code to guava.py - -TESTS: - sage: MS = MatrixSpace(GF(2),4,7) - sage: G = MS([[1,1,1,0,0,0,0], [1,0,0,1,1,0,0], [0,1,0,1,0,1,0], [1,1,0,1,0,0,1]]) - sage: C = LinearCode(G) - sage: C == loads(dumps(C)) - True """ @@ -634,7 +627,5 @@ def __cmp__(self, right): - if not isinstance(right, LinearCode): - return cmp(type(self), type(right)) - return cmp(self.__gen_mat, right.__gen_mat) + raise NotImplementedError def decode(self, right): @@ -785,4 +776,5 @@ EXAMPLES: + """ slength = self.length() @@ -793,9 +785,9 @@ rF = right.base_ring() if slength != rlength: - return False + return 0 if sdim != rdim: - return False + return 0 if sF != rF: - return False + return 0 V = VectorSpace(sF,sdim) sbasis = self.gens() @@ -804,10 +796,10 @@ rcheck = right.check_mat() for c in sbasis: - if rcheck*c: - return False + if rcheck*c != V(0): + return 0 for c in rbasis: - if scheck*c: - return False - return True + if scheck*c != V(0): + return 0 + return 1 def is_permutation_automorphism(self,g): Index: sage/combinat/combinat.py =================================================================== --- sage/combinat/combinat.py (revision 4022) +++ sage/combinat/combinat.py (revision 2664) @@ -16,108 +16,101 @@ \item Bell numbers, \code{bell_number} -\item Bernoulli numbers, \code{bernoulli_number} (though PARI's - bernoulli is better) - -\item Catalan numbers, \code{catalan_number} (not to be confused with - the Catalan constant) +\item Bernoulli numbers, \code{bernoulli_number} (though PARI's bernoulli is + better) + +\item Catalan numbers, \code{catalan_number} (not to be confused with the + Catalan constant) \item Eulerian/Euler numbers, \code{euler_number} (Maxima) -\item Fibonacci numbers, \code{fibonacci} (PARI) and - \code{fibonacci_number} (GAP) The PARI version is better. +\item Fibonacci numbers, \code{fibonacci} (PARI) and \code{fibonacci_number} (GAP) + The PARI version is better. \item Lucas numbers, \code{lucas_number1}, \code{lucas_number2}. -\item Stirling numbers, \code{stirling_number1}, -\code{stirling_number2}. - +\item Stirling numbers, \code{stirling_number1}, \code{stirling_number2}. \end{itemize} Set-theoretic constructions: \begin{itemize} - -\item Combinations of a multiset, \code{combinations}, -\code{combinations_iterator}, and \code{number_of_combinations}. These -are unordered selections without repetition of k objects from a -multiset S. - -\item Arrangements of a multiset, \code{arrangements} and - \code{number_of_arrangements} These are ordered selections without - repetition of k objects from a multiset S. - -\item Derangements of a multiset, \code{derangements} and -\code{number_of_derangements}. +\item Combinations of a multiset, \code{combinations}, \code{combinations_iterator}, +and \code{number_of_combinations}. These are unordered selections without +repetition of k objects from a multiset S. + +\item Arrangements of a multiset, \code{arrangements} and \code{number_of_arrangements} + These are ordered selections without repetition of k objects from a + multiset S. + +\item Derangements of a multiset, \code{derangements} and \code{number_of_derangements}. \item Tuples of a multiset, \code{tuples} and \code{number_of_tuples}. - An ordered tuple of length k of set S is a ordered selection with - repetitions of S and is represented by a sorted list of length k - containing elements from S. - -\item Unordered tuples of a set, \code{unordered_tuple} and - \code{number_of_unordered_tuples}. An unordered tuple of length k - of set S is a unordered selection with repetitions of S and is - represented by a sorted list of length k containing elements from S. - -\item Permutations of a multiset, \code{permutations}, -\code{permutations_iterator}, \code{number_of_permutations}. A -permutation is a list that contains exactly the same elements but + An ordered tuple of length k of set S is a ordered selection with + repetitions of S and is represented by a sorted list of length k + containing elements from S. + +\item Unordered tuples of a set, \code{unordered_tuple} and \code{number_of_unordered_tuples}. + An unordered tuple of length k of set S is a unordered selection with + repetitions of S and is represented by a sorted list of length k + containing elements from S. + +\item Permutations of a multiset, \code{permutations}, \code{permutations_iterator}, +\code{number_of_permutations}. A permutation is a list that contains exactly the same elements but possibly in different order. - \end{itemize} Partitions: \begin{itemize} - -\item Partitions of a set, \code{partitions_set}, - \code{number_of_partitions_set}. An unordered partition of set S is - a set of pairwise disjoint nonempty sets with union S and is - represented by a sorted list of such sets. - -\item Partitions of an integer, \code{partitions_list}, - \code{number_of_partitions_list}. An unordered partition of n is an - unordered sum $n = p_1+p_2 +\ldots+ p_k$ of positive integers and is - represented by the list $p = [p_1,p_2,\ldots,p_k]$, in nonincreasing - order, i.e., $p1\geq p_2 ...\geq p_k$. - -\item Ordered partitions of an integer, \code{ordered_partitions}, - \code{number_of_ordered_partitions}. An ordered partition of n is - an ordered sum $n = p_1+p_2 +\ldots+ p_k$ of positive integers and - is represented by the list $p = [p_1,p_2,\ldots,p_k]$, in - nonincreasing order, i.e., $p1\geq p_2 ...\geq p_k$. - -\item Restricted partitions of an integer, - \code{partitions_restricted}, - \code{number_of_partitions_restricted}. An unordered restricted - partition of n is an unordered sum $n = p_1+p_2 +\ldots+ p_k$ of - positive integers $p_i$ belonging to a given set $S$, and is - represented by the list $p = [p_1,p_2,\ldots,p_k]$, in nonincreasing - order, i.e., $p1\geq p_2 ...\geq p_k$. - -\item \code{partitions_greatest} implements a special type of - restricted partition. - -\item \code{partitions_greatest_eq} is another type of restricted -partition. +\item Partitions of a set, \code{partitions_set}, \code{number_of_partitions_set}. + An unordered partition of set S is a set of pairwise disjoint + nonempty sets with union S and is represented by a sorted list of + such sets. + +\item Partitions of an integer, \code{partitions_list}, \code{number_of_partitions_list}. + An unordered partition of n is an unordered sum + $n = p_1+p_2 +\ldots+ p_k$ of positive integers and is represented by + the list $p = [p_1,p_2,\ldots,p_k]$, in nonincreasing order, i.e., + $p1\geq p_2 ...\geq p_k$. + +\item Ordered partitions of an integer, \code{ordered_partitions}, + \code{number_of_ordered_partitions}. + An ordered partition of n is an ordered sum $n = p_1+p_2 +\ldots+ p_k$ + of positive integers and is represented by + the list $p = [p_1,p_2,\ldots,p_k]$, in nonincreasing order, i.e., + $p1\geq p_2 ...\geq p_k$. + +\item Restricted partitions of an integer, \code{partitions_restricted}, + \code{number_of_partitions_restricted}. + An unordered restricted partition of n is an unordered sum + $n = p_1+p_2 +\ldots+ p_k$ of positive integers $p_i$ belonging to a + given set $S$, and is represented by the list $p = [p_1,p_2,\ldots,p_k]$, + in nonincreasing order, i.e., $p1\geq p_2 ...\geq p_k$. + +\item \code{partitions_greatest} + implements a special type of restricted partition. + +\item \code{partitions_greatest_eq} is another type of restricted partition. \item Tuples of partitions, \code{partition_tuples}, - \code{number_of_partition_tuples}. A $k$-tuple of partitions is - represented by a list of all $k$-tuples of partitions which together - form a partition of $n$. - -\item Powers of a partition, \code{partition_power(pi, k)}. The power - of a partition corresponds to the $k$-th power of a permutation with - cycle structure $\pi$. - -\item Sign of a partition, \code{partition_sign( pi ) } This means the - sign of a permutation with cycle structure given by the partition - pi. - -\item Associated partition, \code{partition_associated( pi )} The - ``associated'' (also called ``conjugate'' in the literature) - partition of the partition pi which is obtained by transposing the + \code{number_of_partition_tuples}. + A $k$-tuple of partitions is represented by a list of all $k$-tuples + of partitions which together form a partition of $n$. + +\item Powers of a partition, \code{partition_power(pi, k)}. + The power of a partition corresponds to the $k$-th power of a + permutation with cycle structure $\pi$. + +\item Sign of a partition, \code{partition_sign( pi ) } + This means the sign of a permutation with cycle structure given by the + partition pi. + +\item Associated partition, \code{partition_associated( pi )} + The ``associated'' (also called ``conjugate'' in the literature) + partition of the partition pi which is obtained by transposing the corresponding Ferrers diagram. -\item Ferrers diagram, \code{ferrers_diagram}. Analogous to the Young - diagram of an irredicible representation of $S_n$. \end{itemize} +\item Ferrers diagram, \code{ferrers_diagram}. + Analogous to the Young diagram of an irredicible representation + of $S_n$. + \end{itemize} Related functions: @@ -266,5 +259,5 @@ [1, 1, 2, 5, 14, 42, 132] sage: maxima.eval("-(1/2)*taylor (sqrt (1-4*x^2), x, 0, 15)") - '-1/2+x^2+x^4+2*x^6+5*x^8+14*x^10+42*x^12+132*x^14' + '-1/2 + x^2 + x^4 + 2*x^6 + 5*x^8 + 14*x^10 + 42*x^12 + 132*x^14' sage: [catalan_number(i) for i in range(-7,7) if i != -1] [0, 0, 0, 0, 0, 0, 1, 1, 2, 5, 14, 42, 132] @@ -294,5 +287,5 @@ [1, 0, -1, 0, 5, 0, -61, 0, 1385, 0] sage: maxima.eval("taylor (2/(exp(x)+exp(-x)), x, 0, 10)") - '1-x^2/2+5*x^4/24-61*x^6/720+277*x^8/8064-50521*x^10/3628800' + '1 - x^2/2 + 5*x^4/24 - 61*x^6/720 + 277*x^8/8064 - 50521*x^10/3628800' sage: [euler_number(i)/factorial(i) for i in range(11)] [1, 0, -1/2, 0, 5/24, 0, -61/720, 0, 277/8064, 0, -50521/3628800] Index: sage/combinat/sloane_functions.py =================================================================== --- sage/combinat/sloane_functions.py (revision 4064) +++ sage/combinat/sloane_functions.py (revision 3537) @@ -35,9 +35,4 @@ sage: a The integer sequence tau(n), which is the number of divisors of n. - -TESTS: - sage: a = sloane.A000001; - sage: a == loads(dumps(a)) - True AUTHORS: @@ -99,5 +94,4 @@ from sage.misc.misc import srange from sage.rings.integer_ring import ZZ -import sage.calculus.all as calculus Integer = ZZ @@ -117,9 +111,4 @@ def _repr_(self): raise NotImplementedError - - def __cmp__(self, other): - if not isinstance(other, SloaneSequence): - return cmp(type(self), type(other)) - return cmp(repr(self), repr(other)) def __call__(self, n): @@ -3397,5 +3386,5 @@ def _eval(self, n): - return arith.binomial(n, int(calculus.floor(n//2))) + return arith.binomial(n,arith.floor(n//2)) class A000292(SloaneSequence): Index: sage/crypto/cipher.py =================================================================== --- sage/crypto/cipher.py (revision 4005) +++ sage/crypto/cipher.py (revision 2447) @@ -28,7 +28,4 @@ self._key = key - def __eq__(self, right): - return type(self) == type(right) and self._parent == right._parent and self._key == right._key - def __repr__(self): return str(self._key) Index: sage/crypto/classical.py =================================================================== --- sage/crypto/classical.py (revision 4005) +++ sage/crypto/classical.py (revision 2784) @@ -44,11 +44,4 @@ sage: e(m) GSVXZGRMGSVSZG - - TESTS: - sage: M = AlphabeticStrings() - sage: E = SubstitutionCryptosystem(M) - sage: E == loads(dumps(E)) - True - """ if not isinstance(S, StringMonoid_class): @@ -148,11 +141,4 @@ sage: e(S("THECATINTHEHAT")) TAHEHTNITACEHT - - EXAMPLES: - sage: S = AlphabeticStrings() - sage: E = TranspositionCryptosystem(S,14) - sage: E == loads(dumps(E)) - True - """ if not isinstance(S, StringMonoid_class): @@ -249,11 +235,4 @@ sage: e(S("THECATINTHEHAT")) TIGFEYOUBQOSMG - - TESTS: - sage: S = AlphabeticStrings() - sage: E = VigenereCryptosystem(S,14) - sage: E == loads(dumps(E)) - True - """ if not isinstance(S, StringMonoid_class): Index: sage/crypto/classical_cipher.py =================================================================== --- sage/crypto/classical_cipher.py (revision 4005) +++ sage/crypto/classical_cipher.py (revision 2688) @@ -32,15 +32,6 @@ sage: e(m) GSVXZGRMGSVSZG - - TESTS: - sage: S = AlphabeticStrings() - sage: E = SubstitutionCryptosystem(S) - sage: E == loads(dumps(E)) - True """ SymmetricKeyCipher.__init__(self, parent, key) - - def __eq__(self, right): - return type(self) == type(right) and self.parent() == right.parent() and self.key() == right.key() def __call__(self, M): @@ -93,12 +84,4 @@ sage: e(m) EHTTACDNAEHTTAH - - - TESTS: - sage: S = AlphabeticStrings() - sage: E = TranspositionCryptosystem(S,14) - sage: E == loads(dumps(E)) - True - """ n = parent.block_length() @@ -148,11 +131,4 @@ sage: e(m) LOEMELXRTYIZHT - - TESTS: - sage: S = AlphabeticStrings() - sage: E = VigenereCryptosystem(S,11) - sage: E == loads(dumps(E)) - True - """ SymmetricKeyCipher.__init__(self, parent, key) Index: sage/crypto/cryptosystem.py =================================================================== --- sage/crypto/cryptosystem.py (revision 4005) +++ sage/crypto/cryptosystem.py (revision 2688) @@ -42,13 +42,4 @@ self._block_length = block_length self._period = period - - def __eq__(self,right): - return type(self) == type(right) and \ - self._cipher_domain == right._cipher_domain and \ - self._cipher_codomain == right._cipher_codomain and \ - self._key_space == right._key_space and \ - self._block_length == right._block_length and \ - self._period == right._period - def plaintext_space(self): Index: sage/crypto/stream.py =================================================================== --- sage/crypto/stream.py (revision 4005) +++ sage/crypto/stream.py (revision 2771) @@ -33,10 +33,4 @@ LFSR cryptosystem over Finite Field of size 2 - TESTS: - sage: E = LFSRCryptosystem(FiniteField(2)) - sage: E == loads(dumps(E)) - True - - TODO: Implement LFSR cryptosytem for arbitrary rings. The current implementation if limitated to the finite field of 2 elements only @@ -51,7 +45,4 @@ SymmetricKeyCryptosystem.__init__(self, S, S, None) self._field = field - - def __eq__(self,right): - return type(self) == type(right) and self._field == right._field def __call__(self, key): Index: sage/crypto/stream_cipher.py =================================================================== --- sage/crypto/stream_cipher.py (revision 4005) +++ sage/crypto/stream_cipher.py (revision 2710) @@ -44,12 +44,4 @@ sage: m == e(e(m)) True - - TESTS: - sage: FF = FiniteField(2) - sage: P. = PolynomialRing(FF) - sage: E = LFSRCryptosystem(FF) - sage: E == loads(dumps(E)) - True - """ SymmetricKeyCipher.__init__(self, parent, key = (poly, IS)) Index: sage/databases/conway.py =================================================================== --- sage/databases/conway.py (revision 3702) +++ sage/databases/conway.py (revision 1097) @@ -2,47 +2,4 @@ Frank Luebeck's tables of Conway polynomials over finite fields. """ - - -## On 3/29/07, David Joyner wrote: -## > I guessed what you would do to create the *.bz2 file -## > and I think it turned out to be right. (You did things the simplest way, -## > as far as I can see.) The file is posted at -## > http://sage.math.washington.edu/home/wdj/patches/conway_table.py.bz2 -## > I think what you did was (a) take the data file from -## > http://www.math.rwth-aachen.de/~Frank.Luebeck/data/ConwayPol/CPimport.txt -## > (b) renamed the file conway_table.py -## > (c) used an editor to make a few changes to the first few and last -## > few lines of the data file, -## > (d) packed it using bzip2. -## > -## > I did this and placed the *bz2 file in the correct directory -## > (as determined by conway.py). Here's a test -## > -## > sage: R = PolynomialRing(GF(2),"x") -## > sage: R(ConwayPolynomials()[2][3]) -## > x^3 + x + 1 -## > -## > If I am reading conway.py correctly then this test shows that the -## > file I created is what you want. -## > -## > If you agree, then I will add the new data (you forwarded by -## > separate emails) to it. -## > -## > Please let me know if this is reasonable. - -## Yes, you did exactly the right thing, which I verified as follows: - -## (1) delete SAGE_ROOT/data/conway_polynomials/* -## (2) put your conway_polynomial.py.bz2 file in a new directory -## /home/was/s/data/src/conway/ -## (3) Start SAGE: -## sage: c = ConwayPolynomials(read_only=False) -## sage: c._init() # builds database -## sage: c.polynomial(3,10) -## [2, 1, 0, 0, 2, 2, 2, 0, 0, 0, 1] -## (4) restart and test: -## sage: conway_polynomial(3,10) -## x^10 + 2*x^6 + 2*x^5 + 2*x^4 + x + 2 - #***************************************************************************** Index: sage/databases/cremona.py =================================================================== --- sage/databases/cremona.py (revision 4053) +++ sage/databases/cremona.py (revision 1097) @@ -256,5 +256,4 @@ sage: c.allcurves(11) {'a1': [[0, -1, 1, -10, -20], 0, 5], 'a3': [[0, -1, 1, 0, 0], 0, 5], 'a2': [[0, -1, 1, -7820, -263580], 0, 1]} - """ def __init__(self, read_only=True): Index: sage/dsage/LICENSE.txt =================================================================== --- sage/dsage/LICENSE.txt (revision 3746) +++ sage/dsage/LICENSE.txt (revision 2888) @@ -1,18 +1,14 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## +# Distributed SAGE +# Copyright (C) 2006 Yi Qiang + +# This program is free software; you can redistribute it and/or +# modify it under the terms of the GNU General Public License +# as published by the Free Software Foundation; either version 2 +# of the License, or (at your option) any later version. +# This program is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU General Public License for more details. +# You should have received a copy of the GNU General Public License +# along with this program; if not, write to the Free Software +# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. Index: sage/dsage/README.txt =================================================================== --- sage/dsage/README.txt (revision 3852) +++ sage/dsage/README.txt (revision 2888) @@ -53,5 +53,5 @@ 2) Setting up a public key database - Authentication of clients is done solely based on public keys. + Authentication of users is done solely based on public keys. To grant a client access to the server, you must first add their username and public key to the file you specified in @@ -128,5 +128,5 @@ id, you can simply type: - print job.result.job.job_id + print job.result.job.id This will print out the id of the job you submitted. Also, the Index: sage/dsage/all.py =================================================================== --- sage/dsage/all.py (revision 3901) +++ sage/dsage/all.py (revision 3634) @@ -1,26 +1,12 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## +"""nodoctest +""" from sage.dsage.dsage import dsage -from sage.dsage.dist_functions.all import * +#from sage.dsage.dist_functions.all import * -def DSage(server=None, port=None, username=None, pubkey_file=None, privkey_file=None): +def DSage(server=None, port=8081, username=None, + pubkey_file=None, privkey_file=None): from sage.dsage.interface.dsage_interface import BlockingDSage return BlockingDSage(server=server, port=port, username=username, pubkey_file=pubkey_file, privkey_file=privkey_file) + Index: age/dsage/database/clientdb.py =================================================================== --- sage/dsage/database/clientdb.py (revision 3866) +++ (revision ) @@ -1,229 +1,0 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -import datetime -import os -import sqlite3 as sqlite - -from twisted.python import log - -import sage.dsage.database.sql_functions as sql_functions -from sage.dsage.misc.config import get_conf - -class ClientDatabase(object): - """ - This class defines the ClientDatabase which is used to store user - authentication credentials and other information. - - """ - - TABLENAME = 'clients' - - CREATE_USER_TABLE = """CREATE TABLE %s - ( - id integer PRIMARY KEY, - username text NOT NULL UNIQUE, - public_key text NOT NULL UNIQUE, - creation_time timestamp, - access_time timestamp, - last_login timestamp, - connected BOOL, - enabled BOOL DEFAULT 1 - ) - """ % TABLENAME - - def __init__(self, test=False): - """ - Parameters: - test -- set to true if you would like to do testing. - - """ - - self.conf = get_conf(type='clientdb') - self.tablename = self.TABLENAME - if test: - self.db_file = 'clientdb_test.db' - else: - self.db_file = self.conf['db_file'] - if not os.path.exists(self.db_file): - dir, file = os.path.split(self.db_file) - if not os.path.isdir(dir): - os.mkdir(dir) - self.con = sqlite.connect(self.db_file, - detect_types=sqlite.PARSE_DECLTYPES|sqlite.PARSE_COLNAMES) - self.con.text_factory = str - - if sql_functions.table_exists(self.con, self.tablename) is None: - sql_functions.create_table(self.con, - self.tablename, - self.CREATE_USER_TABLE) - self.con.commit() - - def _shutdown(self): - self.con.commit() - self.con.close() - - def get_user_and_key(self, username): - """ - Returns a tuple containing the username and public key. - - """ - - query = """SELECT username, public_key FROM clients WHERE username = ?""" - - cur = self.con.cursor() - cur.execute(query, (username,)) - result = cur.fetchone() - - return result - - def get_user(self, username): - """ - Returns a tuple containing all of the clients information. - - WARNING: ORDER OF RETURNED TUPLE MIGHT CHANGE - - """ - - query = """SELECT * FROM clients WHERE username = ?""" - cur = self.con.cursor() - cur.execute(query, (username,)) - result = cur.fetchone() - - return result - - def add_user(self, username, pubkey): - """ - Adds a user to the database. - - """ - - query = """INSERT INTO clients - (username, public_key, creation_time) - VALUES (?, ?, ?) - """ - - try: - f = open(pubkey) - type_, key = f.readlines()[0].split()[:2] - f.close() - if not type_ == 'ssh-rsa': - raise TypeError - except IOError: - key = pubkey - - cur = self.con.cursor() - cur.execute(query, (username, key, datetime.datetime.now())) - self.con.commit() - - def del_user(self, username): - """ - Deletes a user from the database. - - """ - - query = """DELETE FROM clients WHERE username = ?""" - self.con.execute(query, (username,)) - self.con.commit() - - def set_enabled(self, username, enabled=True): - """ - Enables/Disables a clients account. - - Parameters: - username -- str - enabled -- bool - """ - - query = """UPDATE clients - SET enabled = ? - WHERE username = ? - """ - - self.con.execute(query, (enabled, username)) - self.con.commit() - - def get_enabled(self, username): - """ - Returns whether or not a user account is enabled. - - """ - - query = """SELECT enabled FROM clients WHERE username = ?""" - cur = self.con.cursor() - cur.execute(query, (username,)) - result = cur.fetchone() - - return bool(result[0]) - - def set_parameter(self, username, parameter, value): - """ - Sets a particular parameter for the given username. - - """ - - query = """UPDATE clients - SET %s = ? - WHERE username = ? - """ % (parameter) - - self.con.execute(query, (value, username)) - self.con.commit() - - def get_parameter(self, username, parameter): - """ - Returns a particular parameter for the given username. - - """ - - query = """SELECT %s FROM clients WHERE username = ?""" % parameter - cur = self.con.cursor() - cur.execute(query, (username,)) - result = cur.fetchone() - - return result[0] - - def set_connected(self, username, connected=True): - self.set_parameter(username, 'connected', connected) - - def update_login_time(self, username): - """ - Updates the last_login time of the user. - - """ - - query = """UPDATE clients - SET last_login = ? - WHERE username = ? - """ - - self.con.execute(query, (datetime.datetime.now(), username,)) - self.con.commit() - - def get_client_list(self): - """ - Returns a list of clients connected. - - """ - - query = """SELECT username from clients WHERE connected""" - cur = self.con.cursor() - cur.execute(query) - - return [result[0] for result in cur.fetchall()] Index: sage/dsage/database/job.py =================================================================== --- sage/dsage/database/job.py (revision 3866) +++ sage/dsage/database/job.py (revision 3019) @@ -15,5 +15,4 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ @@ -23,17 +22,18 @@ import bz2 import os -import copy + +from twisted.spread import pb from persistent import Persistent class Job(Persistent): + r""" + Defines a Job that gets distributed to clients. + """ - Defines a Job that gets distributed to clients. - - """ - - def __init__(self, id_=None, name=None, code=None, parent=None, - username=None, type_='sage'): - """ + + def __init__(self, id=None, name=None, file=None, parent=None, + author=None, type='sage'): + r""" Creates a new job. @@ -41,7 +41,7 @@ name -- job name id -- job id (must be unique) - code -- job code + file -- job file parent -- sets if the job is a parent job - username -- author of the job (not neccesarily unique) + author -- author of the job (not neccesarily unique) type -- the type of the job (file, string, generator) defaults to string @@ -52,39 +52,30 @@ # Job keywords - self.jdict['job_id'] = id_ self.jdict['name'] = name - self.jdict['code'] = code - self.jdict['username'] = username + self.jdict['id'] = id + self.jdict['num'] = None + self.jdict['file'] = file + self.jdict['parent'] = parent + self.jdict['author'] = author + self.jdict['creation_time'] = datetime.datetime.now() + self.jdict['finish_time'] = None + self.jdict['updated_time'] = None + + # Valid status keywords: + # new, completed, incomplete, processing + self.jdict['status'] = 'new' + + self.jdict['children'] = [] + self.jdict['type'] = type + self.jdict['result'] = None # result should be a pickled object + self.jdict['failures'] = 0 + self.jdict['killed'] = False self.jdict['data'] = [] self.jdict['output'] = '' self.jdict['worker_info'] = None - # Valid status keywords: - # new, completed, incomplete, processing - self.jdict['status'] = 'new' - self.jdict['creation_time'] = datetime.datetime.now() - self.jdict['update_time'] = None - self.jdict['finish_time'] = None - self.jdict['killed'] = False - self.jdict['type'] = type_ - self.jdict['result'] = None # result should be a pickled object - self.jdict['failures'] = 0 - self.jdict['verifiable'] = False # is this job easily verified? - - # These might become deprecated - self.jdict['parent'] = parent - self.jdict['children'] = [] def __str__(self): return str(self.jdict) - - def __setattr__(self, name, value): - if name == 'jdict': - if not self.__dict__.has_key('jdict'): - self.__dict__[name] = value - else: - raise ValueError, 'Do not reassign Job.jdict.' - else: - Persistent.__setattr__(self, name, value) - + def num_of_children(self): return len(self.jdict['children']) @@ -98,29 +89,38 @@ name = property(fget=get_name, fset=set_name, fdel=None, doc='Job name') - def get_code(self): - return self.jdict['code'] - def set_code(self, value): + def get_file(self): + return self.jdict['file'] + def set_file(self, value): if not isinstance(value, str): raise TypeError - self.jdict['code'] = value - code = property(fget=get_code, fset=set_code, fdel=None, - doc='Job code') + self.jdict['file'] = value + file = property(fget=get_file, fset=set_file, fdel=None, + doc='Job file') def get_id(self): - return self.jdict['job_id'] + return self.jdict['id'] def set_id(self, value): if not isinstance(value, str): raise TypeError - self.jdict['job_id'] = value - job_id = property(fget=get_id, fset=set_id, fdel=None, doc='Job ID') + self.jdict['id'] = value + id = property(fget=get_id, fset=set_id, fdel=None, doc='Job ID') + + def get_num(self): + if self.id is None: + return None + s = self.id.find('_') + 1 + return int(self.id[s:]) + def set_num(self): + pass + num = property(fget=get_num, fset=set_num, fdel=None, doc='Job Number') def get_status(self): return self.jdict['status'] def set_status(self, value): - # statuses = ['new', 'completed', 'incomplete', 'processing'] - # if not value in statuses: - # raise TypeError - #if value == 'completed': - # self.finish_time = datetime.datetime.now() + statuses = ['new', 'completed', 'incomplete', 'processing'] + if not value in statuses: + raise TypeError + if value == 'completed': + self.finish_time = datetime.datetime.now() self.jdict['status'] = value status = property(fget=get_status, fset=set_status, fdel=None, @@ -159,9 +159,10 @@ doc='Job output') - def get_username(self): - return self.jdict['username'] - def set_username(self, value): - self.jdict['username'] = value - username = property(fget=get_username, fset=set_username, fdel=None, + def get_author(self): + return self.jdict['author'] + def set_author(self, value): + + self.jdict['author'] = value + author = property(fget=get_author, fset=set_author, fdel=None, doc='Job author') @@ -175,16 +176,15 @@ fdel=None, doc='Job finish time') - def get_update_time(self): - return self.jdict['update_time'] - def set_update_time(self, value): + def get_updated_time(self): + return self.jdict['updated_time'] + def set_updated_time(self, value): if not isinstance(value, datetime.datetime): raise TypeError - self.jdict['update_time'] = value - update_time = property(fget=get_update_time, fset=set_update_time, + self.jdict['updated_time'] = value + updated_time = property(fget=get_updated_time, fset=set_updated_time, fdel=None, doc='Job updated time') def get_creation_time(self): return self.jdict['creation_time'] - def set_creation_time(self, value): if not isinstance(value, datetime.datetime): @@ -229,14 +229,11 @@ worker_info = property(fget=get_worker_info, fset=set_worker_info, fdel=None, doc='Worker info') - - def get_verifiable(self): - return self.jdict['verifiable'] - def set_verifiable(self, value): - if not isinstance(value, bool): - raise TypeError - self.jdict['verifiable'] = value + + def get_data(self): + return self.jdict['data'] + data = property(fget=get_data, fset=None, fdel=None, doc='Job data.') def attach(self, var, obj, file_name=None): - """ + r""" Attaches an object to a job. @@ -251,5 +248,5 @@ try: s = open(file_name, 'rb').read() - s = zlib.compress(s) + s = zlib.compress(f) except: print 'Unable to load %s. ' % file_name @@ -259,11 +256,11 @@ s = cPickle.dumps(obj, 2) s = zlib.compress(s) - except cPickle.PicklingError: - print 'Unable to attach your object.' + except PicklingError: + print 'Unable to attach yor object.' return self.jdict['data'].append((var, s, 'object')) def attach_file(self, file_name): - """ + r""" Attach a file to a job. @@ -273,6 +270,10 @@ """ - f = open(file_name, 'rb').read() - f = zlib.compress(f) + try: + f = open(file_name, 'rb').read() + f = zlib.compress(f) + except: + print 'Unable to read file.' + return # Strip out any hard coded path in the file name @@ -281,16 +282,19 @@ def pickle(self): - """ + r""" Returns a pickled representation of self. """ - s = cPickle.dumps(self, 2) - s = zlib.compress(s) - + try: + s = cPickle.dumps(self, 2) + s = zlib.compress(s) + except: + print 'Error pickling self' + return return s def unpickle(self, pickled_job): - """ + r""" Returns the unpickled version of myself. @@ -298,38 +302,2 @@ return cPickle.loads(zlib.decompress(pickled_job)) - - def reduce(self): - """ - Returns a reduced form of Job.jdict to be sent over the network. - - """ - - # TODO: Figure out what attributes are safe to delete - - # dump and compress the data of the job - jdict = copy.deepcopy(self.jdict) - jdict['data'] = cPickle.dumps(self.jdict['data'], 2) - jdict['data'] = zlib.compress(jdict['data']) - - return jdict - -def expand_job(jdict): - """ - This method recreates a Job object given a jdict. - - """ - - if jdict is None: - return None - - job = Job() - - # decompress and load data - try: - jdict['data'] = zlib.decompress(jdict['data']) - jdict['data'] = cPickle.loads(jdict['data']) - except: - jdict['data'] = None - job.jdict.update(jdict) - - return job Index: sage/dsage/database/jobdb.py =================================================================== --- sage/dsage/database/jobdb.py (revision 3895) +++ sage/dsage/database/jobdb.py (revision 3017) @@ -15,13 +15,11 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ +import sys import datetime import os +import ConfigParser import random -import string -import time -import sqlite3 from twisted.python import log @@ -29,43 +27,31 @@ from ZODB import FileStorage, DB from BTrees import OOBTree +from persistent import Persistent import transaction +import sqlite3 as sqlite + from sage.dsage.database.job import Job -import sage.dsage.database.sql_functions as sql_functions -from sage.dsage.misc.config import get_conf - -class JobDatabase(object): - """ - Implementation of the job database. - Common methods between the implementations should go here. - - """ - - def __init__(self): - self.conf = get_conf(type='jobdb') - self.db_file = self.conf['db_file'] - self.job_failure_threshold = int(self.conf['job_failure_threshold']) - self.log_file = self.conf['log_file'] - self.log_level = int(self.conf['log_level']) - self.prune_in_days = int(self.conf['prune_in_days']) - - def random_string(self, length=10): - """ - Returns a random string - - Parameters: - length -- the length of the string - - """ - - random.seed() - l = list((length*length) * (string.letters + string.digits)) - random.shuffle(l) - s = ''.join(random.sample(l, length)) - - return s - -class JobDatabaseZODB(JobDatabase): - """ + +DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') +# Begin reading configuration +try: + conf_file = os.path.join(DSAGE_DIR, 'server.conf') + config = ConfigParser.ConfigParser() + config.read(conf_file) + + DB_FILE = os.path.expanduser(config.get('db', 'db_file')) + PRUNE_IN_DAYS = config.getint('db', 'prune_in_days') + STALE_IN_DAYS = config.getint('db', 'stale_in_days') + FAILURE_THRESHHOLD = config.getint('db', 'failure_threshhold') + LOG_FILE = config.get('db_log', 'log_file') + LOG_LEVEL = config.getint('db_log', 'log_level') +except: + print "Error reading '%s', please run dsage.setup() or fix manually"%conf_file + sys.exit(-1) +# End reading configuration + +class JobDatabaseZODB(object): + r""" Implementation of DSage's database using ZODB. @@ -76,18 +62,9 @@ """ - # The following effectively turns of the ZODB logger, which is OK for us. - # Without this, one gets this annoying error message a lot: - # No handlers could be found for logger "ZODB.FileStorage" - import logging - logging.getLogger("ZODB.FileStorage").setLevel(10000000) - logging.getLogger("ZODB.lock_file").setLevel(10000000) - logging.getLogger("ZODB.Connection").setLevel(10000000) - def __init__(self, test=False, read_only=False): - JobDatabase.__init__(self) if test: self.db_file = 'test_db.db' else: - self.db_file = self.DB_FILE + self.db_file = DB_FILE if not os.path.exists(self.db_file): dir, file = os.path.split(self.db_file) @@ -95,6 +72,5 @@ os.mkdir(dir) if read_only: - self.storage = FileStorage.FileStorage(self.db_file, - read_only=True) + self.storage = FileStorage.FileStorage(self.db_file, read_only=True) else: self.storage = FileStorage.FileStorage(self.db_file) @@ -116,9 +92,9 @@ self.completed_jobdb = self.dbroot['completed_jobdb'] - if self.get_job_by_id('GLOBALS') == None: + if self.getJobByID('GLOBALS') == None: self.__init_globals() def _shutdown(self): - """ + r""" Shuts down the database by closing all DB connections and storages. @@ -129,29 +105,46 @@ self.db.close() - def get_next_job_id(self): - """ - Increments job_id by one and returns the current job_id - - """ - - gdict = self.__retrieve_globals() + def getJobID(self): + r""" + Increments jobID by one and returns the current jobID + + """ + + gdict = self.__retrieveGlobals() jobNUM = gdict['next_job_num'] gdict['next_job_num'] += 1 - job_id = self.random_string(10) + '_' + '%s' % jobNUM - self.store_job(gdict) - if self.log_level > 1: + jobID = self.random_string(10) + '_' + '%s' % jobNUM + self.storeJob(gdict) + if LOG_LEVEL > 1: log.msg('[DB] Incremented job num to: ', jobNUM) - return job_id + return jobID + + def random_string(self, length): + r""" + Returns a random string + + Parameters: + length -- the length of the string + + """ + + random.seed() + letters = 'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ' + l = list(10 * letters) + random.shuffle(l) + s = ''.join(random.sample(l, length)) + + return s - def __retrieve_globals(self): - return self.get_job_by_id('GLOBALS') + def __retrieveGlobals(self): + return self.getJobByID('GLOBALS') def __init_globals(self): gdict = dict(next_job_num = 1) - self.store_job(gdict) - - def get_job(self): - """ + self.storeJob(gdict) + + def getJob(self): + r""" Returns the first non completed job in the job database. @@ -161,5 +154,5 @@ """ - for job_id, job in self.jobdb.iteritems(): + for jobID, job in self.jobdb.iteritems(): try: if isinstance(job, Job) and job.status == 'new': @@ -168,23 +161,23 @@ return None - def get_job_by_id(self, job_id): - """ + def getJobByID(self, jobID): + r""" Returns a job given a job id. Parameters: - job_id -- the job id (int) - - """ - if not self.has_job(job_id): + jobID -- the job id (int) + + """ + if not self.hasJob(jobID): return None else: - return self.jobdb[job_id] - - def get_jobs_by_username(self, username, is_active, job_name=None): - """ + return self.jobdb[jobID] + + def getJobsByAuthor(self, author, is_active, job_name=None): + r""" Returns jobs created by author. Parameters: - username -- the username name (str) + author -- the author name (str) is_active -- when set to true, only return active jobs (bool) job_name -- the job name to return (default=None) @@ -194,24 +187,24 @@ if is_active: if job_name: - jobs = [job for job in self.get_active_jobs() - if (job.username == username and job.name == job_name)] + jobs = [job for job in self.getActiveJobs() + if (job.author == author and job.name == job_name)] else: - jobs = [job for job in self.get_active_jobs() - if job.username == username] + jobs = [job for job in self.getActiveJobs() + if job.author == author] else: if job_name: - jobs = [job for job in self.get_jobs_list() - if (job.username == username and job.name == job_name)] + jobs = [job for job in self.getJobsList() + if (job.author == author and job.name == job_name)] else: - jobs = [job for job in self.get_jobs_list() - if job.username == username] - - if self.log_level > 3: - log.msg('[JobDatabaseZODB, get_jobs_by_username] ', jobs) + jobs = [job for job in self.getJobsList() + if job.author == author] + + if LOG_LEVEL > 3: + log.msg('[JobDatabaseZODB, getJobsByAuthor] ', jobs) return jobs - def store_job(self, job): - """ + def storeJob(self, job): + r""" Stores a job in the job database. @@ -228,48 +221,48 @@ if isinstance(job, dict): if job.has_key('next_job_num'): - # log.msg('[DB, store_job] Setting job_id to GLOBALS') - job_id = 'GLOBALS' + # log.msg('[DB, storeJob] Setting jobID to GLOBALS') + jobID = 'GLOBALS' elif isinstance(job, Job): - job_id = job.job_id - if not isinstance(job_id, str): - job_id = self.get_next_job_id() - job.update_time = datetime.datetime.now() + jobID = job.id + if not isinstance(jobID, str): + jobID = self.getJobID() + job.updated_time = datetime.datetime.now() else: raise TypeError - self.jobdb[job_id] = job + self.jobdb[jobID] = job # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # Need this hack to notify ZODB that the dict was modified # WITHOUT IT CHANGES WILL NOT BE WRITTEN BACK TO DISK - if job_id != 'GLOBALS': + if jobID != 'GLOBALS': job._p_changed = True # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # transaction.commit() - if self.log_level > 0: - log.msg("[DB] Stored job %s" % (job_id)) - - return job_id - - def remove_job(self, job_id): - """ + if LOG_LEVEL > 0: + log.msg("[DB] Stored job %s" % (jobID)) + + return jobID + + def removeJob(self, jobID): + r""" Removes a job from the database. Parameters: - job_id -- job id (int) + jobID -- job id (int) """ try: - del self.jobdb[job_id] - if self.log_level > 0: - log.msg('[JobDB] Removed job %s from jobdb' % (job_id)) + del self.jobdb[jobID] + if LOG_LEVEL > 0: + log.msg('[JobDB] Removed job %s from jobdb' % (jobID)) transaction.commit() - return job_id + return jobID except: log.msg('[JobDB] Failure removing a job.') raise - def get_active_jobs(self): - """ + def getActiveJobs(self): + r""" Returns a list containing active jobs, i.e. jobs that are currentl being processed. @@ -277,18 +270,18 @@ """ - return [job for job in self.get_jobs_list() + return [job for job in self.getJobsList() if job.status == 'processing'] - def has_job(self, job_id): - """ + def hasJob(self, jobID): + r""" Checks if the database contains a job corresponding to job id. Parameters: - job_id -- the job id (int) + jobID -- the job id (int) """ # For some reason has_key returns 0/1 versus True/False - b = self.jobdb.has_key(job_id) + b = self.jobdb.has_key(jobID) if b > 0: return True @@ -296,6 +289,6 @@ return False - def get_jobs_list(self): - """ + def getJobsList(self): + r""" Returns an ordered list of all the jobs in the database. @@ -305,14 +298,14 @@ sorted_list = [] - for job_id, job in self.jobdb.iteritems(): - if job_id == 'GLOBALS': # Skip the GLOBALS job + for jobID, job in self.jobdb.iteritems(): + if jobID == 'GLOBALS': # Skip the GLOBALS job continue - sorted_list.append((job.job_id, job)) + sorted_list.append((job.num, job)) sorted_list.sort() return [job[1] for job in sorted_list] - def get_completed_jobs_list(self): - """ + def getCompletedJobsList(self): + r""" Returns an ordered list of all the completed jobs in the database. @@ -320,25 +313,25 @@ """ - return [job for job in self.get_jobs_list() + return [job for job in self.getJobsList() if job.status == 'completed'] - def get_in_complete_jobs_list(self): - """ + def getIncompleteJobsList(self): + r""" Returns an ordered list of jobs marked as incomplete. """ - return [job for job in self.get_jobs_list() + return [job for job in self.getJobsList() if job.status == 'incomplete'] - def get_killed_jobs_list(self): - """ + def getKilledJobsList(self): + r""" Returns a list of killed jobs. """ - return [job for job in self.get_jobs_list() if job.killed] - - def new_job(self, job): - """ + return [job for job in self.getJobsList() if job.killed] + + def newJob(self, job): + r""" Stores a new job in the database. @@ -348,294 +341,16 @@ """ - job_id = self.get_next_job_id() - job.job_id = job_id - - return self.store_job(job) - -class JobDatabaseSQLite(JobDatabase): - """ - Implementation of DSage's database using SQLite. - - Parameters: - test -- set to true for unittesting purposes - - """ - - # TODO: SQLite does *NOT* enforce foreign key constraints - # Must do manual checking. - - CREATE_JOBS_TABLE = """CREATE TABLE jobs - (job_id TEXT NOT NULL UNIQUE, - name TEXT, - username TEXT REFERENCES clients(username), - monitor_id TEXT REFERENCES monitors(uuid), - worker_info TEXT, - code TEXT, - data BLOB, - output TEXT, - result BLOB, - status TEXT NOT NULL, - priority INTEGER DEFAULT 10, - type TEXT, - failures INTEGER DEFAULT 0, - creation_time timestamp NOT NULL, - update_time timestamp, - finish_time timestamp, - verifiable BOOL, - killed BOOL DEFAULT 0 - ); - """ - - def __init__(self, test=False): - JobDatabase.__init__(self) - if test: - self.db_file = 'test_jobdb.db' - else: - if not os.path.exists(self.db_file): - dir, file = os.path.split(self.db_file) - if not os.path.isdir(dir): - os.mkdir(dir) - - self.tablename = 'jobs' - self.con = sqlite3.connect( - self.db_file, - detect_types=sqlite3.PARSE_DECLTYPES|sqlite3.PARSE_COLNAMES) - self.con.text_factory = str # Don't want unicode objects - if not sql_functions.table_exists(self.con, self.tablename): - sql_functions.create_table(self.con, - self.tablename, - self.CREATE_JOBS_TABLE) - - def __add_test_data(self): - INSERT_JOB = """INSERT INTO jobs - (uid, - username, - code, - data, - output, - worker_id, - status, - priority, - creation_time, - update_time, - finish_time - ) - VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?); - """ - - dn = lambda: datetime.datetime.now() # short hand - D = [(self.random_string(), 1, None, None, None, 1, - 'new', 1, dn(), dn(), None), - (self.random_string(), 1, None, None, None, 1, - 0, 1, dn(), dn(), None), - (self.random_string(), 1, None, None, None, 1, - 0, 1, dn(), dn(), None)] - - log.msg('Sleeping for 0.5 second to test timestamps...') - time.sleep(0.5) - - D.extend([(self.random_string(), 1, None, None, None, 1, - 0, 1, dn(), dn(), None), - (self.random_string(), 1, None, None, None, 1, - 0, 1, dn(), dn(), None), - (self.random_string(), 1, None, None, None, 1, - 0, 1, dn(), dn(), None)]) - - self.con.executemany(INSERT_JOB, D) - self.con.commit() - - def _shutdown(self): - self.con.commit() - self.con.close() - - def get_job(self, anonymous=False): - """ - Returns the first unprocessed job of the highest priority. - - """ - - if anonymous: - query = "SELECT * FROM jobs WHERE status = 'new' AND killed = 0" - else: - query = "SELECT * FROM jobs WHERE status = 'new' AND killed = 0" - cur = self.con.cursor() - cur.execute(query) - jtuple = cur.fetchone() - - return self.create_jdict(jtuple, cur.description) - - def set_job_uuid(self, job_id, uuid): - query = "UPDATE jobs SET monitor_id=? WHERE job_id=?" - cur = self.con.cursor() - cur.execute(query, (uuid, job_id)) - self.con.commit() - - def get_all_jobs(self): - query = "SELECT * from jobs" - cur = self.con.cursor() - cur.execute(query) - result = cur.fetchall() - - return [self.create_jdict(jtuple, cur.description) - for jtuple in result] - - def get_job_by_id(self, job_id): - query = "SELECT * FROM jobs WHERE job_id = ?" - cur = self.con.cursor() - cur.execute(query, (job_id,)) # Need to cast it to int for SAGE - jtuple = cur.fetchone() - return self.create_jdict(jtuple, cur.description) - - def _get_jobs_by_parameter(self, key, value): - """ - Returns a particular result given a key and value. - - """ - - query = """SELECT * FROM jobs where %s = ?""" % (key) - cur = self.con.cursor() - cur.execute(query, (value,)) - result = cur.fetchall() - - return [self.create_jdict(jtuple, cur.description) - for jtuple in result] - - def _set_parameter(self, job_id, key, value): - query = """UPDATE jobs - SET %s=? - WHERE job_id=?""" % (key) - cur = self.con.cursor() - cur.execute(query, (value, job_id)) - self.con.commit() - - def _update_value(self, job_id, key, value): - """ - Sets the appropriate value for a job in the database. - - """ - - query = """UPDATE jobs - SET %s=? - WHERE job_id=? - """ % (key) - cur = self.con.cursor() - if key == 'data' or key == 'result': # Binary objects - if value != None: - cur.execute(query, (sqlite3.Binary(value), job_id)) - else: - cur.execute(query, (value, job_id)) - self.con.commit() - - def store_job(self, jdict): - """ - Stores a job based on information from Job.jdict. - The keys of the dictionary should correspond to the columns in the - 'jobs' table. - - Parameters: - job -- a sage.dsage.database.Job object - - """ - - job_id = jdict['job_id'] - - if job_id is None: - job_id = self.random_string() - if self.log_level > 3: - log.msg('[JobDB] Creating a new job with id:', job_id) - query = """INSERT INTO jobs - (job_id, status, creation_time) VALUES (?, ?, ?)""" - cur = self.con.cursor() - cur.execute(query, (job_id, 'new', datetime.datetime.now())) - self.con.commit() - - for k, v in jdict.iteritems(): - try: - self._update_value(job_id, k, v) - except (sqlite3.InterfaceError, - sqlite3.OperationalError, - sqlite3.IntegrityError), msg: - if self.log_level > 3: - log.msg('key: %s, value: %s' % (k, v)) - log.msg(msg) - continue - - return self.get_job_by_id(job_id) - - def create_jdict(self, jtuple, row_description): - """ - Creates a jdict out of a job_tuple. - - """ - - if jtuple is None: - return None - - columns = [desc[0] for desc in row_description] - jdict = dict(zip(columns, jtuple)) - - # Convert 0/1 into python booleans - jdict['killed'] = bool(jdict['killed']) - jdict['verifiable'] = bool(jdict['verifiable']) - - # Convert buffer objects back to string - jdict['data'] = str(jdict['data']) - jdict['result'] = str(jdict['result']) - - return jdict - - def get_killed_jobs_list(self): - """ - Returns a list of jobs which have been marked as killed. - - """ - query = "SELECT * from jobs where killed = 1 AND status <> 'completed'" - cur = self.con.cursor() - cur.execute(query) - killed_jobs = cur.fetchall() - return [self.create_jdict(jdict, cur.description) - for jdict in killed_jobs] - - def get_jobs_by_username(self, username, active=True): - """ - Returns a list of jobs belonging to 'username' - - """ - - if active: - query = """SELECT * from jobs WHERE username = ? - AND status IN ('new', 'processing')""" - else: - query = """SELECT * from jobs WHERE username = ? """ - cur = self.con.cursor() - cur.execute(query, (username,)) - - return [self.create_jdict(jtuple, cur.description) for jtuple in cur] - - def has_job(self, job_id): - """ - Checks if the database contains a job with the given uid. - - """ - - job = self.get_job_by_id(job_id) - if job is None: - return False - else: - return True - - def set_killed(self, job_id, killed=True): - self._update_value(job_id, 'killed', killed) - - def get_active_jobs(self): - return self._get_jobs_by_parameter('status', 'processing') - + jobID = self.getJobID() + job.id = jobID + + return self.storeJob(job) + class DatabasePruner(object): - """ + r""" DatabasePruner is responsible for cleaning out the database. """ def __init__(self, jobdb): - """ + r""" Parameters: jobdb -- a JobDatabase object @@ -645,6 +360,6 @@ self.jobdb = jobdb - def clean_old_jobs(self): - """ + def cleanOldJobs(self): + r""" Cleans out jobs that are older than PRUNE_IN_DAYS days. @@ -652,25 +367,28 @@ log.msg('[DatabasePruner] Cleaning out old jobs...') - jobs = self.jobdb.get_jobs_list() + jobs = self.jobdb.getJobsList() for job in jobs: - delta = datetime.datetime.now() - job.update_time - if delta > datetime.timedelta(self.jobdb.prune_in_days): - self.jobdb.remove_job(job.job_id) - log.msg('[DatabasePruner, clean_old_jobs] Deleted job ', - job.job_id) - - def clean_failed_jobs(self): - """ + delta = datetime.datetime.now() - job.updated_time + if delta > datetime.timedelta(PRUNE_IN_DAYS): + self.jobdb.removeJob(job.id) + log.msg('[DatabasePruner, cleanOldJobs] Deleted job ', + job.id) + + def cleanFailedJobs(self): + r""" Cleans out jobs which are marked as having failed. - """ - - jobs = self.jobdb.get_jobs_list() + Failure threshhold is set in FAILURE_THRESHHOLD, if a job + exceeds this threshhold, we remove it from the job database. + + """ + + jobs = self.jobdb.getJobsList() for job in jobs: - if job.failures > self.jobdb.job_failure_threshold: - self.jobdb.remove_job(job.job_id) + if job.failures > FAILURE_THRESHHOLD: + self.jobdb.removeJob(job.id) def prune(self): - self.clean_old_jobs() - self.clean_failed_jobs() + self.cleanOldJobs() + self.cleanFailedJobs() Index: age/dsage/database/monitordb.py =================================================================== --- sage/dsage/database/monitordb.py (revision 3866) +++ (revision ) @@ -1,268 +1,0 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -import datetime -import os -import sqlite3 as sqlite - -from twisted.python import log - -import sage.dsage.database.sql_functions as sql_functions -from sage.dsage.misc.config import get_conf - -class MonitorDatabase(object): - """ - This table keeps track of workers. - - """ - - CREATE_MONITOR_TABLE = """CREATE TABLE monitors - ( - uuid text NOT NULL UNIQUE, - hostname TEXT, - ip TEXT, - workers INTEGER, - sage_version text, - os text, - kernel_version TEXT, - cpus INTEGER, - cpu_speed INTEGER, - cpu_model TEXT, - mem_total INTEGER, - mem_free INTEGER, - connected BOOL, - busy BOOL, - anonymous BOOL DEFAULT 0, - last_connection timestamp - ) - """ - - def __init__(self, test=False): - self.conf = get_conf(type='monitordb') - self.tablename = 'monitors' - if test: - self.db_file = 'monitordb-test.db' - else: - self.db_file = self.conf['db_file'] - if not os.path.exists(self.db_file): - dir, file = os.path.split(self.db_file) - if not os.path.isdir(dir): - os.mkdir(dir) - self.log_level = self.conf['log_level'] - self.log_file = self.conf['log_file'] - self.con = sqlite.connect(self.db_file, - detect_types=sqlite.PARSE_DECLTYPES|sqlite.PARSE_COLNAMES) - self.con.text_factory = str - - if sql_functions.table_exists(self.con, self.tablename) is None: - sql_functions.create_table(self.con, - self.tablename, - self.CREATE_MONITOR_TABLE) - self.con.commit() - - def _set_parameter(self, uuid, key, value): - query = """UPDATE monitors - SET %s=? - WHERE uuid=?""" % (key) - cur = self.con.cursor() - cur.execute(query, (value, uuid)) - self.con.commit() - - def set_anonymous(self, uuid, anonymous=True): - return self._set_parameter(uuid, 'anonymous', anonymous) - - def add_monitor(self, host_info): - query = """INSERT INTO monitors - (uuid, - hostname, - ip, - workers, - sage_version, - os, - kernel_version, - cpus, - cpu_speed, - cpu_model, - mem_total, - mem_free) - VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?) - """ - - uuid = host_info['uuid'] - hostname = host_info['hostname'] - ip = host_info['ip'] - workers = host_info['workers'] - sage_version = host_info['sage_version'] - os = host_info['os'] - kernel_version = host_info['kernel_version'] - cpus = host_info['cpus'] - cpu_speed = host_info['cpu_speed'] - cpu_model = host_info['cpu_model'] - mem_total = host_info['mem_total'] - mem_free = host_info['mem_free'] - - cur = self.con.cursor() - cur.execute(query, (uuid, hostname, ip, workers, sage_version, os, - kernel_version, cpus, cpu_speed, cpu_model, - mem_total, mem_free)) - self.con.commit() - - def get_monitor(self, uuid): - query = """SELECT uuid, hostname, ip, anonymous, sage_version, os FROM monitors - WHERE uuid=?""" - cur = self.con.cursor() - cur.execute(query, (uuid,)) - result = cur.fetchone() - if result is None: - return result - columns = [desc[0] for desc in cur.description] - monitor = dict(zip(columns, result)) - for k, v in monitor.iteritems(): - if k == 'anonymous': - monitor[k] = bool(v) - - return monitor - - def get_monitor_list(self): - """ - Returns a list of connected monitors. - - """ - - query = """SELECT uuid, hostname, ip, anonymous, sage_version, os FROM monitors - WHERE connected""" - cur = self.con.cursor() - cur.execute(query) - result = cur.fetchall() - columns = [desc[0] for desc in cur.description] - monitors = [dict(zip(columns, monitor)) for monitor in result] - for monitor in monitors: - for k, v in monitor.iteritems(): - if k == 'anonymous': - monitor[k] = bool(v) - - return monitors - - def set_connected(self, uuid, connected=True): - """ - Sets the connected status of a worker. - - Parameters: - uuid -- string - connected -- bool - - """ - - cur = self.con.cursor() - if connected: - query = """UPDATE monitors SET connected=1, last_connection=? - WHERE uuid=?""" - cur.execute(query, (datetime.datetime.now(), uuid)) - else: - query = """UPDATE monitors SET connected=0 WHERE uuid=?""" - cur.execute(query, (uuid,)) - - self.con.commit() - - def set_busy(self, uuid, busy): - """ - Sets whether or not a worker is doing a job. - - """ - - if busy: - query = """UPDATE monitors SET busy=1 WHERE uuid=?""" - else: - query = """UPDATE monitors SET busy=0 WHERE uuid=?""" - - cur = self.con.cursor() - cur.execute(query, (uuid,)) - self.con.commit() - - def get_worker_count(self, connected, busy): - """ - Returns the number of workers. - - Parameters: - connected -- bool - busy -- bool - - """ - - if connected and not busy: - query = """SELECT workers FROM monitors WHERE connected AND NOT busy""" - elif connected and busy: - query = """SELECT workers FROM monitors WHERE connected AND busy""" - elif connected: - query = """SELECT workers FROM monitors WHERE connected""" - else: - query = "SELECT workers FROM monitors WHERE NOT connected" - - cur = self.con.cursor() - cur.execute(query) - result = cur.fetchall() - - return sum(w[0] for w in result) - - def get_cpu_speed(self, connected=True, busy=True): - """ - Returns the aggregate cpu speed in Mhz. - - Parameters: - connected -- bool - - """ - - if connected: - query = """SELECT cpu_speed, workers FROM monitors - WHERE connected AND busy""" - else: - query = """SELECT cpu_speed, workers FROM monitors""" - - cur = self.con.cursor() - cur.execute(query) - - result = cur.fetchall() - - cpu_speed = sum([s[0]*s[1] for s in result]) - - return cpu_speed - - def get_cpu_count(self, connected=True): - """ - Returns the number of cpus that are available. - - Parameters: - connected -- bool - - """ - - if connected: - query = """SELECT workers, cpus FROM monitors WHERE connected""" - else: - query = """SELECT workers, cpus FROM monitors""" - - cur = self.con.cursor() - cur.execute(query) - - result = cur.fetchall() - - cpu_count = sum(min(s[0:2]) for s in result) - - return cpu_count Index: age/dsage/database/sql_functions.py =================================================================== --- sage/dsage/database/sql_functions.py (revision 3866) +++ (revision ) @@ -1,61 +1,0 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -from twisted.python import log - -def table_exists(con, tablename): - """ - Check if a given table exists. - If the below query is not None, then the table exists - - """ - - query = """SELECT name FROM sqlite_master - WHERE type = 'table' AND name = ?; - """ - - cur = con.cursor() - cur.execute(query, (tablename,)) - result = cur.fetchone() - return result - -def create_table(con, tablename, query): - """ - Creates a table given the connection. - - """ - - log.msg('Creating table %s...' % tablename) - con.execute(query) - -def fields(cursor): - """ - Given a DB API 2.0 cursor object that has been executed, returns - a dictionary that maps each field name to a column index, 0 and up. - - """ - - results = {} - for column, desc in enumerate(cursor.description): - results[desc[0]] = column - - return results - -def add_trigger(con, trigger): - con.execute(trigger) Index: age/dsage/database/tests/test_clientdb.py =================================================================== --- sage/dsage/database/tests/test_clientdb.py (revision 3866) +++ (revision ) @@ -1,74 +1,0 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -import unittest - -import datetime - -from sage.dsage.database.clientdb import ClientDatabase - -class ClientDatabaseTestCase(unittest.TestCase): - """ - Test cases for DSAGE's ClientDatabase - - """ - - TEST_USERNAMES = ['yi', 'alex', 'dorian', 'robert', 'william', 'martin'] - TEST_EMAILS = ['foo@bar.com', 'bar@foo.com', '1@2.com', '2@4.com', '5@6.com', '6@7.com' ] - TEST_KEYS = ['1', '2', '3', '4', '5', '6'] - - def setUp(self): - self.clientdb = ClientDatabase(test=True) - - def tearDown(self): - query = """DELETE FROM clients""" - cur = self.clientdb.con.cursor() - cur.execute(query) - self.clientdb.con.commit() - self.clientdb._shutdown() - - def testadd_user(self): - for user, key in zip(self.TEST_USERNAMES, self.TEST_KEYS): - self.clientdb.add_user(user, key) - self.assert_(self.clientdb.get_user(user) is not None) - - def testdel_user(self): - for user in self.TEST_USERNAMES: - self.clientdb.del_user(user) - self.assert_(self.clientdb.get_user(user) is None) - - def testset_enabled(self): - username = self.TEST_USERNAMES[0] - self.clientdb.add_user(username, self.TEST_KEYS[0]) - self.clientdb.set_enabled(username, enabled=True) - self.assertEquals(self.clientdb.get_enabled(username), True) - self.clientdb.set_enabled(username, enabled=False) - self.assertEquals(self.clientdb.get_enabled(username), False) - - def testupdate_login_time(self): - username = self.TEST_USERNAMES[0] - self.clientdb.add_user(username, self.TEST_KEYS[0]) - pre_login_time = self.clientdb.get_parameter(username, 'last_login') - self.assertEquals(pre_login_time, None) - self.clientdb.update_login_time(username) - post_login_time = self.clientdb.get_parameter(username, 'last_login') - self.assert_(datetime.datetime.now() > post_login_time) - -if __name__ == '__main__': - unittest.main() Index: sage/dsage/database/tests/test_job.py =================================================================== --- sage/dsage/database/tests/test_job.py (revision 3852) +++ sage/dsage/database/tests/test_job.py (revision 2944) @@ -25,19 +25,22 @@ class JobTestCase(unittest.TestCase): - def testcreate_job(self): + def testcreateJob(self): job = Job() self.assert_(isinstance(job, Job)) - job = Job(id_=10, name='test', code='test', parent='test', - username='test', type_='test') + job = Job(id=10, name='test', file='test', parent='test', + author='test', type='test') self.assert_(isinstance(job, Job)) - def testjob_id(self): + def testjobID(self): job = Job() - self.assertRaises(TypeError, job.job_id, 5) + self.assertRaises(TypeError, job.id, 5) + def testjobNum(self): + job = Job() + self.assertEquals(None, job.num) def testjobFile(self): job = Job() - self.assertRaises(TypeError, job.code, 1) + self.assertRaises(TypeError, job.file, 1) def testjobCreationTime(self): @@ -51,8 +54,8 @@ self.assertRaises(TypeError, job.finish_time, 'test') - def testjobUpdateTime(self): + def testjobUpdatedTime(self): job = Job() - self.assertEquals(job.update_time, None) - self.assertRaises(TypeError, job.update_time, 'test') + self.assertEquals(job.updated_time, None) + self.assertRaises(TypeError, job.updated_time, 'test') def testjobStatus(self): Index: sage/dsage/database/tests/test_jobdb.py =================================================================== --- sage/dsage/database/tests/test_jobdb.py (revision 3866) +++ sage/dsage/database/tests/test_jobdb.py (revision 2944) @@ -15,5 +15,4 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ @@ -23,6 +22,5 @@ from glob import glob -from sage.dsage.database.jobdb import JobDatabaseZODB, JobDatabaseSQLite -from sage.dsage.database.jobdb import DatabasePruner +from sage.dsage.database.jobdb import JobDatabaseZODB, DatabasePruner from sage.dsage.database.job import Job @@ -31,7 +29,7 @@ self.jobdb = JobDatabaseZODB(test=True) - jobs = self.create_jobs(10) + jobs = self.createJobs(10) for job in jobs: - self.jobdb.new_job(job) + self.jobdb.newJob(job) def tearDown(self): @@ -41,125 +39,80 @@ os.remove(file) - def testhas_job(self): - job = self.create_jobs(1) - job_id = self.jobdb.store_job(job[0]) - self.assertEquals(self.jobdb.has_job(job_id), True) - self.assert_(self.jobdb.has_job('GLOBALS') > 0) + def testhasJob(self): + job = self.createJobs(1) + jobID = self.jobdb.storeJob(job[0]) + self.assertEquals(self.jobdb.hasJob(jobID), True) + self.assert_(self.jobdb.hasJob('GLOBALS') > 0) - def testget_next_job_id(self): + def testgetJobID(self): """Attempt to increment Job ID by one. """ - job_id = self.jobdb.get_next_job_id() - job_id1 = self.jobdb.get_next_job_id() + jobID = self.jobdb.getJobID() + jobID1 = self.jobdb.getJobID() - self.assert_(int(job_id[11:]) < int(job_id1[11:])) + self.assert_(int(jobID[11:]) < int(jobID1[11:])) - def testget_job(self): - job = self.jobdb.get_job() + def testgetJob(self): + job = self.jobdb.getJob() self.assert_(isinstance(job, Job) and job.status != 'completed') - def testremove_job(self): - self.assertRaises(KeyError, self.jobdb.remove_job, 'not_a_job_id') + def testremoveJob(self): + self.assertRaises(KeyError, self.jobdb.removeJob, 'not_a_job_id') - job = self.jobdb.get_job() + job = self.jobdb.getJob() self.assertEquals(type(job), Job) - job_id = job.job_id - self.assertEquals(self.jobdb.remove_job(job_id), job_id) - self.assertRaises(KeyError, self.jobdb.remove_job, job_id) + job_id = job.id + self.assertEquals(self.jobdb.removeJob(job_id), job_id) + self.assertRaises(KeyError, self.jobdb.removeJob, job_id) - def teststore_job(self): - jobs = self.create_jobs(10) + def teststoreJob(self): + jobs = self.createJobs(10) for job in jobs: - job_id = self.jobdb.new_job(job) - self.assertEquals(job, self.jobdb.get_job_by_id(job_id)) - self.assert_(self.jobdb.get_job_by_id(job_id).update_time < + job_id = self.jobdb.newJob(job) + self.assertEquals(job, self.jobdb.getJobByID(job_id)) + self.assert_(self.jobdb.getJobByID(job_id).updated_time < datetime.datetime.now()) - def testget_jobs_by_username(self): - jobs = self.jobdb.get_jobs_by_username('Yi Qiang', True) + def testgetJobsByAuthor(self): + jobs = self.jobdb.getJobsByAuthor('Yi Qiang', True) self.assert_(len(jobs) == 0) - jobs = self.jobdb.get_jobs_by_username('Yi Qiang', False, 'unittest') + jobs = self.jobdb.getJobsByAuthor('Yi Qiang', False, 'unittest') self.assert_(len(jobs) > 0) - def testget_active_jobs(self): - jobs = self.jobdb.get_active_jobs() + def testgetActiveJobs(self): + jobs = self.jobdb.getActiveJobs() self.assert_(len(jobs) == 0) - jobs = self.jobdb.get_jobs_list() + jobs = self.jobdb.getJobsList() for job in jobs: job.status = 'processing' - self.jobdb.store_job(job) + self.jobdb.storeJob(job) - jobs = self.jobdb.get_active_jobs() + jobs = self.jobdb.getActiveJobs() self.assert_(len(jobs) == 10) - def testget_jobs_list(self): - jobs = self.jobdb.get_jobs_list() - self.assertEquals(len(jobs), 10) + def testgetJobsList(self): + jobs = self.jobdb.getJobsList() + + for i in xrange(len(jobs)-1): + self.assert_(jobs[i].num < jobs[i+1].num) - def create_jobs(self, n): + def createJobs(self, n): """This method creates n jobs. """ jobs = [] for i in range(n): - jobs.append(Job(name='unittest', username='Yi Qiang')) + jobs.append(Job(name='unittest', author='Yi Qiang')) return jobs -class JobDatabaseSQLiteTestCase(unittest.TestCase): - """ - Unit tests for the SQLite based JobDatabase go here. - - """ - - def setUp(self): - self.jobdb = JobDatabaseSQLite(test=True) - - def tearDown(self): - query = """DELETE FROM jobs""" - cur = self.jobdb.con.cursor() - cur.execute(query) - self.jobdb._shutdown() - - def testget_job(self): - job = Job() - job.status = 'new' - job.killed = False - jdict = self.jobdb.store_job(job.reduce()) - self.assertEquals(jdict['job_id'], self.jobdb.get_job()['job_id']) - - def teststore_job(self): - job = Job() - self.assert_(isinstance(self.jobdb.store_job(job.reduce()), dict)) - - def testget_job_by_id(self): - job = Job() - jdict = self.jobdb.store_job(job.reduce()) - self.assert_(self.jobdb.get_job_by_id(jdict['job_id']) is not None) - - def testhas_job(self): - job = Job() - jdict = self.jobdb.store_job(job.reduce()) - self.assertEquals(self.jobdb.has_job(jdict['job_id']), True) - - def testcreate_jdict(self): - job = Job() - jdict = self.jobdb.store_job(job.reduce()) - self.assert_(isinstance(jdict, dict)) - - def testget_killed_jobs_list(self): - job = Job() - jdict = self.jobdb.store_job(job.reduce()) - self.jobdb.set_killed(jdict['job_id'], killed=True) - self.assertEquals(len(self.jobdb.get_killed_jobs_list()), 1) - class DatabasePrunerTestCase(unittest.TestCase): def setUp(self): self.jobdb = JobDatabaseZODB(test=True) self.pruner = DatabasePruner(self.jobdb) - jobs = self.create_jobs(10) + jobs = self.createJobs(10) for job in jobs: - self.jobdb.new_job(job) + self.jobdb.newJob(job) @@ -170,33 +123,33 @@ os.remove(file) - def testclean_old_jobs(self): - jobs = self.jobdb.get_jobs_list() + def testcleanOldJobs(self): + jobs = self.jobdb.getJobsList() for job in jobs: - job.update_time -= datetime.timedelta(10) - # directly accessing the database because store_job - # automatically updates the update_time - self.jobdb.jobdb[job.job_id] = job + job.updated_time -= datetime.timedelta(10) + # directly accessing the database because storeJob + # automatically updates the updated_time + self.jobdb.jobdb[job.id] = job - self.pruner.clean_old_jobs() + self.pruner.cleanOldJobs() - jobs = self.jobdb.get_jobs_list() + jobs = self.jobdb.getJobsList() self.assertEquals(len(jobs), 0) - def testclean_failed_jobs(self): - jobs = self.jobdb.get_jobs_list() + def testcleanFailedJobs(self): + jobs = self.jobdb.getJobsList() for job in jobs: job.failures += 20 - self.jobdb.store_job(job) + self.jobdb.storeJob(job) - self.pruner.clean_failed_jobs() - jobs = self.jobdb.get_jobs_list() + self.pruner.cleanFailedJobs() + jobs = self.jobdb.getJobsList() self.assertEquals(len(jobs), 0) - def create_jobs(self, n): + def createJobs(self, n): """This method creates n jobs. """ jobs = [] for i in range(n): - jobs.append(Job(name='unittest', username='Yi Qiang')) + jobs.append(Job(name='unittest', author='Yi Qiang')) return jobs Index: sage/dsage/dist_functions/all.py =================================================================== --- sage/dsage/dist_functions/all.py (revision 3837) +++ sage/dsage/dist_functions/all.py (revision 2942) @@ -1,20 +1,2 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## from dist_function import DistributedFunction, DistributedFunctionTest from dist_factor import DistributedFactor Index: sage/dsage/dist_functions/dist_factor.py =================================================================== --- sage/dsage/dist_functions/dist_factor.py (revision 3874) +++ sage/dsage/dist_functions/dist_factor.py (revision 3016) @@ -6,5 +6,5 @@ class DistributedFactor(DistributedFunction): - """ + r""" DistributedFactor uses ECM and QSIEVE to find factors of numbers. @@ -17,7 +17,7 @@ """ - def __init__(self, DSage, n, concurrent=10, verbosity=0, trial_division_limit=10000, - name='DistributedFactor'): - """ + def __init__(self, DSage, n, concurrent=10, verbosity=0, + trial_division_limit=10000, name='DistributedFactor'): + r""" Parameters: DSage -- an instance of a dsage connection @@ -36,5 +36,4 @@ self.n = n self.prime_factors = [] - self.composite_factors = [] self.cur_B1 = 2000 self.curve_count = 50 @@ -42,4 +41,5 @@ self.verbosity = verbosity self.name = name + # Trial division first to peel off some factors for d in prime_range(2, trial_division_limit): @@ -49,9 +49,6 @@ if n == 1: self.done = True - elif is_prime(n): # The last value might be prime - self.done = True - self.prime_factors.append(n) else: - self.composite_factors.append(n) + self.composite_factors = [n] self.outstanding_jobs = [self.qsieve_job()] for i in range(concurrent-1): @@ -65,5 +62,5 @@ if n < 10**40: return self.ecm_job() - job = Job(code=""" + job = Job(file=""" n = %s if is_prime(n): @@ -71,5 +68,7 @@ else: v, t = qsieve(n) - DSAGE_RESULT = [v, [0]*len(v), {}, 'qsieve'] + result = [v, [0]*len(v), {}, 'qsieve'] + save(result, 'result') + DSAGE_RESULT = 'result.sobj' """ % n, name='qsieve') job.n = int(n) # otherwise cPickle will crash @@ -84,11 +83,13 @@ n = self.composite_factors[self.i % len(self.composite_factors)] rate_multiplier = float(self.concurrent / len(self.composite_factors)) - job = Job(code=""" + job = Job(file=""" n = %s if is_prime(n): - DSAGE_RESULT = [[n], [True], {}, 'primality'] + result = [[n], [True], {}, 'primality'] else: e = ECM() - DSAGE_RESULT = [e.find_factor(n, B1=%s, c=%s, I=%s), e.primality, e.last_params, 'ecm'] + result = [e.find_factor(n, B1=%s, c=%s, I=%s), e.primality, e.last_params, 'ecm'] +save(result, 'result') +DSAGE_RESULT = 'result.sobj' """ % (n, self.cur_B1, self.curve_count, rate_multiplier), name='ecm' ) @@ -98,5 +99,5 @@ def process_result(self, job): - """ + r""" For each factor m of n found by the worker, record them by 1) Dividing each element x of composite_factors by gcd(x,m) @@ -107,5 +108,5 @@ """ - + if prod(self.prime_factors) == self.n: self.done = True @@ -120,8 +121,6 @@ try: factors, primality, params, algorithm = result - except Exception, msg: + except: print 'Error in processing result.' - print result - print msg return try: @@ -136,5 +135,6 @@ self.prime_factors.append("BAD FACTORS") # switch the order of indices - result = [(result[0][i], result[1][i]) for i in range(len(result[0]))] + result = [(result[0][i], + result[1][i]) for i in range(len(result[0]))] # Only works for square-free numbers for r, is_prime_factor in result: @@ -176,5 +176,4 @@ else: self.qsieve_count = 0 - to_be_removed_jobs = [] for wrapped_job in self.waiting_jobs: if wrapped_job.algorithm == 'qsieve': @@ -186,13 +185,10 @@ else: wrapped_job.async_kill() - to_be_removed_jobs.append(wrapped_job) + self.waiting_jobs.remove(wrapped_job) else: self.qsieve_count += 1 - for job in to_be_removed_jobs: - self.waiting_jobs.remove(job) + # Need to use async versions of submitting the jobs because + # this method is called from within the reactor thread if self.qsieve_count == 0: self.submit_job(self.qsieve_job(), self.name, async=True) self.submit_job(self.ecm_job(), self.name, async=True) - - self.prime_factors.sort() - self.composite_factors.sort() Index: sage/dsage/dist_functions/dist_function.py =================================================================== --- sage/dsage/dist_functions/dist_function.py (revision 3905) +++ sage/dsage/dist_functions/dist_function.py (revision 3017) @@ -15,17 +15,20 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ import datetime +import copy import cPickle import zlib +from twisted.internet import reactor, task +from twisted.spread import pb + from sage.dsage.database.job import Job -from sage.dsage.interface.dsage_interface import JobWrapper, BlockingJobWrapper -from sage.dsage.twisted.misc import blocking_call_from_thread +from sage.dsage.interface.dsage_interface import JobWrapper, blockingJobWrapper +from sage.dsage.twisted.misc import blockingCallFromThread class DistributedFunction(object): - """ + r""" Parent class for all classes that wish to use Distributed SAGE. @@ -45,12 +48,11 @@ self.name = None self.job_files = [] + # self.checker_task = None self._done = False def __getstate__(self): - import copy - d = copy.copy(self.__dict__) + d = copy(self.__dict__) d['DSage'] = None d['checker_task'] = None - return d @@ -72,6 +74,6 @@ def save(self, filename=None, compress=True): - """ - Saves your distributed job to disk. + r""" + Saves your distributed job to a sobj. """ @@ -87,30 +89,10 @@ f.write(s) f.close() - return filename - def stop(self, verbose=True): - """ - Ends the current DistributedFunction, kills all waiting jobs. - - """ - - for job in self.waiting_jobs: - job.kill() - - self.done = True - - if verbose: - print 'All waiting jobs have been killed. This job is no more.' - def restore(self, dsage): - """ - Reloads a distributed job from disk. - - """ - - from twisted.internet import reactor, task if dsage.remoteobj is None: # XXX This is a hack because dsage.remoteobj is not set yet + from twisted.internet import reactor reactor.callLater(1.0, self.restore, dsage) return @@ -120,71 +102,47 @@ if not len(self.outstanding_jobs) == 0: self.submit_jobs(self.name) - self.checker_task = task.LoopingCall(self.check_results) - reactor.callFromThread(self.checker_task.start, 1.0, now=True) + self.checker_task.start(2.0, now=True) - def submit_job(self, job, job_name='job', async=True): - """ - Submits a job to the server. - - """ - - job.username = self.DSage.username + def submit_job(self, job, job_name='job', async=False): if async: if isinstance(job, Job): - self.waiting_jobs.append(self.DSage.send_job(job, async=True)) + self.waiting_jobs.append(self.DSage.send_job(job, + async=True)) else: - self.waiting_jobs.append(self.DSage.eval(job, job_name=job_name, async=True)) + self.waiting_jobs.append(self.DSage.eval(job, + job_name=job_name, + async=True)) else: if isinstance(job, Job): - self.waiting_jobs.append(self.DSage.send_job(job, async=False)) + self.waiting_jobs.append(self.DSage.send_job(job)) else: - self.waiting_jobs.append(self.DSage.eval(job, job_name=job_name)) + self.waiting_jobs.append(self.DSage.eval(job, + job_name=job_name)) - def submit_jobs(self, job_name='job', async=True): - """ - Repeatedly calls submit_job until we have no more jobs in outstanding_jobs - - """ - + def submit_jobs(self, job_name='job', async=False): for job in self.outstanding_jobs: - try: - self.submit_job(job, job_name, async) - except Exception, msg: - print msg + self.submit_job(job, job_name, async) self.outstanding_jobs = [] def start(self): - from twisted.internet import reactor, task - if self.DSage is None: - print 'Error: Not connected to a DSage server.' - return self.start_time = datetime.datetime.now() reactor.callFromThread(self.submit_jobs, self.name, async=True) - self.checker_task = blocking_call_from_thread(task.LoopingCall, self.check_results) - reactor.callFromThread(self.checker_task.start, 1.0, now=True) - - def process_result(self): - """ - Any class subclassing DistributedFunction should implement this method. - - """ - - pass - + self.checker_task = blockingCallFromThread(task.LoopingCall, + self.check_results) + reactor.callFromThread(self.checker_task.start, + 1.0, now=True) def check_results(self): - from twisted.internet import reactor - from twisted.spread import pb for wrapped_job in self.waiting_jobs: if isinstance(wrapped_job, JobWrapper): try: - wrapped_job.get_job() + wrapped_job.getJob() except pb.DeadReferenceError: - print 'Disconnected from the server, stopping checker_task.' - if self.checker_task.running: - reactor.callFromThread(self.checker_task.stop) + print 'Got pb.DeadReferenceError.' + print 'This will be handled in the future.' + reactor.callFromThread(self.checker_task.stop) break - elif isinstance(wrapped_job, BlockingJobWrapper): - wrapped_job.async_get_job() + else: + wrapped_job.async_getJob() if wrapped_job.status == 'completed': self.waiting_jobs.remove(wrapped_job) @@ -192,20 +150,16 @@ self.processed_jobs.append(wrapped_job) if self.done: + # kill the jobs in the waiting queue for wrapped_job in self.waiting_jobs: if isinstance(wrapped_job, JobWrapper): wrapped_job.kill() - elif isinstance(wrapped_job, BlockingJobWrapper): + else: wrapped_job.async_kill() self.waiting_jobs = [] - if self.checker_task.running: - reactor.callFromThread(self.checker_task.stop) + reactor.callFromThread(self.checker_task.stop) + + self.done = len(self.waiting_jobs) == 0 class DistributedFunctionTest(DistributedFunction): - """ - This is a very simple DistributedFunction. - Only for educational purposes. - - """ - def __init__(self, DSage, n, name='DistributedFunctionTest'): DistributedFunction.__init__(self, DSage) @@ -214,8 +168,6 @@ self.result = 0 self.results = [] - self.code = """DSAGE_RESULT=%s""" - self.outstanding_jobs = [Job(code=self.code % i, username='yqiang') for i in range(1, n+1)] - + self.outstanding_jobs = ["print %s"%i for i in range(1,n+1)] + def process_result(self, job): - self.done = len(self.waiting_jobs) == 0 - self.result += (job.result) + self.result += int(job.output) Index: sage/dsage/dist_functions/dist_povray.py =================================================================== --- sage/dsage/dist_functions/dist_povray.py (revision 3866) +++ sage/dsage/dist_functions/dist_povray.py (revision 3018) @@ -5,5 +5,5 @@ class DistributedPOVRay(DistributedFunction): - """ + r""" DistributedPOVRay distributes rendering of a .pov file. @@ -21,4 +21,7 @@ which is the combination of all the rendered parts. + AUTHOR: + Yi Qiang + """ @@ -73,5 +76,5 @@ self.job_files.append(job_file) - job = Job(code=job_file, name='%s_%04d.ppm' % (self.name, self.n)) + job = Job(file=job_file, name='%s_%04d.ppm' % (self.name, self.n)) for file_ in self.files: Index: age/dsage/doc/dsage.tex =================================================================== --- sage/dsage/doc/dsage.tex (revision 3746) +++ (revision ) @@ -1,28 +1,0 @@ -% -% Distributed SAGE -% -% Created by Yi Qiang on 2007-02-20. -% Copyright (c) 2007 Yi Qiang. All rights reserved. -% -\documentclass[]{howto} -\title{Distributed SAGE HOWTO} -\author{ - Yi Qiang\\ - yqiang@gmail.com -} -\release{1.0} -\date{2007-02-22} - -\begin{document} - -\maketitle - -\begin{abstract} - This document will demonstrate how to use Distributed SAGE. -\end{abstract} - -\section{Introduction} -\sectionauthor{Yi Qiang}{yqiang@gmail.com} - - -\end{document} Index: sage/dsage/dsage.py =================================================================== --- sage/dsage/dsage.py (revision 3914) +++ sage/dsage/dsage.py (revision 3025) @@ -8,100 +8,70 @@ import os -import sage.interfaces.cleaner -from sage.misc.all import DOT_SAGE -import pexpect - -## def spawn(cmd, logfile=None, verbose=True): -## pid = os.fork() -## if pid != 0: -## sage.interfaces.cleaner.cleaner(pid) -## if verbose: -## print "Started %s (pid = %s, logfile = '%s')"%(cmd, pid, logfile) -## return pid -## if pid == 0: -## if not logfile is None: -## cmd += ' 2>&1 > ' + logfile -## os.system(cmd) - -## def start_process(typ, hostname, address, port): -## cmd = 'dsage_%s.py &'%typ -## os.system(cmd) -## dir = '%s/dsage/'%os.environ['DOT_SAGE'] -## pid_file = '%s/server-hostname-address-port.pid'%dir -## while True: -## try: -## if os.path.exists(pid_file): -## return int(open(pid_file).read()) -## except Exception, msg: -## print msg - - class DistributedSage(object): r""" - DistributedSage allows you to do distributed computing using SAGE. + DistributedSage allows you to do distributed computing in SAGE. - To get up and running quickly, run dsage.setup() to run the - configuration utility. - - Note that configuration files will be stored in the - directory \code{\$DOT\_SAGE/dsage}. + To get up and running quickly, run dsage.setup() to run the configuration + utility. + Note that configuration files will be stored in DOT_SAGE/dsage There are three distinct parts of Distributed SAGE: Server Launch the server with dsage.server() - Worker Launch the worker with dsage.worker() - Client Create the DSage object like this: d = DSage() - EXAMPLES: - This starts a server instance on localhost: - + Examples: + This starts a server instance on localhost + sage: dsage.server() + This is currently blocking - The dsage server is currently blocking by default. - - Open another sage instance and type: + Open another sage instance and type sage: dsage.worker() - This starts a worker connecting the localhost. + This starts a worker connecting the localhost - Open yet another terminal and type: + Open yet another terminal and type: + sage: D = DSage() - This creates a connection to the remote server. To do a simple - evaluation, type: + This creates a connection to the remote server. To do a simple + evaluation, type: + sage: job1 = D('2+2') - This sends the job '2+2' to a worker and you can view the - result by typing: + This sends the job 'print 2+2' to a worker and you can view the + result by typing: sage: print job1 - This is the most basic way of interacting with dsage. To do more - complicated tasks, you should look at the DistributedFunction - class. For example, to do distributed integer factorization with - ECM, type this: + This is the most basic way of interacting with dsage. To do more + complicated tasks, you should look at the DistributedFunction class. + For example, to do distributed integer factorization with ECM, type + this: sage: f = DistributedFactor(P, number, name='my_factor') sage: f.start() - To check the result, do + To check the result, do sage: print f.result - To check if it is done, do + To check if it is done, do sage: print f.done Customization: - - To customize how the worker, server, or client behaves, you - can look for their respective conf files in DOT_SAGE/dsage. - The configuration file should be self explanatory. + To customize how the worker, server, or client behaves, you can look + for their respective conf files in DOT_SAGE/dsage. The configuration + file should be self explanatory. + + TODO: + """ def __init__(self): @@ -112,93 +82,55 @@ self.worker(blocking=False) from sage.dsage.interface.dsage_interface import BlockingDSage as DSage - return DSage() -## def server(self, blocking=True, logfile=None): -## r""" -## Run the Distributed SAGE server. + def server(self, blocking=True): + r""" + This is the server of Distributed SAGE -## Doing \code{dsage.server()} will spawn a server process which -## listens by default on port 8081. + Doing dsage.server() will spawn a server process which listens by + default on ports 8081 and 8082. -## INPUT: -## blocking -- boolean (default: True) -- if False the dsage -## server will run and you'll still be able to -## enter commands at the command prompt (though -## logging will make this hard). -## logfile -- only used if blocking=True; the default is -## to log to $DOT_SAGE/dsage/server.log -## """ -## cmd = 'dsage_server.py' -## if not blocking: -## if logfile is None: -## logfile = '%s/dsage/server.log'%DOT_SAGE -## spawn(cmd, logfile) -## else: -## os.system(cmd) + """ - def server(self): + cmd = 'dsage_server.py' + if not blocking: + cmd += '&' + os.system(cmd) + + def worker(self, server=None, port=None, blocking=True): r""" - Run the Distributed SAGE server. + This is the worker of Distributed SAGE + + Typing sage.worker() will launch a worker which by default connects to + localhost on port 8082 to fetch jobs. - Doing \code{dsage.server()} will spawn a server process which - listens by default on port 8081. + Parameters: + hostname -- the server you want to connect to + port -- the port that the server listens on for workers. + """ - cmd = 'dsage_server.py' + + cmd = 'dsage_worker.py' + if isinstance(server, str): + cmd += ' %s' % server + if isinstance(port, int): + cmd += ' %s' % port + + if not blocking: + cmd += '&' + os.system(cmd) - -## def worker(self, server=None, port=None, blocking=True, logfile=None): -## r""" -## Run the Distributed SAGE worker. - -## Typing \code{sage.worker()} will launch a worker which by -## default connects to localhost on port 8081 to fetch jobs. - -## INPUT: - -## server -- (string, default: None) the server you want to -## connect to if None, connects to the server -## specified in .sage/dsage/worker.conf -## port -- (integer, default: None) the port that the server -## listens on for workers. -## blocking -- (bool, default: True) whether or not to make a -## blocking connection. -## logfile -- only used if blocking=True; the default is -## to log to $DOT_SAGE/dsage/worker.log -## """ -## cmd = 'dsage_worker.py' -## if blocking: -## cmd += ' %s' % server -## cmd += ' %s' % port -## os.system(cmd) -## else: -## if not server is None or not port is None: -## args = [str(server), str(port)] -## else: -## args = [] -## if logfile is None: -## logfile = '%s/dsage/worker.log'%DOT_SAGE -## spawn(cmd + ' '.join(args), logfile) - - def worker(self, server=None, port=None): - r""" - Run the Distributed SAGE worker. - - Typing \code{sage.worker()} will launch a worker which by - default connects to localhost on port 8081 to fetch jobs. - - INPUT: - - server -- (string, default: None) the server you want to - connect to if None, connects to the server - specified in .sage/dsage/worker.conf - port -- (integer, default: None) the port that the server - listens on for workers. - """ - cmd = 'dsage_worker.py' - cmd += ' %s' % server - cmd += ' %s' % port - os.system(cmd) + # This is completely outdated now, only kept for historical reference + # def console(self): + # r""" + # This is the IPython console that allows you submit and view jobs. + # + # Simply type dsage.console() to launch it. It is a special ipython + # console because it has a twisted thread running in the background. + # """ + # # this is overwritten below. + # cmd = 'dsage_console.py' + # os.system(cmd) def setup(self): @@ -206,9 +138,9 @@ This is the setup utility which helps you configure dsage. - Type \code{dsage.setup()} to run the configuration for the server, - worker and client. Alternatively, if you want to run the - configuration for just one parts, you can launch - \code{dsage.setup_server()}, \code{dsage.setup\_worker()} - or \code{dsage.setup()}. + Type dsage.setup() to run the configuration for the server, worker and + client. Alternatively, if you want to run the configuration for just + one parts, you can launch dsage.setup_server(), dsage.setup_worker() or + dsage.setup() client + """ cmd = 'dsage_setup.py' @@ -216,21 +148,24 @@ def setup_server(self): - """ + r""" This method runs the configuration utility for the server. """ + cmd = 'dsage_setup.py server' os.system(cmd) def setup_worker(self): - """ + r""" This method runs the configuration utility for the worker. """ + cmd = 'dsage_setup.py worker' os.system(cmd) def setup_client(self): - """ + r""" This method runs the configuration utility for the client. """ + cmd = 'dsage_setup.py client' os.system(cmd) Index: sage/dsage/errors/exceptions.py =================================================================== --- sage/dsage/errors/exceptions.py (revision 3866) +++ sage/dsage/errors/exceptions.py (revision 2885) @@ -54,13 +54,2 @@ class BadKeyException(pb.Error): pass - -class AuthenticationError(pb.Error): - """ - Return this when credential checking has failed. - - """ - - def __init__(self, value, data=None): - Exception.__init__(self, value, data) - self.value = value - self.data = data Index: sage/dsage/interface/dsage_interface.py =================================================================== --- sage/dsage/interface/dsage_interface.py (revision 3903) +++ sage/dsage/interface/dsage_interface.py (revision 3025) @@ -15,9 +15,11 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ +import sys import os +import random import glob +import ConfigParser import copy import cPickle @@ -26,16 +28,20 @@ import time -from sage.dsage.database.job import Job, expand_job -from sage.dsage.twisted.misc import blocking_call_from_thread -from sage.dsage.misc.config import get_conf +from twisted.spread import pb +from twisted.internet import reactor, defer, error, task +from twisted.cred import credentials +from twisted.conch.ssh import keys + +from sage.dsage.database.job import Job +from sage.dsage.twisted.pb import ClientPBClientFactory +from sage.dsage.twisted.misc import blockingCallFromThread +from sage.dsage.errors.exceptions import NoJobException, NotConnectedException class DSageThread(threading.Thread): def run(self): - from twisted.internet import reactor - if not reactor.running: - reactor.run(installSignalHandlers=0) + reactor.run(installSignalHandlers=False) class DSage(object): - """ + r""" This object represents a connection to the distributed SAGE server. """ @@ -43,45 +49,25 @@ def __init__(self, server=None, port=8081, username=None, pubkey_file=None, privkey_file=None): - """ - Parameters: - server -- str - port -- int - username -- str - pubkey_file -- str (Default: None) - privkey_file -- str (Default: None) - - """ - - from twisted.cred import credentials - from twisted.conch.ssh import keys - from twisted.spread import banana - banana.SIZE_LIMIT = 100*1024*1024 # 100 MegaBytes - conf = get_conf(type='client') + + # We will read the values in from the conf file first and let the + # user override the values stored in the conf file by keyword + # parameters + + self._getconf() if server is None: - self.server = self.conf['server'] + self.server = SERVER else: self.server = server - if port is None: - self.port = self.conf['port'] - else: - self.port = port - if username is None: - self.username = self.conf['username'] - else: - self.username = username - if pubkey_file is None: - self.pubkey_file = self.conf['pubkey_file'] - else: - self.pubkey_file = pubkey_file - if privkey_file is None: - self.privkey_file = self.conf['privkey_file'] - else: - self.privkey_file = privkey_file - - self.ssl = int(self.conf['ssl']) - self.log_level = int(conf['log_level']) + + self.port = PORT + self.username = USERNAME + self.pubkey_file = PUBKEY_FILE + self.privkey_file = PRIVKEY_FILE + self.remoteobj = None self.result = None + + passphrase = self._getpassphrase() # public key authentication information @@ -89,5 +75,6 @@ # try getting the private key object without a passphrase first try: - self.priv_key = keys.getPrivateKeyObject(filename=self.privkey_file) + self.priv_key = keys.getPrivateKeyObject( + filename=self.privkey_file) except keys.BadKeyError: passphrase = self._getpassphrase() @@ -98,5 +85,5 @@ self.alg_name = 'rsa' self.blob = keys.makePublicKeyBlob(self.pub_key) - self.data = self.conf['data'] + self.data = DATA self.signature = keys.signData(self.priv_key, self.data) self.creds = credentials.SSHPrivateKey(self.username, @@ -110,16 +97,15 @@ self.connect() - def __repr__(self): - return self.__str__() - def __str__(self): self.check_connected() - self.info_str = 'Connected to: %s:%s' % (self.server, self.port) + self.info_str = 'Connected to: ' \ + + self.server + ':' + str(self.port) return self.info_str + '\r' def __call__(self, cmd, globals_=None, job_name=None): cmd = ['ans = %s\n' % (cmd), - 'print ans\n', - "DSAGE_RESULT = ans\n"] + 'print ans\n' + "save(ans, 'ans')\n" + "DSAGE_RESULT = 'ans.sobj'\n"] return self.eval(''.join(cmd), globals_=globals_, job_name=job_name) @@ -129,5 +115,29 @@ d['remoteobj'] = None return d - + + def _getconf(self): + # randomly generated string we will use to sign + self.DATA = ''.join([chr(i) for i in [random.randint(65, 123) for n in + range(500)]]) + self.DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') + # Begin reading configuration + try: + conf_file = os.path.join(self.DSAGE_DIR, 'client.conf') + config = ConfigParser.ConfigParser() + config.read(conf_file) + + self.LOG_FILE = config.get('log', 'log_file') + self.LOG_LEVEL = config.getint('log', 'log_level') + self.SSL = config.getint('ssl', 'ssl') + self.USERNAME = config.get('auth', 'username') + self.PRIVKEY_FILE = os.path.expanduser(config.get('auth', + 'privkey_file')) + self.PUBKEY_FILE = os.path.expanduser(config.get('auth', + 'pubkey_file')) + self.SERVER = config.get('general', 'server') + self.PORT = config.getint('general', 'port') + except Exception, msg: + raise + def _getpassphrase(self): import getpass @@ -136,14 +146,13 @@ return passphrase - def _catch_failure(self, failure): - from twisted.internet import error + def _catchFailure(self, failure): if failure.check(error.ConnectionRefusedError): - print 'Remote server %s refused the connection.' % (self.server) - else: - print "Error: ", failure.getErrorMessage() - print "Traceback: ", failure.printTraceback() + print 'Remote server refused the connection.' + return + print "Error: ", failure.getErrorMessage() + print "Traceback: ", failure.printTraceback() def _connected(self, remoteobj): - if self.log_level > 0: + if self.LOG_LEVEL > 0: print 'Connected to remote server.\r' self.remoteobj = remoteobj @@ -151,9 +160,8 @@ def _disconnected(self, remoteobj): - print '[DSage] Lost connection to %s' % (self.server) + print 'Lost connection to the server.' self.info_str = 'Not connected.' - def _got_my_jobs(self, jobs, job_name): - from sage.dsage.errors.exceptions import NoJobException + def _gotMyJobs(self, jobs, job_name): if jobs == None: raise NoJobException @@ -162,24 +170,24 @@ for job in jobs if job.name == job_name] - def _killed_job(self, job_id): - pass + def _killedJob(self, jobID): + if jobID: + if self.LOG_LEVEL > 2: + print str(jobID) + ' was successfully killed.' def restore(self, remoteobj): - """ + r""" This method restores a connection to the server. - - """ - + """ self.remoteobj = remoteobj def connect(self): - """ + r""" This methods establishes the conection to the remote server. """ - - from twisted.internet import reactor - from sage.dsage.twisted.pb import PBClientFactory - factory = PBClientFactory() + + # TODO: Send a useful 'mind' object with the login request! + # factory = pb.PBClientFactory() + factory = ClientPBClientFactory() if self.SSL == 1: @@ -195,5 +203,5 @@ return factory.login(self.creds, None).addCallback( self._connected).addErrback( - self._catch_failure) + self._catchFailure) def disconnect(self): @@ -202,5 +210,5 @@ def eval(self, cmd, globals_=None, job_name=None): - """ + r""" eval evaluates a command @@ -214,10 +222,10 @@ self.check_connected() if not job_name or not isinstance(job_name, str): - job_name = 'default job' - - type_ = 'sage' - - job = Job(id_=None, code=cmd, name=job_name, - username=self.username, type_=type_) + job_name = 'default_job' + + type = 'sage' + + job = Job(id=None, file=cmd, name=job_name, + author=self.username, type=type) wrapped_job = JobWrapper(self.remoteobj, job) @@ -229,5 +237,5 @@ def eval_file(self, fname, job_name): - """ + r""" eval_file allows you to evaluate the contents of an entire file. @@ -239,8 +247,8 @@ self.check_connected() - type_ = 'file' + type = 'file' cmd = open(fname).read() - job = Job(id_=None, code=cmd, name=job_name, - username=self.username, type_=type_) + job = Job(id=None, file=cmd, name=job_name, + author=self.username, type=type) wrapped_job = JobWrapper(self.remoteobj, job) @@ -249,5 +257,5 @@ def send_job(self, job): - """ + r""" Sends a Job object to the server. @@ -259,13 +267,13 @@ return wrapped_job - def _got_job_id(self, id_, job): - job.job_id = id_ - job.username = self.username + def _gotJobID(self, id, job): + job.id = id + job.author = self.username self.jobs.append(job) pickled_job = job.pickle() - d = self.remoteobj.callRemote('submit_job', pickled_job) - d.addErrback(self._catch_failure) + d = self.remoteobj.callRemote('submitJob', pickled_job) + d.addErrback(self._catchFailure) # d.addCallback(self._submitted, job) @@ -273,5 +281,4 @@ def eval_dir(self, dir, job_name): - from twisted.internet import defer self.check_connected() os.chdir(dir) @@ -280,27 +287,27 @@ for file in files: sage_cmd = open(file).readlines() - d = self.remoteobj.callRemote('get_next_job_id') - d.addCallback(self._got_id, sage_cmd, job_name, file=True, - type_='spyx') - d.addErrback(self._catch_failure) + d = self.remoteobj.callRemote('getNextJobID') + d.addCallback(self._gotID, sage_cmd, job_name, file=True, + type='spyx') + d.addErrback(self._catchFailure) deferreds.append(d) d_list = defer.DeferredList(deferreds) return d_list - def kill(self, job_id): - """ + def kill(self, jobID): + r""" Kills a job given the job id. Parameters: - job_id -- job id - - """ - - d = self.remoteobj.callRemote('kill_job', job_id) - d.addCallback(self._killed_job) - d.addErrback(self._catch_failure) + jobID -- job id + + """ + + d = self.remoteobj.callRemote('killJob', jobID) + d.addCallback(self._killedJob) + d.addErrback(self._catchFailure) def get_my_jobs(self, is_active=False, job_name=None): - """ + r""" This method returns a list of jobs that belong to you. @@ -315,15 +322,15 @@ self.check_connected() - d = self.remoteobj.callRemote('get_jobs_by_username', + d = self.remoteobj.callRemote('getJobsByAuthor', self.username, is_active, job_name) - d.addCallback(self._got_my_jobs, job_name) - d.addErrback(self._catch_failure) + d.addCallback(self._gotMyJobs, job_name) + d.addErrback(self._catchFailure) return d def cluster_speed(self): - """ + r""" Returns the speed of the cluster. @@ -332,9 +339,7 @@ self.check_connected() - return self.remoteobj.callRemote('get_cluster_speed') + return self.remoteobj.callRemote('getClusterSpeed') def check_connected(self): - from sage.dsage.errors.exceptions import NotConnectedException - if self.remoteobj == None: raise NotConnectedException @@ -343,46 +348,24 @@ class BlockingDSage(DSage): + r"""This is the blocking version of DSage """ - This is the blocking version of the DSage interface. - - """ - - def __init__(self, server=None, port=None, username=None, pubkey_file=None, privkey_file=None): - from twisted.cred import credentials - from twisted.conch.ssh import keys - from twisted.spread import banana - banana.SIZE_LIMIT = 100*1024*1024 # 100 MegaBytes - - self.conf = get_conf(type='client') + + def __init__(self, server=None, port=8081, username=None, + pubkey_file=None, privkey_file=None): + self._getconf() if server is None: - self.server = self.conf['server'] + self.server = self.SERVER else: self.server = server - if port is None: - if self.server == 'localhost': - conf = get_conf(type='server') - self.port = int(conf['client_port']) - else: - self.port = int(self.conf['port']) - else: - self.port = port - if username is None: - self.username = self.conf['username'] - else: - self.username = username - if pubkey_file is None: - self.pubkey_file = self.conf['pubkey_file'] - else: - self.pubkey_file = pubkey_file - if privkey_file is None: - self.privkey_file = self.conf['privkey_file'] - else: - self.privkey_file = privkey_file - - self.data = self.conf['data'] - self.ssl = int(self.conf['ssl']) - self.log_level = int(self.conf['log_level']) + + self.port = self.PORT + self.username = self.USERNAME + self.pubkey_file = self.PUBKEY_FILE + self.privkey_file = self.PRIVKEY_FILE + self.remoteobj = None - self.result = None + self.result = None + + # passphrase = self._getpassphrase() # public key authentication information @@ -402,11 +385,13 @@ self.alg_name = 'rsa' self.blob = keys.makePublicKeyBlob(self.pub_key) + self.data = self.DATA self.signature = keys.signData(self.priv_key, self.data) self.creds = credentials.SSHPrivateKey(self.username, - self.alg_name, - self.blob, - self.data, - self.signature) - + self.alg_name, + self.blob, + self.data, + self.signature) + + self.jobs = [] self.dsage_thread = DSageThread() self.dsage_thread.start() @@ -414,33 +399,30 @@ def connect(self): - """ + r""" This methods establishes the conection to the remote server. """ - - from twisted.internet import reactor - from sage.dsage.twisted.pb import PBClientFactory - - self.factory = PBClientFactory() - - if self.ssl: + + # TODO: Send a useful 'mind' object with the login request! + # factory = pb.PBClientFactory() + factory = ClientPBClientFactory() + + if self.SSL == 1: from twisted.internet import ssl contextFactory = ssl.ClientContextFactory() - blocking_call_from_thread(reactor.connectSSL, + blockingCallFromThread(reactor.connectSSL, self.server, self.port, - self.factory, contextFactory) + factory, contextFactory) else: - blocking_call_from_thread(reactor.connectTCP, + blockingCallFromThread(reactor.connectTCP, self.server, self.port, - self.factory) - - d = self.factory.login(self.creds, None) - d.addCallback(self._connected) - d.addErrback(self._catch_failure) - - return d + factory) + + return factory.login(self.creds, None).addCallback( + self._connected).addErrback( + self._catchFailure) def eval(self, cmd, globals_=None, job_name=None, async=False): - """ + r""" eval evaluates a command @@ -457,8 +439,8 @@ job_name = 'default_job' - type_ = 'sage' - - job = Job(id_=None, code=cmd, name=job_name, - username=self.username, type_=type_) + type = 'sage' + + job = Job(id=None, file=cmd, name=job_name, + author=self.username, type=type) if globals_ is not None: @@ -469,10 +451,10 @@ wrapped_job = JobWrapper(self.remoteobj, job) else: - wrapped_job = BlockingJobWrapper(self.remoteobj, job) + wrapped_job = blockingJobWrapper(self.remoteobj, job) return wrapped_job def send_job(self, job, async=False): - """ + r""" Sends a Job object to the server. @@ -488,38 +470,10 @@ wrapped_job = JobWrapper(self.remoteobj, job) else: - wrapped_job = BlockingJobWrapper(self.remoteobj, job) + wrapped_job = blockingJobWrapper(self.remoteobj, job) return wrapped_job - def get_my_jobs(self, active=True): - """ - This method returns a list of jobs that belong to you. - - Parameters: - active -- set to true to get only active jobs (bool) - - Use this method if you get disconnected from the server and wish to - retrieve your old jobs back. - - """ - - self.check_connected() - - if active: - jdicts = blocking_call_from_thread(self.remoteobj.callRemote, - 'get_jobs_by_username', - self.username, - active) - else: - jdicts = blocking_call_from_thread(self.remoteobj.callRemote, - 'get_jobs_by_username', - self.username, - False) - - return [expand_job(jdict) for jdict in jdicts] - - def cluster_speed(self): - """ + r""" Returns the speed of the cluster. @@ -528,8 +482,9 @@ self.check_connected() - return blocking_call_from_thread(self.remoteobj.callRemote, 'get_cluster_speed') - - def get_monitors_list(self): - """Returns a list of monitors connected to the server. + return blockingCallFromThread(self.remoteobj.callRemote, + 'getClusterSpeed') + + def list_workers(self): + r"""Returns a list of workers connected to the server. """ @@ -537,8 +492,9 @@ self.check_connected() - return blocking_call_from_thread(self.remoteobj.callRemote, 'get_monitor_list') - - def get_clients_list(self): - """ + return blockingCallFromThread(self.remoteobj.callRemote, + 'getWorkerList') + + def list_clients(self): + r""" Returns a list of clients connected to the server. """ @@ -546,18 +502,9 @@ self.check_connected() - return blocking_call_from_thread(self.remoteobj.callRemote, 'get_client_list') - - def get_worker_count(self): - """ - Returns the number of busy and free workers. - - """ - - self.check_connected() - - return blocking_call_from_thread(self.remoteobj.callRemote, 'get_worker_count') - + return blockingCallFromThread(self.remoteobj.callRemote, + 'getClientList') + class JobWrapper(object): - """ + r""" Represents a remote job. @@ -574,10 +521,14 @@ # TODO Make this more complete self._update_job(job) - - # d = self.remoteobj.callRemote('get_next_job_id') - d = self.remoteobj.callRemote('submit_job', job.reduce()) - d.addCallback(self._got_jdict) - d.addErrback(self._catch_failure) - + self.worker_info = self._job.worker_info + + d = self.remoteobj.callRemote('getNextJobID') + d.addCallback(self._gotID) + d.addErrback(self._catchFailure) + + # hack to try and fetch a result after submitting the job + # self.syncJob_task = task.LoopingCall(self.syncJob) + # self.syncJob_task.start(2.0, now=True) + def __repr__(self): if self._job.status == 'completed' and not self._job.output: @@ -591,6 +542,5 @@ d = copy.copy(self.__dict__) d['remoteobj'] = None - d['sync_job_task'] = None - + d['syncJob_task'] = None return d @@ -609,5 +559,4 @@ def wait(self): - from twisted.internet import reactor timeout = 0.1 while self._job.result is None: @@ -620,13 +569,7 @@ f = open(filename, 'w') cPickle.dump(self, f, 2) - return filename - - def restore(self, dsage): - self.remoteobj = dsage.remoteobj - - def _catch_failure(self, failure): - from twisted.internet import error - from twisted.spread import pb + + def _catchFailure(self, failure): if failure.check(pb.DeadReferenceError, error.ConnectionLost): print 'Disconnected from server.' @@ -635,56 +578,52 @@ print "Traceback: ", failure.printTraceback() - def _got_job(self, job): + def _gotJob(self, job): if job == None: return - self._job = expand_job(job) + self._job = self.unpickle(job) self._update_job(self._job) - def _got_jdict(self, jdict): - self._job = expand_job(jdict) - self.job_id = jdict['job_id'] - self._update_job(self._job) - - def get_job(self): - from sage.dsage.errors.exceptions import NotConnectedException - + def _gotID(self, id_): + self._job.id = id_ + self.id = id_ + pickled_job = self._job.pickle() + d = self.remoteobj.callRemote('submitJob', pickled_job) + d.addErrback(self._catchFailure) + + def getJob(self): if self.remoteobj is None: raise NotConnectedException - if self.job_id is None: - return - d = self.remoteobj.callRemote('get_job_by_id', self.job_id) - d.addCallback(self._got_job) - d.addErrback(self._catch_failure) - + if self.id is None: + return + d = self.remoteobj.callRemote('getJobByID', self.id) + d.addCallback(self._gotJob) + d.addErrback(self._catchFailure) return d - def get_job_output(self): + def getJobOutput(self): if self.remoteobj == None: return - d = self.remoteobj.callRemote('get_job_output_by_id', self._job.job_id) - d.addCallback(self._got_job_output) - d.addErrback(self._catch_failure) - + d = self.remoteobj.callRemote('getJobOutputByID', self._job.id) + d.addCallback(self._gotJobOutput) + d.addErrback(self._catchFailure) return d - def _got_job_output(self, output): + def _gotJobOutput(self, output): self.output = output self._job.output = output - def get_job_result(self): + def getJobResult(self): if self.remoteobj == None: return - d = self.remoteobj.callRemote('get_job_result_by_id', self._job.job_id) - d.addCallback(self._got_job_result) - d.addErrback(self._catch_failure) - + d = self.remoteobj.callRemote('getJobResultByID', self._job.id) + d.addCallback(self._gotJobResult) + d.addErrback(self._catchFailure) return d - def _got_job_result(self, result): + def _gotJobResult(self, result): self.result = result self._job.result = result - def sync_job(self): - from twisted.spread import pb + def syncJob(self): if self.remoteobj == None: if self.LOG_LEVEL > 2: @@ -693,20 +632,20 @@ if self.status == 'completed': if self.LOG_LEVEL > 2: - print 'Stopping sync_job' - if self.sync_job_task: - if self.sync_job_task.running: - self.sync_job_task.stop() + print 'Stopping syncJob' + if self.syncJob_task: + if self.syncJob_task.running: + self.syncJob_task.stop() return try: - d = self.remoteobj.callRemote('sync_job', self._job.job_id) + d = self.remoteobj.callRemote('syncJob', self._job.id) except pb.DeadReferenceError: - if self.sync_job_task: - if self.sync_job_task.running: - self.sync_job_task.stop() + if self.syncJob_task: + if self.syncJob_task.running: + self.syncJob_task.stop() return - d.addCallback(self._got_job) - d.addErrback(self._catch_failure) + d.addCallback(self._gotJob) + d.addErrback(self._catchFailure) def write_result(self, filename): @@ -720,112 +659,94 @@ def kill(self): - """ + r""" Kills the current job. """ - if self.job_id is not None: - d = self.remoteobj.callRemote('kill_job', self.job_id) - d.addCallback(self._killed_job) - d.addErrback(self._catch_failure) - return d - else: - return - - def _killed_job(self, job_id): - return - -class BlockingJobWrapper(JobWrapper): - """ - Blocking version of the JobWrapper object. This is to be used - interactively. - - """ - + d = self.remoteobj.callRemote('killJob', self.id) + d.addCallback(self._killedJob) + d.addErrback(self._catchFailure) + return d + + def _killedJob(self, jobID): + if jobID: + if self.LOG_LEVEL > 2: + print str(jobID) + ' was successfully killed.\r' + +class blockingJobWrapper(JobWrapper): def __init__(self, remoteobj, job): self.remoteobj = remoteobj self._job = job + # TODO Make this more complete self._update_job(job) - - jdict = blocking_call_from_thread(self.remoteobj.callRemote, 'submit_job', job.reduce()) - self._job = expand_job(jdict) + self.worker_info = self._job.worker_info + + + # This is kind of stupid, why not just set the job ID when + # submitting the job? + + jobID = blockingCallFromThread(self.remoteobj.callRemote, + 'getNextJobID') + + self._job.id = jobID + pickled_job = self._job.pickle() + d = blockingCallFromThread(self.remoteobj.callRemote, + 'submitJob', pickled_job) def __repr__(self): - if self.killed: - return 'Job %s was killed' % (self.job_id) - if self.status != 'completed': - self.get_job() + self.getJob() if self.status == 'completed' and not self.output: - return 'No output.' - if not self.output: + return 'No output.' + elif not self.output: return 'No output yet.' - else: - return self.output - - def get_job(self): - from sage.dsage.errors.exceptions import NotConnectedException - + + return self.output + + def getJob(self): if self.remoteobj == None: raise NotConnectedException if self.status == 'completed': return - - job = blocking_call_from_thread( - self.remoteobj.callRemote, 'get_job_by_id', self._job.job_id) - - self._update_job(expand_job(job)) - - def async_get_job(self): - return JobWrapper.get_job(self) + + job = blockingCallFromThread(self.remoteobj.callRemote, + 'getJobByID', self._job.id) + + self._update_job(self.unpickle(job)) + + def async_getJob(self): + # if self.remoteobj == None: + # raise NotConnectedException + # d = self.remoteobj.callRemote('getJobByID', self._job.id) + # d.addCallback(self._gotJob) + # d.addErrback(self._catchFailure) + return JobWrapper.getJob(self) + # return d def kill(self): - """ + r""" Kills the current job. """ - - job_id = blocking_call_from_thread(self.remoteobj.callRemote, 'kill_job', self._job.job_id) - self.job_id = job_id - self.killed = True - - return job_id + + jobID = blockingCallFromThread(self.remoteobj.callRemote, + 'killJob', self._job.id) + return jobID def async_kill(self): - """ + r""" async version of kill """ - d = self.remoteobj.callRemote('kill_job', self.job_id) - d.addCallback(self._killed_job) - d.addErrback(self._catch_failure) - + print 'Killing ', self.id + d = self.remoteobj.callRemote('killJob', self.id) + d.addCallback(self._killedJob) + d.addErrback(self._catchFailure) return d - def wait(self, timeout=None): - """ - Waits on a job until it is completed. - - Parameters: - timeout -- number of seconds to wait, if it has not completed by then - it will raise RunTimeError if it is set to None, - it will wait indefinitely until the job is completed - - """ - - import signal - - if timeout is None: - while self.status != 'completed': - time.sleep(1.0) - self.get_job() - else: - def handler(signum, frame): - raise RuntimeError, 'Maximum wait time exceeded.' - signal.signal(signal.SIGALRM, handler) - signal.alarm(timeout) - while self.status != 'completed': - time.sleep(1.0) - self.get_job() - signal.alarm(0) + def wait(self): + timeout = 0.1 + while self.result is None: + time.sleep(timeout) + self.getJob() Index: age/dsage/misc/config.py =================================================================== --- sage/dsage/misc/config.py (revision 3902) +++ (revision ) @@ -1,89 +1,0 @@ -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -""" -Gets the different configuration options for the various components of DSAGE. -""" - -import os -import random -import ConfigParser -import uuid - -def check_version(old_version): - from sage.dsage.__version__ import version - if version != old_version: - raise ValueError, "Incompatible version. You have %s, need %s." % (old_version, version) - -def read_conf(config): - conf = {} - for sec in config.sections(): - conf.update(dict(config.items(sec))) - check_version(conf['version']) - - return conf - -def get_conf(type): - DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') - config = ConfigParser.ConfigParser() - try: - if type == 'client': - conf_file = os.path.join(DSAGE_DIR, 'client.conf') - DATA = ''.join([chr(i) for i in [random.randint(65, 123) for n in range(500)]]) - config.read(conf_file) - conf = read_conf(config) - conf['data'] = DATA - elif type == 'server': - conf_file = os.path.join(DSAGE_DIR, 'server.conf') - config.read(conf_file) - conf = read_conf(config) - elif type == 'monitor': - conf_file = os.path.join(DSAGE_DIR, 'worker.conf') - config.read(conf_file) - if len(config.get('uuid', 'id')) != 36: - config.set('uuid', 'id', str(uuid.uuid1())) - f = open(conf_file, 'w') - config.write(f) - config.read(conf_file) - conf = read_conf(config) - elif type == 'jobdb' or type == 'clientdb' or type == 'monitordb': - conf_file = os.path.join(DSAGE_DIR, 'server.conf') - config.read(conf_file) - conf = read_conf(config) - conf['log_level'] = config.get('db_log', 'log_level') - conf['log_file'] = config.get('db_log', 'log_file') - - return conf - except Exception, msg: - print msg - print "Error reading '%s', run dsage.setup()" % conf_file - -def get_bool(value): - boolean_states = {'0': False, - '1': True, - 'false': False, - 'no': False, - 'off': False, - 'on': True, - 'true': True, - 'yes': True} - if value.lower() not in boolean_states: - raise ValueError, 'Not a boolean: %s' % value - - return boolean_states[value.lower()] Index: age/dsage/misc/constants.py =================================================================== --- sage/dsage/misc/constants.py (revision 3769) +++ (revision ) @@ -1,1 +1,0 @@ -delimiter = '-' * 50 Index: sage/dsage/misc/hostinfo.py =================================================================== --- sage/dsage/misc/hostinfo.py (revision 3866) +++ sage/dsage/misc/hostinfo.py (revision 2885) @@ -31,9 +31,9 @@ return str(self.host_info) - def _catch_failure(self, failure): + def _catchFailure(self, failure): log.msg("Error: ", failure.getErrorMessage()) log.msg("Traceback: ", failure.printTraceback()) - def _gotsysctl(self, output, host_info): + def _gotsysctl(self, output, host_info_mac): d = defer.Deferred() output = output.split('\n') @@ -49,16 +49,13 @@ l = [li.strip() for li in l] if l[0] == 'hw.cpufrequency': - host_info['cpu Mhz'] = str(int(l[1]) / 1000000.0) + host_info_mac['cpu Mhz'] = str(int(l[1]) / 1000000.0) elif l[0] == 'hw.availcpu': - host_info['cpus'] = int(l[1]) + host_info_mac['cpus'] = int(l[1]) elif l[0] == 'hw.physmem': - host_info['MemTotal'] = int(l[1]) + host_info_mac['MemTotal'] = int(l[1]) elif l[0] == 'hw.usermem': - host_info['MemFree'] = (host_info['MemTotal'] - + host_info_mac['MemFree'] = (host_info_mac['MemTotal'] - int(l[1])) / 1024 / 1024 - elif l[0] == 'machdep.cpu.brand_string': - host_info['cpu model'] = l[1] - - self.canonical_info(host_info) + self.canonical_info(host_info_mac) d.callback(self.host_info) return d @@ -66,8 +63,8 @@ def get_host_info(self): platform = sys.platform - host_info = {} if platform == 'linux2' or platform == 'linux': d = defer.Deferred() - host_info['os'] = platform + host_info_linux = {} + host_info_linux['os'] = platform cpuinfo = open('/proc/cpuinfo','r').readlines() @@ -82,11 +79,11 @@ s = line.split(':') if s != ['\n']: - host_info[s[0].strip()] = s[1].strip() + host_info_linux[s[0].strip()] = s[1].strip() - host_info['cpus'] = cpus + host_info_linux['cpus'] = cpus # uptime uptime = open('/proc/uptime', 'r').readline().split(' ') - host_info['uptime'] = uptime[0] + host_info_linux['uptime'] = uptime[0] # memory info @@ -95,37 +92,37 @@ s = line.split(':') if s != ['\n']: - host_info[s[0].strip()] = s[1].strip() + host_info_linux[s[0].strip()] = s[1].strip() # hostname hostname = os.popen('hostname').readline().strip() - host_info['hostname'] = hostname + host_info_linux['hostname'] = hostname # kernel version kernel_version = os.popen('uname -r').readline().strip() - host_info['kernel_version'] = kernel_version + host_info_linux['kernel_version'] = kernel_version - host_info['os'] = platform - d.callback(self.canonical_info(host_info)) + host_info_linux['os'] = platform + d.callback(self.canonical_info(host_info_linux)) return d if platform == 'darwin': """OS X Worker. """ + host_info_mac = {} cmd = '/usr/sbin/sysctl' args = ('-a', 'hw') d = utils.getProcessOutput(cmd, args, errortoo=1) - d.addCallback(self._gotsysctl, host_info) - d.addErrback(self._catch_failure) + d.addCallback(self._gotsysctl, host_info_mac) + d.addErrback(self._catchFailure) return d - + def canonical_info(self, platform_host_info): """Standarize host info so we can parse it easily""" - unify_info = {'model name': 'cpu_model', + unify_info = {'model name': 'cpu_name', 'cpu Mhz': 'cpu_speed', - 'MemTotal': 'mem_total', - 'MemFree': 'mem_free', + 'MemTotal': 'total_mem', + 'MemFree': 'free_mem', 'kernel_version': 'os', - 'cpu family': 'cpu_model', - 'cpu model': 'cpu_model', + 'cpu family': 'cpu_family', 'cache size': 'cpu_cache_size', 'fpu': 'fpu', @@ -142,139 +139,9 @@ except KeyError: pass - - import sage.version - canonical_info['sage_version'] = sage.version.version - + self.host_info = canonical_info return self.host_info -class ClassicHostInfo(object): - """ - Class to gather computer specifications on the running host. - - """ - - def __init__(self): - self.host_info = self.get_host_info(sys.platform) - - def __str__(self): - return str(self.host_info) - - def __repr__(self): - return str(self.host_info) - - def get_host_info(self, platform): - host_info = {} - if platform == 'linux2' or platform == 'linux': - try: - # os - host_info['os'] = platform - # cpu info - cpuinfo = open('/proc/cpuinfo','r').readlines() - - cpus = 0 - for line in cpuinfo: - if 'processor' in line: - cpus += 1 - s = line.split(':') - if s != ['\n']: - host_info[s[0].strip()] = s[1].strip() - - host_info['cpus'] = cpus - - # uptime - uptime = open('/proc/uptime', 'r').readline().split(' ') - host_info['uptime'] = uptime[0] - - # memory info - meminfo = open('/proc/meminfo', 'r').readlines() - for line in meminfo: - s = line.split(':') - if s != ['\n']: - host_info[s[0].strip()] = s[1].strip() - - # hostname - hostname = os.popen('hostname').readline().strip() - host_info['hostname'] = hostname - - # kernel version - kernel_version = os.popen('uname -r').readline().strip() - host_info['kernel_version'] = kernel_version - - except IOError: - raise - - host_info['os'] = platform - return self.canonical_info(host_info) - - if platform == 'darwin': - try: - # os - for line in os.popen('sysctl -a hw machdep').readlines(): - l = line.strip() - if '=' in l: - l = l.split('=') - if ':' in line: - l = l.split(':') - - l = [li.strip() for li in l] - if l[0] == 'hw.cpufrequency': - host_info['cpu MHz'] = str(int(l[1]) / 1000000) - elif l[0] == 'hw.availcpu': - host_info['cpus'] = int(l[1]) - elif l[0] == 'hw.physmem': - host_info['MemTotal'] = l[1] - elif l[0] == 'hw.usermem': - host_info['MemFree'] = int(int(host_info['MemTotal']) - - int(l[1]) / int(1024*2)) - elif l[0] == 'machdep.cpu.brand_string': - host_info['model name'] = l[1] - - # hostname - hostname = os.popen('hostname').readline().strip() - host_info['hostname'] = hostname - - # kernel version - kernel_version = os.popen('uname -r').readline().strip() - host_info['kernel_version'] = kernel_version - except IOError, msg: - log.msg(msg) - raise - - - host_info['os'] = platform - - return self.canonical_info(host_info) - - def canonical_info(self, platform_host_info): - """Standarize host info so we can parse it easily""" - - unify_info = {'model name': 'cpu_model', - 'cpu MHz': 'cpu_speed', - 'MemTotal': 'mem_total', - 'MemFree': 'mem_free', - 'kernel_version': 'kernel_version', - 'processor': 'processors', - 'cache size': 'cpu_cache_size', - 'fpu': 'fpu', - 'hostname': 'hostname', - 'cpus': 'cpus', - 'ip': 'ip', - 'os': 'os' - } - - canonical_info = {} - for k,v in platform_host_info.iteritems(): - try: - canonical_info[unify_info[k]] = v - except KeyError: - pass - - import sage.version - canonical_info['sage_version'] = sage.version.version - - return canonical_info - -if __name__ == 'main': - h = HostInfo().get_host_info() - reactor.run() + if __name__ == 'main': + h = HostInfo().get_host_info() + reactor.run() Index: age/dsage/scripts/dsage_get_stats.py =================================================================== --- sage/dsage/scripts/dsage_get_stats.py (revision 3798) +++ (revision ) @@ -1,37 +1,0 @@ -#!/usr/bin/env python -############################################################################## -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -# -############################################################################## - -from sage.dsage.server.server import DSageServer -from sage.dsage.database.jobdb import JobDatabaseSQLite -from sage.dsage.database.monitordb import MonitorDatabase -from sage.dsage.database.clientdb import ClientDatabase - -def main(): - jobdb = JobDatabaseSQLite() - monitordb = MonitorDatabase() - clientdb = ClientDatabase() - dsage_server = DSageServer(jobdb, monitordb, clientdb) - f = open('dsage.xml', 'w') - f.write(dsage_server.generate_xml_stats()) - f.close() - print 'Wrote dsage.xml...' - -if __name__ == '__main__': - main() Index: sage/dsage/scripts/dsage_server.py =================================================================== --- sage/dsage/scripts/dsage_server.py (revision 3906) +++ sage/dsage/scripts/dsage_server.py (revision 2925) @@ -21,31 +21,40 @@ import sys import os -import socket - - - from optparse import OptionParser import ConfigParser -import socket -from twisted.internet import reactor, error, ssl, task +from twisted.internet import reactor, task from twisted.spread import pb from twisted.python import log from twisted.cred import portal -from sage.dsage.database.jobdb import JobDatabaseZODB, JobDatabaseSQLite -from sage.dsage.database.jobdb import DatabasePruner -from sage.dsage.database.clientdb import ClientDatabase -from sage.dsage.database.monitordb import MonitorDatabase +from sage.dsage.database.jobdb import JobDatabaseZODB, DatabasePruner from sage.dsage.twisted.pb import Realm from sage.dsage.twisted.pb import WorkerPBServerFactory from sage.dsage.twisted.pb import _SSHKeyPortalRoot from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsChecker -from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsCheckerDB from sage.dsage.server.server import DSageServer, DSageWorkerServer -from sage.dsage.misc.constants import delimiter as DELIMITER -from sage.dsage.__version__ import version DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') +# Begin reading configuration +try: + conf_file = os.path.join(DSAGE_DIR, 'server.conf') + config = ConfigParser.ConfigParser() + config.read(conf_file) + + LOG_FILE = config.get('server_log', 'log_file') + LOG_LEVEL = config.getint('server_log', 'log_level') + SSL = config.getint('ssl', 'ssl') + SSL_PRIVKEY = config.get('ssl', 'privkey_file') + SSL_CERT = config.get('ssl', 'cert_file') + WORKER_PORT = config.getint('server', 'worker_port') + CLIENT_PORT = config.getint('server', 'client_port') + PUBKEY_DATABASE = os.path.expanduser(config.get('auth', + 'pubkey_database')) +except: + print "Error reading %s, please fix manually run dsage.setup()" % \ + conf_file + sys.exit(-1) +# End reading configuration def usage(): @@ -71,15 +80,4 @@ return options -def write_stats(dsage_server, stats_file): - # Put this entire thing in a try block, should not cause the server to die in any way. - try: - fname = os.path.join(DSAGE_DIR, stats_file) - f = open(fname, 'w') - f.write(dsage_server.generate_xml_stats()) - f.close() - except Exception, msg: - print 'Error writing stats: %s' % (msg) - return - def startLogging(log_file): """This method initializes the logging facilities for the server. """ @@ -87,116 +85,60 @@ log.startLogging(sys.stdout) else: - print "DSAGE Server logging to file: ", log_file + print "Logging to file: ", log_file server_log = open(log_file, 'a') log.startLogging(server_log) def main(): - """ - Main execution loop of the server. + """Main execution loop of the server.""" - """ + options = usage() + jobdb = JobDatabaseZODB() - try: - conf_file = os.path.join(DSAGE_DIR, 'server.conf') - config = ConfigParser.ConfigParser() - config.read(conf_file) - - LOG_FILE = config.get('server_log', 'log_file') - LOG_LEVEL = config.getint('server_log', 'log_level') - SSL = config.getint('ssl', 'ssl') - SSL_PRIVKEY = config.get('ssl', 'privkey_file') - SSL_CERT = config.get('ssl', 'cert_file') - CLIENT_PORT = config.getint('server', 'client_port') - PUBKEY_DATABASE = os.path.expanduser(config.get('auth', 'pubkey_database')) - STATS_FILE = config.get('general', 'stats_file') - old_version = config.get('general', 'version') - if version != old_version: - raise ValueError, "Incompatible version. You have %s, need %s." % (old_version, version) - except Exception, msg: - print msg - print "Error reading %s, run dsage.setup()" % conf_file - sys.exit(-1) + # Start to prune out old jobs + jobdb_pruner = DatabasePruner(jobdb) + prune_db = task.LoopingCall(jobdb_pruner.prune) + prune_db.start(60*60*24.0, now=True) # start now, interval is one day + + # Create the main DSage object + dsage_server = DSageServer(jobdb, log_level=LOG_LEVEL) + p = _SSHKeyPortalRoot(portal.Portal(Realm(dsage_server))) + + # Get authorized keys + p.portal.registerChecker(PublicKeyCredentialsChecker(PUBKEY_DATABASE)) + + # HACK: unsafeTracebacks should eventually be TURNED off + client_factory = pb.PBServerFactory(p, unsafeTracebacks=True) + + # Create the PBServerFactory for workers + dsage_worker = DSageWorkerServer(jobdb, log_level=LOG_LEVEL) + worker_factory = WorkerPBServerFactory(dsage_worker) + + # We will listen on 2 ports + # One port that is authenticated so clients can submit new jobs + # One port for workers to connect to to receive and submit jobs + if SSL == 1: + from twisted.internet import ssl + sslContext = ssl.DefaultOpenSSLContextFactory( + SSL_PRIVKEY, + SSL_CERT) + + reactor.listenSSL(CLIENT_PORT, + client_factory, + contextFactory = sslContext) + reactor.listenSSL(WORKER_PORT, + worker_factory, + contextFactory = sslContext) + + else: + reactor.listenTCP(CLIENT_PORT, client_factory) + reactor.listenTCP(WORKER_PORT, worker_factory) + + dsage_server.client_factory = client_factory + dsage_server.worker_factory = worker_factory # start logging startLogging(LOG_FILE) - # Job database - jobdb = JobDatabaseSQLite() - - # Worker database - monitordb = MonitorDatabase() - - # Client database - clientdb = ClientDatabase() - - # Create the main DSage object - dsage_server = DSageServer(jobdb, monitordb, clientdb, log_level=LOG_LEVEL) - p = _SSHKeyPortalRoot(portal.Portal(Realm(dsage_server))) - - # Credentials checker - p.portal.registerChecker(PublicKeyCredentialsCheckerDB(clientdb)) - - # HACK: unsafeTracebacks should eventually be TURNED off - client_factory = pb.PBServerFactory(p, unsafeTracebacks=True) - - # Create the looping call that will output the XML file for Dashboard - tsk1 = task.LoopingCall(write_stats, dsage_server, STATS_FILE) - tsk1.start(5.0, now=False) - - # Create the PBServerFactory for workers - # Use this for unauthorized workers - # dsage_worker = DSageWorkerServer(jobdb, log_level=LOG_LEVEL) - # worker_factory = WorkerPBServerFactory(dsage_worker) - - dsage_server.client_factory = client_factory - - attempts = 0 - err_msg = "Could not find an open port after 50 attempts." - NEW_CLIENT_PORT = CLIENT_PORT - while True: - if attempts > 50: - log.err(err_msg) - log.err('Last attempted port: %s' % (NEW_CLIENT_PORT)) - sys.exit(-1) - try: - try: - s = socket.socket(socket.AF_INET, socket.SOCK_STREAM) - s.connect(('', NEW_CLIENT_PORT)) - port_used = True - except socket.error, msg: - port_used = False - if not port_used: - if SSL: - log.msg('Using SSL...') - ssl_context = ssl.DefaultOpenSSLContextFactory(SSL_PRIVKEY, SSL_CERT) - reactor.listenSSL(NEW_CLIENT_PORT, - client_factory, - contextFactory = ssl_context) - break - else: - reactor.listenTCP(NEW_CLIENT_PORT, client_factory) - break - else: - raise SystemError, 'Trying to bind to open port: %s.' % (NEW_CLIENT_PORT) - except (SystemError, error.CannotListenError): - attempts += 1 - NEW_CLIENT_PORT += 1 - - if CLIENT_PORT != NEW_CLIENT_PORT: - log.msg(DELIMITER) - log.msg("***NOTICE***") - log.msg("Changing listening port in server.conf to %s" % (NEW_CLIENT_PORT)) - log.msg(DELIMITER) - config.set('server', 'client_port', NEW_CLIENT_PORT) - config.write(open(conf_file, 'w')) - - log.msg(DELIMITER) - log.msg('DSAGE Server') - log.msg('PID %s'%os.getpid()) - log.msg('Listening on %s' % (NEW_CLIENT_PORT)) - log.msg(DELIMITER) - - # start the reactor. - reactor.run(installSignalHandlers=1) + reactor.run() if __name__ == "__main__": Index: sage/dsage/scripts/dsage_setup.py =================================================================== --- sage/dsage/scripts/dsage_setup.py (revision 3905) +++ sage/dsage/scripts/dsage_setup.py (revision 2891) @@ -24,12 +24,9 @@ import sys -from sage.dsage.database.clientdb import ClientDatabase -from sage.dsage.misc.constants import delimiter as DELIMITER -from sage.dsage.__version__ import version - -DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') +DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') +PUBKEY_DATABASE = os.path.abspath(os.path.join(DSAGE_DIR, + 'authorized_keys.db')) DB_DIR = os.path.join(DSAGE_DIR, 'db/') SAGE_ROOT = os.getenv('SAGE_ROOT') -DSAGE_VERSION = version def check_dsage_dir(): @@ -43,5 +40,4 @@ config = ConfigParser.ConfigParser() config.add_section('general') - config.set('general', 'version', DSAGE_VERSION) config.add_section('ssl') if type == 'client': @@ -71,9 +67,7 @@ config.set('log', 'log_level', '0') # set public key authentication info - print DELIMITER print "Generating public/private key pair for authentication..." print "Your key will be stored in %s/dsage_key"%DSAGE_DIR print "Just hit enter when prompted for a passphrase" - print DELIMITER key_file = os.path.join(DSAGE_DIR, 'dsage_key') cmd = ["ssh-keygen", "-q", "-trsa", "-f%s" % key_file] @@ -84,5 +78,5 @@ config.set('auth', 'pubkey_file', key_file + '.pub') config.write(open(conf_file, 'w')) - print "Client configuration finished.\n" + print "Client configuration finished." def setup_worker(): @@ -92,5 +86,5 @@ config.set('general', 'server', 'localhost') - config.set('general', 'port', 8081) + config.set('general', 'port', 8082) config.set('general', 'nice_level', 20) config.set('general', 'workers', 2) @@ -100,8 +94,7 @@ config.set('log', 'log_level', '0') config.set('general', 'delay', '5') - config.set('general', 'anonymous', False) conf_file = os.path.join(DSAGE_DIR, 'worker.conf') config.write(open(conf_file, 'w')) - print "Worker configuration finished.\n" + print "Worker configuration finished." def setup_server(): @@ -110,4 +103,5 @@ config = get_config('server') config.set('server', 'client_port', 8081) + config.set('server', 'worker_port', 8082) config.set('ssl', 'ssl', 1) config.set('server_log', 'log_file', 'stdout') @@ -115,17 +109,18 @@ config.set('db_log', 'log_file', 'stdout') config.set('db_log', 'log_level', '0') - config.set('auth', 'pubkey_database', os.path.join(DB_DIR, 'dsage.db')) - config.set('db', 'db_file', os.path.join(DB_DIR, 'dsage.db')) + config.set('auth', 'pubkey_database', PUBKEY_DATABASE) + config.set('db', 'db_file', os.path.join(DB_DIR, 'jobdb.fs')) config.set('db', 'prune_in_days', 7) config.set('db', 'stale_in_days', 365) - config.set('db', 'job_failure_threshold', 2) + config.set('db', 'failure_threshhold', 5) config.set('ssl', 'privkey_file', os.path.join(DSAGE_DIR, 'cacert.pem')) - config.set('ssl', 'cert_file', os.path.join(DSAGE_DIR, 'pubcert.pem')) - config.set('general', 'stats_file', 'gauge.xml') - - print DELIMITER + config.set('ssl', 'cert_file', os.path.join(DSAGE_DIR, 'privkey.pem')) + + print "Generating SSL certificate for server..." + print "Creates a private key:" cmd = ['openssl genrsa > %s' % (config.get('ssl', 'privkey_file'))] subprocess.call(cmd, shell=True) + print "Creates a self signed SSL certificate:" cmd = ['openssl req -config %s -new -x509 -key %s -out %s -days \ 1000' % (os.path.join(SAGE_ROOT,'local/openssl/openssl.cnf'), @@ -133,12 +128,5 @@ config.get('ssl', 'cert_file'))] subprocess.call(cmd, shell=True) - print DELIMITER - os.chmod(os.path.join(DSAGE_DIR, 'cacert.pem'), 0600) - - conf_file = os.path.join(DSAGE_DIR, 'server.conf') - config.write(open(conf_file, 'w')) - - print "Server configuration finished.\n\n" - + # add default user c = ConfigParser.ConfigParser() @@ -146,17 +134,19 @@ username = c.get('auth', 'username') pubkey_file = c.get('auth', 'pubkey_file') - clientdb = ClientDatabase() - if clientdb.get_user_and_key(username) is None: - clientdb.add_user(username, pubkey_file) - print 'Added user %s\n' % (username) - else: - (user, key) = clientdb.get_user_and_key(username) - pubkey = open(pubkey_file).read() - if pubkey != key: - clientdb.del_user(username) - clientdb.add_user(username, pubkey_file) - print 'User %s exists, changing public key' % (username) - else: - print 'User %s already exists.' % (username) + add_user(username, pubkey_file) + + conf_file = os.path.join(DSAGE_DIR, 'server.conf') + config.write(open(conf_file, 'w')) + + print "Server configuration finished." + print "\n" + +def add_user(username, pubkey_file): + f = open(pubkey_file) + type, key = f.readlines()[0].split()[:2] + f.close() + f1 = open(PUBKEY_DATABASE, 'a') + f1.write(':'.join([username, key]) + '\n') + f1.close() def setup(): Index: sage/dsage/scripts/dsage_worker.py =================================================================== --- sage/dsage/scripts/dsage_worker.py (revision 3906) +++ sage/dsage/scripts/dsage_worker.py (revision 2965) @@ -16,5 +16,4 @@ # # http://www.gnu.org/licenses/ -# ############################################################################ @@ -22,24 +21,17 @@ import os import ConfigParser +import uuid import cPickle import zlib -import pexpect -import time from twisted.spread import pb from twisted.internet import reactor, defer, error, task from twisted.python import log -from twisted.spread import banana -banana.SIZE_LIMIT = 100*1024*1024 # 100 MegaBytes from sage.interfaces.sage0 import Sage from sage.misc.preparser import preparse_file -from sage.dsage.database.job import Job, expand_job -from sage.dsage.misc.hostinfo import HostInfo, ClassicHostInfo -from sage.dsage.misc.config import get_conf, get_bool +from sage.dsage.misc.hostinfo import HostInfo from sage.dsage.errors.exceptions import NoJobException -from sage.dsage.twisted.pb import PBClientFactory -from sage.dsage.misc.constants import delimiter as DELIMITER pb.setUnjellyableForClass(HostInfo, HostInfo) @@ -47,4 +39,24 @@ DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') +# Begin reading configuration +try: + conf_file = os.path.join(DSAGE_DIR, 'worker.conf') + config = ConfigParser.ConfigParser() + config.read(conf_file) + + LOG_FILE = config.get('log', 'log_file') + LOG_LEVEL = config.getint('log','log_level') + SSL = config.getint('ssl', 'ssl') + WORKERS = config.getint('general', 'workers') + SERVER = config.get('general', 'server') + PORT = config.getint('general', 'port') + DELAY = config.getint('general', 'delay') +except: + print "Error reading %s, please fix manually or run dsage.setup()" % \ + conf_file + sys.exit(-1) +# End reading configuration + +# OUTPUT MARKERS shared by Worker and Monitor START_MARKER = '___BEGIN___' END_MARKER = '___END___' @@ -54,5 +66,5 @@ class Worker(object): - """ + r""" This class represents a worker object that does the actual calculation. @@ -67,8 +79,6 @@ self.free = True self.job = None - self.conf = get_conf('monitor') - self.log_level = self.conf['log_level'] - self.delay = self.conf['delay'] - if self.log_level > 3: + + if LOG_LEVEL > 3: self.sage = Sage(logfile=DSAGE_DIR + '/%s-pexpect.log'\ % self.id) @@ -82,20 +92,16 @@ # Initialize getting of jobs - self.get_job() - - def _catch_failure(self, failure): - log.msg("Error: ", failure.getErrorMessage()) - log.msg("Traceback: ", failure.printTraceback()) - - def get_job(self): + self.getJob() + + def getJob(self): + # print 'Ok so far.' try: - if self.log_level > 3: - log.msg('Worker %s: Getting job...' % (self.id)) - d = self.remoteobj.callRemote('get_job') + d = self.remoteobj.callRemote('getJob') except Exception, msg: - log.msg(msg) - log.msg('[Worker: %s, get_job] Disconnected from remote server.'\ + print 'Error getting job.' + print msg + log.msg('[Worker: %s, getJob] Disconnected from remote server.'\ % self.id) - reactor.callLater(self.delay, self.get_job) + reactor.callLater(DELAY, self.getJob) return d.addCallback(self.gotJob) @@ -104,33 +110,29 @@ return d - def gotJob(self, jdict): - """ - gotJob is a callback for the remoteobj's get_job method. + def gotJob(self, job): + r""" + gotJob is a callback for the remoteobj's getJob method. Parameters: - job -- Job object returned by remote's 'get_job' method - - """ - - if self.log_level > 3: - log.msg('[Worker %s, gotJob] %s' % (self.id, jdict)) - - self.job = expand_job(jdict) - - if not isinstance(self.job, Job): + job -- Job object returned by remote's 'getJob' method + + """ + + if not isinstance(job, str): raise NoJobException - log.msg('[Worker: %s] Got job (%s, %s)' % (self.id, self.job.name, self.job.job_id)) + self.job = unpickle(job) + log.msg('[Worker: %s] Got job (%s, %s)' % (self.id, + self.job.name, + self.job.id)) try: self.doJob(self.job) - except Exception, msg: - log.msg(msg) - d = self.remoteobj.callRemote('job_failed', self.job.job_id, msg) - d.addErrback(self._catch_failure) - self.restart() - - def job_done(self, output, result, completed): - """ - job_done is a callback for doJob. Called when a job completes. + except Exception, e: + print e + raise + + def jobDone(self, output, result, completed, worker_info): + r""" + jobDone is a callback for doJob. Called when a job completes. Parameters: @@ -138,18 +140,21 @@ result -- the result of processing the job, a pickled object completed -- whether or not the job is completely finished (bool) + worker_info -- user@host, os.uname() (tuple) """ try: - d = self.remoteobj.callRemote('job_done', - self.job.job_id, + d = self.remoteobj.callRemote('jobDone', + self.job.id, output, result, - completed) + completed, + worker_info) except Exception, msg: log.msg(msg) - log.msg('[Worker: %s, job_done] Disconnected, reconnecting in %s'\ - % (self.id, self.delay)) - reactor.callLater(self.delay, self.job_done, output, result, completed) + log.msg('[Worker: %s, jobDone] Disconnected, reconnecting in %s'\ + % (self.id, DELAY)) + reactor.callLater(DELAY, self.jobDone, output, + result, completed, worker_info) d = defer.Deferred() d.errback(error.ConnectionLost()) @@ -162,5 +167,7 @@ def noJob(self, failure): - """ + # TODO: Probably do not need this errback, look into consolidating + # with failedJob + r""" noJob is an errback that catches the NoJobException. @@ -172,24 +179,15 @@ sleep_time = 5.0 if failure.check(NoJobException): - if self.log_level > 3: - log.msg('[Worker %s, noJob] Sleeping for %s seconds' % (self.id, sleep_time)) - reactor.callLater(sleep_time, self.get_job) - else: - print "Error: ", failure.getErrorMessage() - print "Traceback: ", failure.printTraceback() - - def setup_tmp_dir(self, job): - """ - Creates the temporary directory for the worker. - - """ - + reactor.callLater(5.0, self.getJob) + + def setupTempDir(self, job): + # change to a temporary directory cur_dir = os.getcwd() # keep a reference to the current directory tmp_dir = os.path.join(DSAGE_DIR, 'tmp_worker_files') - tmp_job_dir = os.path.join(tmp_dir, job.job_id) + tmp_job_dir = os.path.join(tmp_dir, job.id) + self.tmp_job_dir = tmp_job_dir if not os.path.isdir(tmp_dir): os.mkdir(tmp_dir) - if not os.path.isdir(tmp_job_dir): - os.mkdir(tmp_job_dir) + os.mkdir(tmp_job_dir) os.chdir(tmp_job_dir) self.sage.eval("os.chdir('%s')" % tmp_job_dir) @@ -197,6 +195,6 @@ return tmp_job_dir - def extract_job_data(self, job): - """ + def extractJobData(self, job): + r""" Extracts all the data that is in a job object. @@ -204,39 +202,38 @@ if isinstance(job.data, list): - if self.log_level > 2: + if LOG_LEVEL > 2: log.msg('Extracting job data...') - try: - for var, data, kind in job.data: - try: - data = zlib.decompress(data) - except Exception, msg: - log.msg(msg) - continue - if kind == 'file': - f = open(var, 'wb') - f.write(data) - f.close() - if self.log_level > 2: - log.msg('[Worker: %s] Extracted %s. ' % (self.id, f)) - if kind == 'object': - fname = var + '.sobj' - if self.log_level > 2: - log.msg('Object to be loaded: %s' % fname) - f = open(fname, 'wb') - f.write(data) - f.close() - self.sage.eval("%s = load('%s')" % (var, fname)) - if self.log_level > 2: - log.msg('[Worker: %s] Loaded %s' % (self.id, fname)) - except Exception, msg: - log.err(msg) - - def write_job_file(self, job): - """ + for var, data, kind in job.data: + # Uncompress data + try: + data = zlib.decompress(data) + except Exception, msg: + log.msg(msg) + continue + if kind == 'file': + # Write out files to current dir + f = open(var, 'wb') + f.write(data) + if LOG_LEVEL > 2: + log.msg('[Worker: %s] Extracted %s. ' % (self.id, f)) + if kind == 'object': + # Load object into the SAGE worker + fname = var + '.sobj' + if LOG_LEVEL > 3: + log.msg('Object to be loaded: %s' % fname) + f = open(fname, 'wb') + f.write(data) + f.close() + self.sage.eval("%s = load('%s')" % (var, fname)) + if LOG_LEVEL > 2: + log.msg('[Worker: %s] Loaded %s' % (self.id, fname)) + + def writeJobFile(self, job): + r""" Writes out the job file to be executed to disk. """ - - parsed_file = preparse_file(job.code, magic=False, do_time=False, ignore_prompts=False) + parsed_file = preparse_file(job.file, magic=False, + do_time=False, ignore_prompts=False) job_filename = str(job.name) + '.py' @@ -249,5 +246,6 @@ job_file.write(END) job_file.close() - if self.log_level > 2: + + if LOG_LEVEL > 2: log.msg('[Worker: %s] Wrote job file. ' % (self.id)) @@ -255,5 +253,5 @@ def doJob(self, job): - """ + r""" doJob is the method that drives the execution of a job. @@ -263,19 +261,18 @@ """ - if self.log_level > 3: - log.msg('[Worker %s, doJob] Beginning job execution...' % (self.id)) - self.free = False d = defer.Deferred() - self.tmp_job_dir = self.setup_tmp_dir(job) - self.extract_job_data(job) - - job_filename = self.write_job_file(job) - - f = os.path.join(self.tmp_job_dir, job_filename) + tmp_job_dir = self.setupTempDir(job) + self.extractJobData(job) + + job_filename = self.writeJobFile(job) + + f = os.path.join(tmp_job_dir, job_filename) self.sage._send("execfile('%s')" % (f)) - if self.log_level > 2: + if LOG_LEVEL > 2: log.msg('[Worker: %s] File to execute: %s' % (self.id, f)) + if LOG_LEVEL > 3: + log.msg('[Worker: %s] Called sage._send()' % (self.id)) d.callback(True) @@ -284,45 +281,22 @@ def stop(self): - """ - Stops the current worker and resets it's internal state. + r""" + stop() kills the current running job. """ - - INTERRUPT_TRIES = 10 - timeout = 0.05 - for i in range(INTERRUPT_TRIES): - try: - self.sage._expect.sendline(chr(3)) # send ctrl-c - self.sage._expect.expect(self.sage._prompt, timeout=timeout) - self.sage._expect.expect(self.sage._prompt, timeout=timeout) - success = True - break - except (pexpect.TIMEOUT, pexpect.EOF), msg: - if self.log_level > 3: - log.err("Trying again to interrupt SAGE (try %s)..." % i) - - self.sage.reset() + + self.sage.quit() self.free = True self.job = None + self.sage = None def start(self): - """ - Starts a new worker if it does not exist already. - - """ - - if self.sage is None: - if self.log_level > 3: - self.sage = Sage(logfile=DSAGE_DIR + '/%s-pexpect.out' % self.id) - else: - self.sage = Sage() - self.get_job() + if LOG_LEVEL > 3: + self.sage = Sage(logfile=DSAGE_DIR + '/%s-pexpect.out' % self.id) + else: + self.sage = Sage() + self.getJob() def restart(self): - """ - Restarts the current worker. - - """ - log.msg('[Worker: %s] Restarting...' % (self.id)) self.stop() @@ -330,5 +304,5 @@ class Monitor(object): - """ + r""" This class represents a monitor that controls workers. @@ -341,58 +315,21 @@ """ - def __init__(self, server, port): - self.conf = get_conf('monitor') - self.uuid = self.conf['id'] - self.workers = int(self.conf['workers']) - self.log_file = self.conf['log_file'] - self.log_level = self.conf['log_level'] - self.delay = float(self.conf['delay']) - self.anonymous = get_bool(self.conf['anonymous']) - self.ssl = get_bool(self.conf['ssl']) - if server is None: - self.server = self.conf['server'] - else: - self.server = server - if port is None: - if self.server == 'localhost': - self.port = int(get_conf('server')['client_port']) - else: - self.port = int(self.conf['port']) - else: - self.port = port + def __init__(self, hostname, port): + self.hostname = hostname + self.port = port self.remoteobj = None self.connected = False self.reconnecting = False - self.worker_pool = None - - self.host_info = ClassicHostInfo().host_info - self.host_info['uuid'] = self.uuid - self.host_info['workers'] = self.workers - - self._startLogging(self.log_file) - - if not self.anonymous: - from twisted.cred import credentials - from twisted.conch.ssh import keys - self._get_auth_info() - # public key authentication information - self.pubkey_str =keys.getPublicKeyString(filename=self.pubkey_file) - # try getting the private key object without a passphrase first - try: - self.priv_key = keys.getPrivateKeyObject(filename=self.privkey_file) - except keys.BadKeyError: - pphrase = self._getpassphrase() - self.priv_key = keys.getPrivateKeyObject(filename=self.privkey_file, - passphrase=pphrase) - self.pub_key = keys.getPublicKeyObject(self.pubkey_str) - self.alg_name = 'rsa' - self.blob = keys.makePublicKeyBlob(self.pub_key) - self.data = self.DATA - self.signature = keys.signData(self.priv_key, self.data) - self.creds = credentials.SSHPrivateKey(self.username, - self.alg_name, - self.blob, - self.data, - self.signature) + self.workers = None + + # Start twisted logging facility + self._startLogging(LOG_FILE) + + if len(config.get('uuid', 'id')) != 36: + config.set('uuid', 'id', str(uuid.uuid1())) + f = open(conf_file, 'w') + config.write(f) + + self.identifier = config.get('uuid', 'id') def _startLogging(self, log_file): @@ -403,29 +340,5 @@ server_log = open(log_file, 'a') log.startLogging(server_log) - - def _get_auth_info(self): - import random - self.DATA = ''.join([chr(i) for i in [random.randint(65, 123) for n in - range(500)]]) - self.DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') - # Begin reading configuration - try: - conf_file = os.path.join(self.DSAGE_DIR, 'client.conf') - config = ConfigParser.ConfigParser() - config.read(conf_file) - - self.username = config.get('auth', 'username') - self.privkey_file = os.path.expanduser(config.get('auth', 'privkey_file')) - self.pubkey_file = os.path.expanduser(config.get('auth', 'pubkey_file')) - except Exception, msg: - print msg - raise - - def _getpassphrase(self): - import getpass - passphrase = getpass.getpass('Passphrase (Hit enter for None): ') - - return passphrase - + def _connected(self, remoteobj): self.remoteobj = remoteobj @@ -434,22 +347,20 @@ self.reconnecting = False - if self.worker_pool == None: # Only pool workers the first time - self.pool_workers(self.remoteobj) - else: - for worker in self.worker_pool: + if self.workers == None: # Only pool workers the first time + self.poolWorkers(self.remoteobj) + else: + for worker in self.workers: worker.remoteobj = self.remoteobj # Update workers - # self.submit_host_info() + self.submitHostInfo() def _disconnected(self, remoteobj): - log.err('Lost connection to the server.') + log.msg('Lost connection to the server.') self.connected = False self._retryConnect() - def _got_killed_jobs(self, killed_jobs): + def _gotKilledJobsList(self, killed_jobs): if killed_jobs == None: return - # reconstruct the Job objects from the jdicts - killed_jobs = [expand_job(jdict) for jdict in killed_jobs] - for worker in self.worker_pool: + for worker in self.workers: if worker.job is None: continue @@ -457,32 +368,29 @@ continue for job in killed_jobs: - if job is None or worker.job is None: + if job == None or worker.job == None: continue - if worker.job.job_id == job.job_id: - log.msg('[Worker: %s] Processing a killed job, restarting...' % worker.id) + job = unpickle(job) + if worker.job.id == job.id: + log.msg('[Worker: %s] Processing a killed job, \ + restarting...' % worker.id) worker.restart() def _retryConnect(self): - log.err('[Monitor] Disconnected, reconnecting in %s' % self.delay) - reactor.callLater(self.delay, self.connect) + log.msg('[Monitor] Disconnected, reconnecting in %s' % DELAY) + reactor.callLater(DELAY, self.connect) def _catchConnectionFailure(self, failure): # If we lost the connection to the server somehow - # if failure.check(error.ConnectionRefusedError, + #if failure.check(error.ConnectionRefusedError, # error.ConnectionLost, # pb.DeadReferenceError): - self.connected = False self._retryConnect() - - log.err("Error: ", failure.getErrorMessage()) - log.err("Traceback: ", failure.printTraceback()) - - def _catch_failure(self, failure): - log.err("Error: ", failure.getErrorMessage()) - log.err("Traceback: ", failure.printTraceback()) - + # else: + # log.msg("Error: ", failure.getErrorMessage()) + # log.msg("Traceback: ", failure.printTraceback()) + def connect(self): - """ + r""" This method connects the monitor to a remote PB server. @@ -493,42 +401,29 @@ factory = pb.PBClientFactory() - log.msg(DELIMITER) - log.msg('DSAGE Worker') - log.msg('PID %s'%os.getpid()) - log.msg('Connecting to %s:%s' % (self.server, self.port)) - log.msg(DELIMITER) - - self.factory = PBClientFactory() - if self.ssl == 1: + if SSL == 1: from twisted.internet import ssl contextFactory = ssl.ClientContextFactory() - reactor.connectSSL(self.server, self.port, - self.factory, contextFactory) - else: - reactor.connectTCP(self.server, self.port, self.factory) - - if not self.anonymous: - log.msg('Connecting as authenticated worker...\n') - d = self.factory.login(self.creds, (pb.Referenceable(), self.host_info)) - else: - log.msg('Connecting as anonymous worker...\n') - d = self.factory.login('Anonymous', (pb.Referenceable(), self.host_info)) + reactor.connectSSL(self.hostname, self.port, + factory, contextFactory) + else: + reactor.connectTCP(self.hostname, self.port, factory) + + d = factory.getRootObject() d.addCallback(self._connected) d.addErrback(self._catchConnectionFailure) - return d - def pool_workers(self, remoteobj): - """ - pool_workers creates as many workers as specified in worker.conf. - - """ - - log.msg('[Monitor] Starting %s workers...' % (self.workers)) - self.worker_pool = [Worker(remoteobj, x) for x in range(self.workers)] - - def check_output(self): - """ - check_output periodically polls workers for new output. + def poolWorkers(self, remoteobj): + r""" + poolWorkers creates as many workers as specified in worker.conf. + + """ + + self.workers = [Worker(remoteobj, x) for x in range(WORKERS)] + log.msg('Initialized ' + str(len(self.workers)) + ' workers.') + + def checkForJobOutput(self): + r""" + checkForJobOutput periodically polls workers for new output. This figures out whether or not there is anything new output that we @@ -537,8 +432,8 @@ """ - if self.worker_pool == None: + if self.workers == None: return - for worker in self.worker_pool: + for worker in self.workers: if worker.job == None: continue @@ -546,59 +441,59 @@ continue - if self.log_level > 1: - log.msg('[Monitor] Checking for job output of worker %s' % (worker.id)) + # log.msg('[Monitor] Checking for job output') try: done, output, new = worker.sage._so_far() except Exception, msg: - log.err('Exception raised when checking output.') - log.err(msg) + log.msg(msg) continue if new == '' or new.isspace(): continue if done: - worker.free = True + # Checks to see if the job created a result var sobj = worker.sage.get('DSAGE_RESULT') - timeout = 0.1 - while sobj == '' or sobj.isspace(): + if sobj == '' or sobj.isspace(): + if LOG_LEVEL > 1: + log.msg('Something went wrong, it should not be empty.') + worker.sage._get() sobj = worker.sage.get('DSAGE_RESULT') - time.sleep(timeout) - if 'NameError: name \'DSAGE_RESULT\' is not defined' in sobj: - if self.log_level > 1: + if sobj == '' or sobj.isspace(): + worker.sage._get() + sobj = worker.sage.get('DSAGE_RESULT') + else: + if LOG_LEVEL > 1: + log.msg('Got DSAGE_RESULT second time') + + # DSAGE_RESULT does not exist + if 'Traceback' in sobj or 'NameError' in sobj: + if LOG_LEVEL > 1: log.msg('DSAGE_RESULT does not exist') result = cPickle.dumps('No result saved.', 2) else: + os.chdir(worker.tmp_job_dir) try: - os.chdir(worker.tmp_job_dir) - worker.sage.eval("os.chdir('%s')" % (worker.tmp_job_dir)) - worker.sage.eval("save(DSAGE_RESULT, 'result', compress=True)") - result = open('result.sobj', 'rb').read() # Already in compressed form. + result = open(sobj, 'rb').read() except Exception, msg: - if self.log_level > 1: - log.err(msg) - result = cPickle.dumps(msg, 2) - log.msg("[Worker: %s] Job '%s' finished" % (worker.id, worker.job.job_id)) + if LOG_LEVEL > 1: + log.msg(msg) + result = cPickle.dumps('Error in reading result.', 2) + worker.free = True + log.msg("Job '%s' finished" % worker.job.name) else: - result = cPickle.dumps('Job not done yet.', 2) - - sanitized_output = self.clean_output(new) - if self.check_failure(sanitized_output): - s = ['[Monitor] Error in result for ', - '%s:%s ' % (worker.job.name, worker.job.job_id), - 'Worker ID:%s' % (worker.id)] - log.err(''.join(s)) - log.err('[Monitor] Traceback: \n%s' % sanitized_output) - d = self.remoteobj.callRemote('job_failed', worker.job.job_id, sanitized_output) - d.addErrback(self._catch_failure) - worker.restart() - continue - d = worker.job_done(sanitized_output, result, done) + result = 'No result yet.' + + worker_info = (os.getenv('USER') + '@' + os.uname()[1], + ' '.join(os.uname()[2:])) + sanitized_output = self.sanitizeOutput(new) + + if self.checkOutputForFailure(sanitized_output): + log.msg('[Monitor] Error in result for job %s %s done by \ +Worker: %s ' % (worker.job.name, worker.job.id, worker.id)) + log.msg('[Monitor] Traceback: \n%s' % sanitized_output) + d = self.remoteobj.callRemote('jobFailed', worker.job.id) + + d = worker.jobDone(sanitized_output, result, done, worker_info) d.addErrback(self._catchConnectionFailure) - def check_failure(self, sage_output): - """ - Checks for signs of exceptions or errors in the output. - - """ - + def checkOutputForFailure(self, sage_output): if sage_output == None: return False @@ -613,7 +508,7 @@ return False - def check_killed_jobs(self): - """ - check_killed_jobs retrieves a list of killed job ids. + def checkForKilledJobs(self): + r""" + checkForKilledJobs retrieves a list of killed job ids. """ @@ -621,15 +516,28 @@ if not self.connected: return - - killed_jobs = self.remoteobj.callRemote('get_killed_jobs_list') - killed_jobs.addCallback(self._got_killed_jobs) - killed_jobs.addErrback(self._catch_failure) - - def clean_output(self, sage_output): - """ - clean_output attempts to clean up the output string from sage. - - """ - + # try: + killed_jobs = self.remoteobj.callRemote('getKilledJobsList') +# except: +# if not self.reconnecting: +# self._retryConnect() +# return + killed_jobs.addCallback(self._gotKilledJobsList) + + def jobUpdated(self, id): + r""" + jobUpdated is a callback that gets called when there is new output + from checkForJobOutput. + + """ + + print str(id) + ' was updated!' + + def sanitizeOutput(self, sage_output): + r""" + sanitizeOutput attempts to clean up the output string from sage. + + """ + + # log.msg("Before cleaning output: ", sage_output) begin = sage_output.find(START_MARKER) if begin != -1: @@ -646,60 +554,75 @@ output = output.replace('\r', '') + # log.msg("After cleaning output: ", output) return output - def start_looping_calls(self): - """ - start_looping_calls prepares and starts our periodic checking methods. - - """ - - self.tsk1 = task.LoopingCall(self.check_output) + def _gotHostInfo(self, h): + + # attach the workers uuid to the dictionary returned by + # HostInfo().get_host_info + h['uuid'] = self.identifier + + d = self.remoteobj.callRemote("submitHostInfo", h) + d.addErrback(self._catchConnectionFailure) + log.msg('Submitted host info') + + def submitHostInfo(self): + r""" + Sends the workers hardware specs to the server. + + """ + + h = HostInfo().get_host_info() + h.addCallback(self._gotHostInfo) + h.addErrback(self._catchConnectionFailure) + + def startLoopingCalls(self): + r""" + startLoopingCalls prepares and starts our periodic checking methods. + + """ + + # submits the output to the server + self.tsk1 = task.LoopingCall(self.checkForJobOutput) self.tsk1.start(0.1, now=False) - interval = 5.0 - self.tsk2 = task.LoopingCall(self.check_killed_jobs) - self.tsk2.start(interval, now=False) - - def stop_looping_calls(self): - """ - stops the looping calls. - - """ - + + # checks for killed jobs + self.tsk2 = task.LoopingCall(self.checkForKilledJobs) + self.tsk2.start(5.0, now=False) + + def stopLoopingCalls(self): + r""" + Stops the looping calls. + + """ + self.tsk.stop() self.tsk1.stop() self.tsk2.stop() def main(): - """ + r""" argv[1] == hostname argv[2] == port """ - + + if len(sys.argv) == 1: + monitor = Monitor(SERVER, PORT) + if len(sys.argv) == 2: + monitor = Monitor(sys.argv[1], PORT) if len(sys.argv) == 3: - hostname, port = sys.argv[1:3] try: - port = int(port) - except: - port = None - if hostname == 'None': - hostname = None - else: - try: - hostname = str(hostname) - except Exception, msg: - print msg - hostname = None - else: - hostname = port = None - - monitor = Monitor(hostname, port) + port = int(sys.argv[2]) + except Exception, e: + print e + port = PORT + monitor = Monitor(sys.argv[1], port) monitor.connect() - monitor.start_looping_calls() - + monitor.startLoopingCalls() try: reactor.run() except: - sys.exit() + sys.exist(-1) if __name__ == '__main__': Index: sage/dsage/server/client_tracker.py =================================================================== --- sage/dsage/server/client_tracker.py (revision 3866) +++ sage/dsage/server/client_tracker.py (revision 2942) @@ -20,5 +20,5 @@ def add(avatar): - """ + r""" Adds an avatar to clients_list. @@ -28,5 +28,5 @@ def remove(avatar): - """ + r""" Removes the avatar from the client_list. Index: sage/dsage/server/server.py =================================================================== --- sage/dsage/server/server.py (revision 3895) +++ sage/dsage/server/server.py (revision 3600) @@ -19,7 +19,4 @@ import zlib import cPickle -import datetime -import xml.dom.minidom -import cStringIO from twisted.spread import pb @@ -27,12 +24,13 @@ from sage.dsage.misc.hostinfo import HostInfo +import sage.dsage.server.worker_tracker as worker_tracker +import sage.dsage.server.client_tracker as client_tracker from sage.dsage.server.hostinfo_tracker import hostinfo_list from sage.dsage.errors.exceptions import BadTypeError -from sage.dsage.database.job import expand_job pb.setUnjellyableForClass(HostInfo, HostInfo) class DSageServer(pb.Root): - """ + r""" This class represents Distributed Sage server which does all the coordination of distributing jobs, creating new jobs and accepting job @@ -40,7 +38,6 @@ """ - - def __init__(self, jobdb, monitordb, clientdb, log_level=0): - """ + def __init__(self, jobdb, log_level=0): + r""" Initializes the Distributed Sage PB Server. @@ -52,13 +49,11 @@ self.jobdb = jobdb - self.monitordb = monitordb - self.clientdb = clientdb - self.LOG_LEVEL = log_level + self.log_level = log_level def unpickle(self, pickled_job): return cPickle.loads(zlib.decompress(pickled_job)) - def get_job(self, anonymous=False): - """ + def getJob(self): + r""" Returns a job to the client. @@ -68,28 +63,20 @@ """ - if anonymous: - jdict = self.jobdb.get_job(anonymous=True) - else: - jdict = self.jobdb.get_job(anonymous=False) - if jdict == None: - if self.LOG_LEVEL > 3: - log.msg('[DSage, get_job]' + ' Job db is empty.') + job = self.jobdb.getJob() + + if job == None: + if self.log_level > 2: + log.msg('[DSage]' + ' Job db is empty.') return None else: - if self.LOG_LEVEL > 3: - log.msg('[DSage, get_job]' + ' Returning Job %s to client' % (jdict['job_id'])) - jdict['status'] = 'processing' - jdict = self.jobdb.store_job(jdict) - - return jdict - - def set_job_uuid(self, job_id, uuid): - return self.jobdb.set_job_uuid(job_id, uuid) - - def set_busy(self, uuid, busy): - return self.monitordb.set_busy(uuid, busy=busy) - - def get_job_by_id(self, job_id): - """ + if self.log_level > 3: + log.msg('[DSage, getJob]' + ' Returning Job (%s, %s) to client' + % (job.id, job.name)) + job.status = 'processing' + self.jobdb.storeJob(job) + return job.pickle() + + def getJobByID(self, jobID): + r""" Returns a job by the job id. @@ -99,11 +86,8 @@ """ - jdict = self.jobdb.get_job_by_id(job_id) - uuid = jdict['monitor_id'] - jdict['worker_info'] = self.monitordb.get_monitor(uuid) - - return jdict - - def get_job_result_by_id(self, job_id): + job = self.jobdb.getJobByID(jobID) + return job.pickle() + + def getJobResultByID(self, jobID): """Returns the job result. @@ -113,10 +97,8 @@ """ - jdict = self.jobdb.get_job_by_id(job_id) - job = expand_job(jdict) - + job = self.jobdb.getJobByID(jobID) return job.result - def get_job_output_by_id(self, job_id): + def getJobOutputByID(self, jobID): """Returns the job output. @@ -126,72 +108,77 @@ """ - job = self.jobdb.get_job_by_id(job_id) + job = self.jobdb.getJobByID(jobID) return job.output - def sync_job(self, job_id): - raise NotImplementedError - # job = self.jobdb.get_job_by_id(job_id) + def syncJob(self, jobID): + job = self.jobdb.getJobByID(jobID) # new_job = copy.deepcopy(job) # print new_job # # Set file, data to 'Omitted' so we don't need to transfer it - # new_job.code = 'Omitted...' + # new_job.file = 'Omitted...' # new_job.data = 'Omitted...' - # return job.pickle() - - def get_jobs_by_username(self, username, active=False): - """ - Returns jobs created by username. - - Parameters: - username -- the username (str) - active -- when set to True, only return active jobs (bool) + return job.pickle() + + def getJobsByAuthor(self, author, is_active, job_name): + r""" + Returns jobs created by author. + + Parameters: + author -- the author name (str) + is_active -- when set to True, only return active jobs (bool) job_name -- the job name (optional) """ - jobs = self.jobdb.get_jobs_by_username(username, active) - - if self.LOG_LEVEL > 3: + jobs = self.jobdb.getJobsByAuthor(author, is_active, job_name) + + if self.log_level > 3: log.msg(jobs) return jobs - def submit_job(self, jdict): - """ + def submitJob(self, pickled_job): + r""" Submits a job to the job database. Parameters: - jdict -- the internal dictionary of a Job object + pickled_job -- a pickled_Job object """ - - if self.LOG_LEVEL > 3: - log.msg('[DSage, submit_job] %s' % (jdict)) - - if jdict['code'] is None: + try: + if self.log_level > 3: + log.msg('[DSage, submitJob] Trying to unpickle job') + job = self.unpickle(pickled_job) + except: return False - if jdict['name'] is None: - jdict['name'] = 'Default' - jdict['update_time'] = datetime.datetime.now() - - return self.jobdb.store_job(jdict) - - def get_all_jobs(self): - """ - Returns a list of all jobs in the database. - - """ - return self.jobdb.get_all_jobs() - - def get_active_jobs(self): - """ + if job.file is None: + return False + if job.name is None: + job.name = 'defaultjob' + if job.id is None: + job.id = self.jobdb.getJobID() + + if self.log_level > 0: + log.msg('[DSage, submitJob] Job (%s %s) submitted' % (job.id, + job.name)) + return self.jobdb.storeJob(job) + + def getJobsList(self): + r""" + Returns an ordered list of jobs in the database. + + """ + return self.jobdb.getJobsList() + + def getActiveJobs(self): + r""" Returns a list of active jobs""" - return self.jobdb.get_active_jobs() - - def get_active_clients_list(self): - """ + return self.jobdb.getActiveJobs() + + def getActiveClientList(self): + r""" Returns a list of active clients. @@ -200,83 +187,82 @@ raise NotImplementedError - def get_killed_jobs_list(self): - """ - Returns a list of killed job jdicts. - """ - - killed_jobs = self.jobdb.get_killed_jobs_list() - return killed_jobs - - def get_next_job_id(self): - """ + def getKilledJobsList(self): + r""" + Returns a list of killed jobs. + """ + + killed_jobs = self.jobdb.getKilledJobsList() + return [job.pickle() for job in killed_jobs] + + def getNextJobID(self): + r""" Returns the next job id. """ - if self.LOG_LEVEL > 0: - log.msg('[DSage, get_next_job_id] Returning next job ID') + if self.log_level > 0: + log.msg('[DSage, getNextJobID] Returning next job ID') - return self.jobdb.get_next_job_id() - - def job_done(self, job_id, output, result, completed): - """ - job_done is called by the workers check_output method. - - Parameters: - job_id -- job id (str) + return self.jobdb.getJobID() + + def jobDone(self, jobID, output, result, completed, worker_info): + r""" + jobDone is called by the workers checkForJobOutput method. + + Parameters: + jobID -- job id (str) output -- the stdout from the worker (string) result -- the result from the client (compressed pickle string) result could be 'None' completed -- whether or not the job is completed (bool) - - """ - - if self.LOG_LEVEL > 0: - log.msg('[DSage, job_done] Job %s called back' % (job_id)) - if self.LOG_LEVEL > 3: - log.msg('[DSage, job_done] Output: %s ' % output) - log.msg('[DSage, job_done] completed: %s ' % completed) - - jdict = self.get_job_by_id(job_id) + worker_info -- ''.join(os.uname()) + + """ + + if self.log_level > 0: + log.msg('[DSage, jobDone] Job %s called back' % (jobID)) + if self.log_level > 2: + log.msg('[DSage, jobDone] Output: %s ' % output) + log.msg('[DSage, jobDone] Result: Some binary data...') + log.msg('[DSage, jobDone] completed: %s ' % completed) + log.msg('[DSage, jobDone] worker_info: %s ' % str(worker_info)) + + job = self.unpickle(self.getJobByID(jobID)) + + if self.log_level > 3: + log.msg('[DSage, jobDone] result type' , type(result)) + output = str(output) - if jdict['output'] is not None: # Append new output to existing output - jdict['output'] += output + if job.output is not None: # Append new output to existing output + job.output = job.output + output else: - jdict['output'] = output + job.output = output if completed: - jdict['result'] = result - jdict['status'] = 'completed' - - jdict['update_time'] = datetime.datetime.now() - - return self.jobdb.store_job(jdict) - - def job_failed(self, job_id, traceback): - """ - job_failed is called when a remote job fails. - - Parameters: - job_id -- the job id (str) + job.result = result + job.status = 'completed' + job.worker_info = worker_info + + return self.jobdb.storeJob(job) + + def jobFailed(self, jobID): + r""" + jobFailed is called when a remote job fails. + + Parameters: + jobID -- the job id (str) """ - job = expand_job(self.jobdb.get_job_by_id(job_id)) + job = self.jobdb.getJobByID(jobID) job.failures += 1 - job.output = traceback - - if job.failures > self.jobdb.job_failure_threshold: - job.status = 'failed' - else: - job.status = 'new' # Put job back in the queue - - if self.LOG_LEVEL > 1: - s = ['[DSage, job_failed] Job %s failed ' % (job_id), - '%s times. ' % (job.failures)] - log.msg(''.join(s)) - - return self.jobdb.store_job(job.reduce()) - - def kill_job(self, job_id, reason): - """ + job.status = 'new' # Put job back in the queue + + if self.log_level > 1: + log.msg('[DSage, jobFailed] Job %s failed' % jobID) + + self.jobdb.storeJob(job) + + def killJob(self, jobID, reason): + r""" Kills a job. @@ -285,17 +271,19 @@ """ - if job_id == None: - if self.LOG_LEVEL > 0: - log.msg('[DSage, kill_job] No such job id %s' % job_id) + job = self.unpickle(self.getJobByID(jobID)) + if job == None: + if self.log_level > 0: + log.msg('[DSage, killJob] No such job id') return None else: - self.jobdb.set_killed(job_id, killed=True) - if self.LOG_LEVEL > 0: - log.msg('Killed job %s' % (job_id)) + job.killed = True + self.jobdb.storeJob(job) + if self.log_level > 0: + log.msg('Job %s was killed because %s ' % (jobID, reason)) - return job_id - - def get_monitor_list(self): - """ + return jobID + + def getWorkerList(self): + r""" Returns a list of workers as a 3 tuple. @@ -305,16 +293,17 @@ """ - return self.monitordb.get_monitor_list() + + return worker_tracker.worker_list - def get_client_list(self): - """ + def getClientList(self): + r""" Returns a list of clients. """ - return self.clientdb.get_client_list() - - def get_cluster_speed(self): - """ + return client_tracker.client_list + + def getClusterSpeed(self): + r""" Returns an approximation of the total CPU speed of the cluster. @@ -322,5 +311,5 @@ cluster_speed = 0 - if self.LOG_LEVEL > 3: + if self.log_level > 3: log.msg(hostinfo_list) log.msg(len(hostinfo_list)) @@ -332,27 +321,12 @@ return cluster_speed - - def get_worker_count(self): - """ - Returns a list of busy and free workers. - - """ - - count = {} - free_workers = self.monitordb.get_worker_count(connected=True, busy=False) - working_workers = self.monitordb.get_worker_count(connected=True, busy=True) - - count['free'] = free_workers - count['working'] = working_workers - - return count - - def submit_host_info(self, h): - """ + + def submitHostInfo(self, h): + r""" Takes a dict of workers machine specs. """ - if self.LOG_LEVEL > 0: + if self.log_level > 0: log.msg(h) if len(hostinfo_list) == 0: @@ -362,225 +336,35 @@ if h['uuid'] not in h.values(): hostinfo_list.append(h) - - def generate_xml_stats(self): - """ - This method returns a an XML document to be consumed by the Dashboard - widget - - """ - - def create_gauge(doc): - gauge = doc.createElement('gauge') - doc.appendChild(gauge) - - return doc, gauge - - def add_totalAgentCount(doc, gauge): - totalAgentCount = doc.createElement('totalAgentCount') - gauge.appendChild(totalAgentCount) - working_workers = self.monitordb.get_worker_count(connected=True, - busy=True) - free_workers = self.monitordb.get_worker_count(connected=True, - busy=False) - disconnected_workers = self.monitordb.get_worker_count( - connected=False, - busy=False) - total_workers = (working_workers + - free_workers + - disconnected_workers) - count = doc.createTextNode(str(total_workers)) - totalAgentCount.appendChild(count) - - return doc, totalAgentCount - - def add_onlineAgentCount(doc, gauge): - onlineAgentCount = doc.createElement('onlineAgentCount') - gauge.appendChild(onlineAgentCount) - free_workers = self.monitordb.get_worker_count(connected=True, - busy=False) - busy_workers = self.monitordb.get_worker_count(connected=True, - busy=True) - count = doc.createTextNode(str(free_workers + busy_workers)) - onlineAgentCount.appendChild(count) - - return doc, onlineAgentCount - - def add_offlineAgentCount(doc, gauge): - offlineAgentCount = doc.createElement('offlineAgentCount') - gauge.appendChild(offlineAgentCount) - worker_count = self.monitordb.get_worker_count(connected=False, - busy=False) - count = doc.createTextNode(str(worker_count)) - offlineAgentCount.appendChild(count) - - return doc, offlineAgentCount - - def add_workingAgentCount(doc, gauge): - workingAgentCount = doc.createElement('workingAgentCount') - gauge.appendChild(workingAgentCount) - worker_count = self.monitordb.get_worker_count(connected=True, - busy=True) - count = doc.createTextNode(str(worker_count)) - workingAgentCount.appendChild(count) - - return doc, workingAgentCount - - def add_availableAgentCount(doc, gauge): - availableAgentCount = doc.createElement('availableAgentCount') - gauge.appendChild(availableAgentCount) - worker_count = self.monitordb.get_worker_count(connected=True, - busy=False) - count = doc.createTextNode(str(worker_count)) - availableAgentCount.appendChild(count) - - return doc, availableAgentCount - - def add_unavailableAgentCount(doc, gauge): - unavailableAgentCount = doc.createElement('unavailableAgentCount') - gauge.appendChild(unavailableAgentCount) - worker_count = self.monitordb.get_worker_count(connected=True, - busy=True) - count = doc.createTextNode(str(worker_count)) - unavailableAgentCount.appendChild(count) - - return doc, unavailableAgentCount - - def add_workingMegaHertz(doc, gauge): - workingMegaHertz = doc.createElement('workingMegaHertz') - gauge.appendChild(workingMegaHertz) - cpu_speed = self.monitordb.get_cpu_speed(connected=True, busy=True) - mhz = doc.createTextNode(str(cpu_speed)) - workingMegaHertz.appendChild(mhz) - - return doc, workingMegaHertz - - def add_availableProcessorCount(doc, gauge): - pass - - def add_unavailableProcessorCount(doc, gauge): - pass - - def add_onlineProcessorCount(doc, gauge): - onlineProcessorCount = doc.createElement('onlineProcessorCount') - gauge.appendChild(onlineProcessorCount) - cpu_count = self.monitordb.get_cpu_count(connected=True) - c = doc.createTextNode(str(cpu_count)) - onlineProcessorCount.appendChild(c) - - return doc, onlineProcessorCount - - def add_offlineProcessorCount(doc, gauge): - offlineProcessorCount = doc.createElement('offlineProcessorCount') - gauge.appendChild(offlineProcessorCount) - cpu_count = self.monitordb.get_cpu_count(connected=False) - c = doc.createTextNode(str(cpu_count)) - offlineProcessorCount.appendChild(c) - - return doc, offlineProcessorCount - - def add_workingProcessorCount(doc, gauge): - workingProcessorCount = doc.createElement('workingProcessorCount') - gauge.appendChild(workingProcessorCount) - worker_count = self.monitordb.get_cpu_count(connected=True) - pcount = doc.createTextNode(str(worker_count)) - workingProcessorCount.appendChild(pcount) - - return doc, workingProcessorCount - - def add_workingAgentPercentage(doc, gauge): - workingAgentPercentage = doc.createElement( - 'workingAgentPercentage') - gauge.appendChild(workingAgentPercentage) - working_workers = self.monitordb.get_worker_count(connected=True, - busy=True) - free_workers = self.monitordb.get_worker_count(connected=True, - busy=False) - disconnected_workers = self.monitordb.get_worker_count( - connected=False, - busy=False) - total_workers = (working_workers + - free_workers + - disconnected_workers) - - if total_workers != 0: - worker_percentage = float(working_workers / total_workers) * 100 - else: - worker_percentage = 0.0 - percentage = doc.createTextNode(str(worker_percentage)) - workingAgentPercentage.appendChild(percentage) - - return doc, workingAgentPercentage - - def add_date(doc, gauge): - date = datetime.datetime.now() - - year = doc.createElement('Year') - gauge.appendChild(year) - year.appendChild(doc.createTextNode(str(date.year))) - - seconds = doc.createElement('Seconds') - gauge.appendChild(seconds) - seconds.appendChild(doc.createTextNode(str(date.second))) - - minutes = doc.createElement('Minutes') - gauge.appendChild(minutes) - minutes.appendChild(doc.createTextNode(str(date.minute))) - - return doc, year, seconds, minutes - - doc = xml.dom.minidom.Document() - doc, gauge = create_gauge(doc) - - add_totalAgentCount(doc, gauge) - add_onlineAgentCount(doc, gauge) - add_offlineAgentCount(doc, gauge) - add_availableAgentCount(doc, gauge) - add_unavailableAgentCount(doc, gauge) - add_workingAgentCount(doc, gauge) - add_workingAgentPercentage(doc, gauge) - - add_onlineProcessorCount(doc, gauge) - add_offlineAgentCount(doc, gauge) - add_availableProcessorCount(doc, gauge) - add_unavailableProcessorCount(doc, gauge) - add_workingProcessorCount(doc, gauge) - add_workingMegaHertz(doc, gauge) - - add_date(doc, gauge) - s = cStringIO.StringIO() - doc.writexml(s, newl='\n') - - return s.getvalue() class DSageWorkerServer(DSageServer): - """ + r""" Exposes methods to workers. """ - def remote_get_job(self): - return DSageServer.get_job(self) - - def remote_job_done(self, job_id, output, result, completed, worker_info): - if not (isinstance(job_id, str) or isinstance(completed, bool)): - log.msg('BadType in remote_job_done') + def remote_getJob(self): + return DSageServer.getJob(self) + + def remote_jobDone(self, jobID, output, result, completed, worker_info): + if not (isinstance(jobID, str) or isinstance(completed, bool)): + log.msg('BadType in remote_jobDone') raise BadTypeError() - return DSageServer.job_done(self, job_id, output, result, + return DSageServer.jobDone(self, jobID, output, result, completed, worker_info) - def remote_job_failed(self, job_id, traceback): - if not isinstance(job_id, str): - log.msg('BadType in remote_job_failed') + def remote_jobFailed(self, jobID): + if not isinstance(jobID, str): + log.msg('BadType in remote_jobFailed') raise BadTypeError() - return DSageServer.job_failed(self, job_id, traceback) - - def remote_get_killed_jobs_list(self): - return DSageServer.get_killed_jobs_list(self) - - def remote_submit_host_info(self, hostinfo): + return DSageServer.jobFailed(self, jobID) + + def remote_getKilledJobsList(self): + return DSageServer.getKilledJobsList(self) + + def remote_submitHostInfo(self, hostinfo): if not isinstance(hostinfo, dict): - log.msg('BadType in remote_submit_host_info') + log.msg('BadType in remote_submitHostInfo') raise BadTypeError() - return DSageServer.submit_host_info(self, hostinfo) - + return DSageServer.submitHostInfo(self, hostinfo) + Index: age/dsage/server/tests/test_server.py =================================================================== --- sage/dsage/server/tests/test_server.py (revision 3866) +++ (revision ) @@ -1,185 +1,0 @@ -############################################################################ -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# This code is distributed in the hope that it will be useful, -# but WITHOUT ANY WARRANTY; without even the implied warranty of -# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -# General Public License for more details. -# -# The full text of the GPL is available at: -# -# http://www.gnu.org/licenses/ -############################################################################ - -import unittest -import datetime -import os -from glob import glob - -from sage.dsage.database.job import Job, expand_job -from sage.dsage.database.jobdb import JobDatabaseSQLite -from sage.dsage.database.monitordb import MonitorDatabase -from sage.dsage.database.clientdb import ClientDatabase -from sage.dsage.server.server import DSageServer - -class DSageServerTestCase(unittest.TestCase): - """ - Tests for DSageServer go here. - - """ - - def setUp(self): - self.jobdb = JobDatabaseSQLite(test=True) - self.monitordb = MonitorDatabase(test=True) - self.clientdb = ClientDatabase(test=True) - self.dsage_server = DSageServer(self.jobdb, - self.monitordb, - self.clientdb, - log_level=5) - for job in self.create_jobs(10): - self.dsage_server.submit_job(job.reduce()) - - def tearDown(self): - self.dsage_server.jobdb._shutdown() - files = glob('*.db*') - for file in files: - os.remove(file) - - def testget_job(self): - jdict = self.dsage_server.get_job() - self.assertEquals(type(jdict), dict) - job = expand_job(jdict) - self.assert_(isinstance(job, Job)) - - def testget_job_by_id(self): - job = Job() - job.code = '2+2' - jdict = self.dsage_server.submit_job(job.reduce()) - self.assertEquals(type(jdict['job_id']), str) - - def testget_job_result_by_id(self): - job = self.create_jobs(1)[0] - job = expand_job(self.dsage_server.get_job()) - job.result = 'test' - jdict = self.dsage_server.submit_job(job.reduce()) - self.assertEquals( - self.dsage_server.get_job_result_by_id(jdict['job_id']), - 'test') - - def testget_jobs_by_username(self): - self.assertEquals( - type(self.dsage_server.get_jobs_by_username('yqiang')), - list) - self.assertEquals( - len(self.dsage_server.get_jobs_by_username('test')), - 0) - - job = expand_job(self.dsage_server.get_job()) - job.username = 'testing123' - job.code = '' - jdict = self.dsage_server.submit_job(job.reduce()) - j = expand_job(self.dsage_server.get_jobs_by_username('testing123')[0]) - self.assertEquals(j.username, job.username) - - def testsubmit_job(self): - jobs = self.create_jobs(10) - for job in jobs: - jdict = self.dsage_server.submit_job(job.reduce()) - self.assertEquals(type(jdict), dict) - j = expand_job(self.dsage_server.get_job_by_id(jdict['job_id'])) - self.assert_(isinstance(j, Job)) - - def testget_all_jobs(self): - jobs = self.dsage_server.get_all_jobs() - self.assertEquals(len(jobs), 10) - - def testget_active_jobs(self): - jobs = self.dsage_server.get_all_jobs() - for job in jobs: - job = expand_job(job) - job.status = 'processing' - jdict = self.dsage_server.submit_job(job.reduce()) - jobs = self.dsage_server.get_active_jobs() - self.assert_(len(jobs) == 10) - for job in jobs: - job = expand_job(job) - self.assert_(isinstance(job, Job)) - self.assert_(job.status == 'processing') - self.assert_(job.update_time < datetime.datetime.now()) - - def testget_active_clients_list(self): - clients = self.dsage_server.get_client_list() - self.assertEquals(len(clients), 0) - self.assertEquals(type(clients), list) - - def testget_killed_jobs_list(self): - jobs = self.dsage_server.get_killed_jobs_list() - self.assertEquals(len(jobs), 0) - - jobs = self.dsage_server.get_all_jobs() - for job in jobs: - job = expand_job(job) - job.killed = True - self.dsage_server.submit_job(job.reduce()) - - jobs = self.dsage_server.get_killed_jobs_list() - self.assertEquals(len(jobs), 10) - - for job in jobs: - job = expand_job(job) - self.assert_(isinstance(job, Job)) - self.assertEquals(job.killed, True) - self.assert_(job.update_time < datetime.datetime.now()) - - def testjob_done(self): - job = expand_job(self.dsage_server.get_job()) - result = 'done' - output = 'done ' - completed = True - jdict = self.dsage_server.job_done(job.job_id, output, result, completed) - job = expand_job(self.dsage_server.get_job_by_id(jdict['job_id'])) - self.assertEquals(job.output, output) - self.assertEquals(job.result, result) - self.assertEquals(job.status, 'completed') - - job = expand_job(self.dsage_server.get_job()) - result = ['testing', '123'] - output = 'testing' - completed = False - jdict = self.dsage_server.job_done(job.job_id, output, result, completed) - job = expand_job(self.dsage_server.get_job_by_id(jdict['job_id'])) - self.assert_(isinstance(job.output, str)) - self.assert_(job.status != 'completed') - - def testjob_failed(self): - job = expand_job(self.dsage_server.get_job()) - self.dsage_server.job_failed(job.job_id, 'Failure') - job = expand_job(self.dsage_server.get_job_by_id(job.job_id)) - self.assertEquals(job.failures, 1) - self.assertEquals(job.output, 'Failure') - self.dsage_server.job_failed(job.job_id, 'Another Failure') - job = expand_job(self.dsage_server.get_job_by_id(job.job_id)) - self.assertEquals(job.failures, 2) - self.assertEquals(job.output, 'Another Failure') - - def testkill_job(self): - job = expand_job(self.dsage_server.get_job()) - reason = 'test' - id = self.dsage_server.kill_job(job.job_id, reason) - job = expand_job(self.dsage_server.get_job_by_id(id)) - self.assertEquals(job.killed, True) - - def create_jobs(self, n): - """This method creates n jobs. """ - - jobs = [] - for i in range(n): - jobs.append(Job(name='unittest', username='yqiang', code='2+2')) - - return jobs - Index: sage/dsage/server/worker_tracker.py =================================================================== --- sage/dsage/server/worker_tracker.py (revision 3866) +++ sage/dsage/server/worker_tracker.py (revision 2942) @@ -17,21 +17,21 @@ ############################################################################ -"""This is a dummy module that keeps a list of connected workers. """ +"""This is a dummy class that keeps a list of connected workers. """ worker_list = [] -def add(worker): - """ +def add(avatar): + r""" Adds an avatar to worker_list. """ - worker_list.append(worker) + worker_list.append(avatar) -def remove(worker): - """ +def remove(avatar): + r""" Removes the avatar from the worker_list. """ - worker_list.remove(worker) + worker_list.remove(avatar) Index: sage/dsage/tests/data/authorized_keys.db =================================================================== --- sage/dsage/tests/data/authorized_keys.db (revision 2885) +++ sage/dsage/tests/data/authorized_keys.db (revision 2885) @@ -0,0 +1,3 @@ +yi:AAAAB3NzaC1yc2EAAAABIwAAAQEAppDp75P57zx6XRCUFUjRh5HrtIKE2Xp6iO39rXALiQmXag+KvvcWL38bk3Vr/X1nAunRAbcudVMkfj05oEZKyhC/XHJ1zoNi/Yj9sqABSZITQeXuU2tftNY7bFQ+WldR3vOdJoItqRdP7yGpCmvd8wpeKex7rJ4+ZpMZCYCil2axdBEltTsoexvFFzDdC4Vrbol4zz+dcgYfEmum4Fm9ovp9QCwR+Ukyru9KA1oHXUZO8MvbLgwpdlvJaV/OffQ11PFFrYPVmFg5APqhpItVf5l1D5Z2rYjTIfvUm9XOHKr+tHFf/M2fSIs/zDseg86wBvKpKpxzFp6Tn8C7FB1CSQ== +admin:AAAAB3NzaC1yc2EAAAABIwAAAQEAppDp75P57zx6XRCUFUjRh5HrtIKE2Xp6iO39rXALiQmXag+KvvcWL38bk3Vr/X1nAunRAbcudVMkfj05oEZKyhC/XHJ1zoNi/Yj9sqABSZITQeXuU2tftNY7bFQ+WldR3vOdJoItqRdP7yGpCmvd8wpeKex7rJ4+ZpMZCYCil2axdBEltTsoexvFFzDdC4Vrbol4zz+dcgYfEmum4Fm9ovp9QCwR+Ukyru9KA1oHXUZO8MvbLgwpdlvJaV/OffQ11PFFrYPVmFg5APqhpItVf5l1D5Z2rYjTIfvUm9XOHKr+tHFf/M2fSIs/zDseg86wBvKpKpxzFp6Tn8C7FB1CSQ== +alex:AAAAB3NzaC1yc2EAAAABIwAAAQEAzeF0N+GaxdWvvKVRmRKwzknuygigpZHKSY35LF59aWX8yBF9ZkXWXIiWWaLv+OtmT/I3Vn9564WLFIZKD3AfhCV156uZ5398XSIdJAwQxD9c3S+I/iS9769kJsA0QmALbM3yvHat3x53skPWfdhyOeRuJInnnJwcTFTvX8VtnzMvMnYChfrj+9gJyPVO+5GTNkCeuieStvD5GrBYHI1l/UNAeCjjkcYjndVRXWNXjWlUBI1D3TcEW//6T8YBmH3XkJFly9/C0ZpDavJ9kmzung35utIyG6XHAl1T700a9D9u6oRTNdcdrlwb6YzleAaqBeCn+vrLi7FjspFpz83eZw== Index: sage/dsage/tests/test_server.py =================================================================== --- sage/dsage/tests/test_server.py (revision 2885) +++ sage/dsage/tests/test_server.py (revision 2885) @@ -0,0 +1,31 @@ +############################################################################ +# +# DSAGE: Distributed SAGE +# +# Copyright (C) 2006, 2007 Yi Qiang +# +# Distributed under the terms of the GNU General Public License (GPL) +# +# This code is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# General Public License for more details. +# +# The full text of the GPL is available at: +# +# http://www.gnu.org/licenses/ +############################################################################ + +#import unittest +#import os + +#class ServerTestCase(unittest.TestCase): +# def testgetAuthorizedKeys(self): +# cur = os.getcwd() +# os.chdir('../dsage/tests/data') +# authorized_keys = getAuthorizedKeys('authorized_keys.db') +# for username, key in authorized_keys.iteritems(): +# self.assert_(isinstance(username, str)) +# self.assert_(isinstance(key, str)) +# os.chdir(cur) +# Index: age/dsage/tests/testdoc.py =================================================================== --- sage/dsage/tests/testdoc.py (revision 3883) +++ (revision ) @@ -1,20 +1,0 @@ -"""nodoctest -These test that DSage is *really* working for normal users locally -on their system: - -WARNING: Currently these non-blocking startups leave processes -hanging around! - - sage: dsage.server(blocking=False) - sage: dsage.worker(blocking=False) - sage: d = DSage() - sage: sleep(0.5) - sage: a = d('2 + 3') - sage: a.wait() - sage: a - 5 - sage: v = [d('%s^2'%i) for i in range(100,103)] - sage: _ = [x.wait() for x in v] - sage: print v - [10000, 10201, 10404] -""" Index: sage/dsage/twisted/misc.py =================================================================== --- sage/dsage/twisted/misc.py (revision 3837) +++ sage/dsage/twisted/misc.py (revision 2940) @@ -18,10 +18,10 @@ import threading, sys +from twisted.internet import defer, reactor +from twisted.python.failure import Failure # This code is from # http://twistedmatrix.com/trac/ticket/1042 -def blocking_call_from_thread(func, *args, **kwargs): - from twisted.internet import defer, reactor - from twisted.python.failure import Failure +def blockingCallFromThread(func, *args, **kwargs): # print func # print args Index: sage/dsage/twisted/pb.py =================================================================== --- sage/dsage/twisted/pb.py (revision 3895) +++ sage/dsage/twisted/pb.py (revision 3024) @@ -18,27 +18,20 @@ from twisted.spread import pb -from twisted.spread import banana -banana.SIZE_LIMIT = 100*1024*1024 # 100 MegaBytes - from zope.interface import implements from twisted.cred import portal, credentials -from twisted.cred.credentials import ISSHPrivateKey -from twisted.cred.credentials import Anonymous from twisted.spread.interfaces import IJellyable from twisted.spread.pb import IPerspective, AsReferenceable from twisted.python import log +from twisted.internet import defer from sage.dsage.misc.hostinfo import HostInfo +from sage.dsage.server.server import DSageServer +import sage.dsage.server.client_tracker as client_tracker import sage.dsage.server.worker_tracker as worker_tracker -from sage.dsage.errors.exceptions import BadTypeError, BadJobError +from sage.dsage.errors.exceptions import BadTypeError pb.setUnjellyableForClass(HostInfo, HostInfo) class WorkerPBServerFactory(pb.PBServerFactory): - """ - This factory serves workers requests. - - """ - def __init__(self, root): pb.PBServerFactory.__init__(self, root) @@ -62,39 +55,29 @@ worker_tracker.remove((broker, host, port)) -class PBClientFactory(pb.PBClientFactory): - """ - Custom implementation of the PBClientFactory that supports logging in - with public key as well as anonymous credentials. - - """ - - def login(self, creds, mind=None): - if ISSHPrivateKey.providedBy(creds): - d = self.getRootObject() - d.addCallback(self._cbSendUsername, - creds.username, - creds.algName, - creds.blob, - creds.sigData, - creds.signature, - mind) - - return d - else: - d = self.getRootObject() - d.addCallback(self._cbAnonymousLogin, mind) - return d + + +class ClientPBClientFactory(pb.PBClientFactory): + def login(self, creds, client=None): + if not isinstance(creds, credentials.SSHPrivateKey): + return defer.fail(TypeError()) + + d = self.getRootObject() + d.addCallback(self._cbSendUsername, + creds.username, + creds.algName, + creds.blob, + creds.sigData, + creds.signature, + client) + + return d def _cbSendUsername(self, root, username, alg_name, blob, sig_data, - signature, mind): + signature, client): + d = root.callRemote("login", username, alg_name, blob, sig_data, - signature, mind) + signature, client) return d - def _cbAnonymousLogin(self, root, mind): - d = root.callRemote("login_anonymous", mind) - - return d - class _SSHKeyPortalRoot(pb._PortalRoot): def rootObject(self, broker): @@ -113,11 +96,5 @@ return d - - def remote_login_anonymous(self, mind): - d = self.portal.login(Anonymous(), mind, IPerspective) - d.addCallback(self._loggedIn) - - return d - + def _loggedIn(self, (interface, perspective, logout)): if not IJellyable.providedBy(perspective): @@ -128,242 +105,124 @@ class DefaultPerspective(pb.Avatar): + r""" + Custom implementation of pb.Avatar so we can keep track of the broker. + """ - Custom implementation of pb.Avatar so we can keep track of the broker. + + current_connections = 0 + + def perspectiveMessageReceived(self, broker, message, args, kw): + self.broker = broker + + return pb.Avatar.perspectiveMessageReceived(self, broker, + message, args, kw) + + def attached(self, avatar, mind): + self.current_connections += 1 + client_tracker.add((avatar, mind)) + + def detached(self, avatar, mind): + self.current_connections -= 1 + client_tracker.remove((avatar, mind)) + + +class UserPerspective(DefaultPerspective): + r""" + Defines the perspective of a regular user to the server. """ - + def __init__(self, DSageServer, avatarID): self.DSageServer = DSageServer self.avatarID = avatarID - self.connections = 0 log.msg('%s connected' % self.avatarID) - def perspectiveMessageReceived(self, broker, message, args, kw): - self.broker = broker - - return pb.Avatar.perspectiveMessageReceived(self, broker, - message, args, kw) - - def attached(self, avatar, mind): - self.connections += 1 - if isinstance(mind, tuple): - self.mind = mind - self.host_info = mind[1] - self.host_info['ip'] = mind[0].broker.transport.getPeer().host - self.host_info['port'] = mind[0].broker.transport.getPeer().port - uuid = self.host_info['uuid'] - if self.DSageServer.monitordb.get_monitor(uuid) is None: - self.DSageServer.monitordb.add_monitor(self.host_info) - self.DSageServer.monitordb.set_connected(uuid, connected=True) - else: - self.DSageServer.clientdb.update_login_time(self.avatarID) - self.DSageServer.clientdb.set_connected(self.avatarID, connected=True) - - def detached(self, avatar, mind): - self.connections -= 1 - log.msg('%s disconnected' % (self.avatarID)) - if isinstance(mind, tuple): - self.DSageServer.monitordb.set_connected(self.host_info['uuid'], connected=False) - else: - self.DSageServer.clientdb.set_connected(self.avatarID, connected=False) - -class AnonymousMonitorPerspective(DefaultPerspective): - """ - Defines the perspective of an anonymous worker. - - """ - - def __init__(self, DSageServer, avatarID): - DefaultPerspective.__init__(self, DSageServer, avatarID) - - def attached(self, avatar, mind): - self.connections += 1 - self.mind = mind - self.host_info = mind[1] - self.host_info['ip'] = mind[0].broker.transport.getPeer().host - self.host_info['port'] = mind[0].broker.transport.getPeer().port - uuid = self.host_info['uuid'] - if self.DSageServer.monitordb.get_monitor(uuid) is None: - self.DSageServer.monitordb.add_monitor(self.host_info) - self.DSageServer.monitordb.set_connected(uuid, connected=True) - self.DSageServer.monitordb.set_anonymous(uuid, anonymous=True) - - def detached(self, avatar, mind): - self.connections -= 1 - log.msg('%s disconnected' % (self.avatarID)) - self.DSageServer.monitordb.set_connected(self.host_info['uuid'], connected=False) - - def perspective_get_job(self): - """ - Returns jobs only marked as doable by anonymous workers. - - """ - - uuid = self.mind[1]['uuid'] - jdict = self.DSageServer.get_job(anonymous=True) - if jdict is not None: - self.DSageServer.set_job_uuid(jdict['job_id'], uuid) - self.DSageServer.set_busy(uuid, busy=True) - else: - self.DSageServer.set_busy(uuid, busy=False) - - return jdict - - def perspective_get_killed_jobs_list(self): - return self.DSageServer.get_killed_jobs_list() - - - def perspective_job_failed(self, job_id, traceback): - if not isinstance(job_id, str): - log.msg('Bad job_id [%s] passed to perspective_job_failed' % (job_id)) - raise BadTypeError() - - uuid = self.mind[1]['uuid'] - self.DSageServer.set_busy(uuid, busy=False) - - return self.DSageServer.job_failed(job_id, traceback) - - def perspective_job_done(self, job_id, output, result, completed): - if not (isinstance(job_id, str) or isinstance(completed, bool)): - log.msg('Bad job_id passed to perspective_job_done') - log.msg('job_id: %s' % (job_id)) - log.msg('output: %s' % (output)) - log.msg('completed: %s' % (completed)) - raise BadTypeError() - if completed: - uuid = self.mind[1]['uuid'] - self.DSageServer.set_busy(uuid, busy=False) - - return self.DSageServer.job_done(job_id, output, result, completed) - - def perspective_submit_host_info(self, hostinfo): - if not isinstance(hostinfo, dict): - raise BadTypeError() - return self.DSageServer.submit_host_info(hostinfo) - -class MonitorPerspective(AnonymousMonitorPerspective): - """ - Defines the perspective of an authenticated worker to the server. - - """ - def __init__(self, DSageServer, avatarID): - DefaultPerspective.__init__(self, DSageServer, avatarID) - - def attached(self, avatar, mind): - self.connections += 1 - self.mind = mind - self.host_info = mind[1] - self.host_info['ip'] = mind[0].broker.transport.getPeer().host - self.host_info['port'] = mind[0].broker.transport.getPeer().port - uuid = self.host_info['uuid'] - if self.DSageServer.monitordb.get_monitor(uuid) is None: - self.DSageServer.monitordb.add_monitor(self.host_info) - self.DSageServer.monitordb.set_connected(uuid, connected=True) - self.DSageServer.monitordb.set_anonymous(uuid, anonymous=False) - - def perspective_get_job(self): - """ - Returns jobs to authenticated workers. - - """ - - uuid = self.mind[1]['uuid'] - jdict = self.DSageServer.get_job(anonymous=False) - if jdict is not None: - self.DSageServer.set_job_uuid(jdict['job_id'], uuid) - self.DSageServer.set_busy(uuid, busy=True) - else: - self.DSageServer.set_busy(uuid, busy=False) - - return jdict - -class UserPerspective(DefaultPerspective): - """ - Defines the perspective of a regular user to the server. - - """ - def __init__(self, DSageServer, avatarID): - DefaultPerspective.__init__(self, DSageServer, avatarID) - - def perspective_get_job_by_id(self, job_id): - if not isinstance(job_id, str): - log.msg('Bad job_id [%s] passed to get_job_by_id' % (job_id)) - raise BadTypeError() - # log.msg('Returning job %s to %s' % (job_id, self.avatarID)) - job = self.DSageServer.get_job_by_id(job_id) + def perspective_getJob(self): + return self.DSageServer.getJob() + + def perspective_getNextJobID(self): + job_id = self.DSageServer.getNextJobID() + + return job_id + + def perspective_getJobByID(self, jobID): + if not isinstance(jobID, str): + raise BadTypeError() + print 'Bad jobID passed to getJobByID' + log.msg('Returning job %s to %s' % (jobID, self.avatarID)) + job = self.DSageServer.getJobByID(jobID) return job - def perspective_get_jobs_by_username(self, username, active=True): - if not (isinstance(username, str)): - log.msg('Bad username [%s] passed to perspective_get_jobs_by_username' % (username)) - raise BadTypeError() - - jobs = self.DSageServer.get_jobs_by_username(username, active) + def perspective_getJobsByAuthor(self, author, job_name, is_active): + if not (isinstance(author, str) or + isinstance(is_active, bool) or + isinstance(job_name, str)): + print 'Bad jobID passed to perspective_getJobsByAuthor' + raise BadTypeError() + + jobs = self.DSageServer.getJobsByAuthor(author, job_name, is_active) return jobs - def perspective_get_job_result_by_id(self, job_id): - if not isinstance(job_id, str): - log.msg('Bad job_id [%s] passed to perspective_get_job_result_by_id' % (job_id)) - raise BadTypeError() - - return self.DSageServer.get_job_result_by_id(job_id) - - def perspective_get_job_output_by_id(self, job_id): - if not isinstance(job_id, str): - log.msg('Bad job_id [%s] passed to get_job_output_by_id' % (job_id)) - raise BadTypeError() - - return self.DSageServer.get_job_output_by_id(job_id) - - def perspective_sync_job(self, job_id): - if not isinstance(job_id, str): + def perspective_getJobResultByID(self, jobID): + if not isinstance(jobID, str): + print 'Bad jobID passed to perspective_getJobResultByID' + raise BadTypeError() + + return self.DSageServer.getJobResultByID(jobID) + + def perspective_getJobOutputByID(self, jobID): + if not isinstance(jobID, str): + print 'Bad jobID passed to getJobOutputByID' + raise BadTypeError() + + return self.DSageServer.getJobOutputByID(jobID) + + def perspective_syncJob(self, jobID): + if not isinstance(jobID, str): return None - return self.DSageServer.sync_job(job_id) - - def perspective_submit_job(self, jdict): - if jdict is None: - raise BadJobError() - if jdict['username'] != self.avatarID: - log.msg('username does not match credentials') - log.msg('claim: %s' % jdict['username']) - log.msg('actual: %s' % self.avatarID) - raise BadJobError() - - return self.DSageServer.submit_job(jdict) - - def perspective_kill_job(self, job_id, reason=None): - if not isinstance(job_id, str): - log.msg('Bad job_id [%s] passed to perspective_kill_job' % job_id) - raise BadTypeError() - - return self.DSageServer.kill_job(job_id, reason) - - def perspective_get_cluster_speed(self): - return self.DSageServer.get_cluster_speed() - - def perspective_get_monitor_list(self): - # return [x[1] for x in self.DSageServer.get_worker_list()] - return self.DSageServer.get_monitor_list() - - def perspective_get_client_list(self): - return self.DSageServer.get_client_list() - - def perspective_get_worker_count(self): - return self.DSageServer.get_worker_count() - - def perspective_submit_host_info(self, hostinfo): - if not isinstance(hostinfo, dict): - raise BadTypeError() - return self.DSageServer.submit_host_info(hostinfo) - - def perspective_get_killed_jobs_list(self): - return self.DSageServer.get_killed_jobs_list() - + return self.DSageServer.syncJob(jobID) + + def perspective_submitJob(self, pickled_job): + return self.DSageServer.submitJob(pickled_job) + + def perspective_jobDone(self, jobID, output, result, + completed, worker_info): + if not (isinstance(jobID, str) or isinstance(completed, bool)): + print 'Bad jobID passed to perspective_jobDone' + raise BadTypeError() + + return self.DSageServer.jobDone(jobID, output, result, + completed, worker_info) + + def perspective_jobFailed(self, jobID): + if not isinstance(jobID, str): + print 'Bad jobID passed to perspective_jobFailed' + raise BadTypeError() + + return self.DSageServer.jobFailed(jobID) + + def perspective_killJob(self, jobID, reason=None): + if not isinstance(jobID, str): + print 'Bad jobID passed to perspective_killJob' + raise BadTypeError() + + return self.DSageServer.killJob(jobID, reason) + + def perspective_getClusterSpeed(self): + return self.DSageServer.getClusterSpeed() + + def perspective_getWorkerList(self): + return [x[1:] for x in self.DSageServer.getWorkerList()] + + def perspective_getClientList(self): + return [avatar[0].avatarID for avatar in + self.DSageServer.getClientList()] + class AdminPerspective(UserPerspective): - """ + r""" Defines the perspective of the admin. @@ -372,5 +231,5 @@ def __init__(self, DSageServer, avatarID): UserPerspective.__init__(self, DSageServer, avatarID) - + class Realm(object): implements(portal.IRealm) @@ -379,16 +238,13 @@ self.DSageServer = DSageServer - def requestAvatar(self, avatarID, mind, *interfaces): + def requestAvatar(self, avatarID, mind, *interfaces): if not pb.IPerspective in interfaces: raise NotImplementedError, "No supported avatar interface." else: if avatarID == 'admin': - avatar = AdminPerspective(self.DSageServer, avatarID) - elif avatarID == 'Anonymous' and mind: - avatar = AnonymousMonitorPerspective(self.DSageServer, avatarID) - elif mind: - avatar = MonitorPerspective(self.DSageServer, avatarID) + avatar = AdminPerspective(self.DSageServer) else: avatar = UserPerspective(self.DSageServer, avatarID) avatar.attached(avatar, mind) - return pb.IPerspective, avatar, lambda a=avatar:a.detached(avatar, mind) + return pb.IPerspective, avatar, lambda a=avatar:a.detached(avatar, + mind) Index: sage/dsage/twisted/pubkeyauth.py =================================================================== --- sage/dsage/twisted/pubkeyauth.py (revision 3898) +++ sage/dsage/twisted/pubkeyauth.py (revision 2925) @@ -1,9 +1,9 @@ ############################################################################ -# -# DSAGE: Distributed SAGE -# -# Copyright (C) 2006, 2007 Yi Qiang -# -# Distributed under the terms of the GNU General Public License (GPL) +# +# DSAGE: Distributed SAGE +# +# Copyright (C) 2006, 2007 Yi Qiang +# +# Distributed under the terms of the GNU General Public License (GPL) # # This code is distributed in the hope that it will be useful, @@ -22,32 +22,18 @@ from twisted.conch.ssh import keys from twisted.cred import checkers, credentials -from twisted.cred.credentials import IAnonymous from zope.interface import implements from twisted.internet import defer -from twisted.python import log -from twisted.spread import pb - -from sage.dsage.database.clientdb import ClientDatabase -from sage.dsage.errors.exceptions import AuthenticationError class PublicKeyCredentialsChecker(object): - """ - This class provides authentication checking using ssh public keys. - - """ - implements(checkers.ICredentialsChecker) - credentialInterfaces = (credentials.ISSHPrivateKey, credentials.IAnonymous) - + credentialInterfaces = (credentials.ISSHPrivateKey,) + def __init__(self, pubkeydb): self.authorizedKeys = self.getAuthorizedKeys(pubkeydb) - + def requestAvatarId(self, credentials): - if IAnonymous.providedBy(credentials): - return 'Anonymous' - # read the authentication table to make sure we have a fresh copy self.authorizedKeys = self.getAuthorizedKeys(self.file_name) - + if self.authorizedKeys.has_key(credentials.username): userKey = self.authorizedKeys[credentials.username] @@ -56,5 +42,5 @@ if not credentials.signature: return defer.fail(error.ValidPublicKey()) - + pubKey = keys.getPublicKeyObject(data=credentials.blob) if keys.verifySignature(pubKey, credentials.signature, @@ -65,8 +51,8 @@ else: return defer.fail(error.ConchError("Invalid username.")) - + def getAuthorizedKeys(self, file_name): self.file_name = file_name - authorized_keys = {} + authorized_keys = {} try: f = open(file_name) @@ -78,45 +64,35 @@ except: raise - + return authorized_keys class PublicKeyCredentialsCheckerDB(object): implements(checkers.ICredentialsChecker) - credentialInterfaces = (credentials.ISSHPrivateKey, credentials.IAnonymous) - - def __init__(self, clientdb): - if not isinstance(clientdb, ClientDatabase): - raise TypeError - self.clientdb = clientdb - + credentialInterfaces = (credentials.ISSHPrivateKey,) + + def __init__(self, userdb): + self.userdb = userdb + + def getUser(self, username): + if not self.userdb.has_key('username'): + return False + return self.userdb[username] + def requestAvatarId(self, credentials): - if IAnonymous.providedBy(credentials): - return 'Anonymous' - try: - user, key = self.get_user(credentials.username) - except TypeError: - log.msg("Invalid username: '%s'" % credentials.username) - return defer.fail(AuthenticationError('Login failed.')) + user = self.getUser(credentials.username) if user: - if not credentials.blob == base64.decodestring(key): - log.msg('Invalid key for user %s' % (credentials.username)) - return defer.fail(AuthenticationError('Login failed.')) + userKey = user['public_key'] + if not credentials.blob == base64.decodestring(userKey): + return defer.fail(error.ConchError("Invalid key.")) if not credentials.signature: - log.msg('No signature for user %s ' % (credentials.username)) - return defer.fail(AuthenticationError('Login failed.')) - pub_key = keys.getPublicKeyObject(data=credentials.blob) - if keys.verifySignature(pub_key, credentials.signature, + return defer.fail(error.ValidPublicKey()) + + pubKey = keys.getPublicKeyObject(data=credentials.blob) + if keys.verifySignature(pubKey, credentials.signature, credentials.sigData): - # If we get to this stage, it means the user is already - # logged in - self.clientdb.update_login_time(credentials.username) return credentials.username else: - log.msg('Invalid signature.') - return defer.fail(AuthenticationError('Login failed.')) + return defer.fail(error.ConchError("Invalid signature.")) else: - log.msg('Invalid username.') - return defer.fail(AuthenticationError('Login failed.')) - - def get_user(self, username): - return self.clientdb.get_user_and_key(username) + return defer.fail(error.ConchError("Invalid username.")) + Index: sage/dsage/twisted/tests/test_pb.py =================================================================== --- sage/dsage/twisted/tests/test_pb.py (revision 2964) +++ sage/dsage/twisted/tests/test_pb.py (revision 2964) @@ -0,0 +1,184 @@ +############################################################################ +# +# DSAGE: Distributed SAGE +# +# Copyright (C) 2006, 2007 Yi Qiang +# +# Distributed under the terms of the GNU General Public License (GPL) +# +# This code is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# General Public License for more details. +# +# The full text of the GPL is available at: +# +# http://www.gnu.org/licenses/ +############################################################################ + +import unittest +import datetime +import os +from glob import glob +from random import randint +from cPickle import dumps, loads +import zlib + +from sage.dsage.database.job import Job +from sage.dsage.database.jobdb import JobDatabaseZODB +from sage.dsage.server.server import DSageServer + +class DSageTestCase(unittest.TestCase): + def unpickle(self, pickled_job): + return loads(zlib.decompress(pickled_job)) + + def setUp(self): + self.jobdb = JobDatabaseZODB(test=True) + self.dsage_server = DSageServer(self.jobdb, log_level=5) + for job in self.createJobs(10): + self.dsage_server.jobdb.newJob(job) + + def tearDown(self): + self.dsage_server.jobdb._shutdown() + files = glob('*.db*') + for file in files: + os.remove(file) + + def testgetJob(self): + pickled_job = self.dsage_server.getJob() + self.assertEquals(type(pickled_job), str) + job = self.unpickle(pickled_job) + self.assert_(isinstance(job, Job)) + + def testgetJobByID(self): + job = self.createJobs(1) + for j in job: + jobID = self.jobdb.storeJob(j) + self.assert_(isinstance(jobID, str)) + + def testgetJobResultsByID(self): + job = self.unpickle(self.dsage_server.getJob()) + job.result = 'test' + job.file = '' + id = self.dsage_server.submitJob(job.pickle()) + self.assert_(self.dsage_server.getJobResultByID(id) == 'test') + + def testgetJobsByAuthor(self): + self.assert_(isinstance( + self.dsage_server.getJobsByAuthor('Yi Qiang', + 'unittest', + True), list)) + + self.assert_(len(self.dsage_server.getJobsByAuthor('test', + False, + None)) == 0) + + job = self.unpickle(self.dsage_server.getJob()) + job.author = 'test' + job.file = '' + id = self.dsage_server.submitJob(job.pickle()) + self.assert_(self.dsage_server.getJobsByAuthor('test', + False, + None)[0].author == 'test') + + def testsubmitJob(self): + jobs = self.createJobs(10) + for job in jobs: + job.file = "" + id = self.dsage_server.submitJob(job.pickle()) + self.assertEquals(type(id), str) + j = self.unpickle(self.dsage_server.getJobByID(id)) + self.assert_(isinstance(j, Job)) + + def testgetJobsList(self): + jobs = self.dsage_server.getJobsList() + self.assertEquals(len(jobs), 10) + for i in xrange(len(jobs)-1): + self.assert_(isinstance(jobs[i], Job)) + self.assert_(jobs[i].num < jobs[i+1].num) + + def testgetActiveJobs(self): + jobs = self.dsage_server.getJobsList() + for job in jobs: + job.status = 'processing' + id = self.dsage_server.submitJob(job.pickle()) + jobs = self.dsage_server.getActiveJobs() + self.assert_(len(jobs) == 10) + for job in jobs: + self.assert_(isinstance(job, Job)) + self.assert_(job.status == 'processing') + self.assert_(job.updated_time < datetime.datetime.now()) + + def testgetActiveClientsList(self): + pass + + def testgetKilledJobsList(self): + jobs = self.dsage_server.getKilledJobsList() + self.assertEquals(len(jobs), 0) + + jobs = self.dsage_server.getJobsList() + for job in jobs: + job.killed = True + self.dsage_server.submitJob(job.pickle()) + + jobs = self.dsage_server.getKilledJobsList() + self.assertEquals(len(jobs), 10) + + for job in jobs: + job = self.unpickle(job) + self.assert_(isinstance(job, Job)) + self.assertEquals(job.killed, True) + self.assert_(job.updated_time < datetime.datetime.now()) + + def testgetNextJobID(self): + id = self.dsage_server.getNextJobID() + self.assertEquals(type(id), str) + self.assert_(id != self.dsage_server.getNextJobID()) + + def testjobDone(self): + job = self.unpickle(self.dsage_server.getJob()) + result = 'done' + output = 'done ' + completed = True + id = self.dsage_server.jobDone(job.id, output, result, completed, + ('yi@test', 'no info provided')) + job = self.unpickle(self.dsage_server.getJobByID(id)) + self.assertEquals(job.output, output) + self.assertEquals(job.result, result) + self.assertEquals(job.status, 'completed') + + job = self.unpickle(self.dsage_server.getJob()) + result = ['testing', '123'] + output = 'testing' + completed = False + id = self.dsage_server.jobDone(job.id, output, result, completed, + ('yi@test', 'no info provided')) + job = self.unpickle(self.dsage_server.getJobByID(id)) + self.assert_(isinstance(job.output, str)) + self.assert_(job.status != 'completed') + + def testjobFailed(self): + job = self.unpickle(self.dsage_server.getJob()) + self.dsage_server.jobFailed(job.id) + job = self.unpickle(self.dsage_server.getJobByID(job.id)) + self.assertEquals(job.failures, 1) + self.dsage_server.jobFailed(job.id) + job = self.unpickle(self.dsage_server.getJobByID(job.id)) + self.assertEquals(job.failures, 2) + + def testkillJob(self): + job = self.unpickle(self.dsage_server.getJob()) + reason = 'test' + id = self.dsage_server.killJob(job.id, reason) + job = self.unpickle(self.dsage_server.getJobByID(id)) + self.assertEquals(job.killed, True) + + def createJobs(self, n): + """This method creates n jobs. """ + + jobs = [] + for i in range(n): + jobs.append(Job(name='unittest', author='Yi Qiang')) + + return jobs + Index: sage/dsage/twisted/tests/test_pubkeyauth.py =================================================================== --- sage/dsage/twisted/tests/test_pubkeyauth.py (revision 3905) +++ sage/dsage/twisted/tests/test_pubkeyauth.py (revision 2944) @@ -27,14 +27,12 @@ from twisted.cred import portal, credentials from twisted.conch.ssh import keys +import twisted.conch from sage.dsage.twisted.pb import Realm from sage.dsage.server.server import DSageServer from sage.dsage.twisted.pb import _SSHKeyPortalRoot -from sage.dsage.twisted.pb import PBClientFactory -from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsCheckerDB -from sage.dsage.database.jobdb import JobDatabaseSQLite -from sage.dsage.database.monitordb import MonitorDatabase -from sage.dsage.database.clientdb import ClientDatabase -from sage.dsage.errors.exceptions import AuthenticationError +from sage.dsage.twisted.pb import ClientPBClientFactory +from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsChecker +from sage.dsage.database.jobdb import JobDatabaseZODB DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') @@ -47,4 +45,5 @@ LOG_FILE = config.get('server_log', 'log_file') SSL = config.getint('ssl', 'ssl') + WORKER_PORT = config.getint('server', 'worker_port') CLIENT_PORT = config.getint('server', 'client_port') PUBKEY_DATABASE = os.path.expanduser(config.get('auth', @@ -68,21 +67,14 @@ class PublicKeyCredentialsCheckerTest(unittest.TestCase): - def setUp(self): - self.jobdb = JobDatabaseSQLite(test=True) - self.monitordb = MonitorDatabase(test=True) - self.clientdb = ClientDatabase(test=True) - self.dsage_server = DSageServer(self.jobdb, - self.monitordb, - self.clientdb, - log_level=5) - self.realm = Realm(self.dsage_server) - self.p = _SSHKeyPortalRoot(portal.Portal(Realm(self.dsage_server))) - self.clientdb = ClientDatabase(test=True) - self.p.portal.registerChecker( - PublicKeyCredentialsCheckerDB(self.clientdb)) + def setUp(self): + self.jobdb = JobDatabaseZODB(test=True) + self.dsage = DSageServer(self.jobdb, log_level=5) + self.realm = Realm(self.dsage) + self.p = _SSHKeyPortalRoot(portal.Portal(Realm(self.dsage))) + self.p.portal.registerChecker(PublicKeyCredentialsChecker(PUBKEY_DATABASE)) self.client_factory = pb.PBServerFactory(self.p) self.hostname = 'localhost' - self.r = reactor.listenTCP(0, self.client_factory) - self.port = self.r.getHost().port + self.port = CLIENT_PORT + self.r = reactor.listenTCP(CLIENT_PORT, self.client_factory) # public key authentication information @@ -102,10 +94,5 @@ self.data, self.signature) - c = ConfigParser.ConfigParser() - c.read(os.path.join(DSAGE_DIR, 'client.conf')) - username = c.get('auth', 'username') - pubkey_file = c.get('auth', 'pubkey_file') - self.clientdb.add_user(username, pubkey_file) - + def tearDown(self): self.connection.disconnect() @@ -117,10 +104,10 @@ def testLogin(self): - factory = PBClientFactory() + """Tests the login method. """ + factory = ClientPBClientFactory() self.connection = reactor.connectTCP(self.hostname, self.port, factory) d = factory.login(self.creds, None) d.addCallback(self._LoginConnected) - return d @@ -129,5 +116,5 @@ def testBadLogin(self): - factory = PBClientFactory() + factory = ClientPBClientFactory() self.connection = reactor.connectTCP(self.hostname, self.port, factory) @@ -138,5 +125,5 @@ def testBadLogin2(self): - factory = PBClientFactory() + factory = ClientPBClientFactory() self.connection = reactor.connectTCP(self.hostname, self.port, factory) bad_creds = credentials.SSHPrivateKey('this user name should not exit', @@ -150,8 +137,8 @@ def _BadLoginFailure(self, failure): - self.assertEquals(failure.type, str(AuthenticationError)) + self.assertEquals(failure.type, str(twisted.conch.error.ConchError)) def testBadLogin3(self): - factory = PBClientFactory() + factory = ClientPBClientFactory() self.connection = reactor.connectTCP(self.hostname, self.port, factory) bad_creds = credentials.SSHPrivateKey(self.username, Index: sage/dsage/twisted/tests/test_remote.py =================================================================== --- sage/dsage/twisted/tests/test_remote.py (revision 3905) +++ sage/dsage/twisted/tests/test_remote.py (revision 2944) @@ -23,5 +23,4 @@ import cPickle import zlib -import uuid from twisted.trial import unittest @@ -30,17 +29,14 @@ from twisted.cred import portal, credentials from twisted.conch.ssh import keys -from twisted.python import log from sage.dsage.twisted.pb import Realm from sage.dsage.server.server import DSageServer from sage.dsage.twisted.pb import _SSHKeyPortalRoot -from sage.dsage.twisted.pb import PBClientFactory -from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsCheckerDB -from sage.dsage.database.jobdb import JobDatabaseSQLite -from sage.dsage.database.monitordb import MonitorDatabase -from sage.dsage.database.clientdb import ClientDatabase +from sage.dsage.twisted.pb import ClientPBClientFactory +from sage.dsage.twisted.pubkeyauth import PublicKeyCredentialsChecker +from sage.dsage.database.jobdb import JobDatabaseZODB from sage.dsage.database.job import Job from sage.dsage.errors.exceptions import BadJobError -from sage.dsage.misc.hostinfo import ClassicHostInfo + DSAGE_DIR = os.path.join(os.getenv('DOT_SAGE'), 'dsage') @@ -53,6 +49,8 @@ LOG_FILE = config.get('server_log', 'log_file') SSL = config.getint('ssl', 'ssl') + WORKER_PORT = config.getint('server', 'worker_port') CLIENT_PORT = config.getint('server', 'client_port') - PUBKEY_DATABASE = os.path.expanduser(config.get('auth', 'pubkey_database')) + PUBKEY_DATABASE = os.path.expanduser(config.get('auth', + 'pubkey_database')) conf_file = os.path.join(DSAGE_DIR, 'client.conf') @@ -65,22 +63,7 @@ PRIVKEY_FILE = os.path.expanduser(config.get('auth', 'privkey_file')) PUBKEY_FILE = os.path.expanduser(config.get('auth', 'pubkey_file')) - - conf_file = os.path.join(DSAGE_DIR, 'worker.conf') - config = ConfigParser.ConfigParser() - config.read(conf_file) - if len(config.get('uuid', 'id')) != 36: - config.set('uuid', 'id', str(uuid.uuid1())) - f = open(conf_file, 'w') - config.write(f) - UUID = config.get('uuid', 'id') - WORKERS = config.getint('general', 'workers') - -except Exception, msg: - log.msg(msg) +except: raise # End reading configuration -hf = ClassicHostInfo().host_info -hf['uuid'] = UUID -hf['workers'] = WORKERS Data = ''.join([chr(i) for i in [random.randint(65, 123) for n in @@ -88,29 +71,18 @@ class ClientRemoteCallsTest(unittest.TestCase): - """ - Tests of remote procedure calls go here. - - """ - def unpickle(self, pickled_job): return cPickle.loads(zlib.decompress(pickled_job)) def setUp(self): - self.jobdb = JobDatabaseSQLite(test=True) - self.monitordb = MonitorDatabase(test=True) - self.clientdb = ClientDatabase(test=True) - self.dsage_server = DSageServer(self.jobdb, - self.monitordb, - self.clientdb, - log_level=5) - self.realm = Realm(self.dsage_server) - self.p = _SSHKeyPortalRoot(portal.Portal(self.realm)) - self.clientdb = ClientDatabase(test=True) - self.p.portal.registerChecker(PublicKeyCredentialsCheckerDB(self.clientdb)) + self.jobdb = JobDatabaseZODB(test=True) + self.dsage = DSageServer(self.jobdb, log_level=5) + self.realm = Realm(self.dsage) + self.p = _SSHKeyPortalRoot(portal.Portal(Realm(self.dsage))) + self.p.portal.registerChecker(PublicKeyCredentialsChecker(PUBKEY_DATABASE)) self.client_factory = pb.PBServerFactory(self.p) self.hostname = 'localhost' - self.server = reactor.listenTCP(0, self.client_factory) - self.port = self.server.getHost().port - + self.port = CLIENT_PORT + self.r = reactor.listenTCP(CLIENT_PORT, self.client_factory) + # public key authentication information self.username = USERNAME @@ -129,10 +101,5 @@ self.data, self.signature) - c = ConfigParser.ConfigParser() - c.read(os.path.join(DSAGE_DIR, 'client.conf')) - username = c.get('auth', 'username') - pubkey_file = c.get('auth', 'pubkey_file') - self.clientdb.add_user(username, pubkey_file) - + def tearDown(self): self.connection.disconnect() @@ -141,17 +108,55 @@ for file in files: os.remove(file) - return self.server.stopListening() - - def _catch_failure(self, failure, *args): - log.msg("Error: ", failure.getErrorMessage()) - log.msg("Traceback: ", failure.printTraceback()) - + return self.r.stopListening() + + def testremoteGetJobEmptyQueue(self): + """Tests perspective_getJob on an empty database""" + factory = ClientPBClientFactory() + self.connection = reactor.connectTCP(self.hostname, self.port, + factory) + + d = factory.login(self.creds, None) + d.addCallback(self._LoginConnected) + return d + + def _LoginConnected(self, remoteobj): + d = remoteobj.callRemote('getJob') + d.addCallback(self._gotNoJob) + return d + + def _gotNoJob(self, job): + self.assertEquals(job, None) + + def testremoteGetJob(self): + """Tests perspective_getJob""" + jobs = self.createJobs(10) + for job in jobs: + self.jobdb.newJob(job) + + factory = ClientPBClientFactory() + self.connection = reactor.connectTCP(self.hostname, self.port, + factory) + + d = factory.login(self.creds, None) + d.addCallback(self._LoginConnected1) + return d + + def _LoginConnected1(self, remoteobj): + d = remoteobj.callRemote('getJob') + d.addCallback(self._gotJob) + return d + + def _gotJob(self, job): + self.assert_(isinstance(job, str)) + import cPickle, zlib + job = self.unpickle(job) + self.assert_(isinstance(job, Job)) + def testremoteSubmitJob(self): - """tests perspective_submit_job""" - jobs = self.create_jobs(1) - - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, - self.port, + """tests perspective_submitJob""" + jobs = self.createJobs(1) + + factory = ClientPBClientFactory() + self.connection = reactor.connectTCP(self.hostname, self.port, factory) @@ -162,19 +167,17 @@ def _LoginConnected2(self, remoteobj, jobs): job = jobs[0] - job.code = "2+2" - d = remoteobj.callRemote('submit_job', job.reduce()) - d.addCallback(self._got_jdict) - return d - - def _got_jdict(self, jdict): - self.assertEquals(type(jdict), dict) - self.assertEquals(type(jdict['job_id']), str) + job.file = "" + d = remoteobj.callRemote('submitJob', job.pickle()) + d.addCallback(self._gotJobID) + return d + + def _gotJobID(self, jobID): + self.assertEquals(type(jobID), str) def testremoteSubmitBadJob(self): - """tests perspective_submit_job""" - - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, - self.port, + """tests perspective_submitJob""" + + factory = ClientPBClientFactory() + self.connection = reactor.connectTCP(self.hostname, self.port, factory) @@ -184,5 +187,5 @@ def _LoginConnected3(self, remoteobj): - d = remoteobj.callRemote('submit_job', None) + d = remoteobj.callRemote('submitJob', None) d.addErrback(self._gotNoJobID) return d @@ -191,171 +194,13 @@ self.assertEquals(BadJobError, failure.check(BadJobError)) - def create_jobs(self, n): + def createJobs(self, n): """This method creates n jobs. """ jobs = [] for i in range(n): - jobs.append(Job(name='unittest', username=self.username)) + jobs.append(Job(name='unittest', author='Yi Qiang')) return jobs -class MonitorRemoteCallsTest(unittest.TestCase): - """ - Tests remote calls for monitors. - - """ - - def setUp(self): - self.jobdb = JobDatabaseSQLite(test=True) - self.monitordb = MonitorDatabase(test=True) - self.clientdb = ClientDatabase(test=True) - self.dsage_server = DSageServer(self.jobdb, - self.monitordb, - self.clientdb, - log_level=5) - self.realm = Realm(self.dsage_server) - self.p = _SSHKeyPortalRoot(portal.Portal(self.realm)) - self.p.portal.registerChecker( - PublicKeyCredentialsCheckerDB(self.clientdb)) - self.client_factory = pb.PBServerFactory(self.p) - self.hostname = 'localhost' - self.server = reactor.listenTCP(0, self.client_factory) - self.port = self.server.getHost().port - # public key authentication information - self.username = USERNAME - self.pubkey_file = PUBKEY_FILE - self.privkey_file = PRIVKEY_FILE - self.public_key_string = keys.getPublicKeyString( - filename=self.pubkey_file) - self.private_key = keys.getPrivateKeyObject(filename=self.privkey_file) - self.public_key = keys.getPublicKeyObject(self.public_key_string) - self.alg_name = 'rsa' - self.blob = keys.makePublicKeyBlob(self.public_key) - self.data = Data - self.signature = keys.signData(self.private_key, self.data) - self.creds = credentials.SSHPrivateKey(self.username, - self.alg_name, - self.blob, - self.data, - self.signature) - c = ConfigParser.ConfigParser() - c.read(os.path.join(DSAGE_DIR, 'client.conf')) - username = c.get('auth', 'username') - pubkey_file = c.get('auth', 'pubkey_file') - self.clientdb.add_user(username, pubkey_file) - - def tearDown(self): - self.connection.disconnect() - self.jobdb._shutdown() - files = glob('*.db*') - for file in files: - os.remove(file) - return self.server.stopListening() - - def testremote_get_job(self): - job = Job() - job.code = "2+2" - self.dsage_server.submit_job(job.reduce()) - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, - self.port, - factory) - d = factory.login(self.creds, (pb.Referenceable(), hf)) - d.addCallback(self._logged_in) - d.addCallback(self._get_job) - - return d - - def _logged_in(self, remoteobj): - self.assert_(remoteobj is not None) - - return remoteobj - - def _get_job(self, remoteobj): - d = remoteobj.callRemote('get_job') - d.addCallback(self._got_job) - - return d - - def _got_job(self, jdict): - self.assertEquals(type(jdict), dict) - - def testremote_job_done(self): - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, self.port, factory) - d = factory.login(self.creds, (pb.Referenceable(), hf)) - job = Job() - job.code = "2+2" - jdict = self.dsage_server.submit_job(job.reduce()) - d.addCallback(self._logged_in) - d.addCallback(self._job_done, jdict) - - return d - - def _job_done(self, remoteobj, jdict): - job_id = jdict['job_id'] - result = jdict['result'] - d = remoteobj.callRemote('job_done', job_id, 'Nothing.', result, False) - d.addCallback(self._done_job) - - return d - - def _done_job(self, jdict): - self.assertEquals(type(jdict), dict) - self.assertEquals(jdict['status'], 'new') - self.assertEquals(jdict['output'], 'Nothing.') - - def testremote_job_failed(self): - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, - self.port, - factory) - job = Job() - job.code = "2+2" - jdict = self.dsage_server.submit_job(job.reduce()) - d = factory.login(self.creds, (pb.Referenceable(), hf)) - d.addCallback(self._logged_in) - d.addCallback(self._job_failed, jdict) - - return d - - def _job_failed(self, remoteobj, jdict): - d = remoteobj.callRemote('job_failed', jdict['job_id'], 'Failure') - d.addCallback(self._failed_job) - - return d - - def _failed_job(self, jdict): - self.assertEquals(type(jdict), dict) - self.assertEquals(jdict['failures'], 1) - self.assertEquals(jdict['output'], 'Failure') - - def testget_killed_jobs_list(self): - factory = PBClientFactory() - self.connection = reactor.connectTCP(self.hostname, - self.port, - factory) - - job = Job() - job.code = "2+2" - job.killed = True - jdict = self.dsage_server.submit_job(job.reduce()) - d = factory.login(self.creds, (pb.Referenceable(), hf)) - d.addCallback(self._logged_in) - d.addCallback(self._get_killed_jobs_list) - d.addCallback(self._got_killed_jobs_list, jdict) - - return d - - def _get_killed_jobs_list(self, remoteobj): - d = remoteobj.callRemote('get_killed_jobs_list') - - return d - - def _got_killed_jobs_list(self, killed_jobs_list, jdict): - self.assertEquals(len(killed_jobs_list), 1) - self.assertEquals(killed_jobs_list[0]['job_id'], jdict['job_id']) - - if __name__ == 'main': unittest.main() Index: sage/dsage/twisted/tests/test_server.py =================================================================== --- sage/dsage/twisted/tests/test_server.py (revision 2925) +++ sage/dsage/twisted/tests/test_server.py (revision 2925) @@ -0,0 +1,31 @@ +############################################################################ +# +# DSAGE: Distributed SAGE +# +# Copyright (C) 2006, 2007 Yi Qiang +# +# Distributed under the terms of the GNU General Public License (GPL) +# +# This code is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# General Public License for more details. +# +# The full text of the GPL is available at: +# +# http://www.gnu.org/licenses/ +############################################################################ + +#import unittest +#import os + +#class ServerTestCase(unittest.TestCase): +# def testgetAuthorizedKeys(self): +# cur = os.getcwd() +# os.chdir('../dsage/tests/data') +# authorized_keys = getAuthorizedKeys('authorized_keys.db') +# for username, key in authorized_keys.iteritems(): +# self.assert_(isinstance(username, str)) +# self.assert_(isinstance(key, str)) +# os.chdir(cur) +# Index: sage/ext/cdefs.pxi =================================================================== --- sage/ext/cdefs.pxi (revision 3922) +++ sage/ext/cdefs.pxi (revision 3292) @@ -113,14 +113,4 @@ void mpz_xor (mpz_t rop, mpz_t op1, mpz_t op2) int mpz_root (mpz_t rop, mpz_t op, unsigned long int n) - - int mpz_odd_p (mpz_t op) - int mpz_even_p (mpz_t op) - - int mpz_perfect_power_p (mpz_t op) - int mpz_perfect_square_p (mpz_t op) - - int mpz_jacobi (mpz_t a, mpz_t b) - int mpz_kronecker (mpz_t a, mpz_t b) - int mpz_kronecker_si (mpz_t a, long b) # The mpq type Index: sage/ext/interactive_constructors_c.pyx =================================================================== --- sage/ext/interactive_constructors_c.pyx (revision 3973) +++ sage/ext/interactive_constructors_c.pyx (revision 1854) @@ -34,11 +34,13 @@ sage: GF(9,'c') Finite Field in c of size 3^2 - sage: c^3 - c^3 + sage: c + Traceback (most recent call last): + ... + NameError: name 'c' is not defined sage: inject_on(verbose=False) sage: GF(9,'c') Finite Field in c of size 3^2 - sage: c^3 - 2*c + 1 + sage: c + c ROLL YOUR OWN: If a constructor you would like to auto inject Index: sage/functions/all.py =================================================================== --- sage/functions/all.py (revision 4050) +++ sage/functions/all.py (revision 2106) @@ -1,6 +1,4 @@ from piecewise import Piecewise - -piecewise = Piecewise from transcendental import (exponential_integral_1, @@ -8,4 +6,5 @@ zeta, zeta_symmetric) +# This is too terrible code. #from elementary import (cosine, sine, exponential, # ElementaryFunction, @@ -13,9 +12,10 @@ from special import (bessel_I, bessel_J, bessel_K, bessel_Y, - hypergeometric_U, + hypergeometric_U, incomplete_gamma, spherical_bessel_J, spherical_bessel_Y, spherical_hankel1, spherical_hankel2, spherical_harmonic, jacobi, - inverse_jacobi, dilog, + inverse_jacobi, sinh, cosh, + tanh, coth, sech, csch, dilog, lngamma, exp_int, error_fcn) @@ -36,4 +36,4 @@ from constants import (pi, e, NaN, golden_ratio, log2, euler_gamma, catalan, - khinchin, twinprime, merten, brun, I) + khinchin, twinprime, merten, brun) Index: sage/functions/constants.py =================================================================== --- sage/functions/constants.py (revision 4065) +++ sage/functions/constants.py (revision 3290) @@ -19,5 +19,5 @@ euler_gamma sage: catalan # the Catalon constant - catalan + K sage: khinchin # Khinchin's constant khinchin @@ -54,13 +54,13 @@ can be coerced into other systems or evaluated. sage: a = pi + e*4/5; a - pi + 4*e/5 + (pi + ((e*4)/5)) sage: maxima(a) - %pi+4*%e/5 - sage: RealField(15)(a) # 15 *bits* of precision - 5.316 - sage: gp(a) - 5.316218116357029426750873360 # 32-bit - 5.3162181163570294267508733603616328824 # 64-bit - sage: print mathematica(a) # optional + %pi + 4*%e/5 + sage: a.str(15) # 15 *bits* of precision + '5.316' + sage: gp(a) + 5.316218116357029426750873360 # 32-bit + 5.3162181163570294267508733603616328824 # 64-bit + sage: mathematica(a) # optional 4 E --- + Pi @@ -102,16 +102,12 @@ EXAMPLES: Arithmetic with constants - sage: f = I*(e+1); f - (e + 1)*I - sage: f^2 - -(e + 1)^2 sage: pp = pi+pi; pp - 2*pi + (pi + pi) sage: R(pp) 6.2831853071795864769252867665590057683943387987502116419499 - sage: s = (1 + e^pi); s - e^pi + 1 + sage: s = (1 + e^pi);s + (1 + (e^pi)) sage: R(s) 24.140692632779269005729086367948547380266106242600211993445 @@ -119,6 +115,6 @@ 23.140692632779269005729086367948547380266106242600211993445 - sage: l = (1-log2)/(1+log2); l - (1 - log(2))/(log(2) + 1) + sage: l = (1-log2)/(1+log2);l + ((1 - log2)/(1 + log2)) sage: R(l) 0.18123221829928249948761381864650311423330609774776013488056 @@ -160,31 +156,30 @@ from functions import Function_gen, Function_arith, Function, FunctionRing_class - ###################### # Ring of Constants ###################### -## class ConstantRing_class(FunctionRing_class): -## def _repr_(self): -## return "Ring of Real Mathematical Constants" - -## def __cmp__(self, right): -## if isinstance(right, ConstantRing_class): -## return 0 -## return -1 +class ConstantRing_class(FunctionRing_class): + def _repr_(self): + return "Ring of Real Mathematical Constants" + + def __cmp__(self, right): + if isinstance(right, ConstantRing_class): + return 0 + return -1 -## def __call__(self, x): -## try: -## return self._coerce_(x) -## except TypeError: -## return Constant_gen(x) - -## def _coerce_impl(self, x): -## if isinstance(x, (sage.rings.integer.Integer, -## sage.rings.rational.Rational, int, long)): -## return Constant_gen(x) -## raise TypeError, 'no canonical coercion of element into self.' - -## ConstantRing = ConstantRing_class() + def __call__(self, x): + try: + return self._coerce_(x) + except TypeError: + return Constant_gen(x) + + def _coerce_impl(self, x): + if isinstance(x, (sage.rings.integer.Integer, + sage.rings.rational.Rational, int, long)): + return Constant_gen(x) + raise TypeError, 'no canonical coercion of element into self.' + +ConstantRing = ConstantRing_class() @@ -192,35 +187,9 @@ # Constant functions ###################### -import sage.calculus.calculus class Constant(Function): def __init__(self, conversions={}): self._conversions = conversions - RingElement.__init__(self, sage.calculus.calculus.SR) - - def _has_op(self, x): - return False - - def substitute(self, *args, **kwds): - return self - - def _recursive_sub(self, kwds): - return self - - def _recursive_sub(self, kwds): - return self - - def _recursive_sub_over_ring(self, kwds, ring): - return ring(self) - - def variables(self): - return [] - - def _ser(self): - try: - return self.__ser - except AttributeError: - self.__ser = sage.calculus.calculus.SR._coerce_impl(self) - return self.__ser + RingElement.__init__(self, ConstantRing) def _neg_(self): @@ -233,31 +202,23 @@ return Integer(int(float(self))) - def _latex_(self): - return '\\text{%s}'%self - - def _complex_mpfr_field_(self, R): - return R(self._mpfr_(R._real_field())) - - def _real_double_(self, R): - return R(float(self)) - - def _complex_double_(self, R): - return R(float(self)) - # The following adds formal arithmetic support for generic constant def _add_(self, right): - return self._ser() + right + return Constant_arith(self, right, operator.add) def _sub_(self, right): - return self._ser() - right + return Constant_arith(self, right, operator.sub) def _mul_(self, right): - return self._ser() * right + return Constant_arith(self, right, operator.mul) def _div_(self, right): - return self._ser() / right + return Constant_arith(self, right, operator.div) def __pow__(self, right): - return self._ser() ** right + try: + right = self.parent()._coerce_(right) + except TypeError: + raise TypeError, "computation of %s^%s not defined"%(self, right) + return Constant_arith(self, right, operator.pow) def _interface_is_cached_(self): @@ -299,5 +260,6 @@ Function_arith.__init__(self, x, y, op) Constant.__init__(self) - + + class Pi(Constant): """ @@ -319,5 +281,5 @@ 3.1415926535897932384626433832795028841971693993751058209749 sage: pp = pi+pi; pp - 2*pi + (pi + pi) sage: R(pp) 6.2831853071795864769252867665590057683943387987502116419499 @@ -333,5 +295,5 @@ 'matlab':'pi','maple':'Pi','octave':'pi','pari':'Pi'}) - def _repr_(self, simplify=True): + def _repr_(self): return "pi" @@ -348,6 +310,6 @@ return R.pi() - def _real_double_(self,R): - return R.pi() + def _real_double_(self): + return sage.rings.all.RD.pi() def __abs__(self): @@ -367,72 +329,4 @@ pi = Pi() - -class I_class(Constant): - """ - The formal square root of -1. - - EXAMPLES: - sage: I - I - sage: I^2 - -1 - sage: float(I) - Traceback (most recent call last): - ... - TypeError - sage: gp(I) - I - sage: RR(I) - Traceback (most recent call last): - ... - TypeError - sage: C = ComplexField(200); C - Complex Field with 200 bits of precision - sage: C(I) - 1.0000000000000000000000000000000000000000000000000000000000*I - sage: z = I + I; z - 2*I - sage: C(z) - 2.0000000000000000000000000000000000000000000000000000000000*I - sage: maxima(2*I) - 2*%i - """ - def __init__(self): - Constant.__init__(self, - {'axiom':'%i', - 'maxima':'%i','gp':'I','mathematica':'I', - 'matlab':'i','maple':'I','octave':'i','pari':'I'}) - - def _repr_(self, simplify=True): - return "I" - - def _latex_(self): - return "i" - - def _mathml_(self): - return "&i;" - - def __float__(self): - raise TypeError - - def _mpfr_(self, R): - raise TypeError - - def _complex_mpfr_field_(self, R): - return R.gen() - - def _complex_double_(self, C): - return C.gen() - - def _real_double_(self, R): - raise TypeError - - def __abs__(self): - return Integer(1) - - def floor(self): - raise TypeError - -I = I_class() class E(Constant): @@ -448,5 +342,5 @@ 2.7182818284590452353602874713526624977572470936999595749670 sage: em = 1 + e^(1-e); em - e^(1 - e) + 1 + (1 + (e^(1 - e))) sage: R(em) 1.1793740787340171819619895873183164984596816017589156131574 @@ -470,5 +364,5 @@ 'octave':'e'}) - def _repr_(self, simplify=True): + def _repr_(self): return 'e' @@ -485,6 +379,6 @@ return Integer(2) - def _real_double_(self, R): - return R(1).exp() + def _real_double_(self): + return sage.rings.all.RD.e() # This just gives a string in singular anyways, and it's @@ -497,4 +391,6 @@ ee = e + + class NotANumber(Constant): """ @@ -505,5 +401,5 @@ {'matlab':'NaN'}) - def _repr_(self, simplify=True): + def _repr_(self): return 'NaN' @@ -511,6 +407,6 @@ return R('NaN') #??? nan in mpfr: void mpfr_set_nan (mpfr_t x) - def _real_double_(self, R): - return R.nan() + def _real_double_(self): + return sage.rings.all.RD.nan() NaN = NotANumber() @@ -528,7 +424,7 @@ 1.6180339887498948482045868343656381177203091798057628621354 sage: grm = maxima(golden_ratio);grm - (sqrt(5)+1)/2 + (sqrt(5) + 1)/2 sage: grm + grm - sqrt(5)+1 + sqrt(5) + 1 sage: float(grm + grm) 3.2360679774997898 @@ -539,5 +435,5 @@ 'pari':'(1+sqrt(5))/2','octave':'(1+sqrt(5))/2', 'kash':'(1+Sqrt(5))/2'}) - def _repr_(self, simplify=True): + def _repr_(self): return 'golden_ratio' @@ -548,5 +444,5 @@ return float(0.5)*(float(1.0)+math.sqrt(float(5.0))) - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -554,5 +450,5 @@ 1.61803398875 """ - return R('1.61803398874989484820458') + return sage.rings.all.RDF(1.61803398874989484820458) def _mpfr_(self,R): #is this OK for _mpfr_ ? @@ -576,6 +472,6 @@ sage: R(log2) 0.69314718055994530941723212145817656807550013436025525412068 - sage: l = (1-log2)/(1+log2); l - (1 - log(2))/(log(2) + 1) + sage: l = (1-log2)/(1+log2);l + ((1 - log2)/(1 + log2)) sage: R(l) 0.18123221829928249948761381864650311423330609774776013488056 @@ -596,5 +492,5 @@ 'pari':'log(2)','octave':'log(2)'}) - def _repr_(self, simplify=True): + def _repr_(self): return 'log2' @@ -605,5 +501,5 @@ return math.log(2) - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -611,5 +507,5 @@ 0.69314718056 """ - return R.log2() + return sage.rings.all.RD.log2() def _mpfr_(self,R): @@ -633,6 +529,6 @@ sage: R(euler_gamma) 0.57721566490153286060651209008240243104215933593992359880577 - sage: eg = euler_gamma + euler_gamma; eg - 2*euler_gamma + sage: eg = euler_gamma + euler_gamma;eg + (euler_gamma + euler_gamma) sage: R(eg) 1.1544313298030657212130241801648048620843186718798471976115 @@ -641,8 +537,7 @@ Constant.__init__(self, {'kash':'EulerGamma(R)','maple':'gamma', - 'mathematica':'EulerGamma','pari':'Euler', - 'maxima':'%gamma', 'maxima':'euler_gamma'}) - - def _repr_(self, simplify=True): + 'mathematica':'EulerGamma','pari':'Euler'}) + + def _repr_(self): return 'euler_gamma' @@ -653,5 +548,5 @@ return R.euler_constant() - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -659,5 +554,5 @@ 0.577215664902 """ - return R.euler_constant() + return sage.rings.all.RD.euler() def floor(self): @@ -672,19 +567,20 @@ EXAMPLES: - sage: catalan^2 + merten - merten + catalan^2 """ def __init__(self): Constant.__init__(self, {'mathematica':'Catalan','kash':'Catalan(R)', #kash: R is default prec - 'maple':'Catalan', 'maxima':'catalan'}) + 'maple':'Catalan'}) - def _repr_(self, simplify=True): - return 'catalan' + def _repr_(self): + return 'K' + + def _latex_(self): + return 'K' def _mpfr_(self, R): return R.catalan_constant() - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -693,5 +589,5 @@ 0.915965594177 """ - return R('0.91596559417721901505460351493252') + return sage.rings.all.RDF(0.91596559417721901505460351493252) def __float__(self): @@ -721,10 +617,14 @@ Khinchin sage: m.N(200) # optional - 2.6854520010653064453097148354817956938203822939944629530511523455572188595371520028011411749318476979951534659052880900828976777164109630517925334832596683818523154213321194996260393285220448194096180686641664289 # 32-bit - 2.6854520010653064453097148354817956938203822939944629530511523455572188595371520028011411749318476979951534659052880900828976777164109630517925334832596683818523154213321194996260393285220448194096181 # 64-bit + 2.685452001065306445309714835481795693820382293994462953051152345557 # 32-bit + > 218859537152002801141174931847697995153465905288090082897677716410963051 # 32-bit + > 7925334832596683818523154213321194996260393285220448194096181 # 32-bit + 2.685452001065306445309714835481795693820382293994462953051152345557 # 64-bit + > 218859537152002801141174931847697995153465905288090082897677716410963051 # 64-bit + > 7925334832596683818523154213321194996260393285220448194096181 # 64-bit """ def __init__(self): Constant.__init__(self, - {'maxima':'khinchin', 'mathematica':'Khinchin'}) #Khinchin is only implemented in Mathematica + {'mathematica':'Khinchin'}) #Khinchin is only implemented in Mathematica # digits come from http://pi.lacim.uqam.ca/piDATA/khintchine.txt @@ -732,5 +632,5 @@ self.__bits = len(self.__value)*3-1 # underestimate - def _repr_(self, simplify=True): + def _repr_(self): return 'khinchin' @@ -740,5 +640,5 @@ raise NotImplementedError, "Khinchin's constant only available up to %s bits"%self.__bits - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -746,5 +646,5 @@ 2.68545200107 """ - return R('2.685452001065306445309714835481795693820') + return sage.rings.all.RDF(2.685452001065306445309714835481795693820) @@ -772,5 +672,5 @@ """ def __init__(self): - Constant.__init__(self,{'maxima':'twinprime'}) #Twin prime is not implemented in any other algebra systems. + Constant.__init__(self,{}) #Twin prime is not implemented in any other algebra systems. #digits come from http://www.gn-50uma.de/alula/essays/Moree/Moree-details.en.shtml @@ -783,5 +683,5 @@ return Integer(0) - def _repr_(self, simplify=True): + def _repr_(self): return 'twinprime' @@ -791,5 +691,5 @@ raise NotImplementedError, "Twin Prime constant only available up to %s bits"%self.__bits - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -797,5 +697,5 @@ 0.660161815847 """ - return R('0.660161815846869573927812110014555778432') + return sage.rings.all.RDF(0.660161815846869573927812110014555778432) def __float__(self): @@ -824,5 +724,5 @@ """ def __init__(self): - Constant.__init__(self,{'maxima':'merten'}) #Merten's constant is not implemented in any other algebra systems. + Constant.__init__(self,{}) #Merten's constant is not implemented in any other algebra systems. # digits come from Sloane's tables at http://www.research.att.com/~njas/sequences/table?a=77761&fmt=0 @@ -835,5 +735,5 @@ return Integer(0) - def _repr_(self, simplify=True): + def _repr_(self): return 'merten' @@ -852,5 +752,5 @@ raise NotImplementedError, "Merten's constant only available up to %s bits"%self.__bits - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -858,5 +758,5 @@ 0.261497212848 """ - return R('0.261497212847642783755426838608695859051') + return sage.rings.all.RDF(0.261497212847642783755426838608695859051) def __float__(self): @@ -867,5 +767,4 @@ """ return 0.261497212847642783755426838608695859051 - merten = Merten() @@ -888,5 +787,5 @@ """ def __init__(self): - Constant.__init__(self,{'maxima':"brun"}) #Brun's constant is not implemented in any other algebra systems. + Constant.__init__(self,{}) #Brun's constant is not implemented in any other algebra systems. # digits come from Sloane's tables at http://www.research.att.com/~njas/sequences/table?a=65421&fmt=0 @@ -899,5 +798,5 @@ return Integer(1) - def _repr_(self, simplify=True): + def _repr_(self): return 'brun' @@ -916,5 +815,5 @@ raise NotImplementedError, "Brun's constant only available up to %s bits"%self.__bits - def _real_double_(self, R): + def _real_double_(self): """ EXAMPLES: @@ -922,5 +821,5 @@ 1.9021605831 """ - return R('1.9021605831040') + return sage.rings.all.RDF(1.9021605831040) def __float__(self): @@ -934,2 +833,49 @@ brun=Brun() +class UniversalPolynomialElement(Constant): + """ + A universal indeterminate. + + EXAMPLES: + sage: x + x + sage: x.parent() + Univariate Polynomial Ring in x over Rational Field + """ + def __init__(self, name): + self._name = name + Constant.__init__(self, + {'axiom':name, + 'maxima':name, + 'gp':name,'kash':name, + 'mathematica':name, + 'matlab':name, + 'maple':name, + 'octave':name, + 'pari':name}) + + def _repr_(self): + return self._name + + def _latex_(self): + return self._name + + def _mathml_(self): + return "%s"%self._name + + def __float__(self): + raise TypeError + + def _mpfr_(self, R): + raise TypeError + + def _real_double_(self): + raise TypeError + + def __abs__(self): + raise TypeError + + def floor(self): + raise TypeError + +x = UniversalPolynomialElement('x') Index: sage/functions/functions.py =================================================================== --- sage/functions/functions.py (revision 4061) +++ sage/functions/functions.py (revision 3290) @@ -2,4 +2,14 @@ SAGE Functions Class +EXAMPLES: + sage: f = 5*sin(x) + sage: f + (5*sin(x)) + sage: f(2) + (5*sin(2)) + sage: f(pi) + (5*sin(((1*pi) + 0))) + sage: float(f(pi)) + 6.1232339957367663e-16 """ import weakref @@ -103,4 +113,6 @@ def _coerce_impl(self, x): + if is_Polynomial(x): + return self(x) return self(x) @@ -206,6 +218,11 @@ """ EXAMPLES: - sage: s = singular(e); s + sage: singular(e) 2.71828182845905 + sage: P = e.parent() + sage: old_prec = P.set_precision(200) + sage: singular(e) + 2.7182818284590452353602874713526624977572470936999595749670 + sage: _ = P.set_precision(old_prec) """ try: @@ -247,16 +264,16 @@ EXAMPLES: sage: s = e + pi - sage: bool(s == 0) + sage: s == 0 False sage: t = e^2 +pi - sage: bool(s == t) + sage: s == t False - sage: bool(s == s) + sage: s == s True - sage: bool(t == t) + sage: t == t True - sage: bool(s < t) + sage: s < t True - sage: bool(t < s) + sage: t < s False """ @@ -318,18 +335,18 @@ sage: s = (pi + pi) * e + e sage: s - 2*e*pi + e + (((pi + pi)*e) + e) sage: RR(s) 19.7977502738062 sage: maxima(s) - 2*%e*%pi+%e + 2*%e*%pi + %e sage: t = e^2 + pi + 2/3; t - pi + e^2 + 2/3 + (((e^2) + pi) + 2/3) sage: RR(t) 11.1973154191871 sage: maxima(t) - %pi+%e^2+2/3 + %pi + %e^2 + 2/3 sage: t^e - (pi + e^2 + 2/3)^e + ((((e^2) + pi) + 2/3)^e) sage: RR(t^e) 710.865247688858 @@ -343,16 +360,9 @@ self.__op = op # a binary operator, e.g., operator.sub - def _maxima_init_(self): - x = self.__x - y = self.__y - op = self.__op - return '(%s) %s (%s)'%(x._maxima_init_(), symbols[op] ,y._maxima_init_()) - - def _repr_(self): """ EXAMPLES: sage: log2 * e + pi^2/2 - e*log(2) + pi^2/2 + ((log2*e) + ((pi^2)/2)) """ return '(%s%s%s)'%(self.__x, symbols[self.__op], self.__y) @@ -362,9 +372,9 @@ EXAMPLES: sage: latex(log2 * e + pi^2/2) - {e \cdot \log \left( 2 \right)} + \frac{{\pi}^{2} }{2} + \log(2) \cdot e + \frac{\pi^{2}}{2} sage: latex(NaN^3 + 1/golden_ratio) - {\text{NaN}}^{3} + \frac{2}{\sqrt{ 5 } + 1} + \text{NaN}^{3} + \frac{1}{\phi} sage: latex(log2 + euler_gamma + catalan + khinchin + twinprime + merten + brun) - \text{twinprime} + \text{merten} + \text{khinchin} + \gamma + \text{catalan} + \text{brun} + \log \left( 2 \right) + \log(2) + \gamma + K + \text{khinchin} + \text{twinprime} + \text{merten} + \text{brun} """ if self.__op == operator.div: @@ -390,5 +400,5 @@ EXAMPLES: sage: gap(e + pi) - "pi + e" + "5.85987448204884" """ return '"%s"'%self.str() @@ -431,5 +441,5 @@ EXAMPLES: sage: maxima(e + pi) - %pi+%e + %pi + %e """ return self.__op(self.__x._maxima_(maxima), self.__y._maxima_(maxima)) @@ -459,5 +469,5 @@ EXAMPLES: sage: singular(e + pi) - pi + e + 5.85987448204884 """ return '"%s"'%self.str() @@ -480,7 +490,7 @@ sage: a = pi/2 + e sage: a - pi/2 + e + ((pi/2) + e) sage: maxima(a) - %pi/2+%e + %pi/2 + %e sage: RR(a) 4.28907815525394 @@ -490,5 +500,5 @@ sage: b = e + 5/7 sage: maxima(b) - %e+5/7 + %e + 5/7 sage: RR(b) 3.43256754274476 Index: sage/functions/orthogonal_polys.py =================================================================== --- sage/functions/orthogonal_polys.py (revision 4016) +++ sage/functions/orthogonal_polys.py (revision 3301) @@ -386,9 +386,9 @@ sage: t = PolynomialRing(QQ, "t").gen() sage: gen_legendre_P(2,0,t) - '3*(1-t)^2/2-3*(1-t)+1' + '3*(1 - t)^2/2 - 3*(1 - t) + 1' sage: legendre_P(2,t) 3/2*t^2 - 1/2 sage: gen_legendre_P(3,1,t) - '-6*(5*(1-t)^2/4-5*(1-t)/2+1)*sqrt(1-t^2)' + '-6*(5*(1 - t)^2/4 - 5*(1 - t)/2 + 1)*sqrt(1 - t^2)' """ _init() @@ -412,7 +412,7 @@ sage: t = PolynomialRing(QQ, "t").gen() sage: gen_legendre_Q(2,0,t) - '(3*log(-(t+1)/(t-1))*t^2-6*t-log(-(t+1)/(t-1)))/4' + '(3*log( - (t + 1)/(t - 1))*t^2 - 6*t - log( - (t + 1)/(t - 1)))/4' sage: legendre_Q(2,t) - '(3*log(-(t+1)/(t-1))*t^2-6*t-log(-(t+1)/(t-1)))/4' + '(3*log( - (t + 1)/(t - 1))*t^2 - 6*t - log( - (t + 1)/(t - 1)))/4' sage: gen_legendre_Q(3,1,0.5) 2.49185259171 @@ -523,5 +523,5 @@ sage: t = PolynomialRing(QQ, 't').gen() sage: legendre_Q(2,t) - '(3*log(-(t+1)/(t-1))*t^2-6*t-log(-(t+1)/(t-1)))/4' + '(3*log( - (t + 1)/(t - 1))*t^2 - 6*t - log( - (t + 1)/(t - 1)))/4' sage: legendre_Q(3,0.5) -0.198654771479 Index: sage/functions/piecewise.py =================================================================== --- sage/functions/piecewise.py (revision 4058) +++ sage/functions/piecewise.py (revision 3636) @@ -99,12 +99,4 @@ from sage.rings.all import QQ, RR, Integer, Rational -from sage.interfaces.maxima import maxima -from sage.calculus.calculus import SR, var - -def meval(x): - from sage.calculus.calculus import symbolic_expression_from_maxima_element - return symbolic_expression_from_maxima_element(maxima(x)) - - class PiecewisePolynomial: def __init__(self, list_of_pairs): @@ -141,4 +133,5 @@ sage: f.latex() '\\begin{array}{ll} \\left\\{ 1,& 0 < x < 1 ,\\right. \\end{array}' + """ x = PolynomialRing(QQ,'x').gen() @@ -150,5 +143,5 @@ a = intvls[i][0] b = intvls[i][1] - tex.append(repr(f(x))) + tex.append(str(f(x))) tex.append(",& %s < x < %s ,\\"%(a,b)) tex = tex[:-2] @@ -434,19 +427,18 @@ def critical_points(self): """ - Return the critical points of this piecewise function. - - WARNINGS: Uses maxima, which prints the warning to use results - with caution. Only works for piecewise functions whose parts - are polynomials with real critical not occurring on the - interval endpoints. + Function to return the critical points. Uses maxima, which + prints the warning to use results with caution. Only works for + piecewise functions whose parts are polynomials with real + critical not occurring on the interval endpoints. EXAMPLES: sage: x = PolynomialRing(QQ, 'x').0 sage: f1 = x^0 - sage: f2 = 10*x - x^2 - sage: f3 = 3*x^4 - 156*x^3 + 3036*x^2 - 26208*x - sage: f = Piecewise([[(0,3),f1],[(3,10),f2],[(10,20),f3]]) + sage: f2 = 1-x + sage: f3 = 2*x + sage: f4 = 10*x-x^2 + sage: f = Piecewise([[(0,1),f1],[(1,2),f2],[(2,3),f3],[(3,10),f4]]) sage: f.critical_points() - [5.0, 12.000000000000171, 12.9999999999996, 14.000000000000229] + [5.0] """ maxima = sage.interfaces.all.maxima @@ -455,20 +447,13 @@ N = len(fcns) crit_pts = [] - I = self.intervals() for i in range(N): maxima.eval("eqn:diff(%s,x)=0"%fcns[i]) ans = maxima.eval("allroots(eqn)") - while True: - start = ans.find('x=') - if start == -1: - break - ans = ans[start+2:] - end = ans.find(',') - if end == -1: - end = ans.find(']') - r = float(ans[:end]) - if I[i][0] < r < I[i][1]: + if "[x =" in ans: + i1 = ans.index("[x =") + i2 = ans.index("]") + r = eval(ans[i1+4:i2]) + if self.intervals()[i][0] < r < self.intervals()[i][1]: crit_pts.append(r) - ans = ans[end+1:] return crit_pts @@ -565,11 +550,11 @@ sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.integral() - pi/2 + (pi/2) """ maxima = sage.interfaces.all.maxima x = PolynomialRing(QQ,'x').gen() ints = [maxima('%s'%p[1](x)).integral('x', p[0][0], p[0][1]) \ - for p in self.list()] - return meval(repr(sum(ints))) + for p in self.list()] + return sage_eval(str(sum(ints)).replace("%","")) def convolution(self,other): @@ -611,5 +596,5 @@ R1 = f0.parent() xx = R1.gen() - var = repr(xx) + var = str(xx) if len(f.intervals())==1 and len(g.intervals())==1: f = f.unextend() @@ -619,6 +604,6 @@ b1 = g.intervals()[0][0] b2 = g.intervals()[0][1] - i1 = repr(f0).replace(var,repr(uu)) - i2 = repr(g0).replace(var,"("+repr(tt-uu)+")") + i1 = str(f0).replace(var,str(uu)) + i2 = str(g0).replace(var,"("+str(tt-uu)+")") cmd1 = "integrate((%s)*(%s),%s,%s,%s)"%(i1,i2, uu, a1, tt-b1) ## if a1+b1 < tt < a2+b1 cmd2 = "integrate((%s)*(%s),%s,%s,%s)"%(i1,i2, uu, tt-b2, tt-b1) ## if a1+b2 < tt < a2+b1 @@ -629,10 +614,8 @@ conv3 = maxima.eval(cmd3) conv4 = maxima.eval(cmd4) - # this is a very, very, very ugly hack - x = PolynomialRing(QQ,'x').gen() - fg1 = sage_eval(conv1.replace("tt",var), {'x':x}) ## should be = R2(conv1) - fg2 = sage_eval(conv2.replace("tt",var), {'x':x}) ## should be = R2(conv2) - fg3 = sage_eval(conv3.replace("tt",var), {'x':x}) ## should be = R2(conv3) - fg4 = sage_eval(conv4.replace("tt",var), {'x':x}) ## should be = R2(conv4) + fg1 = sage_eval(conv1.replace("tt",var)) ## should be = R2(conv1) + fg2 = sage_eval(conv2.replace("tt",var)) ## should be = R2(conv2) + fg3 = sage_eval(conv3.replace("tt",var)) ## should be = R2(conv3) + fg4 = sage_eval(conv4.replace("tt",var)) ## should be = R2(conv4) if a1-b11 or len(g.intervals())>1: z = Piecewise([[(-3*abs(N-M),3*abs(N-M)),0*xx**0]]) @@ -677,5 +660,5 @@ sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.derivative() - Piecewise defined function with 2 parts, [[(0, pi/2), 0], [(pi/2, pi), 0]] + Piecewise defined function with 2 parts, [[(0, (pi/2)), 0], [((pi/2), pi), 0]] """ maxima = sage.interfaces.all.maxima @@ -684,7 +667,5 @@ diffs = [maxima('%s'%p[1](x)).diff('x') \ for p in self.list()] - dlist = [[(p[0][0], p[0][1]), - R(sage_eval(repr(maxima('%s'%p[1](x)).diff('x')).replace("%",""), - {'x':x}))] for p in self.list()] + dlist = [[(p[0][0], p[0][1]), R(sage_eval(str(maxima('%s'%p[1](x)).diff('x')).replace("%","")))] for p in self.list()] return Piecewise(dlist) @@ -749,5 +730,5 @@ sage: f = Piecewise([[(-1,1),f]]) sage: f.fourier_series_cosine_coefficient(2,1) - 1/pi^2 + (1/(pi^2)) sage: f = lambda x:x^2 sage: f = Piecewise([[(-pi,pi),f]]) @@ -758,5 +739,5 @@ sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.fourier_series_cosine_coefficient(5,pi) - -3/(5*pi) + (-3/(5*pi)) """ maxima = sage.interfaces.all.maxima @@ -766,11 +747,11 @@ fcn = '(%s)*cos('%p[1](x) + 'pi*x*%s/%s)/%s'%(n,L,L) fcn = fcn.replace("pi","%"+"pi") - a = repr(p[0][0]).replace("pi","%"+"pi") - b = repr(p[0][1]).replace("pi","%"+"pi") + a = str(p[0][0]).replace("pi","%"+"pi") + b = str(p[0][1]).replace("pi","%"+"pi") cmd = "integrate("+fcn+", x, %s, %s )"%(a, b) int = maxima(cmd).trigsimp() ints.append(int) ans = sum(ints) - return meval(repr(ans)) + return sage_eval(str(ans).replace("%","")) def fourier_series_sine_coefficient(self,n,L): @@ -798,11 +779,11 @@ fcn = '(%s)*sin('%p[1](x) + 'pi*x*%s/%s)/%s'%(n,L,L) fcn = fcn.replace("pi","%"+"pi") - a = repr(p[0][0]).replace("pi","%"+"pi") - b = repr(p[0][1]).replace("pi","%"+"pi") + a = str(p[0][0]).replace("pi","%"+"pi") + b = str(p[0][1]).replace("pi","%"+"pi") cmd = "integrate("+fcn+", x, %s, %s )"%(a, b) int = maxima(cmd).trigsimp() ints.append(int) ans = sum(ints) - return meval(repr(ans)) + return sage_eval(str(ans).replace("%","")) def fourier_series_partial_sum(self,N,L): @@ -819,19 +800,20 @@ sage: f = Piecewise([[(-1,1),f]]) sage: f.fourier_series_partial_sum(3,1) - cos(2*pi*x)/pi^2 - (4*cos(pi*x)/pi^2) + 1/3 + '1/3 + ((-4/(pi^2))*cos(1*pi*x/1) + 0*sin(1*pi*x/1)) + ((1/(pi^2))*cos(2*pi*x/1) + 0*sin(2*pi*x/1))' sage: f1 = lambda x:-1 sage: f2 = lambda x:2 sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.fourier_series_partial_sum(3,pi) - -3*sin(2*x)/pi + sin(x)/pi - (3*cos(x)/pi) + 1/4 + '1/4 + ((-3/pi)*cos(1*pi*x/pi) + (1/pi)*sin(1*pi*x/pi)) + (0*cos(2*pi*x/pi) + (-3/pi)*sin(2*pi*x/pi))' + """ a0 = self.fourier_series_cosine_coefficient(0,L) - A = [repr(self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] - B = [repr(self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + A = [str(self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + B = [str(self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] FS = ["("+A[i] +" + " + B[i]+")" for i in range(0,N-1)] - sumFS = repr(a0/2)+" + " + sumFS = str(a0/2)+" + " for s in FS: sumFS = sumFS+s+ " + " - return meval(sumFS[:-3]) + return sumFS[:-3] def fourier_series_partial_sum_cesaro(self,N,L): @@ -848,20 +830,20 @@ sage: f = Piecewise([[(-1,1),f]]) sage: f.fourier_series_partial_sum_cesaro(3,1) - cos(2*pi*x)/(3*pi^2) - (8*cos(pi*x)/(3*pi^2)) + 1/3 + '1/3 + ((2/3*(-4/(pi^2)))*cos(1*pi*x/1) + 0*sin(1*pi*x/1)) + ((1/3*(1/(pi^2)))*cos(2*pi*x/1) + 0*sin(2*pi*x/1))' sage: f1 = lambda x:-1 sage: f2 = lambda x:2 sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.fourier_series_partial_sum_cesaro(3,pi) - -sin(2*x)/pi + 2*sin(x)/(3*pi) - (2*cos(x)/pi) + 1/4 + '1/4 + ((2/3*(-3/pi))*cos(1*pi*x/pi) + (2/3*(1/pi))*sin(1*pi*x/pi)) + (0*cos(2*pi*x/pi) + (1/3*(-3/pi))*sin(2*pi*x/pi))' """ a0 = self.fourier_series_cosine_coefficient(0,L) - A = [repr((1-n/N)*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] - B = [repr((1-n/N)*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + A = [str((1-n/N)*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + B = [str((1-n/N)*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] FS = ["("+A[i] +" + " + B[i]+")" for i in range(0,N-1)] - sumFS = repr(a0/2)+" + " + sumFS = str(a0/2)+" + " for s in FS: sumFS = sumFS+s+ " + " - return meval(sumFS[:-3]) + return sumFS[:-3] def fourier_series_partial_sum_hann(self,N,L): @@ -878,19 +860,20 @@ sage: f = Piecewise([[(-1,1),f]]) sage: f.fourier_series_partial_sum_hann(3,1) - 0.500000000000000*(cos(2*pi/3) + 1)*cos(2*pi*x)/pi^2 - (2.00000000000000*(cos(pi/3) + 1)*cos(pi*x)/pi^2) + 1/3 + '1/3 + ((1+cos(pi*1/3))*(0.5*(-4/(pi^2)))*cos(1*pi*x/1) + (1+cos(pi*1/3))*0.0*sin(1*pi*x/1)) + ((1+cos(pi*2/3))*(0.5*(1/(pi^2)))*cos(2*pi*x/1) + (1+cos(pi*2/3))*0.0*sin(2*pi*x/1))' sage: f1 = lambda x:-1 sage: f2 = lambda x:2 sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.fourier_series_partial_sum_hann(3,pi) - -1.50000000000000*(cos(2*pi/3) + 1)*sin(2*x)/pi + 0.500000000000000*(cos(pi/3) + 1)*sin(x)/pi - (1.50000000000000*(cos(pi/3) + 1)*cos(x)/pi) + 1/4 + '1/4 + ((1+cos(pi*1/3))*(0.5*(-3/pi))*cos(1*pi*x/pi) + (1+cos(pi*1/3))*(0.5*(1/pi))*sin(1*pi*x/pi)) + ((1+cos(pi*2/3))*0.0*cos(2*pi*x/pi) + (1+cos(pi*2/3))*(0.5*(-3/pi))*sin(2*pi*x/pi))' + """ a0 = self.fourier_series_cosine_coefficient(0,L) - A = ["(1+cos(pi*%s/%s))*"%(n,N)+repr((0.5)*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] - B = ["(1+cos(pi*%s/%s))*"%(n,N)+repr((0.5)*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + A = ["(1+cos(pi*%s/%s))*"%(n,N)+str((0.5)*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + B = ["(1+cos(pi*%s/%s))*"%(n,N)+str((0.5)*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] FS = ["("+A[i] +" + " + B[i]+")" for i in range(0,N-1)] - sumFS = repr(a0/2)+" + " + sumFS = str(a0/2)+" + " for s in FS: sumFS = sumFS+s+ " + " - return meval(sumFS[:-3]) + return sumFS[:-3] def fourier_series_partial_sum_filtered(self,N,L,F): @@ -908,19 +891,20 @@ sage: f = Piecewise([[(-1,1),f]]) sage: f.fourier_series_partial_sum_filtered(3,1,[1,1,1]) - cos(2*pi*x)/pi^2 - (4*cos(pi*x)/pi^2) + 1/3 + '1/3 + ((1*(-4/(pi^2)))*cos(1*pi*x/1) + 0*sin(1*pi*x/1)) + ((1*(1/(pi^2)))*cos(2*pi*x/1) + 0*sin(2*pi*x/1))' sage: f1 = lambda x:-1 sage: f2 = lambda x:2 sage: f = Piecewise([[(0,pi/2),f1],[(pi/2,pi),f2]]) sage: f.fourier_series_partial_sum_filtered(3,pi,[1,1,1]) - -3*sin(2*x)/pi + sin(x)/pi - (3*cos(x)/pi) + 1/4 + '1/4 + ((1*(-3/pi))*cos(1*pi*x/pi) + (1*(1/pi))*sin(1*pi*x/pi)) + (0*cos(2*pi*x/pi) + (1*(-3/pi))*sin(2*pi*x/pi))' + """ a0 = self.fourier_series_cosine_coefficient(0,L) - A = [repr((F[n])*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] - B = [repr((F[n])*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + A = [str((F[n])*self.fourier_series_cosine_coefficient(n,L))+"*cos(%s*pi*x/%s)"%(n,L) for n in range(1,N)] + B = [str((F[n])*self.fourier_series_sine_coefficient(n,L))+"*sin(%s*pi*x/%s)"%(n,L) for n in range(1,N)] FS = ["("+A[i] +" + " + B[i]+")" for i in range(0,N-1)] - sumFS = repr(a0/2)+" + " + sumFS = str(a0/2)+" + " for s in FS: sumFS = sumFS+s+ " + " - return meval(sumFS[:-3]) + return sumFS[:-3] def plot_fourier_series_partial_sum(self,N,L,xmin,xmax, **kwds): @@ -957,6 +941,6 @@ pi = 3.14159265 xi = xmin + i*h - yi = ff.replace("pi",repr(RR(pi))) - yi = sage_eval(yi.replace("x",repr(xi))) + yi = ff.replace("pi",str(RR(pi))) + yi = sage_eval(yi.replace("x",str(xi))) pts.append([xi,yi]) return line(pts, **kwds) @@ -995,6 +979,6 @@ pi = 3.14159265 xi = xmin + i*h - yi = ff.replace("pi",repr(RR(pi))) - yi = sage_eval(yi.replace("x",repr(xi))) + yi = ff.replace("pi",str(RR(pi))) + yi = sage_eval(yi.replace("x",str(xi))) pts.append([xi,yi]) return line(pts, **kwds) @@ -1033,6 +1017,6 @@ pi = 3.14159265 xi = xmin + i*h - yi = ff.replace("pi",repr(RR(pi))) - yi = sage_eval(yi.replace("x",repr(xi))) + yi = ff.replace("pi",str(RR(pi))) + yi = sage_eval(yi.replace("x",str(xi))) pts.append([xi,yi]) return line(pts, **kwds) @@ -1073,6 +1057,6 @@ pi = 3.14159265 xi = xmin + i*h - yi = ff.replace("pi",repr(RR(pi))) - yi = sage_eval(yi.replace("x",repr(xi))) + yi = ff.replace("pi",str(RR(pi))) + yi = sage_eval(yi.replace("x",str(xi))) pts.append([xi,yi]) return line(pts, **kwds) @@ -1155,5 +1139,5 @@ 0 sage: f.cosine_series_coefficient(3,1) - -4/(9*pi^2) + (-4/(9*(pi^2))) sage: f1 = lambda x:-1 sage: f2 = lambda x:2 @@ -1162,7 +1146,7 @@ 0 sage: f.cosine_series_coefficient(3,pi) - 2/pi + (2/pi) sage: f.cosine_series_coefficient(111,pi) - 2/(37*pi) + (2/(37*pi)) """ @@ -1173,12 +1157,11 @@ fcn = '2*(%s)*cos('%p[1](x) + 'pi*x*%s/%s)/%s'%(n,L,L) fcn = fcn.replace("pi","%"+"pi") - a = repr(p[0][0]).replace("pi","%"+"pi") - b = repr(p[0][1]).replace("pi","%"+"pi") + a = str(p[0][0]).replace("pi","%"+"pi") + b = str(p[0][1]).replace("pi","%"+"pi") cmd = "integrate("+fcn+", x, %s, %s )"%(a, b) I = maxima(cmd).trigsimp() ints.append(I) ans = sum(ints) - return meval(repr(ans)) - + return sage_eval(str(ans).replace("%","")) def sine_series_coefficient(self,n,L): @@ -1204,5 +1187,6 @@ 0 sage: f.sine_series_coefficient(3,1) - 4/(3*pi) + (4/(3*pi)) + """ maxima = sage.interfaces.all.maxima @@ -1212,48 +1196,54 @@ fcn = '2*(%s)*sin('%p[1](x) + 'pi*x*%s/%s)/%s'%(n,L,L) fcn = fcn.replace("pi","%"+"pi") - a = repr(p[0][0]).replace("pi","%"+"pi") - b = repr(p[0][1]).replace("pi","%"+"pi") + a = str(p[0][0]).replace("pi","%"+"pi") + b = str(p[0][1]).replace("pi","%"+"pi") cmd = "integrate("+fcn+", x, %s, %s )"%(a, b) I = maxima(cmd).trigsimp() ints.append(I) ans = sum(ints) - return meval(repr(ans)) - - def laplace(self, x, s): - r""" - Returns the Laplace transform of self with respect to the - variable var. - - INPUT: - x -- variable of self - s -- variable of Laplace transform. - + return sage_eval(str(ans).replace("%","")) + + def laplace_transform(self,var = "s",latex_output=0): + r""" + Returns the laplace transform of self, as a function of var. We assume that a piecewise function is 0 outside of its domain and that the left-most endpoint of the domain is 0. EXAMPLES: - sage: f = Piecewise([[(0,1),1],[(1,2), 1-x]]) - sage: f.laplace(x, s) - -e^(-s)/s - (e^(-s)/s^2) + (s + 1)*e^(-2*s)/s^2 + 1/s - sage: f.laplace(x, w) - -e^(-w)/w - (e^(-w)/w^2) + (w + 1)*e^(-2*w)/w^2 + 1/w - - sage: f = Piecewise([[(1,2), 1-y]]) - sage: f.laplace(y, t) - (t + 1)*e^(-2*t)/t^2 - (e^(-t)/t^2) - """ - x = var(x) - s = var(s) + sage: f1 = lambda x:1 + sage: f2 = lambda x:1-x + sage: f = Piecewise([[(0,1),f1],[(1,2),f2]]) + sage: f.laplace_transform() + '1/s - e^-s/s + (s + 1)*e^-(2*s)/s^2 - e^-s/s^2' + sage: f.laplace_transform("w",latex_output=1) + ' - {{e^{ - w}}\\over{w}} - {{e^{ - w}}\\over{w^2}} + {{\\left(w + 1\\right)\\,e^{ - 2\\,w}}\\over{w^2}} + {{1}\\over{w}}' + sage: f.laplace_transform("w",True) + ' - {{e^{ - w}}\\over{w}} - {{e^{ - w}}\\over{w^2}} + {{\\left(w + 1\\right)\\,e^{ - 2\\,w}}\\over{w^2}} + {{1}\\over{w}}' + sage: f.laplace_transform("w") + '1/w - e^-w/w + (w + 1)*e^-(2*w)/w^2 - e^-w/w^2' + + """ + maxima = sage.interfaces.all.maxima + x = PolynomialRing(QQ,'x').gen() ints = [] for p in self.list(): - g = SR(p[1]) - fcn = maxima('(%s)*exp(-%s*%s)'%(g._maxima_init_(), s, x)) - ints.append(fcn.integral(x, p[0][0], p[0][1])) + fcn = '(%s)*exp(-%s*x)'%(p[1](x),var) + ints.append(maxima(fcn).integral('x', p[0][0], p[0][1])) ans = "" + ans_latex = "" for i in range(len(ints)-1): - ans = ans+repr(ints[i]) + " + " - ans = ans+repr(ints[len(ints)-1]) - return meval(ans) - + ans = ans+str(ints[i]).replace("%","")+" + " + ans_latex = ans_latex+str(ints[i])+" + " + ans = ans+str(ints[len(ints)-1]).replace("%","") + ans_latex = ans_latex + str(ints[len(ints)-1]) + + if latex_output == 0: + return ans + if latex_output == 1: + ans0 = maxima.eval("tex("+ans_latex+")") + ans0 = ans0.replace("$$","") + ans0 = ans0.replace("false","") + return ans0 + def __add__(self,other): """ Index: sage/functions/special.py =================================================================== --- sage/functions/special.py (revision 4053) +++ sage/functions/special.py (revision 2641) @@ -1,3 +1,3 @@ -r""" +r"""nodoctest -- TODO remove Special Functions @@ -5,6 +5,5 @@ -- David Joyner (2006-13-06) -This module provides easy access to many of Maxima and PARI's -special functions. +Some of Maxima's and Pari's special functions are wrapped. Maxima's special functions package (which includes spherical harmonic @@ -332,17 +331,12 @@ from sage.rings.rational_field import RationalField from sage.rings.real_mpfr import RealField -from sage.rings.complex_field import ComplexField from sage.misc.sage_eval import sage_eval -from sage.rings.all import ZZ, QQ, RR +from sage.rings.all import QQ, RR import sage.rings.commutative_ring as commutative_ring import sage.rings.ring as ring -from sage.interfaces.maxima import maxima - -def meval(x): - from sage.calculus.calculus import symbolic_expression_from_maxima_element - return symbolic_expression_from_maxima_element(maxima(x)) - from functions import * + +from sage.misc.functional import exp _done = False @@ -361,9 +355,4 @@ return RR, a -def _setup_CC(prec): - from sage.libs.pari.all import pari - CC = ComplexField(prec) - a = pari.set_real_precision(int(prec/3.3)+1) ## 3.3 < log(10,2) - return CC, a def bessel_I(nu,z,alg = "pari",prec=53): @@ -410,7 +399,7 @@ EXAMPLES: sage: bessel_I(1,1,"pari",500) - 0.565159103992485027207696027609863307328899621621092009480294489479255640964371134092664997766814410064677886055526302676857637684917179812041131208121 + 0.56515910399248502720769602760986330732889962162109200948029448947925564096437113409266499776681441006467788605552630267685763768491717981204113120812118 sage: bessel_I(1,1) - 0.565159103992485 + 0.56515910399248503 sage: bessel_I(2,1.1,"maxima") # last few digits are random 0.16708949925104899 @@ -427,5 +416,5 @@ return b else: - return sage_eval(maxima.eval("bessel_i(%s,%s)"%(float(nu),float(z)))) + return eval(maxima.eval("bessel_i(%s,%s)"%(float(nu),float(z)))) def bessel_J(nu,z,alg="pari",prec=53): @@ -484,12 +473,10 @@ if alg=="pari": from sage.libs.pari.all import pari - K,a = _setup(prec) - if not (z in K): - K, a = _setup_CC(prec) - b = K(pari(z).besselj(nu)) + R,a = _setup(prec) + b = R(pari(z).besselj(nu)) pari.set_real_precision(a) return b else: - return meval("bessel_j(%s,%s)"%(nu, z)) + return RR(maxima.eval("bessel_j(%s,%s)"%(float(nu),float(z)))) def bessel_K(nu,z,prec=53): @@ -513,7 +500,7 @@ EXAMPLES: sage: bessel_K(1,1) - 0.601907230197235 + 0.60190723019723458 sage: bessel_K(1,1,500) - 0.601907230197234574737540001535617339261586889968106456017767959168553582946237840168863706958258215354644099783140050908469292813493294605655726961996 + 0.60190723019723457473754000153561733926158688996810645601776795916855358294623784016886370695825821535464409978314005090846929281349329460565572696199608 """ from sage.libs.pari.all import pari @@ -564,7 +551,7 @@ EXAMPLES: sage: hypergeometric_U(1,1,1) - 0.596347362323194 + 0.59634736232319407 sage: hypergeometric_U(1,1,1,70) - 0.59634736232319407434 + 0.59634736232319407434152 """ from sage.libs.pari.all import pari @@ -574,23 +561,59 @@ return b -def spherical_bessel_J(n, var): +def incomplete_gamma(s,x,prec=53): + r""" + Implements the incomplete Gamma function. + + INPUT: + s, x -- ocmplex numbers. + prec -- bits of precision. + + The argument x and s are complex numbers + (x must be a positive real number if s = 0). + The result returned is $\int_x^\infty e^{-t}t^{s-1}dt$. + + EXAMPLES: + sage: incomplete_gamma(0.1,6,200) + 119.99999984701215693242493354706493878953914933130704861011488 + sage: incomplete_gamma(0,6,200) + 120.00000000000000000000000000000000000000000000000000000000000 + sage: incomplete_gamma(0.3,6,200) + 119.99990598341125737887779259683594390225182610507857843438320 + sage: incomplete_gamma(0.3,6) + 119.99990598341125 + sage: incomplete_gamma(0.5,6) + 119.99830020752132 + sage: incomplete_gamma(0.5,6,100) + 119.99830020752131890111421425093 + """ + from sage.libs.pari.all import pari + R,a = _setup(prec) + b = R(pari(x).incgam(s)) + pari.set_real_precision(a) + return b + +def spherical_bessel_J(n,x): r""" Returns the spherical Bessel function of the first kind for integers n > -1. - Reference: A&S 10.1.8 page 437 and A&S 10.1.15 page 439. EXAMPLES: + sage: x = PolynomialRing(QQ, 'x').gen() sage: spherical_bessel_J(2,x) - ((-(1 - (24/(8*x^2))))*sin(x) - (3*cos(x)/x))/x + '( - (1 - 24/(8*x^2))*sin(x) - 3*cos(x)/x)/x' + + Here I = sqrt(-1). + """ _init() - return meval("spherical_bessel_j(%s,%s)"%(ZZ(n),var)) - -def spherical_bessel_Y(n,var): + R = x.parent() + y = R.gen() + return maxima.eval("spherical_bessel_j(%s,%s)"%(n,y)).replace("%i","I") + +def spherical_bessel_Y(n,x): r""" Returns the spherical Bessel function of the second kind for integers n > -1. - Reference: A&S 10.1.9 page 437 and A&S 10.1.15 page 439. @@ -598,10 +621,15 @@ sage: x = PolynomialRing(QQ, 'x').gen() sage: spherical_bessel_Y(2,x) - (-(3*sin(x)/x - (1 - (24/(8*x^2)))*cos(x)))/x + '-(3*sin(x)/x - (1 - 24/(8*x^2))*cos(x))/x' + + Here I = sqrt(-1). + """ _init() - return meval("spherical_bessel_y(%s,%s)"%(ZZ(n),var)) - -def spherical_hankel1(n,var): + R = x.parent() + y = R.gen() + return maxima.eval("spherical_bessel_y(%s,%s)"%(n,y)).replace("%i","I") + +def spherical_hankel1(n,x): r""" Returns the spherical Hankel function of the first @@ -611,8 +639,12 @@ EXAMPLES: sage: spherical_hankel1(2,'x') - -3*I*(-x^2/3 - I*x + 1)*e^(I*x)/x^3 + '-3*I*( - x^2/3 - I*x + 1)*%e^(I*x)/x^3' + + Here I = sqrt(-1). + """ _init() - return meval("spherical_hankel1(%s,%s)"%(ZZ(n),var)) + y = str(x) + return maxima.eval("spherical_hankel1(%s,%s)"%(n,y)).replace("%i","I") def spherical_hankel2(n,x): @@ -624,5 +656,5 @@ EXAMPLES: sage: spherical_hankel2(2,'x') - '3*I*(-x^2/3+I*x+1)*%e^-(I*x)/x^3' + '3*I*( - x^2/3 + I*x + 1)*%e^-(I*x)/x^3' Here I = sqrt(-1). @@ -640,11 +672,30 @@ EXAMPLES: + sage: x = PolynomialRing(QQ, 'x').gen() + sage: y = PolynomialRing(QQ, 'y').gen() sage: spherical_harmonic(3,2,x,y) - 15*sqrt(7)*cos(x)*sin(x)^2*e^(2*I*y)/(4*sqrt(30)*sqrt(pi)) + '15*sqrt(7)*cos(x)*sin(x)^2*e^(2*I*y)/(4*sqrt(30)*sqrt(pi))' sage: spherical_harmonic(3,2,1,2) - 15*sqrt(7)*e^(4*I)*cos(1)*sin(1)^2/(4*sqrt(30)*sqrt(pi)) + -0.25556469795208248 - 0.29589824630616246*I + + Here I = sqrt(-1). + """ _init() - return meval("spherical_harmonic(%s,%s,%s,%s)"%(ZZ(m),ZZ(n),x,y)) + if not(is_Polynomial(x) and is_Polynomial(y)): + s1 = maxima.eval("spherical_harmonic(%s,%s,%s,%s)"%(m,n,x,y)) + s2 = s1.replace("%i","I") + s3 = s2.replace("%pi","pi") + s4 = s3.replace("%e","CC(e)") + return sage_eval(s4) + R = x.parent() + x1 = R.gen() + R = y.parent() + y1 = R.gen() + s1 = maxima.eval("spherical_harmonic(%s,%s,%s,%s)"%(m,n,x,y)) + s2 = s1.replace("%i","I") + s3 = s2.replace("%pi","pi") + s4 = s3.replace("%e","e") + return s4 ####### elliptic functions and integrals @@ -659,19 +710,18 @@ EXAMPLES: sage: jacobi("sn",1,1) - tanh(1) + 0.76159415595576485 sage: jacobi("cd",1,1/2) - jacobi_cd(1, 1/2) - sage: RDF(jacobi("cd",1,1/2)) - 0.724009721659 - sage: RDF(jacobi("cn",1,1/2)); RDF(jacobi("dn",1,1/2)); RDF(jacobi("cn",1,1/2)/jacobi("dn",1,1/2)) - 0.595976567672 - 0.823161001632 - 0.724009721659 - sage: jsn = jacobi("sn",x,1) - sage: P = plot(jsn,0,1) - sage.: P.show() - """ - _init() - return meval("jacobi_%s(%s,%s)"%(sym, x, m)) + 0.72400972165937116 + sage: jacobi("cn",1,1/2);jacobi("dn",1,1/2);jacobi("cn",1,1/2)/jacobi("dn",1,1/2) + 0.59597656767214113 + 0.82316100163159622 + 0.72400972165937116 + sage: jsn = lambda x: jacobi("sn",x,1) + sage: P= plot(jsn,0,1) + + Now to view this, just type show(P). + + """ + return eval(maxima.eval("jacobi_%s(%s,%s)"%(sym, float(x), float(m)))) def inverse_jacobi(sym,x,m): @@ -683,17 +733,15 @@ EXAMPLES: sage: jacobi("sn",1/2,1/2) - jacobi_sn(1/2, 1/2) - sage: float(jacobi("sn",1/2,1/2)) 0.4707504736556572 - sage: float(inverse_jacobi("sn",0.47,1/2)) + sage: inverse_jacobi("sn",0.47,1/2) 0.4990982313222197 - sage: float(inverse_jacobi("sn",0.4707504,0.5)) + sage: inverse_jacobi("sn",0.4707504,1/2) 0.49999991146655459 - sage: P = plot(inverse_jacobi('sn', x, 0.5), 0, 1, plot_points=20) + sage: ijsn = lambda x: inverse_jacobi("sn",x,1/2) + sage: P= plot(ijsn,0,1) Now to view this, just type show(P). """ - _init() - return meval("inverse_jacobi_%s(%s,%s)"%(sym, x,m)) + return eval(maxima.eval("inverse_jacobi_%s(%s,%s)"%(sym, float(x),float(m)))) #### elliptic integrals @@ -702,35 +750,39 @@ #### of Jacobi elliptic functions but faster to evaluate directly) -## def sinh(t): -## try: -## return t.sinh() -## except AttributeError: -## from sage.calculus.calculus import exp -## return (exp(t)-exp(-t))/2 - -## def cosh(t): -## try: -## return t.cosh() -## except AttributeError: -## from sage.calculus.calculus import exp -## return (exp(t)+exp(-t))/2 - -## def coth(t): -## try: -## return t.coth() -## except AttributeError: -## return 1/tanh(t) - -## def sech(t): -## try: -## return t.sech() -## except AttributeError: -## return 1/cosh(t) - -## def csch(t): -## try: -## return t.csch() -## except AttributeError: -## return 1/sinh(t) +def sinh(t): + try: + return t.sinh() + except AttributeError: + return (exp(t)-exp(-t))/2 + +def cosh(t): + try: + return t.cosh() + except AttributeError: + return (exp(t)+exp(-t))/2 + +def tanh(t): + try: + return t.tanh() + except AttributeError: + return sinh(t)/cosh(t) + +def coth(t): + try: + return t.coth() + except AttributeError: + return 1/tanh(t) + +def sech(t): + try: + return t.sech() + except AttributeError: + return 1/cosh(t) + +def csch(t): + try: + return t.csch() + except AttributeError: + return 1/sinh(t) def dilog(t): Index: sage/functions/transcendental.py =================================================================== --- sage/functions/transcendental.py (revision 4055) +++ sage/functions/transcendental.py (revision 3301) @@ -148,11 +148,16 @@ sage: zeta(RR(2)) 1.6449340668482264364724151666460251892189499012067984377356 - sage: zeta(I) - 0.00330022368532410 - 0.418155449141322*I """ try: return s.zeta() except AttributeError: - return ComplexField()(s).zeta() + return RealField()(s).zeta() + +## prec = s.prec() +## s = pari.new_with_prec(s, prec) +## z = s.zeta()._sage_() +## if z.prec() < prec: +## raise RuntimeError, "Error computing zeta(%s) -- precision loss."%s +## return z def zeta_symmetric(s): Index: sage/geometry/lattice_polytope.py =================================================================== --- sage/geometry/lattice_polytope.py (revision 4061) +++ sage/geometry/lattice_polytope.py (revision 2915) @@ -1098,5 +1098,5 @@ Return a string representation of this face. """ - return repr(self._vertices) + return str(self._vertices) def boundary_points(self): Index: sage/graphs/graph.py =================================================================== --- sage/graphs/graph.py (revision 4065) +++ sage/graphs/graph.py (revision 3592) @@ -57,5 +57,5 @@ sage: d = {0: [1,4,5], 1: [2,6], 2: [3,7], 3: [4,8], 4: [9], 5: [7, 8], 6: [8,9], 7: [9]} sage: G = Graph(d); G - Graph on 10 vertices + A graph on 10 vertices sage: G.save('sage.png') @@ -71,5 +71,5 @@ sage: s = ':I`AKGsaOs`cI]Gb~' sage: G = Graph(s); G - Looped multi-graph on 10 vertices + A looped multi-graph on 10 vertices sage: G.save('sage.png') @@ -90,5 +90,5 @@ [0 0 0 0 1 0 1 1 0 0] sage: G = Graph(M); G - Graph on 10 vertices + A graph on 10 vertices sage: G.save('sage.png') @@ -109,5 +109,5 @@ [ 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 1] sage: G = Graph(M); G - Graph on 10 vertices + A graph on 10 vertices sage: G.save('sage.png') @@ -165,5 +165,5 @@ sage: d = {0 : graphs.DodecahedralGraph(), 1 : graphs.FlowerSnark(),2 : graphs.MoebiusKantorGraph(), 3 : graphs.PetersenGraph() } sage: d[2] - Moebius-Kantor Graph: Graph on 16 vertices + Moebius-Kantor Graph: A graph on 16 vertices sage: T = graphs.TetrahedralGraph() sage: T.vertices() @@ -171,5 +171,5 @@ sage: T.associate(d) sage: T.obj(1) - Flower Snark: Graph on 20 vertices + Flower Snark: A graph on 20 vertices 4. Database @@ -287,5 +287,5 @@ EXAMPLES: sage: g = Graph({0:[1,2,3], 2:[5]}); g - Graph on 5 vertices + A graph on 5 vertices sage: 2 in g True @@ -321,6 +321,5 @@ if name != "No Name" and (not name is None): return self._nxg.name - else: - return repr(self) + else: return repr(self) def _latex_(self): @@ -387,10 +386,10 @@ sage: d = {0: [1,4,5], 1: [2,6], 2: [3,7], 3: [4,8], 4: [9], 5: [7, 8], 6: [8,9], 7: [9]} sage: G = Graph(d); G - Graph on 10 vertices + A graph on 10 vertices sage: G.name("Petersen Graph"); G 'Petersen Graph' - Petersen Graph: Graph on 10 vertices + Petersen Graph: A graph on 10 vertices sage: G.name(set_to_none=True); G - Graph on 10 vertices + A graph on 10 vertices """ if not new is None: @@ -411,14 +410,14 @@ EXAMPLE: sage: G = Graph(); G - Graph on 0 vertices + A graph on 0 vertices sage: G.loops(True); G True - Looped graph on 0 vertices + A looped graph on 0 vertices sage: D = DiGraph(); D - Digraph on 0 vertices + A digraph on 0 vertices sage: D.loops(True); D True - Looped digraph on 0 vertices + A looped digraph on 0 vertices """ if not new is None: @@ -479,8 +478,8 @@ EXAMPLES: sage: G = Graph(); G.add_vertex(); G - Graph on 1 vertex + A graph on 1 vertex sage: D = DiGraph(); D.add_vertex(); D - Digraph on 1 vertex + A digraph on 1 vertex """ if name is None: # then find an integer to use as a key @@ -518,5 +517,5 @@ sage: D = DiGraph({0:[1,2,3,4,5],1:[2],2:[3],3:[4],4:[5],5:[1]}) sage: D.delete_vertex(0); D - Digraph on 5 vertices + A digraph on 5 vertices """ self._nxg.delete_node(vertex) @@ -530,5 +529,5 @@ sage: D = DiGraph({0:[1,2,3,4,5],1:[2],2:[3],3:[4],4:[5],5:[1]}) sage: D.delete_vertices([1,2,3,4,5]); D - Digraph on 1 vertex + A digraph on 1 vertex """ self._nxg.delete_nodes_from(vertices) @@ -564,5 +563,5 @@ sage: d = {0 : graphs.DodecahedralGraph(), 1 : graphs.FlowerSnark(), 2 : graphs.MoebiusKantorGraph(), 3 : graphs.PetersenGraph() } sage: d[2] - Moebius-Kantor Graph: Graph on 16 vertices + Moebius-Kantor Graph: A graph on 16 vertices sage: T = graphs.TetrahedralGraph() sage: T.vertices() @@ -570,5 +569,5 @@ sage: T.associate(d) sage: T.obj(1) - Flower Snark: Graph on 20 vertices + Flower Snark: A graph on 20 vertices """ for v in self.vertices(): @@ -587,5 +586,5 @@ sage: d = {0 : graphs.DodecahedralGraph(), 1 : graphs.FlowerSnark(), 2 : graphs.MoebiusKantorGraph(), 3 : graphs.PetersenGraph() } sage: d[2] - Moebius-Kantor Graph: Graph on 16 vertices + Moebius-Kantor Graph: A graph on 16 vertices sage: T = graphs.TetrahedralGraph() sage: T.vertices() @@ -593,5 +592,5 @@ sage: T.associate(d) sage: T.obj(1) - Flower Snark: Graph on 20 vertices + Flower Snark: A graph on 20 vertices """ return self._assoc[vertex] @@ -649,95 +648,20 @@ Uses a dictionary or permutation to relabel the (di)graph. If perm is a dictionary, each old vertex v is a key in the - dictionary, and its new label is d[v]. If perm is a list, - we think of it as a map i \mapsto perm[i] (only for graphs - with V = {0,1,...,n-1} ). If perm is a per mutation, the - permutation is simply applied to the graph, under the - assumption that V = {0,1,...,n-1} is the vertex set, and + dictionary, and its new label is d[v]. If perm is a permuta- + tion, the permutation is simply applied to the graph, under + the assumption that V = {0,1,...,n-1} is the vertex set, and the permutation acts on the set {1,2,...,n}, where we think of n = 0. - - EXAMPLES: - sage: G = Graph({0:[1],1:[2],2:[]}) - sage: G.am() - [0 1 0] - [1 0 1] - [0 1 0] - - Relabeling using a list: - sage: G.relabel([0,2,1]) - sage: G.am() - [0 0 1] - [0 0 1] - [1 1 0] - - Relabeling using a dictionary: - sage: G.relabel({0:2,2:0}) - sage: G.am() - [0 1 1] - [1 0 0] - [1 0 0] - - Relabeling using a SAGE permutation: - sage: from sage.groups.perm_gps.permgroup import SymmetricGroup - sage: S = SymmetricGroup(3) - sage: gamma = S('(3,2)') - sage: G.relabel(gamma) - sage: G.am() - [0 0 1] - [0 0 1] - [1 1 0] - """ - if type(perm) == list: - if isinstance(self, Graph): - oldd = self._nxg.adj - newd = {} - for v in oldd.iterkeys(): - oldtempd = oldd[v] - newtempd = {} - for w in oldtempd.iterkeys(): - newtempd[perm[w]] = oldtempd[w] - newd[perm[v]] = newtempd - if inplace: - self._nxg.adj = newd - else: - G = self.copy() - G._nxg.adj = newd - return G - else: # DiGraph - oldsucc = self._nxg.succ - oldpred = self._nxg.pred - newsucc = {} - newpred = {} - for v in oldsucc.iterkeys(): - oldtempsucc = oldsucc[v] - newtempsucc = {} - for w in oldtempsucc.iterkeys(): - newtempsucc[perm[w]] = oldtempsucc[w] - newsucc[perm[v]] = newtempsucc - for v in oldpred.iterkeys(): - oldtemppred = oldpred[v] - newtemppred = {} - for w in oldtemppred.iterkeys(): - newtemppred[perm[w]] = oldtemppred[w] - newpred[perm[v]] = newtemppred - if inplace: - self._nxg.adj = newsucc - self._nxg.succ = self._nxg.adj - self._nxg.pred = newpred - else: - D = self.copy() - D._nxg.adj = newsucc - D._nxg.succ = D._nxg.adj - D._nxg.pred = newpred - return D - from sage.groups.perm_gps.permgroup_element import PermutationGroupElement - if type(perm) == PermutationGroupElement: + """ + from sage.groups.perm_gps.permgroup import SymmetricGroup + S = SymmetricGroup(2) + if type(perm) == type(S('(1,2)')): n = self.order() dict = {} - llist = perm.list() + list = perm.list() for i in range(1,n): - dict[i] = llist[i-1]%n + dict[i] = list[i-1]%n if n > 0: - dict[0] = llist[n-1]%n + dict[0] = list[n-1]%n perm = dict if type(perm) == type({}): @@ -900,5 +824,5 @@ pos = None if pos is None: - pos = graph_fast.spring_layout_fast(self) + pos = networkx.drawing.spring_layout(self._nxg) else: for v in pos: @@ -1029,9 +953,7 @@ multiple graphs, the first graph is taken) 'adjacency_matrix' -- a square SAGE matrix M, with M[i][j] equal to the number - of edges \{i,j\} - 'labeled_adjacency_matrix' -- a square SAGE matrix M, with M[i][j] equal to the - label of the single edge \{i,j\} + of edges \{i,j\} 'incidence_matrix' -- a SAGE matrix, with one column C for each edge, where - if C represents \{i, j\}, C[i] is -1 and C[j] is 1 + if C represents \{i, j\}, C[i] is -1 and C[j] is 1 boundary -- a list of boundary vertices, if none, graph is considered as a 'graph without boundary' @@ -1045,9 +967,9 @@ sage: g = networkx.Graph({0:[1,2,3], 2:[5]}) sage: Graph(g) - Graph on 5 vertices + A graph on 5 vertices 2. A dictionary of dictionaries: sage: g = Graph({0:{1:'x',2:'z',3:'a'}, 2:{5:'out'}}); g - Graph on 5 vertices + A graph on 5 vertices The labels ('x', 'z', 'a', 'out') are labels for edges. For example, 'out' is @@ -1057,5 +979,5 @@ 3. A dictionary of lists: sage: g = Graph({0:[1,2,3], 2:[5]}); g - Graph on 5 vertices + A graph on 5 vertices 4. A numpy matrix or ndarray: @@ -1063,5 +985,5 @@ sage: A = numpy.array([[0,1,1],[1,0,1],[1,1,0]]) sage: Graph(A) - Graph on 3 vertices + A graph on 3 vertices 5. A graph6 or sparse6 string: @@ -1070,5 +992,5 @@ sage: s = ':I`AKGsaOs`cI]Gb~' sage: Graph(s) - Looped multi-graph on 10 vertices + A looped multi-graph on 10 vertices There are also list functions to take care of lists of graphs: @@ -1076,5 +998,5 @@ sage: s = ':IgMoqoCUOqeb\n:I`AKGsaOs`cI]Gb~\n:I`EDOAEQ?PccSsge\N\n' sage: graphs_list.from_sparse6(s) - [Looped multi-graph on 10 vertices, Looped multi-graph on 10 vertices, Looped multi-graph on 10 vertices] + [A looped multi-graph on 10 vertices, A looped multi-graph on 10 vertices, A looped multi-graph on 10 vertices] 6. A SAGE matrix: @@ -1096,5 +1018,5 @@ [0 0 0 0 1 0 1 1 0 0] sage: Graph(M) - Graph on 10 vertices + A graph on 10 vertices B. an incidence matrix: @@ -1108,5 +1030,5 @@ [ 0 0 0 0 0] sage: Graph(M) - Graph on 6 vertices + A graph on 6 vertices """ def __init__(self, data=None, pos=None, loops=False, format=None, boundary=None, **kwds): @@ -1160,5 +1082,5 @@ self._nxg = networkx.XGraph(d) elif format == 'sparse6': - from math import ceil, floor + from sage.rings.arith import ceil, floor from sage.misc.functional import log n = data.find('\n') @@ -1167,5 +1089,5 @@ s = data[:n] n, s = graph_fast.N_inverse(s[1:]) - k = int(ceil(log(n,2))) + k = ceil(log(n,2)) l = [graph_fast.binary(ord(i)-63) for i in s] for i in range(len(l)): @@ -1174,5 +1096,5 @@ b = [] x = [] - for i in range(int(floor(len(bits)/(k+1)))): + for i in range(floor(len(bits)/(k+1))): b.append(int(bits[(k+1)*i:(k+1)*i+1],2)) x.append(int(bits[(k+1)*i+1:(k+1)*i+k+1],2)) @@ -1217,16 +1139,4 @@ e.append((i,j)) self._nxg.add_edges_from(e) - elif format == 'weighted_adjacency_matrix': - d = {} - for i in range(data.nrows()): - d[i] = {} - self._nxg = networkx.XGraph(d, selfloops = loops, **kwds) - e = [] - for i,j in data.nonzero_positions(): - if i < j: - e.append((i,j,data[i][j])) - elif i == j and loops: - e.append((i,j,data[i][j])) - self._nxg.add_edges_from(e) elif format == 'incidence_matrix': b = True @@ -1257,5 +1167,10 @@ def _repr_(self): - name = "" + if not self._nxg.name is None and not self._nxg.name == "": + name = self._nxg.name + name = name + ": " + else: + name = "" + name += "A " if self.loops(): name += "looped " @@ -1267,7 +1182,4 @@ else: name += "ices" - name = name.capitalize() - if not self._nxg.name is None and not self._nxg.name == "": - name = self._nxg.name + ": " + name return name @@ -1286,5 +1198,5 @@ EXAMPLE: sage: graphs.PetersenGraph().to_directed() - Digraph on 10 vertices + A digraph on 10 vertices """ return DiGraph(self._nxg.to_directed(), pos=self._pos) @@ -1296,5 +1208,5 @@ EXAMPLE: sage: graphs.PetersenGraph().to_undirected() - Petersen graph: Graph on 10 vertices + Petersen graph: A graph on 10 vertices """ return self.copy() @@ -1317,8 +1229,8 @@ EXAMPLE: sage: G = Graph(multiedges=True); G - Multi-graph on 0 vertices + A multi-graph on 0 vertices sage: G.multiple_edges(False); G False - Graph on 0 vertices + A graph on 0 vertices """ if not new is None: @@ -1389,5 +1301,5 @@ sage: H = Graph() sage: H.add_edges( G.edge_iterator() ); H - Graph on 20 vertices + A graph on 20 vertices """ self._nxg.add_edges_from( edges ) @@ -1910,7 +1822,7 @@ # encode bit vector - from math import ceil + from sage.rings.arith import ceil from sage.misc.functional import log - k = int(ceil(log(n,2))) + k = ceil(log(n,2)) v = 0 i = 0 @@ -2003,11 +1915,11 @@ sage: G = graphs.CompleteGraph(9) sage: H = G.subgraph([0,1,2]); H - Graph on 3 vertices + A graph on 3 vertices sage: G - Complete graph: Graph on 9 vertices + Complete graph: A graph on 9 vertices sage: K = G.subgraph([0,1,2], inplace=True); K - Subgraph of (Complete graph): Graph on 3 vertices + Subgraph of (Complete graph): A graph on 3 vertices sage: G - Subgraph of (Complete graph): Graph on 3 vertices + Subgraph of (Complete graph): A graph on 3 vertices sage: G is K True @@ -2197,5 +2109,5 @@ raise NotImplementedError, "Search algorithm does not support multiple edges yet." else: - from sage.graphs.graph_isom import search_tree, perm_group_elt + from sage.graphs.graph_isom import search_tree from sage.groups.perm_gps.permgroup import PermutationGroup if partition is None: @@ -2205,5 +2117,5 @@ else: a = search_tree(self, partition, dict=False, lab=False, dig=self.loops()) - a = PermutationGroup([perm_group_elt(aa) for aa in a]) + a = PermutationGroup(a) if translation: return a,b @@ -2273,7 +2185,7 @@ sage: D = graphs.DodecahedralGraph() sage: E = D.canonical_label(); E - Dodecahedron: Graph on 20 vertices + Dodecahedron: A graph on 20 vertices sage: D.canonical_label(proof=True) - (Dodecahedron: Graph on 20 vertices, {0: 0, 1: 19, 2: 16, 3: 15, 4: 9, 5: 1, 6: 10, 7: 8, 8: 14, 9: 12, 10: 17, 11: 11, 12: 5, 13: 6, 14: 2, 15: 4, 16: 3, 17: 7, 18: 13, 19: 18}) + (Dodecahedron: A graph on 20 vertices, {0: 0, 1: 19, 2: 16, 3: 15, 4: 9, 5: 1, 6: 10, 7: 8, 8: 14, 9: 12, 10: 17, 11: 11, 12: 5, 13: 6, 14: 2, 15: 4, 16: 3, 17: 7, 18: 13, 19: 18}) sage: D.is_isomorphic(E) True @@ -2330,9 +2242,9 @@ sage: g = networkx.DiGraph({0:[1,2,3], 2:[5]}) sage: DiGraph(g) - Digraph on 5 vertices + A digraph on 5 vertices 2. A dictionary of dictionaries: sage: g = DiGraph({0:{1:'x',2:'z',3:'a'}, 2:{5:'out'}}); g - Digraph on 5 vertices + A digraph on 5 vertices The labels ('x', 'z', 'a', 'out') are labels for arcs. For example, 'out' is @@ -2342,5 +2254,5 @@ 3. A dictionary of lists: sage: g = DiGraph({0:[1,2,3], 2:[5]}); g - Digraph on 5 vertices + A digraph on 5 vertices 4. A numpy matrix or ndarray: @@ -2348,5 +2260,5 @@ sage: A = numpy.array([[0,1,0],[1,0,0],[1,1,0]]) sage: DiGraph(A) - Digraph on 3 vertices + A digraph on 3 vertices 5. A SAGE matrix: @@ -2363,5 +2275,5 @@ [0 0 0 0 0] sage: DiGraph(M) - Digraph on 5 vertices + A digraph on 5 vertices B. an incidence matrix: @@ -2375,5 +2287,5 @@ [ 0 0 0 0 0] sage: DiGraph(M) - Digraph on 6 vertices + A digraph on 6 vertices """ @@ -2411,16 +2323,4 @@ e.append((i,j)) self._nxg.add_edges_from(e) - elif format == 'weighted_adjacency_matrix': - d = {} - for i in range(data.nrows()): - d[i] = {} - self._nxg = networkx.XDiGraph(d, selfloops = loops, **kwds) - e = [] - for i,j in data.nonzero_positions(): - if i != j: - e.append((i,j,data[i][j])) - elif i == j and loops: - e.append((i,j,data[i][j])) - self._nxg.add_edges_from(e) elif format == 'incidence_matrix': b = True @@ -2454,5 +2354,10 @@ def _repr_(self): - name = "" + if not self._nxg.name is None and not self._nxg.name == "": + name = self._nxg.name + name = name + ": " + else: + name = "" + name += "A " if self.loops(): name += "looped " @@ -2464,7 +2369,4 @@ else: name += "ices" - name = name.capitalize() - if not self._nxg.name is None and not self._nxg.name == "": - name = self._nxg.name + ": " + name return name @@ -2482,5 +2384,5 @@ EXAMPLE: sage: DiGraph({0:[1,2,3],4:[5,1]}).to_directed() - Digraph on 6 vertices + A digraph on 6 vertices """ return self.copy() @@ -2517,8 +2419,8 @@ EXAMPLE: sage: D = DiGraph(multiedges=True); D - Multi-digraph on 0 vertices + A multi-digraph on 0 vertices sage: D.multiple_arcs(False); D False - Digraph on 0 vertices + A digraph on 0 vertices """ if not new is None: @@ -2599,5 +2501,5 @@ sage: H = DiGraph() sage: H.add_arcs( G.arc_iterator() ); H - Digraph on 20 vertices + A digraph on 20 vertices """ self._nxg.add_edges_from( arcs ) @@ -3229,11 +3131,11 @@ sage: D = graphs.CompleteGraph(9).to_directed() sage: H = D.subgraph([0,1,2]); H - Digraph on 3 vertices + A digraph on 3 vertices sage: D - Digraph on 9 vertices + A digraph on 9 vertices sage: K = D.subgraph([0,1,2], inplace=True); K - Subgraph of (None): Digraph on 3 vertices + Subgraph of (None): A digraph on 3 vertices sage: D - Subgraph of (None): Digraph on 3 vertices + Subgraph of (None): A digraph on 3 vertices sage: D is K True @@ -3343,5 +3245,5 @@ raise NotImplementedError, "Search algorithm does not support multiple edges yet." else: - from sage.graphs.graph_isom import search_tree, perm_group_elt + from sage.graphs.graph_isom import search_tree from sage.groups.perm_gps.permgroup import PermutationGroup if partition is None: @@ -3351,5 +3253,5 @@ else: a = search_tree(self, partition, dict=False, lab=False, dig=True) - a = PermutationGroup([perm_group_elt(aa) for aa in a]) + a = PermutationGroup(a) if translation: return a,b @@ -3374,12 +3276,12 @@ b,a = self.canonical_label(proof=True) d,c = other.canonical_label(proof=True) + map = {} + cc = c.items() + for vert in self.vertices(): + for aa,bb in cc: + if bb == a[vert]: + map[vert] = aa + break if enum(b) == enum(d): - map = {} - cc = c.items() - for vert in self.vertices(): - for aa,bb in cc: - if bb == a[vert]: - map[vert] = aa - break return True, map else: @@ -3420,5 +3322,5 @@ spring = False if pos3d is None: - pos3d = graph_fast.spring_layout_fast(g, dim=3) + pos3d = networkx.spring_layout(g._nxg, dim=3) try: for v in verts: @@ -3454,29 +3356,13 @@ """ Used for isomorphism checking. - - EXAMPLES: - sage: from sage.graphs.graph import enum - sage: enum(graphs.DodecahedralGraph()) - 646827340296833569479885332381965103655612500627043016896502674924517797573929148319427466126170568392555309533861838850L - sage: enum(graphs.MoebiusKantorGraph()) - 29627597595494233374689380190219099810725571659745484382284031717525232288040L - sage: enum(graphs.FlowerSnark()) - 645682215283153372602620320081348424178216159521280462146968720908564261127120716040952785862033320307812724373694972050L - sage: enum(graphs.CubeGraph(3)) - 6100215452666565930L # 32-bit - 6100215452666565930 # 64-bit - sage: enum(graphs.CubeGraph(4)) - 31323620658472264895128471376615338141839885567113523525061169966087480352810L - sage: enum(graphs.CubeGraph(5)) - 56178607138625465573345383656463935701397275938329921399526324254684498525419117323217491887221387354861371989089284563861938014744765036177184164647909535771592043875566488828479926184925998575521710064024379281086266290501476331004707336065735087197243607743454550839234461575558930808225081956823877550090L - sage: enum(graphs.CubeGraph(6)) - 17009933328531023098235951265708015080189260525466600242007791872273951170067729430659625711869482140011822425402311004663919203785115296476561677814427201708237805402966561863692388687547518491537427897858240566495945005294876576523289206747123399572439707189803821880345487300688962557172856432472391025950779306221469432919735886988596366979797317084123956762362685536557279604675024249987913439836592296340787741671304722135394212035449285260308821361913500205796919484488876249630521666898413890977354122918711285458724686283296097840711521153201188450783978019001984591992381570913097193343212274205747843852376395748070926193308573472616983062165141386183945049871456376379041631456999916186868438148001405477879591035696239287238767746380404501285533026300096772164676955425088646172718295360584249310479706751274583871684827338312536787740914529353458829503642591918761588296961192261166874864565050490306157300749101788751129640698534818737753110920871293122429238702542726347017441416450649382146313791818349648006634724962025571237208317435310419071153813687071275479812184286929976456778629116002591936357623320676067640749567446551071011889378108453641887998273235139859889734259803684619153716302058849155208478850L """ + from sage.rings.integer import Integer M = graph.am() - enumeration = 0 - n = graph.order() - for i, j in M.nonzero_positions(): - enumeration += 1 << ((n-(i+1))*n + n-(j+1)) - return enumeration - - + string = '' + for r in M.rows(): + for c in r: + string += str(c) + if string=='': string='0' + return Integer(string,2) + + Index: sage/graphs/graph_database.py =================================================================== --- sage/graphs/graph_database.py (revision 3734) +++ sage/graphs/graph_database.py (revision 3586) @@ -161,5 +161,5 @@ # Inspect and display graphs individually: sage: glist[0] - Graph on 5 vertices + A graph on 5 vertices sage.: glist[8].show(layout='circular') Index: sage/graphs/graph_fast.pyx =================================================================== --- sage/graphs/graph_fast.pyx (revision 3744) +++ sage/graphs/graph_fast.pyx (revision 3154) @@ -2,12 +2,10 @@ Graph Theory SageX functions -AUTHORS: - -- Robert L. Miller (2007-02-13): initial version - -- Robert W. Bradshaw (2007-03-31): fast spring layout algorithms +AUTHOR: + -- Robert L. Miller (2007-02-13): initial version """ #***************************************************************************** # Copyright (C) 2007 Robert L. Miller -# 2007 Robert W. Bradshaw # # Distributed under the terms of the GNU General Public License (GPL) @@ -15,220 +13,5 @@ #***************************************************************************** -include "../ext/interrupt.pxi" -include '../ext/cdefs.pxi' -include '../ext/stdsage.pxi' -from random import random - -cdef extern from *: - double sqrt(double) - -def spring_layout_fast_split(G, iterations=50, dim=2, vpos=None): - """ - Graphs each component of G separately, placing them adjacent to - each other. This is done because on a disconnected graph, the - spring layout will push components further and further from each - other without bound, resulting in very tight clumps for each - component. - - NOTE: - If the axis are scaled to fit the plot in a square, the - horizontal distance may end up being "squished" due to - the several adjacent components. - - EXAMPLE: - sage: G = graphs.DodecahedralGraph() - sage: for i in range(10): G.add_cycle(range(100*i, 100*i+3)) - sage: N = G.plot() - - AUTHOR: - Robert Bradshaw - """ - Gs = G.connected_components_subgraphs() - pos = {} - left = 0 - buffer = 1/sqrt(len(G)) - for g in Gs: - cur_pos = spring_layout_fast(g, iterations, dim, vpos) - xmin = min([x[0] for x in cur_pos.values()]) - xmax = max([x[0] for x in cur_pos.values()]) - if len(g) > 1: - buffer = (xmax - xmin)/sqrt(len(g)) - for v, loc in cur_pos.iteritems(): - loc[0] += left - xmin + buffer - pos[v] = loc - left += xmax - xmin + buffer - return pos - -def spring_layout_fast(G, iterations=50, dim=2, vpos=None): - """ - Spring force model layout - - This function primarily acts as a wrapper around run_spring, - converting to and from raw c types. - - This kind of speed cannot be achieved by naive pyrexification of the - function alone, especially if we require a function call (let alone - an object creation) every time we want to add a pair of doubles. - """ - - G = G.networkx_graph() - vlist = list(G) # this defines a consistant order - - cdef int i, j, x - cdef int n = G.order() - if n == 0: - return {} - - cdef double* pos = sage_malloc(n * dim * sizeof(double)) - if pos is NULL: - raise MemoryError, "error allocating scratch space for spring layout" - - # convert or create the starting positions as a flat list of doubles - if vpos is None: # set the initial positions randomly in 1x1 box - for i from 0 <= i < n*dim: - pos[i] = random() - else: - for i from 0 <= i < n: - loc = vpos[vlist[i]] - for x from 0 <= x sage_malloc( (2 * len(G.edges()) + 2) * sizeof(int) ) - if elist is NULL: - sage_free(pos) - raise MemoryError, "error allocating scratch space for spring layout" - - cdef int cur_edge = 0 - - for i from 0 <= i < n: - for j from i < j < n: - if G.has_edge(vlist[i], vlist[j]): - elist[cur_edge] = i - elist[cur_edge+1] = j - cur_edge += 2 - - # finish the list with -1, -1 which never gets matched - # but does get compared against when looking for the "next" edge - elist[cur_edge] = -1 - elist[cur_edge+1] = -1 - - run_spring(iterations, dim, pos, elist, n) - - # put the data back into a position dictionary - vpos = {} - for i from 0 <= i < n: - vpos[vlist[i]] = [pos[i*dim+x] for x from 0 <= x < dim] - - sage_free(pos) - sage_free(elist) - - return vpos - - -cdef run_spring(int iterations, int dim, double* pos, int* edges, int n): - """ - Find a locally optimal layout for this graph, according to the - constraints that neighboring nodes want to be a fixed distance - from each other, and non-neighboring nodes always repel. - - This is not a true physical model of mutually-replusive particles - with springs, rather it is more a model of such things traveling, - without any inertia, through an (ever thickening) fluid. - - TODO: The inertial model could be incorperated (with F=ma) - TODO: Are the hard-coded constants here optimal? - - INPUT: - iterations -- number of steps to take - dim -- number of dimensions of freedom - pos -- already initalized initial positions - Each vertext is stored as [dim] consecutive doubles. - These doubles are then placed consecutively in the array. - For example, if dim=3, we would have - pos = [x_1, y_1, z_1, x_2, y_2, z_2, ... , x_n, y_n, z_n] - edges -- List of edges, sorted lexographically by the first - (smallest) vertex, terminated by -1, -1. - The first two entries represent the first edge, and so on. - n -- number of vertices in the graph - - OUTPUT: - Modifies contents of pos. - - AUTHOR: - Robert Bradshaw - """ - - cdef int cur_iter, cur_edge - cdef int i, j, x - - cdef double t = 1, dt = t/iterations, k = sqrt(1.0/n) - cdef double square_dist, force, scale - cdef double* disp_i - cdef double* disp_j - cdef double* delta - - cdef double* disp = sage_malloc((n+1) * dim * sizeof(double)) - if disp is NULL: - raise MemoryError, "error allocating scratch space for spring layout" - delta = &disp[n*dim] - - _sig_on - - for cur_iter from 0 <= cur_iter < iterations: - cur_edge = 1 # offset by one for fast checking against 2nd element first - # zero out the disp vectors - memset(disp, 0, n * dim * sizeof(double)) - for i from 0 <= i < n: - disp_i = disp + (i*dim) - for j from i < j < n: - disp_j = disp + (j*dim) - - for x from 0 <= x < dim: - delta[x] = pos[i*dim+x] - pos[j*dim+x] - - square_dist = delta[0] * delta[0] - for x from 1 <= x < dim: - square_dist += delta[x] * delta[x] - - if square_dist < 0.01: - square_dist = 0.01 - - # they repel according to the (capped) inverse square law - force = k*k/square_dist - - # and if they are neighbors, attract according Hooke's law - if edges[cur_edge] == j and edges[cur_edge-1] == i: - force -= sqrt(square_dist)/k - cur_edge += 2 - - # add this factor into each of the involved points - for x from 0 <= x < dim: - disp_i[x] += delta[x] * force - disp_j[x] -= delta[x] * force - - # now update the positions - for i from 0 <= i < n: - disp_i = disp + (i*dim) - - square_dist = disp_i[0] * disp_i[0] - for x from 1 <= x < dim: - square_dist += disp_i[x] * disp_i[x] - - scale = t / (1 if square_dist < 0.01 else sqrt(square_dist)) - - for x from 0 <= x < dim: - pos[i*dim+x] += disp_i[x] * scale - - t -= dt - - _sig_off - - sage_free(disp) - - - +include '../ext/cdefs.pxi' def binary(n, length=None): Index: sage/graphs/graph_generators.py =================================================================== --- sage/graphs/graph_generators.py (revision 3734) +++ sage/graphs/graph_generators.py (revision 3586) @@ -318,5 +318,5 @@ sage: G = graphs.ClawGraph() sage: G - Claw graph: Graph on 4 vertices + Claw graph: A graph on 4 vertices """ pos_dict = {0:[0,1],1:[-1,0],2:[0,0],3:[1,0]} @@ -1136,5 +1136,5 @@ sage: F = graphs.FlowerSnark() sage: F - Flower Snark: Graph on 20 vertices + Flower Snark: A graph on 20 vertices sage: F.graph6_string() 'ShCGHC@?GGg@?@?Gp?K??C?CA?G?_G?Cc' @@ -1178,5 +1178,5 @@ sage: FRUCHT = graphs.FruchtGraph() sage: FRUCHT - Frucht graph: Graph on 12 vertices + Frucht graph: A graph on 12 vertices sage: FRUCHT.graph6_string() 'KhCKM?_EGK?L' @@ -1220,5 +1220,5 @@ sage: H = graphs.HeawoodGraph() sage: H - Heawood graph: Graph on 14 vertices + Heawood graph: A graph on 14 vertices sage: H.graph6_string() 'MhEGHC@AI?_PC@_G_' @@ -1259,5 +1259,5 @@ sage: MK = graphs.MoebiusKantorGraph() sage: MK - Moebius-Kantor Graph: Graph on 16 vertices + Moebius-Kantor Graph: A graph on 16 vertices sage: MK.graph6_string() 'OhCGKE?O@?ACAC@I?Q_AS' @@ -1332,5 +1332,5 @@ sage: T = graphs.ThomsenGraph() sage: T - Thomsen graph: Graph on 6 vertices + Thomsen graph: A graph on 6 vertices sage: T.graph6_string() 'EFz_' Index: sage/graphs/graph_isom.py =================================================================== --- sage/graphs/graph_isom.py (revision 3880) +++ sage/graphs/graph_isom.py (revision 3596) @@ -31,5 +31,4 @@ ############################################################################## -from sage.graphs.graph import Graph, DiGraph def finer(Pi1, Pi2): @@ -139,6 +138,6 @@ return l -def orbit_partition(gamma, list_perm=False): - r""" +def orbit_partition(G, gamma): + """ Assuming that G is a graph on vertices {0,1,...,n-1}, and gamma is an element of SymmetricGroup(n), returns the partition of the vertex set @@ -147,8 +146,4 @@ determined by a cyclic representation of gamma. - INPUT: - list_perm -- if True, assumes gamma is a list representing the map - i \mapsto gamma[i]. - EXAMPLES: sage: import sage.graphs.graph_isom @@ -157,38 +152,20 @@ sage: S = SymmetricGroup(10) sage: gamma = S('(10,1,2,3,4)(5,6,7)(8,9)') - sage: orbit_partition(gamma) + sage: orbit_partition(G,gamma) [[1, 2, 3, 4, 0], [5, 6, 7], [8, 9]] sage: gamma = S('(10,5)(1,6)(2,7)(3,8)(4,9)') - sage: orbit_partition(gamma) + sage: orbit_partition(G,gamma) [[1, 6], [2, 7], [3, 8], [4, 9], [5, 0]] """ - if list_perm: - n = len(gamma) - seen = [1] + [0]*(n-1) - i = 0 - p = 0 - partition = [[0]] - while sum(seen) < n: - if gamma[i] != partition[p][0]: - partition[p].append(gamma[i]) - i = gamma[i] - seen[i] = 1 - else: - i = min([j for j in range(n) if seen[j] == 0]) - partition.append([i]) - p += 1 - seen[i] = 1 - return partition - else: - n = len(gamma.list()) - l = [] - for i in range(1,n+1): - orb = gamma.orbit(i) - if orb not in l: l.append(orb) - for i in l: - for j in range(len(i)): - if i[j] == n: - i[j] = 0 - return l + n = len(gamma.list()) + l = [] + for i in range(1,n+1): + orb = gamma.orbit(i) + if orb not in l: l.append(orb) + for i in l: + for j in range(len(i)): + if i[j] == n: + i[j] = 0 + return l def sat225(Pi, n): @@ -224,7 +201,12 @@ """ i = 0 - for u in W: - if G._nxg.adj[u].has_key(v): - i += 1 + if G.is_directed(): + for u in W: + if G.has_arc(u,v): + i += 1 + else: + for u in W: + if G.has_edge(u,v): + i += 1 return i @@ -504,13 +486,9 @@ return prod([l for l in LL if l!=0]) -def get_permutation(eta, nu, list_perm=False): - r""" +def get_permutation(eta, nu): + """ Given two terminal nodes of the search tree, eta and nu, each last partition is discrete, and the order of the partition determines a permutation gamma such that gamma(eta) = nu. Returns the partition gamma. - - INPUT: - list_perm -- if True, returns a list L representing the map i \mapsto - L[i]. EXAMPLE: @@ -523,71 +501,46 @@ sage: get_permutation(eta, nu) (1,8,7,14,15,16,17,18,19,20)(12,4,11,3,10,2,9,6,13,5) - sage: get_permutation(eta, nu, list_perm=True) - [1, 8, 9, 10, 11, 12, 13, 14, 7, 6, 2, 3, 4, 5, 15, 16, 17, 18, 19, 0] - """ - a = nu[-1] - b = eta[-1] + """ + from sage.rings.integer import Integer + from sage.groups.perm_gps.permgroup import SymmetricGroup + a = nu[len(nu)-Integer(1)] + b = eta[len(eta)-Integer(1)] n = len(b) - if list_perm: - gamma = [] - i = 0 - while len(gamma) < n: - for j in range(n): - if b[j][0] == i: - gamma.append(a[j][0]) - i += 1 + S = SymmetricGroup(n) + gamma = [] + for i in range(len(b)): + if b[i][0] != a[i][0]: + gamma.append([b[i][0],a[i][0]]) + i = 0 + while i < len(gamma): + if gamma[i][0] == gamma[i][-1]: + i += 1 + else: + for j in range(i+1,len(gamma)): + if gamma[i][-1] == gamma[j][0]: + gamma[i] = gamma[i] + gamma[j][1:] + gamma.pop(j) break - return gamma + for i in range(len(gamma)): + gamma[i] = gamma[i][1:] + if len(gamma) == 0: + gamma = S('()') else: - from sage.groups.perm_gps.permgroup import SymmetricGroup - S = SymmetricGroup(n) - gamma = [] - for i in range(len(b)): - if b[i][0] != a[i][0]: - gamma.append([b[i][0],a[i][0]]) - i = 0 - while i < len(gamma): - if gamma[i][0] == gamma[i][-1]: - i += 1 - else: - for j in range(i+1,len(gamma)): - if gamma[i][-1] == gamma[j][0]: - gamma[i] = gamma[i] + gamma[j][1:] - gamma.pop(j) - break - for i in range(len(gamma)): - gamma[i] = gamma[i][1:] - if len(gamma) == 0: - gamma = S('()') - else: - gamma = S(str(gamma)[1:-1].replace('[','(').replace(']',')').\ - replace(' ', '').replace('(0','('+str(n)).replace(',0',','+str(n))) - return gamma - -def term_pnest_graph(G, nu, enumer=False): + gamma = S(str(gamma)[1:-1].replace('[','(').replace(']',')').\ + replace(' ', '').replace('(0','('+str(n)).replace(',0',','+str(n))) + return gamma + +def term_pnest_graph(G, nu): """ BDM's G(nu): returns the graph G, relabeled in the order found in nu[last]. Assumes nu is a terminal partition nest in T(G, Pi). """ - n = G.order() + ord = nu[len(nu)-1] d = {} - for i in range(n): - d[nu[-1][i][0]] = i - if enumer: - # we know that the vertex set is {0,...,n-1}... - numbr = 0 - if isinstance(G, Graph): - for i,j,l in G.edge_iterator(): - numbr += 1<<((n-(d[i]+1))*n + n-(d[j]+1)) - numbr += 1<<((n-(d[j]+1))*n + n-(d[i]+1)) - elif isinstance(G, DiGraph): - for i,j,l in G.arc_iterator(): - numbr += 1<<((n-(d[i]+1))*n + n-(d[j]+1)) - return numbr - else: - ord = nu[-1] - H = G.copy() - H.relabel(d) - return H + for i in range(len(nu[len(nu)-1])): + d[nu[len(nu)-1][i][0]] = i + H = G.copy() + H.relabel(d) + return H def search_tree(G, Pi, lab=True, dig=False, dict=False, proof=False): @@ -629,5 +582,5 @@ sage: from sage.groups.perm_gps.permgroup import PermutationGroup sage: import sage.graphs.graph_isom - sage: from sage.graphs.graph_isom import search_tree, perm_group_elt + sage: from sage.graphs.graph_isom import search_tree sage: from sage.graphs.graph import enum @@ -636,9 +589,9 @@ sage: a,b = search_tree(G, Pi) sage: print a, enum(b) - [[0, 19, 3, 2, 6, 5, 4, 17, 18, 11, 10, 9, 13, 12, 16, 15, 14, 7, 8, 1], [0, 1, 8, 9, 13, 14, 7, 6, 2, 3, 19, 18, 17, 4, 5, 15, 16, 12, 11, 10], [0, 19, 18, 11, 12, 16, 17, 4, 3, 2, 1, 8, 7, 6, 5, 15, 14, 13, 9, 10], [1, 8, 9, 10, 11, 12, 13, 14, 7, 6, 2, 3, 4, 5, 15, 16, 17, 18, 19, 0]] 17318942212009113839976787462421724338461987195898671092180383421848885858584973127639899792828728124797968735273000 + [(16,14)(13,12)(7,17)(6,4)(9,11)(8,18)(2,3)(1,19), (14,5)(17,12)(4,13)(6,7)(18,11)(3,9)(2,8)(19,10), (16,14,5)(7,4,12)(6,17,13)(8,3,11)(2,18,9)(1,19,10), (1,8,7,14,15,16,17,18,19,20)(12,4,11,3,10,2,9,6,13,5)] 17318942212009113839976787462421724338461987195898671092180383421848885858584973127639899792828728124797968735273000 sage: c = search_tree(G, Pi, lab=False) sage: print c - [[0, 19, 3, 2, 6, 5, 4, 17, 18, 11, 10, 9, 13, 12, 16, 15, 14, 7, 8, 1], [0, 1, 8, 9, 13, 14, 7, 6, 2, 3, 19, 18, 17, 4, 5, 15, 16, 12, 11, 10], [0, 19, 18, 11, 12, 16, 17, 4, 3, 2, 1, 8, 7, 6, 5, 15, 14, 13, 9, 10], [1, 8, 9, 10, 11, 12, 13, 14, 7, 6, 2, 3, 4, 5, 15, 16, 17, 18, 19, 0]] - sage: DodecAut = PermutationGroup([perm_group_elt(aa) for aa in a]) + [(16,14)(13,12)(7,17)(6,4)(9,11)(8,18)(2,3)(1,19), (14,5)(17,12)(4,13)(6,7)(18,11)(3,9)(2,8)(19,10), (16,14,5)(7,4,12)(6,17,13)(8,3,11)(2,18,9)(1,19,10), (1,8,7,14,15,16,17,18,19,20)(12,4,11,3,10,2,9,6,13,5)] + sage: DodecAut = PermutationGroup(a) sage: DodecAut.character_table() [ 1 1 1 1 1 1 1 1 1 1] @@ -652,5 +605,5 @@ [ 5 1 -1 1 0 0 -1 0 0 5] [ 5 -1 -1 1 0 0 1 0 0 -5] - sage: DodecAut2 = PermutationGroup([perm_group_elt(cc) for cc in c]) + sage: DodecAut2 = PermutationGroup(c) sage: DodecAut2.character_table() [ 1 1 1 1 1 1 1 1 1 1] @@ -669,7 +622,7 @@ sage: a,b = search_tree(G, Pi) sage: print a, enum(b) - [[0, 1, 2, 7, 5, 4, 6, 3, 9, 8], [0, 1, 6, 8, 5, 4, 2, 9, 3, 7], [0, 4, 3, 8, 5, 1, 9, 2, 6, 7], [1, 0, 4, 9, 6, 2, 5, 3, 7, 8]] 8716441511243809436161868448 + [(9,8)(3,7)(4,5), (3,8)(7,9)(6,2)(4,5), (6,9,7,2,3,8)(4,5,1), (1,10)(7,3,9,8)(4,6,5,2)] 8716441511243809436161868448 sage: c = search_tree(G, Pi, lab=False) - sage: PAut = PermutationGroup([perm_group_elt(aa) for aa in a]) + sage: PAut = PermutationGroup(a) sage: PAut.character_table() [ 1 1 1 1 1 1 1] @@ -680,5 +633,5 @@ [ 5 -1 1 -1 -1 1 0] [ 6 0 -2 0 0 0 1] - sage: PAut = PermutationGroup([perm_group_elt(cc) for cc in c]) + sage: PAut = PermutationGroup(c) sage: PAut.character_table() [ 1 1 1 1 1 1 1] @@ -699,10 +652,10 @@ sage: a,b = search_tree(G, Pi) sage: print a, enum(b) - [[0, 3, 2, 1, 6, 5, 4, 7], [0, 1, 4, 5, 2, 3, 6, 7], [0, 3, 6, 5, 2, 1, 4, 7], [1, 0, 3, 2, 5, 4, 7, 6]] 520239721777506480 + [(6,4)(1,3), (4,2)(3,5), (6,4,2)(1,3,5), (1,8)(6,7)(3,2)(5,4)] 520239721777506480 sage: c = search_tree(G, Pi, lab=False) - sage: PermutationGroup([perm_group_elt(aa) for aa in a]).order() + sage: PermutationGroup(a).order() 48 - sage: PermutationGroup([perm_group_elt(cc) for cc in c]).order() + sage: PermutationGroup(c).order() 48 sage: DodecAut.order() @@ -751,14 +704,14 @@ [] 0 [] 0 [] [] 0 [] 0 [] - [[1, 0]] 0 [[1, 0]] 0 [[1, 0]] - [[1, 0]] 0 [[1, 0]] 0 [[1, 0]] + [(1,2)] 0 [(1,2)] 0 [(1,2)] + [(1,2)] 0 [(1,2)] 0 [(1,2)] [] 6 [] 6 [] [] 6 [] 6 [] - [[1, 0]] 6 [[1, 0]] 6 [[1, 0]] - [[1, 0]] 6 [[1, 0]] 6 [[1, 0]] - + [(1,2)] 6 [(1,2)] 6 [(1,2)] + [(1,2)] 6 [(1,2)] 6 [(1,2)] + sage: graph3 = all_labeled_graphs(3) sage: part3 = all_ordered_partitions(range(3)) - sage: for G in graph3: # long time (~30 secs) + sage: for G in graph3: # long time ... for Pi in part3: ... a,b = search_tree(G, Pi) @@ -769,30 +722,30 @@ [] 0 [] 0 [] [] 0 [] 0 [] - [[0, 2, 1]] 0 [[0, 2, 1]] 0 [[0, 2, 1]] - [[0, 2, 1]] 0 [[0, 2, 1]] 0 [[0, 2, 1]] + [(2,1)] 0 [(2,1)] 0 [(2,1)] + [(2,1)] 0 [(2,1)] 0 [(2,1)] [] 0 [] 0 [] [] 0 [] 0 [] - [[2, 1, 0]] 0 [[2, 1, 0]] 0 [[2, 1, 0]] - [[2, 1, 0]] 0 [[2, 1, 0]] 0 [[2, 1, 0]] + [(2,3)] 0 [(2,3)] 0 [(2,3)] + [(2,3)] 0 [(2,3)] 0 [(2,3)] [] 0 [] 0 [] [] 0 [] 0 [] - [[1, 0, 2]] 0 [[1, 0, 2]] 0 [[1, 0, 2]] - [[1, 0, 2]] 0 [[1, 0, 2]] 0 [[1, 0, 2]] - [[1, 0, 2]] 0 [[1, 0, 2]] 0 [[1, 0, 2]] - [[2, 1, 0]] 0 [[2, 1, 0]] 0 [[2, 1, 0]] - [[1, 0, 2]] 0 [[1, 0, 2]] 0 [[1, 0, 2]] - [[0, 2, 1]] 0 [[0, 2, 1]] 0 [[0, 2, 1]] - [[2, 1, 0]] 0 [[2, 1, 0]] 0 [[2, 1, 0]] - [[0, 2, 1]] 0 [[0, 2, 1]] 0 [[0, 2, 1]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] 0 [[0, 2, 1], [1, 0, 2]] - [] 10 [] 10 [] - [] 10 [] 10 [] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] + [(1,3)] 0 [(1,3)] 0 [(1,3)] + [(1,3)] 0 [(1,3)] 0 [(1,3)] + [(1,3)] 0 [(1,3)] 0 [(1,3)] + [(2,3)] 0 [(2,3)] 0 [(2,3)] + [(1,3)] 0 [(1,3)] 0 [(1,3)] + [(2,1)] 0 [(2,1)] 0 [(2,1)] + [(2,3)] 0 [(2,3)] 0 [(2,3)] + [(2,1)] 0 [(2,1)] 0 [(2,1)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [(2,1), (1,3)] 0 [(2,1), (1,3)] 0 [(2,1), (1,3)] + [] 10 [] 10 [] + [] 10 [] 10 [] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] [] 68 [] 68 [] [] 160 [] 160 [] @@ -806,13 +759,13 @@ [] 10 [] 10 [] [] 10 [] 10 [] - [[0, 2, 1]] 160 [[0, 2, 1]] 160 [[0, 2, 1]] - [] 10 [] 10 [] - [[0, 2, 1]] 160 [[0, 2, 1]] 160 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] - [[0, 2, 1]] 10 [[0, 2, 1]] 10 [[0, 2, 1]] + [(2,1)] 160 [(2,1)] 160 [(2,1)] + [] 10 [] 10 [] + [(2,1)] 160 [(2,1)] 160 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] + [(2,1)] 10 [(2,1)] 10 [(2,1)] [] 68 [] 68 [] [] 160 [] 160 [] @@ -821,6 +774,6 @@ [] 10 [] 10 [] [] 10 [] 10 [] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] [] 160 [] 160 [] [] 68 [] 68 [] @@ -828,15 +781,15 @@ [] 68 [] 68 [] [] 10 [] 10 [] - [[2, 1, 0]] 160 [[2, 1, 0]] 160 [[2, 1, 0]] - [] 10 [] 10 [] - [] 10 [] 10 [] - [[2, 1, 0]] 160 [[2, 1, 0]] 160 [[2, 1, 0]] - [] 10 [] 10 [] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] - [[2, 1, 0]] 10 [[2, 1, 0]] 10 [[2, 1, 0]] + [(2,3)] 160 [(2,3)] 160 [(2,3)] + [] 10 [] 10 [] + [] 10 [] 10 [] + [(2,3)] 160 [(2,3)] 160 [(2,3)] + [] 10 [] 10 [] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] + [(2,3)] 10 [(2,3)] 10 [(2,3)] [] 78 [] 78 [] [] 170 [] 170 [] @@ -849,18 +802,18 @@ [] 228 [] 228 [] [] 228 [] 228 [] - [[1, 0, 2]] 228 [[1, 0, 2]] 228 [[1, 0, 2]] - [[1, 0, 2]] 228 [[1, 0, 2]] 228 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [] 170 [] 170 [] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [] 170 [] 170 [] - [] 170 [] 170 [] - [] 170 [] 170 [] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] - [[1, 0, 2]] 78 [[1, 0, 2]] 78 [[1, 0, 2]] + [(1,3)] 228 [(1,3)] 228 [(1,3)] + [(1,3)] 228 [(1,3)] 228 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [] 170 [] 170 [] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [] 170 [] 170 [] + [] 170 [] 170 [] + [] 170 [] 170 [] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] + [(1,3)] 78 [(1,3)] 78 [(1,3)] [] 160 [] 160 [] [] 68 [] 68 [] @@ -873,18 +826,18 @@ [] 10 [] 10 [] [] 10 [] 10 [] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 160 [[1, 0, 2]] 160 [[1, 0, 2]] - [] 10 [] 10 [] - [[1, 0, 2]] 160 [[1, 0, 2]] 160 [[1, 0, 2]] - [] 10 [] 10 [] - [] 10 [] 10 [] - [] 10 [] 10 [] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] - [[1, 0, 2]] 10 [[1, 0, 2]] 10 [[1, 0, 2]] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 160 [(1,3)] 160 [(1,3)] + [] 10 [] 10 [] + [(1,3)] 160 [(1,3)] 160 [(1,3)] + [] 10 [] 10 [] + [] 10 [] 10 [] + [] 10 [] 10 [] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] + [(1,3)] 10 [(1,3)] 10 [(1,3)] [] 170 [] 170 [] [] 78 [] 78 [] @@ -893,99 +846,101 @@ [] 228 [] 228 [] [] 228 [] 228 [] - [[2, 1, 0]] 228 [[2, 1, 0]] 228 [[2, 1, 0]] - [[2, 1, 0]] 228 [[2, 1, 0]] 228 [[2, 1, 0]] - [] 78 [] 78 [] - [] 170 [] 170 [] - [] 78 [] 78 [] - [] 78 [] 78 [] - [] 170 [] 170 [] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [] 170 [] 170 [] - [] 170 [] 170 [] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [] 170 [] 170 [] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] - [[2, 1, 0]] 78 [[2, 1, 0]] 78 [[2, 1, 0]] + [(2,3)] 228 [(2,3)] 228 [(2,3)] + [(2,3)] 228 [(2,3)] 228 [(2,3)] + [] 78 [] 78 [] + [] 170 [] 170 [] + [] 78 [] 78 [] + [] 78 [] 78 [] + [] 170 [] 170 [] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [] 170 [] 170 [] + [] 170 [] 170 [] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [] 170 [] 170 [] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [(2,3)] 78 [(2,3)] 78 [(2,3)] + [(2,3)] 78 [(2,3)] 78 [(2,3)] [] 228 [] 228 [] [] 228 [] 228 [] - [[0, 2, 1]] 228 [[0, 2, 1]] 228 [[0, 2, 1]] - [[0, 2, 1]] 228 [[0, 2, 1]] 228 [[0, 2, 1]] - [] 170 [] 170 [] - [] 78 [] 78 [] - [] 78 [] 78 [] - [] 78 [] 78 [] - [] 170 [] 170 [] - [] 78 [] 78 [] - [] 78 [] 78 [] - [] 78 [] 78 [] - [] 170 [] 170 [] - [] 170 [] 170 [] - [] 170 [] 170 [] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [] 170 [] 170 [] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] - [[0, 2, 1]] 78 [[0, 2, 1]] 78 [[0, 2, 1]] + [(2,1)] 228 [(2,1)] 228 [(2,1)] + [(2,1)] 228 [(2,1)] 228 [(2,1)] + [] 170 [] 170 [] + [] 78 [] 78 [] + [] 78 [] 78 [] + [] 78 [] 78 [] + [] 170 [] 170 [] + [] 78 [] 78 [] + [] 78 [] 78 [] + [] 78 [] 78 [] + [] 170 [] 170 [] + [] 170 [] 170 [] + [] 170 [] 170 [] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [] 170 [] 170 [] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] + [(2,1)] 78 [(2,1)] 78 [(2,1)] [] 238 [] 238 [] [] 238 [] 238 [] - [[0, 2, 1]] 238 [[0, 2, 1]] 238 [[0, 2, 1]] - [[0, 2, 1]] 238 [[0, 2, 1]] 238 [[0, 2, 1]] + [(2,1)] 238 [(2,1)] 238 [(2,1)] + [(2,1)] 238 [(2,1)] 238 [(2,1)] [] 238 [] 238 [] [] 238 [] 238 [] - [[2, 1, 0]] 238 [[2, 1, 0]] 238 [[2, 1, 0]] - [[2, 1, 0]] 238 [[2, 1, 0]] 238 [[2, 1, 0]] + [(2,3)] 238 [(2,3)] 238 [(2,3)] + [(2,3)] 238 [(2,3)] 238 [(2,3)] [] 238 [] 238 [] [] 238 [] 238 [] - [[1, 0, 2]] 238 [[1, 0, 2]] 238 [[1, 0, 2]] - [[1, 0, 2]] 238 [[1, 0, 2]] 238 [[1, 0, 2]] - [[1, 0, 2]] 238 [[1, 0, 2]] 238 [[1, 0, 2]] - [[2, 1, 0]] 238 [[2, 1, 0]] 238 [[2, 1, 0]] - [[1, 0, 2]] 238 [[1, 0, 2]] 238 [[1, 0, 2]] - [[0, 2, 1]] 238 [[0, 2, 1]] 238 [[0, 2, 1]] - [[2, 1, 0]] 238 [[2, 1, 0]] 238 [[2, 1, 0]] - [[0, 2, 1]] 238 [[0, 2, 1]] 238 [[0, 2, 1]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] - [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] 238 [[0, 2, 1], [1, 0, 2]] + [(1,3)] 238 [(1,3)] 238 [(1,3)] + [(1,3)] 238 [(1,3)] 238 [(1,3)] + [(1,3)] 238 [(1,3)] 238 [(1,3)] + [(2,3)] 238 [(2,3)] 238 [(2,3)] + [(1,3)] 238 [(1,3)] 238 [(1,3)] + [(2,1)] 238 [(2,1)] 238 [(2,1)] + [(2,3)] 238 [(2,3)] 238 [(2,3)] + [(2,1)] 238 [(2,1)] 238 [(2,1)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] + [(2,1), (1,3)] 238 [(2,1), (1,3)] 238 [(2,1), (1,3)] sage: C = graphs.CubeGraph(1) sage: gens = search_tree(C, [C.vertices()], lab=False) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() + sage: PermutationGroup(gens).order() 2 sage: C = graphs.CubeGraph(2) sage: gens = search_tree(C, [C.vertices()], lab=False) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() + sage: PermutationGroup(gens).order() 8 sage: C = graphs.CubeGraph(3) sage: gens = search_tree(C, [C.vertices()], lab=False) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() + sage: PermutationGroup(gens).order() 48 sage: C = graphs.CubeGraph(4) sage: gens = search_tree(C, [C.vertices()], lab=False) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() + sage: PermutationGroup(gens).order() 384 sage: C = graphs.CubeGraph(5) - sage: gens = search_tree(C, [C.vertices()], lab=False) # long time (~8 secs) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() # long time + sage: gens = search_tree(C, [C.vertices()], lab=False) # long time + sage: PermutationGroup(gens).order() # long time 3840 sage: C = graphs.CubeGraph(6) - sage: gens = search_tree(C, [C.vertices()], lab=False) # long time (~50 secs) - sage: PermutationGroup([perm_group_elt(aa) for aa in gens]).order() # long time + sage: gens = search_tree(C, [C.vertices()], lab=False) # long time + sage: PermutationGroup(gens).order() # long time 46080 """ from copy import copy + from sage.groups.perm_gps.permgroup import SymmetricGroup from sage.rings.infinity import Infinity n = G.order() + S = SymmetricGroup(n) Pi = copy(Pi) @@ -1118,5 +1073,5 @@ elif k < hzf: state = 8 ## BDM had !=, broke at G = Graph({0:[],1:[],2:[]}), Pi = [[0,1,2]] else: - gamma = get_permutation(eta.values(), nu.values(), list_perm=True) + gamma = get_permutation(eta.values(), nu.values()) # print gamma if G == G.relabel(gamma, inplace=False): # if G^gamma == G: @@ -1128,8 +1083,8 @@ if (not lab) or (qzb < 0): state = 6 elif (qzb > 0) or (k < len(rho)): state = 9 - elif (term_pnest_graph(G, nu.values(), enumer=True) > term_pnest_graph(G, rho.values(), enumer=True)): state = 9 - elif (term_pnest_graph(G, nu.values(), enumer=True) < term_pnest_graph(G, rho.values(), enumer=True)): state = 6 + elif (term_pnest_graph(G, nu.values()) > term_pnest_graph(G, rho.values())): state = 9 + elif (term_pnest_graph(G, nu.values()) < term_pnest_graph(G, rho.values())): state = 6 else: - gamma = get_permutation(nu.values(), rho.values(), list_perm=True) + gamma = get_permutation(nu.values(), rho.values()) # print gamma state = 10 @@ -1145,10 +1100,10 @@ # print 'state: 10' l = min([l+1,L]) - Omega[l] = min_cell_reps(orbit_partition(gamma, list_perm=True)) - Phi[l] = fix(orbit_partition(gamma, list_perm=True)) - if finer( orbit_partition(gamma, list_perm=True), Theta ): + Omega[l] = min_cell_reps(orbit_partition(G, gamma)) + Phi[l] = fix(orbit_partition(G, gamma)) + if finer( orbit_partition(G, gamma), Theta ): state = 11 else: - Theta = vee( orbit_partition(gamma, list_perm=True), Theta ) + Theta = vee( orbit_partition(G, gamma), Theta ) output.append(gamma) if tvc in min_cell_reps(Theta) and lab: ## added "and lab" @@ -1274,26 +1229,4 @@ return output -def perm_group_elt(lperm): - """ - Given a list permutation of the set {0, 1, ..., n-1}, - returns the corresponding PermutationGroupElement where - we take 0 = n. - """ - from sage.groups.perm_gps.permgroup import SymmetricGroup - n = len(lperm) - S = SymmetricGroup(n) - Part = orbit_partition(lperm, list_perm=True) - gens = [] - for z in Part: - if len(z) > 1: - if 0 in z: - zed = z.index(0) - generator = z[:zed] + [n] + z[zed+1:] - gens.append(tuple(generator)) - else: - gens.append(tuple(z)) - E = S(gens) - return E - # Benchmarking functions @@ -1310,5 +1243,5 @@ sage: Glist = {} sage: Giso = {} - sage: for n in range(1,5): # long time (~9 secs) + sage: for n in range(1,5): # long time ... Glist[n] = all_labeled_graphs(n) ... Giso[n] = [] @@ -1393,5 +1326,5 @@ sage: Glist = {} sage: Giso = {} - sage.: for n in range(1,4): # long time (~130 secs) + sage: for n in range(1,4): # long time ... Glist[n] = all_labeled_digraphs_with_loops(n) ... Giso[n] = [] @@ -1404,5 +1337,5 @@ ... if not inn: ... Giso[n].append(b) - sage.: for n in Giso: # long time (depends on previous) + sage: for n in Giso: # long time (depends on previous) ... print n, len(Giso[n]) 1 2 Index: sage/graphs/graph_list.py =================================================================== --- sage/graphs/graph_list.py (revision 3734) +++ sage/graphs/graph_list.py (revision 3586) @@ -58,5 +58,5 @@ sage: l = ['N@@?N@UGAGG?gGlKCMO','XsGGWOW?CC?C@HQKHqOjYKC_uHWGX?P?~TqIKA`OA@SAOEcEA??'] sage: graphs_list.from_graph6(l) - [Graph on 14 vertices, Graph on 25 vertices] + [A graph on 14 vertices, A graph on 25 vertices] """ from sage.graphs.graph import Graph @@ -99,5 +99,5 @@ sage: l = [':P_`cBaC_ACd`C_@BC`ABDHaEH_@BF_@CHIK_@BCEHKL_BIKM_BFGHI',':f`??KO?B_OOSCGE_?OWONDBO?GOJBDO?_SSJdApcOIG`?og_UKEbg?_SKFq@[CCBA`p?oYMFp@gw]Qaa@xEMHDb@hMCBCbQ@ECHEcAKKQKFPOwo[PIDQ{KIHEcQPOkVKEW_WMNKqPWwcRKOOWSKIGCqhWt??___WMJFCahWzEBa`xOu[MpPPKqYNoOOOKHHDBPs|??__gWMKEcAHKgTLErqA?A@a@G{kVLErs?GDBA@XCs\\NggWSOJIDbHh@?A@aF'] sage: graphs_list.from_sparse6(l) - [Looped multi-graph on 17 vertices, Looped multi-graph on 39 vertices] + [A looped multi-graph on 17 vertices, A looped multi-graph on 39 vertices] """ from sage.graphs.graph import Graph Index: sage/groups/abelian_gps/dual_abelian_group_element.py =================================================================== --- sage/groups/abelian_gps/dual_abelian_group_element.py (revision 4063) +++ sage/groups/abelian_gps/dual_abelian_group_element.py (revision 3290) @@ -270,6 +270,5 @@ if is_ComplexField(F): I = F.gen() - PI = F(pi) - ans = prod([exp(2*PI*I*expsX[i]*expsg[i]/invs[i]) for i in range(len(expsX))]) + ans = prod([exp(2*pi*I*expsX[i]*expsg[i]/invs[i]) for i in range(len(expsX))]) return ans ans = F(1) ## assumes F is the cyclotomic field Index: sage/groups/group.pyx =================================================================== --- sage/groups/group.pyx (revision 3977) +++ sage/groups/group.pyx (revision 2419) @@ -121,20 +121,4 @@ return True - def cayley_graph(self): - from sage.graphs.graph import DiGraph - arrows = {} - for g in self: - for s in self.gens(): - gs = g*s - if not gs == g: - try: - _ = arrows[g] - except KeyError: - arrows[g] = {} - - arrows[g][gs] = s - - return DiGraph(arrows) - cdef class AlgebraicGroup(Group): """ Index: sage/gsl/dft.py =================================================================== --- sage/gsl/dft.py (revision 4063) +++ sage/gsl/dft.py (revision 3627) @@ -67,6 +67,8 @@ from sage.rings.real_mpfr import RR from sage.rings.all import CC, I -from sage.calculus.all import sin, cos -from sage.functions.constants import pi +from math import sin +from math import cos +from sage.functions.constants import Pi +pi = Pi() from sage.gsl.fft import FastFourierTransform from sage.gsl.dwt import WaveletTransform @@ -317,7 +319,6 @@ J = self.index_object() ## must be = range(N) N = len(J) - S = self.list() - PI = F(pi) - FT = [sum([S[i]*cos(2*PI*i/N) for i in J]) for j in J] + S = self.list() + FT = [sum([S[i]*cos(2*pi*i/N) for i in J]) for j in J] return IndexedSequence(FT,J) @@ -328,5 +329,4 @@ EXAMPLES: sage: J = range(5) - sage: I = CC.0; pi = CC(pi) sage: A = [exp(-2*pi*i*I/5) for i in J] sage: s = IndexedSequence(A,J) @@ -338,7 +338,6 @@ J = self.index_object() ## must be = range(N) N = len(J) - S = self.list() - PI = F(pi) - FT = [sum([S[i]*sin(2*PI*i/N) for i in J]) for j in J] + S = self.list() + FT = [sum([S[i]*sin(2*pi*i/N) for i in J]) for j in J] return IndexedSequence(FT,J) Index: sage/gsl/integration.pyx =================================================================== --- sage/gsl/integration.pyx (revision 4062) +++ sage/gsl/integration.pyx (revision 3365) @@ -75,5 +75,5 @@ We check this with a symbolic integration: - sage: (sin(x)^3+sin(x)).integral(x,0,pi) + sage: maxima('sin(x)^3+sin(x)').integral(x,0,pi) 10/3 @@ -95,5 +95,5 @@ rule=4: 41 pt rule rule=5: 51 pt rule - rule=6: 61 pt rule + rule=6: 61 pt sule Higher key values are more accurate for smooth functions but lower key values deal better with discontinuities. @@ -102,10 +102,4 @@ numerical_integral returns a tuple whose first component is the answer and whose second component is an error estimate. - - REMARK: - There is also a method \code{nintegral} on symbolic expressions - that implements numerical integration using Maxima. It is potentially - very useful for symbolic expressions. - MORE EXAMPLES: @@ -144,16 +138,10 @@ One can integrate any real-valued callable function: - sage: numerical_integral(lambda x: abs(zeta(x)), [1.1,1.5]) # slightly random output + sage: numerical_integral(zeta, [1.1,1.5]) # slightly random output (1.8488570602160455, 2.052643677492633e-14) - - We can also numerically integrate symbolic expressions using either this - function (which uses GSL) or the native integration (which uses Maxima): - sage: exp(-1/x).nintegral(x, 1, 2) # via maxima - (0.50479221787318396, 5.6043194293440752e-15, 21, 0) - sage: numerical_integral(exp(-1/x), 1, 2) - (0.50479221787318407, 5.6043194293440744e-15) + IMPLEMENTATION NOTES: - Uses calls to the GSL -- the GNU Scientific Library -- C library. + Uses GSL -- the GNU Scientific Library AUTHORS: Index: sage/interfaces/all.py =================================================================== --- sage/interfaces/all.py (revision 3690) +++ sage/interfaces/all.py (revision 3117) @@ -18,5 +18,4 @@ from mathematica import mathematica, mathematica_console, Mathematica from matlab import matlab, matlab_console, matlab_version, Matlab -from mupad import mupad, mupad_console, Mupad # NOT functional yet from mwrank import mwrank, Mwrank, mwrank_console from octave import octave, octave_console, octave_version, Octave Index: sage/interfaces/cleaner.py =================================================================== --- sage/interfaces/cleaner.py (revision 4016) +++ sage/interfaces/cleaner.py (revision 2973) @@ -1,5 +1,2 @@ -"""nodoctest -""" - ############################################################################### # SAGE: System for Algebra and Geometry Experimentation @@ -18,7 +15,6 @@ F = '%s/spawned_processes'%misc.SAGE_TMP -def cleaner(pid, cmd=''): - if cmd != '': - cmd = cmd.strip().split()[0] +def cleaner(pid, cmd): + cmd = cmd.strip().split()[0] # This is safe, since only this process writes to this file. if os.path.exists(F): Index: sage/interfaces/expect.py =================================================================== --- sage/interfaces/expect.py (revision 4061) +++ sage/interfaces/expect.py (revision 3117) @@ -72,10 +72,4 @@ os.environ['PATH'] = ':'.join([v for v in p if v.strip() != '.']) -class AsciiArtString(str): - def __init__(self, x): - str.__init__(self, x) - - def __repr__(self): - return str(self) @@ -345,7 +339,7 @@ self._expect.close = dummy except Exception, msg: - pass + print msg except Exception, msg: - pass + print msg def cputime(self): @@ -356,18 +350,4 @@ def quit(self, verbose=False): - """ - EXAMPLES: - sage: a = maxima('y') - sage: a - y - sage: maxima.quit() - sage: a # since the representation is cached - y - sage: a._check_valid() - Traceback (most recent call last): - ... - ValueError: The maxima session in which this object was defined is no longer running. - """ - self._session_number += 1 if self._expect is None: return @@ -376,16 +356,18 @@ # by shell scripts, and killing the shell script doesn't # kill the binary. - E = self._expect if verbose: print "Exiting spawned %s process."%self try: - E.sendline(self._quit_string()) + self._expect.sendline(self._quit_string()) self._so_far(wait=0.25) - os.killpg(E.pid, 9) - os.kill(E.pid, 9) - except (RuntimeError, OSError), msg: + os.killpg(self._expect.pid, 9) + os.kill(self._expect.pid, 9) + except OSError, msg: pass + #try: + # self._expect.close(9) + #except Exception: + # pass self._expect = None - return def _quit_string(self): @@ -473,28 +455,4 @@ raise KeyboardInterrupt, "Ctrl-c pressed while running %s"%self - def interrupt(self, tries=20, timeout=0.3): - E = self._expect - if E is None: - return True - success = False - try: - for i in range(tries): - E.sendline(self._quit_string()) - E.sendline(chr(3)) - try: - E.expect(self._prompt, timeout=timeout) - success= True - break - except (pexpect.TIMEOUT, pexpect.EOF), msg: - #print msg - pass - except Exception, msg: - pass - if success: - pass - else: - self.quit() - return success - def eval(self, code, strip=True): """ @@ -504,6 +462,5 @@ (ignored in the base class). """ - if not isinstance(code, str): - raise TypeError, 'input code must be a string.' + code = str(code) code = code.strip() try: @@ -512,5 +469,5 @@ self._keyboard_interrupt() except TypeError, s: - raise TypeError, 'error evaluating "%s":\n%s'%(code,s) + return 'error evaluating "%s":\n%s'%(code,s) def execute(self, *args, **kwds): @@ -783,5 +740,5 @@ def _reduce(self): - return repr(self) + return str(self) def _r_action(self, x): # used for coercion @@ -824,6 +781,6 @@ try: P = self.parent() - if P is None or P._session_number == BAD_SESSION or self._session_number == -1 or \ - P._session_number != self._session_number: + if P is None is None or P._session_number == BAD_SESSION or self._session_number == -1 or \ + (P._restart_on_ctrlc and P._session_number != self._session_number): raise ValueError, "The %s session in which this object was defined is no longer running."%P.name() except AttributeError: Index: sage/interfaces/gap.py =================================================================== --- sage/interfaces/gap.py (revision 4059) +++ sage/interfaces/gap.py (revision 3634) @@ -592,7 +592,4 @@ return s - def __nonzero__(self): - return self.bool() - def __len__(self): """ Index: sage/interfaces/macaulay2.py =================================================================== --- sage/interfaces/macaulay2.py (revision 4059) +++ sage/interfaces/macaulay2.py (revision 3157) @@ -96,5 +96,5 @@ import os -from expect import Expect, ExpectElement, AsciiArtString +from expect import Expect, ExpectElement from sage.misc.misc import verbose @@ -161,5 +161,5 @@ if strip: ans = remove_output_labels(ans) - return AsciiArtString(ans) + return ans @@ -377,7 +377,7 @@ return self.parent().new('%s %% %s'%(self.name(), x.name())) - def __nonzero__(self): + def is_zero(self): P = self.parent() - return P.eval('%s == 0'%self.name()) == 'false' + return P.eval('%s == 0'%self.name()) == 'true' def sage_polystring(self): Index: sage/interfaces/maple.py =================================================================== --- sage/interfaces/maple.py (revision 3690) +++ sage/interfaces/maple.py (revision 3134) @@ -260,5 +260,5 @@ def _install_hints(self): """ - Hints for installing Maple on your computer. + Hints for installing mathematica on your computer. AUTHOR: Index: sage/interfaces/mathematica.py =================================================================== --- sage/interfaces/mathematica.py (revision 4026) +++ sage/interfaces/mathematica.py (revision 2124) @@ -78,7 +78,7 @@ sage: c = m(5) - sage: print m('b + c x') + sage: m('b + c x') b + c x - sage: print m('b') + c*m('x') + sage: m('b') + c*m('x') b + 5 x @@ -182,5 +182,5 @@ sage: x = mathematica(pi/2) - sage: print x + sage: x Pi -- @@ -193,4 +193,10 @@ sage: loads(dumps(n)) == n True + +This example illustrates saving to a file in the local directory +and to one in the \sage database directory. + + sage.: n.save('n') + sage.: n.db('n') AUTHOR: @@ -216,6 +222,5 @@ import os -from expect import (Expect, ExpectElement, ExpectFunction, - FunctionElement, AsciiArtString) +from expect import Expect, ExpectElement, ExpectFunction, FunctionElement from sage.misc.misc import verbose @@ -316,7 +321,7 @@ s = Expect.eval(self, code) if strip: - return AsciiArtString(clean_output(s)) + return clean_output(s) else: - return AsciiArtString(s) + return s #def _keyboard_interrupt(self): @@ -436,9 +441,9 @@ def __repr__(self): P = self._check_valid() - return P.get(self._name, ascii_art=False).strip() + return P.get(self._name, ascii_art=True) def __str__(self): P = self._check_valid() - return P.get(self._name, ascii_art=True) + return P.get(self._name, ascii_art=False).strip() def str(self): Index: sage/interfaces/maxima.py =================================================================== --- sage/interfaces/maxima.py (revision 4058) +++ sage/interfaces/maxima.py (revision 3622) @@ -32,29 +32,37 @@ sage: F = maxima.factor('x^5 - y^5') sage: F - -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4) + -(y - x)*(y^4 + x*y^3 + x^2*y^2 + x^3*y + x^4) sage: type(F) Note that Maxima objects can also be displayed using ``ASCII art''; -to see a normal linear representation of any Maxima object x. -Just use the print command: +to see a normal linear representation of any Maxima object x, use \code{str(x)}. - sage: print F + sage: F.display2d() 4 3 2 2 3 4 - (y - x) (y + x y + x y + x y + x ) -You can always use \code{repr(x)} to obtain the linear representation -of an object. This can be useful for moving maxima data to other -systems. - sage: repr(F) - '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)' +We can make this the default: + sage: maxima.display2d(True) + sage: F + 4 3 2 2 3 4 + - (y - x) (y + x y + x y + x y + x ) + +You can always use \code{x.str()} to obtain the linear representation +of an object, even without changing the display2d flag. This can +be useful for moving maxima data to other systems. sage: F.str() - '-(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4)' + '-(y - x)*(y^4 + x*y^3 + x^2*y^2 + x^3*y + x^4)' + sage: maxima.display2d(False) + sage: F + -(y - x)*(y^4 + x*y^3 + x^2*y^2 + x^3*y + x^4) + + The \code{maxima.eval} command evaluates an expression in maxima -and returns the result as a \emph{string} not a maxima object. +and returns the result as a string. sage: print maxima.eval('factor(x^5 - y^5)') - -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4) + -(y - x)*(y^4 + x*y^3 + x^2*y^2 + x^3*y + x^4) We can create the polynomial $f$ as a Maxima polynomial, then call @@ -63,7 +71,7 @@ sage: f = maxima('x^5 - y^5') sage: f^2 - (x^5-y^5)^2 + (x^5 - y^5)^2 sage: f.factor() - -(y-x)*(y^4+x*y^3+x^2*y^2+x^3*y+x^4) + -(y - x)*(y^4 + x*y^3 + x^2*y^2 + x^3*y + x^4) Control-C interruption works well with the maxima interface, @@ -82,7 +90,7 @@ sage: a = maxima('(1 + sqrt(2))^5'); a - (sqrt(2)+1)^5 + (sqrt(2) + 1)^5 sage: a.expand() - 29*sqrt(2)+41 + 29*sqrt(2) + 41 sage: a = maxima('(1 + sqrt(2))^5') @@ -102,22 +110,22 @@ sage: f = maxima('(x + 3*y + x^2*y)^3') sage: f.expand() - x^6*y^3+9*x^4*y^3+27*x^2*y^3+27*y^3+3*x^5*y^2+18*x^3*y^2+27*x*y^2+3*x^4*y+9*x^2*y+x^3 + x^6*y^3 + 9*x^4*y^3 + 27*x^2*y^3 + 27*y^3 + 3*x^5*y^2 + 18*x^3*y^2 + 27*x*y^2 + 3*x^4*y + 9*x^2*y + x^3 sage: f.subst('x=5/z') - (5/z+25*y/z^2+3*y)^3 + (5/z + 25*y/z^2 + 3*y)^3 sage: g = f.subst('x=5/z') sage: h = g.ratsimp(); h - (27*y^3*z^6+135*y^2*z^5+(675*y^3+225*y)*z^4+(2250*y^2+125)*z^3+(5625*y^3+1875*y)*z^2+9375*y^2*z+15625*y^3)/z^6 + (27*y^3*z^6 + 135*y^2*z^5 + (675*y^3 + 225*y)*z^4 + (2250*y^2 + 125)*z^3 + (5625*y^3 + 1875*y)*z^2 + 9375*y^2*z + 15625*y^3)/z^6 sage: h.factor() - (3*y*z^2+5*z+25*y)^3/z^6 + (3*y*z^2 + 5*z + 25*y)^3/z^6 sage: eqn = maxima(['a+b*c=1', 'b-a*c=0', 'a+b=5']) sage: s = eqn.solve('[a,b,c]'); s - [[a=(25*sqrt(79)*%i+25)/(6*sqrt(79)*%i-34),b=(5*sqrt(79)*%i+5)/(sqrt(79)*%i+11),c=(sqrt(79)*%i+1)/10],[a=(25*sqrt(79)*%i-25)/(6*sqrt(79)*%i+34),b=(5*sqrt(79)*%i-5)/(sqrt(79)*%i-11),c=-(sqrt(79)*%i-1)/10]] + [[a = (25*sqrt(79)*%i + 25)/(6*sqrt(79)*%i - 34),b = (5*sqrt(79)*%i + 5)/(sqrt(79)*%i + 11),c = (sqrt(79)*%i + 1)/10],[a = (25*sqrt(79)*%i - 25)/(6*sqrt(79)*%i + 34),b = (5*sqrt(79)*%i - 5)/(sqrt(79)*%i - 11),c = - (sqrt(79)*%i - 1)/10]] Here is an example of solving an algebraic equation: sage: maxima('x^2+y^2=1').solve('y') - [y=-sqrt(1-x^2),y=sqrt(1-x^2)] + [y = - sqrt(1 - x^2),y = sqrt(1 - x^2)] sage: maxima('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').solve('y') - [y=-sqrt((-y^2-x^2)*sqrt(y^2+x^2)+x^2),y=sqrt((-y^2-x^2)*sqrt(y^2+x^2)+x^2)] + [y = - sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2),y = sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2)] You can even nicely typeset the solution in latex: @@ -129,20 +137,20 @@ sage: e = maxima('sin(u + v) * cos(u)^3'); e - cos(u)^3*sin(v+u) + cos(u)^3*sin(v + u) sage: f = e.trigexpand(); f - cos(u)^3*(cos(u)*sin(v)+sin(u)*cos(v)) + cos(u)^3*(cos(u)*sin(v) + sin(u)*cos(v)) sage: f.trigreduce() - (sin(v+4*u)+sin(v-2*u))/8+(3*sin(v+2*u)+3*sin(v))/8 + (sin(v + 4*u) + sin(v - 2*u))/8 + (3*sin(v + 2*u) + 3*sin(v))/8 sage: w = maxima('3 + k*%i') sage: f = w^2 + maxima('%e')^w sage: f.realpart() - %e^3*cos(k)-k^2+9 + %e^3*cos(k) - k^2 + 9 sage: f = maxima('x^3 * %e^(k*x) * sin(w*x)'); f x^3*%e^(k*x)*sin(w*x) sage: f.diff('x') - k*x^3*%e^(k*x)*sin(w*x)+3*x^2*%e^(k*x)*sin(w*x)+w*x^3*%e^(k*x)*cos(w*x) + k*x^3*%e^(k*x)*sin(w*x) + 3*x^2*%e^(k*x)*sin(w*x) + w*x^3*%e^(k*x)*cos(w*x) sage: f.integrate('x') - (((k*w^6+3*k^3*w^4+3*k^5*w^2+k^7)*x^3+(3*w^6+3*k^2*w^4-3*k^4*w^2-3*k^6)*x^2+(-18*k*w^4-12*k^3*w^2+6*k^5)*x-6*w^4+36*k^2*w^2-6*k^4)*%e^(k*x)*sin(w*x)+((-w^7-3*k^2*w^5-3*k^4*w^3-k^6*w)*x^3+(6*k*w^5+12*k^3*w^3+6*k^5*w)*x^2+(6*w^5-12*k^2*w^3-18*k^4*w)*x-24*k*w^3+24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8+4*k^2*w^6+6*k^4*w^4+4*k^6*w^2+k^8) + (((k*w^6 + 3*k^3*w^4 + 3*k^5*w^2 + k^7)*x^3 + (3*w^6 + 3*k^2*w^4 - 3*k^4*w^2 - 3*k^6)*x^2 + ( - 18*k*w^4 - 12*k^3*w^2 + 6*k^5)*x - 6*w^4 + 36*k^2*w^2 - 6*k^4)*%e^(k*x)*sin(w*x) + (( - w^7 - 3*k^2*w^5 - 3*k^4*w^3 - k^6*w)*x^3 + (6*k*w^5 + 12*k^3*w^3 + 6*k^5*w)*x^2 + (6*w^5 - 12*k^2*w^3 - 18*k^4*w)*x - 24*k*w^3 + 24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8 + 4*k^2*w^6 + 6*k^4*w^4 + 4*k^6*w^2 + k^8) sage: f = maxima('1/x^2') @@ -151,8 +159,8 @@ sage: g = maxima('f/sinh(k*x)^4') sage: g.taylor('x', 0, 3) - f/(k^4*x^4)-2*f/(3*k^2*x^2)+11*f/45-62*k^2*f*x^2/945 + f/(k^4*x^4) - 2*f/(3*k^2*x^2) + 11*f/45 - 62*k^2*f*x^2/945 sage: maxima.taylor('asin(x)','x',0, 10) - x+x^3/6+3*x^5/40+5*x^7/112+35*x^9/1152 + x + x^3/6 + 3*x^5/40 + 5*x^7/112 + 35*x^9/1152 \subsection{Examples involving matrices} @@ -170,5 +178,5 @@ [[0,4],[3,1]] sage: A.eigenvectors() - [[[0,4],[3,1]],[1,0,0,-4],[0,1,0,-2],[0,0,1,-4/3],[1,2,3,4]] + [[[0,4],[3,1]],[1,0,0, - 4],[0,1,0, - 2],[0,0,1, - 4/3],[1,2,3,4]] We can also compute the echelon form in \sage: @@ -186,5 +194,5 @@ sage: _ = maxima.eval("f(t) := t*sin(t)") sage: maxima("laplace(f(t),t,s)") - 2*s/(s^2+1)^2 + 2*s/(s^2 + 1)^2 sage: maxima("laplace(delta(t-3),t,s)") #Dirac delta function @@ -193,10 +201,10 @@ sage: _ = maxima.eval("f(t) := exp(t)*sin(t)") sage: maxima("laplace(f(t),t,s)") - 1/(s^2-2*s+2) + 1/(s^2 - 2*s + 2) sage: _ = maxima.eval("f(t) := t^5*exp(t)*sin(t)") sage: maxima("laplace(f(t),t,s)") - 360*(2*s-2)/(s^2-2*s+2)^4-480*(2*s-2)^3/(s^2-2*s+2)^5+120*(2*s-2)^5/(s^2-2*s+2)^6 - sage: print maxima("laplace(f(t),t,s)") + 360*(2*s - 2)/(s^2 - 2*s + 2)^4 - 480*(2*s - 2)^3/(s^2 - 2*s + 2)^5 + 120*(2*s - 2)^5/(s^2 - 2*s + 2)^6 + sage: maxima("laplace(f(t),t,s)").display2d() 3 5 360 (2 s - 2) 480 (2 s - 2) 120 (2 s - 2) @@ -206,11 +214,11 @@ sage: maxima("laplace(diff(x(t),t),t,s)") - s*?%laplace(x(t),t,s)-x(0) + s*?%laplace(x(t),t,s) - x(0) sage: maxima("laplace(diff(x(t),t,2),t,s)") - -?%at('diff(x(t),t,1),t=0)+s^2*?%laplace(x(t),t,s)-x(0)*s + -?%at('diff(x(t),t,1),t = 0) + s^2*?%laplace(x(t),t,s) - x(0)*s It is difficult to read some of these without the 2d representation: - sage: print maxima("laplace(diff(x(t),t,2),t,s)") + sage.: maxima("laplace(diff(x(t),t,2),t,s)").display2d() ! d ! 2 @@ -254,5 +262,5 @@ sage: S = maxima('nusum(exp(1+2*i/n),i,1,n)') - sage: print S + sage.: S.display2d() 2/n + 3 2/n + 1 %e %e @@ -265,5 +273,5 @@ sage: T = S*maxima('2/n') sage: T.tlimit('n','inf') - %e^3-%e + %e^3 - %e \subsection{Miscellaneous} @@ -276,5 +284,5 @@ Defining functions in maxima: sage: maxima.eval('fun[a] := a^2') - 'fun[a]:=a^2' + 'fun[a] := a^2' sage: maxima('fun[10]') 100 @@ -290,8 +298,19 @@ \subsection{Latex Output} -To tex a maxima object do this: +The latex output of Maxima is not perfect. E.g., + + sage: maxima.eval('tex(sin(u) + sinh(v^2))') + '$$\\sinhv^2 + \\sinu$$false' + +Notice the lack of space after the sin macro, which is a latex syntax +error. In \sage this is automatically fixed via a substition for +trig functions, which may have potentially bad side effects: sage: latex(maxima('sin(u) + sinh(v^2)')) \sinh v^2+\sin u + +It would be nice if somebody would fix this problem. One way would +be to improve Maxima by making the fix to Maxima and giving this back +to the Maxima people. Here's another example: @@ -319,10 +338,4 @@ sage: maxima(sin(x)) sin(x) - -A long complicated input expression: - - sage: maxima._eval_line('((((((((((0) + ((1) / ((n0) ^ (0)))) + ((1) / ((n1) ^ (1)))) + ((1) / ((n2) ^ (2)))) + ((1) / ((n3) ^ (3)))) + ((1) / ((n4) ^ (4)))) + ((1) / ((n5) ^ (5)))) + ((1) / ((n6) ^ (6)))) + ((1) / ((n7) ^ (7)))) + ((1) / ((n8) ^ (8)))) + ((1) / ((n9) ^ (9)));') - '1/n9^9+1/n8^8+1/n7^7+1/n6^6+1/n5^5+1/n4^4+1/n3^3+1/n2^2+1/n1+1' - """ @@ -349,11 +362,15 @@ from pexpect import EOF -import random - import sage.rings.all +#import sage.rings.complex_number2 as complex_number from sage.misc.misc import verbose, DOT_SAGE, SAGE_ROOT from sage.misc.multireplace import multiple_replace + +SAGE_START = '_s_start_' +SAGE_END = '_s_stop_' +cnt = 0 +seq = 0 COMMANDS_CACHE = '%s/maxima_commandlist_cache.sobj'%DOT_SAGE @@ -372,5 +389,8 @@ def __call__(self, x): import sage.rings.all - return Expect.__call__(self, x) + if sage.rings.all.is_Infinite(x): + return Expect.__call__(self, 'inf') + else: + return Expect.__call__(self, x) def __init__(self, script_subdirectory=None, logfile=None, server=None): @@ -380,14 +400,11 @@ # TODO: Input and output prompts in maxima can be changed by # setting inchar and outchar.. - eval_using_file_cutoff = 256 + eval_using_file_cutoff = 200 self.__eval_using_file_cutoff = eval_using_file_cutoff - STARTUP = '%s/local/bin/sage-maxima.lisp'%SAGE_ROOT - if not os.path.exists(STARTUP): - raise RuntimeError, 'You must get the file local/bin/sage-maxima.lisp' Expect.__init__(self, name = 'maxima', prompt = '\(\%i[0-9]+\)', - command = 'maxima -p "%s"'%STARTUP, - maxread = 10000, + command = "maxima --disable-readline", + maxread = 1, # CRUCIAL to use less buffering for maxima (or get all kinds of hangs on OS X and 64-bit machines, etc! script_subdirectory = script_subdirectory, restart_on_ctrlc = False, @@ -398,11 +415,5 @@ logfile = logfile, eval_using_file_cutoff=eval_using_file_cutoff) - self._display_prompt = '' # must match what is in the file local/ibn/sage-maxima.lisp!! - self._output_prompt_re = re.compile('\(\%o[0-9]+\)') - self._ask = ['zero or nonzero?', 'an integer?', 'positive, negative, or zero?', 'positive or negative?'] - self._prompt_wait = [self._prompt] + [re.compile(x) for x in self._ask] - self._error_re = re.compile('(debugmode|Incorrect syntax|Maxima encountered a Lisp error)') self._display2d = False - def __getattr__(self, attrname): @@ -412,6 +423,28 @@ def _start(self): + # For some reason sending a single input line at startup avoids + # lots of weird timing issues when doing doctests. Expect._start(self) - self._eval_line('0;') + self(1) + + # this doesn't work. + #def x_start(self): + # Expect._start(self) + # self._expect.sendline('inchar:"__SAGE__";') + # self._change_prompt('__SAGE__[0-9]+\)') + # self.expect().expect('__SAGE__[0-9]+\)') + + def _eval_line_using_file(self, line, tmp): + F = open(tmp, 'w') + F.write(line) + F.close() + if self._expect is None: + self._start() + # For some reason this trivial comp + # keeps certain random freezes from occuring. Do not remove this. + # The space before the \n is also important. + self._expect.sendline('0;batchload("%s"); \n'%tmp) + self._expect.expect(self._prompt) + return '' def __reduce__(self): @@ -421,132 +454,82 @@ return 'quit();' - def _sendline(self, str): - self._send(str) - os.write(self._expect.child_fd, os.linesep) - - def _send(self, str): + def _eval_line(self, line, reformat=True, allow_use_file=False, + wait_for_prompt=True): + if not wait_for_prompt: + return Expect._eval_line(self, line) + line = line.rstrip().rstrip(';') + if line == '': + return '' + global seq + seq += 1 + start = SAGE_START + str(seq) + end = SAGE_END + str(seq) + line = '%s;\n%s; %s;'%(start, line, end) if self._expect is None: self._start() - os.write(self._expect.child_fd, str) - - def _expect_expr(self, expr=None): - if expr is None: - expr = self._prompt_wait - if self._expect is None: - self._start() + if allow_use_file and self.__eval_using_file_cutoff and \ + len(line) > self.__eval_using_file_cutoff: + return self._eval_line_using_file(line, tmp) try: - i = self._expect.expect(expr) - if i > 0: - v = self._expect.before - j = v.find('Is ') - v = v[j:] - msg = "Computation failed since Maxima requested additional constraints (use assume):\n" + v + self._ask[i-1] - self._send(chr(3)) - self._send(chr(3)) - self._expect_expr() - raise ValueError, msg - except KeyboardInterrupt, msg: - #print self._expect.before - i = 0 - while True: - try: - print "Control-C pressed. Interrupting Maxima. Please wait..." - self._send('quit;\n'+chr(3)) - self._send('quit;\n'+chr(3)) - self.interrupt() - self.interrupt() - except KeyboardInterrupt: - i += 1 - if i > 10: - break - pass - else: - break - raise KeyboardInterrupt, msg - - def _interrupt(self): - self._send('quit;\n'+chr(3)) - self._expect_expr() - self._send('quit;\n'+chr(3)) - self._expect_expr() - - def _before(self): - return self._expect.before - - def _batch(self, str, batchload=True): - F = open(tmp, 'w') - F.write(str) - F.close() - if batchload: - cmd = 'batchload("%s");'%tmp - else: - cmd = 'batch("%s");'%tmp - self._sendline(cmd) - self._expect_expr() - out = self._before() - self._error_check(str, out) - return out - - def _error_check(self, str, out): - r = self._error_re - m = r.search(out) - if not m is None: - self._error_msg(str, out) - - def _error_msg(self, str, out): - raise TypeError, "Error executing code in Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s"%(str, out) - - def _eval_line(self, line, reformat=True, allow_use_file=False, - wait_for_prompt=True): - if len(line) == 0: + E = self._expect + #print "in = '%s'"%line + E.sendline(line) + self._expect.expect(end) + # We have timeouts below, since getting the end above + # means the computation completed, but on some systems + # (Cygwin) the expect interface can sometimes hang getting + # the final prompts. + try: + self._expect.expect(end, timeout=1) + out = self._expect.before + self._expect.expect(self._prompt, timeout=1) + out += self._expect.before + except pexpect.TIMEOUT: + out = self._expect.before + if not '(%o' in out: + self._expect.expect(self._prompt) + + except EOF: + if self._quit_string() in line: + return '' + except KeyboardInterrupt: + self._keyboard_interrupt() return '' - line = line.rstrip() - if line[-1] != '$' and line[-1] != ';': - line += ';' - - self._synchronize() - - if len(line) > self.__eval_using_file_cutoff: - a = self(line) - return repr(a) - else: - self._sendline(line) - - if not wait_for_prompt: - return - - self._expect_expr(self._display_prompt) - self._expect_expr() - out = self._before() - self._error_check(line, out) - + + if 'Incorrect syntax:' in out: + raise RuntimeError, out + + import os + if cygwin: + # for reasons I can't deduce yet, maxima behaves somewhat + # differently under cygwin... + out = out.lstrip(';') + else: + i = out.rfind(start) + j = out.rfind(end) + out = out[i+len(start):j] + if not reformat: return out - - r = self._output_prompt_re - m = r.search(out) - if m is None: - o = out[:-2] - else: - o = out[m.end()+1:-2] - o = ''.join([x.strip() for x in o.split()]) - return o - - i = o.rfind('(%o') - return o[:i] - - - def _synchronize(self): - if self._expect is None: return - r = random.randrange(2147483647) - s = str(r+1) - cmd = "1+%s;\n"%r - self._send(cmd) - self._expect_expr() - if not s in self._before(): - self._expect_expr(s) - self._expect_expr() - - + if 'error' in out: + return out + out = out.lstrip() + i = out.find('(%o') + out0 = out[:i].strip() + i += out[i:].find(')') + out1 = out[i+1:].strip() + out = out0 + out1 + out = ''.join(out.split()) # no whitespace + i = out.rfind(';;') + if i != -1: + out = out[i+2:] + out = out.replace('-', ' - ').replace('+',' + ').replace('=',' = ').replace(': =',' :=').replace('^ - ','^-') + if out[:3] == ' - ': + out = '-' + out[3:] + out = out.replace('E - ', 'E-') + out = out.replace('%e - ', '%e-') + i = out.rfind('(%o') + return out[:i] + ########################################### @@ -641,5 +624,5 @@ return 'false' - def function(self, args, defn, rep=None, latex=None): + def function(self, args, defn, repr=None, latex=None): """ Return the Maxima function with given arguments @@ -650,5 +633,5 @@ defn -- a string (or Maxima expression) that defines a function of the arguments in Maxima. - rep -- an optional string; if given, this is how the function will print. + repr -- an optional string; if given, this is how the function will print. EXAMPLES: @@ -658,13 +641,12 @@ sage: f = maxima.function('x,y', 'sin(x)+cos(y)') sage: f(2,3.5) - sin(2)-.9364566872907963 + sin(2) - .9364566872907963 sage: f sin(x)+cos(y) - sage: g = f.integrate('z') - sage: g - (cos(y)+sin(x))*z + sage: g = f.integrate('z'); g + (cos(y) + sin(x))*z sage: g(1,2,3) - 3*(cos(2)+sin(1)) + 3*(cos(2) + sin(1)) The function definition can be a maxima object: @@ -674,24 +656,19 @@ gamma(x)*sin(x) sage: t(2) - sin(2) + sin(2) sage: float(t(2)) 0.90929742682568171 sage: loads(t.dumps()) gamma(x)*sin(x) + + """ name = self._next_var_name() - if isinstance(defn, MaximaElement): - defn = defn.str() - elif not isinstance(defn, str): - defn = str(defn) - if isinstance(args, MaximaElement): - args = args.str() - elif not isinstance(args, str): - args = str(args) - cmd = '%s(%s) := %s'%(name, args, defn) - maxima._eval_line(cmd) - if rep is None: - rep = defn - f = MaximaFunction(self, name, rep, args, latex) + defn = str(defn) + args = str(args) + maxima.eval('%s(%s) := %s'%(name, args, defn)) + if repr is None: + repr = defn + f = MaximaFunction(self, name, repr, args, latex) return f @@ -699,20 +676,11 @@ """ Set the variable var to the given value. - - INPUT: - var -- string - value -- string - """ - if not isinstance(value, str): - raise TypeError - cmd = '%s : %s$'%(var, value.rstrip(';')) - if len(cmd) > self.__eval_using_file_cutoff: - self._batch(cmd, batchload=True) - else: - self._eval_line(cmd) - #self._sendline(cmd) - #self._expect_expr() - #out = self._before() - #self._error_check(cmd, out) + """ + cmd = '%s : %s$"";'%(var, str(value).rstrip(';')) + out = self._eval_line(cmd, reformat=False, allow_use_file=True) + + if out.find("error") != -1: + raise TypeError, "Error executing code in Maxima\nCODE:\n\t%s\nMaxima ERROR:\n\t%s"%(cmd, out) + def get(self, var): @@ -720,15 +688,17 @@ Get the string value of the variable var. """ - s = self._eval_line('%s;'%var) + s = self._eval_line('%s'%var) return s def clear(self, var): - """ - Clear the variable named var. - """ - try: - self._eval_line('kill(%s)$'%var, reformat=False) - except TypeError: - pass + """ + Clear the variable named var. + """ + if self._expect is None: + return + try: + self._expect.sendline('kill(%s);\n'%var) + except: # program around weirdness in pexpect + pass def console(self): @@ -738,25 +708,25 @@ return maxima_version() -## def display2d(self, flag=True): -## """ -## Set the flag that determines whether Maxima objects are -## printed using their 2-d ASCII art representation. When the -## maxima interface starts the default is that objects are not -## represented in 2-d. - -## INPUT: -## flag -- bool (default: True) - -## EXAMPLES -## sage: maxima('1/2') -## 1/2 -## sage: maxima.display2d(True) -## sage: maxima('1/2') -## 1 -## - -## 2 -## sage: maxima.display2d(False) -## """ -## self._display2d = bool(flag) + def display2d(self, flag=True): + """ + Set the flag that determines whether Maxima objects are + printed using their 2-d ASCII art representation. When the + maxima interface starts the default is that objects are not + represented in 2-d. + + INPUT: + flag -- bool (default: True) + + EXAMPLES + sage: maxima('1/2') + 1/2 + sage: maxima.display2d(True) + sage: maxima('1/2') + 1 + - + 2 + sage: maxima.display2d(False) + """ + self._display2d = bool(flag) def plot2d(self, *args): @@ -890,12 +860,12 @@ EXAMPLES: - sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1]) - y=3*x-2*%e^(x-1) - sage: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y']) - y=%k1*%e^x+%k2*%e^-x+3*x - sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y']) - y=(%c-3*(-x-1)*%e^-x)*%e^x - sage: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1]) - y=-%e^-1*(5*%e^x-3*%e*x-3*%e) + sage.: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y'], [1,1,1]) + y = 3*x - 2*%e^(x - 1) + sage.: maxima.de_solve('diff(y,x,2) + 3*x = y', ['x','y']) + y = %k1*%e^x + %k2*%e^ - x + 3*x + sage.: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y']) + y = (%c - 3*( - x - 1)*%e^ - x)*%e^x + sage.: maxima.de_solve('diff(y,x) + 3*x = y', ['x','y'],[1,1]) + y = - %e^ - 1*(5*%e^x - 3*%e*x - 3*%e) """ if not isinstance(vars, str): @@ -928,13 +898,13 @@ EXAMPLES: - sage: maxima.clear('x'); maxima.clear('f') - sage: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2]) - f(x)=x*%e^x+%e^x + sage.: maxima.clear('x'); maxima.clear('f') + sage.: maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"], [0,1,2]) + f(x) = x*%e^x + %e^x - sage: maxima.clear('x'); maxima.clear('f') - sage: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"]) - sage: f - f(x)=x*%e^x*(?%at('diff(f(x),x,1),x=0))-f(0)*x*%e^x+f(0)*%e^x - sage: print f + sage.: maxima.clear('x'); maxima.clear('f') + sage.: f = maxima.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x),x)-f(x)", ["x","f"]) + sage.: f + f(x) = x*%e^x*(at('diff(f(x),x,1),x = 0)) - f(0)*x*%e^x + f(0)*%e^x + sage.: f.display2d() ! x d ! x x @@ -969,6 +939,6 @@ sage: eqns = ["x + z = y","2*a*x - y = 2*a^2","y - 2*z = 2"] sage: vars = ["x","y","z"] - sage: maxima.solve_linear(eqns, vars) - [x=a+1,y=2*a,z=a-1] + sage.: maxima.solve_linear(eqns, vars) + [x = a + 1,y = 2*a,z = a - 1] """ eqs = "[" @@ -986,33 +956,33 @@ return self('linsolve(%s, %s)'%(eqs, vrs)) -## def unit_quadratic_integer(self, n): -## r""" -## Finds a unit of the ring of integers of the quadratic number -## field $\Q(\sqrt{n})$, $n>1$, using the qunit maxima command. - -## EXAMPLE: -## sage: u = maxima.unit_quadratic_integer(101) -## sage: u.parent() -## Number Field in a with defining polynomial x^2 - 101 -## sage: u -## a + 10 -## sage: u = maxima.unit_quadratic_integer(13) -## sage: u -## 5*a + 18 -## sage: u.parent() -## Number Field in a with defining polynomial x^2 - 13 -## """ -## from sage.rings.all import QuadraticField, Integer -## # Take square-free part so sqrt(n) doesn't get simplified further by maxima -## # (The original version of this function would yield wrong answers if -## # n is not squarefree.) -## n = Integer(n).square_free_part() -## if n < 1: -## raise ValueError, "n (=%s) must be >= 1"%n -## s = str(self('qunit(%s)'%n)).lower() -## r = re.compile('sqrt\(.*\)') -## s = r.sub('a', s) -## a = QuadraticField(n, 'a').gen() -## return eval(s) + def unit_quadratic_integer(self, n): + r""" + Finds a unit of the ring of integers of the quadratic number + field $\Q(\sqrt{n})$, $n>1$, using the qunit maxima command. + + EXAMPLE: + sage: u = maxima.unit_quadratic_integer(101) + sage: u.parent() + Number Field in a with defining polynomial x^2 - 101 + sage: u + a + 10 + sage: u = maxima.unit_quadratic_integer(13) + sage: u + 5*a + 18 + sage: u.parent() + Number Field in a with defining polynomial x^2 - 13 + """ + from sage.rings.all import QuadraticField, Integer + # Take square-free part so sqrt(n) doesn't get simplified further by maxima + # (The original version of this function would yield wrong answers if + # n is not squarefree.) + n = Integer(n).square_free_part() + if n < 1: + raise ValueError, "n (=%s) must be >= 1"%n + s = str(self('qunit(%s)'%n)).lower() + r = re.compile('sqrt\(.*\)') + s = r.sub('a', s) + a = QuadraticField(n, 'a').gen() + return eval(s) def plot_list(self, ptsx, ptsy, options=None): @@ -1033,6 +1003,6 @@ EXAMPLES: - sage: zeta_ptsx = [ (pari(1/2 + i*I/10).zeta().real()).precision(1) for i in range (70,150)] - sage: zeta_ptsy = [ (pari(1/2 + i*I/10).zeta().imag()).precision(1) for i in range (70,150)] + sage.: zeta_ptsx = [ (pari(1/2 + i*I/10).zeta().real()).precision(1) for i in range (70,150)] + sage.: zeta_ptsy = [ (pari(1/2 + i*I/10).zeta().imag()).precision(1) for i in range (70,150)] sage.: maxima.plot_list(zeta_ptsx, zeta_ptsy) sage.: opts='[gnuplot_preamble, "set nokey"], [gnuplot_term, ps], [gnuplot_out_file, "zeta.eps"]' @@ -1092,20 +1062,4 @@ return P('%s(%s)'%(self.name(), x)) - def __str__(self): - """ - Printing an object explicitly gives ASCII art: - - EXAMPLES: - sage: f = maxima('1/(x-1)^3'); f - 1/(x-1)^3 - sage: print f - 1 - -------- - 3 - (x - 1) - - """ - return self.display2d(onscreen=False) - def __cmp__(self, other): """ @@ -1131,21 +1085,13 @@ # thanks to David Joyner for telling me about using "is". P = self.parent() - try: - if P.eval("is (%s < %s)"%(self.name(), other.name())) == P._true_symbol(): - return -1 - elif P.eval("is (%s > %s)"%(self.name(), other.name())) == P._true_symbol(): - return 1 - elif P.eval("is (%s = %s)"%(self.name(), other.name())) == P._true_symbol(): - return 0 - except TypeError: - pass - return cmp(repr(self),repr(other)) - # everything is supposed to be comparable in Python, so we define - # the comparison thus when no comparable in interfaced system. - - def sage_object(self): - from sage.calculus.calculus import symbolic_expression_from_maxima_string - return symbolic_expression_from_maxima_string(self.name(), maxima=self.parent()) - + if P.eval("is (%s < %s)"%(self.name(), other.name())) == P._true_symbol(): + return -1 + elif P.eval("is (%s > %s)"%(self.name(), other.name())) == P._true_symbol(): + return 1 + elif P.eval("is (%s = %s)"%(self.name(), other.name())) == P._true_symbol(): + return 0 + else: + return -1 # everything is supposed to be comparable in Python, so we define + # the comparison thus when no comparable in interfaced system. def numer(self): return self.comma('numer') @@ -1170,16 +1116,15 @@ def str(self): - P = self._check_valid() + self._check_valid() + P = self.parent() return P.get(self._name) def __repr__(self): - try: - return self.__repr - except AttributeError: - pass - P = self._check_valid() - r = P.get(self._name) - self.__repr = r - return r + self._check_valid() + P = self.parent() + if P._display2d: + return self.display2d(onscreen=False) + else: + return P.get(self._name) def display2d(self, onscreen=True): @@ -1194,17 +1139,17 @@ P = self.parent() s = P._eval_line('display2d : true; %s'%self.name(), reformat=False) - P._eval_line('display2d : false;', reformat=False) - - r = P._output_prompt_re - - m = r.search(s) - s = s[m.start():] - i = s.find('\n') - s = s[i+1 + len(P._display_prompt):] - m = r.search(s) - if not m is None: - s = s[:m.start()] + ' '*(m.end() - m.start()) + s[m.end():].rstrip() - # if ever want to dedent, see - # http://mail.python.org/pipermail/python-list/2006-December/420033.html + P._eval_line('display2d : false', reformat=False) + if not cygwin: + i = s.find('true') + i += s[i:].find('\n') + s = s[i+1:] + i = s.find('true') + i += s[i:].find('\n') + j = s.rfind('(%o') + s = s[i:j-2] + i = s.find('(%o') + j = i + s[i:].find(')') + s = s[:i] + ' '*(j-i+1) + s[j+1:] + s = s.lstrip('\n') if onscreen: print s @@ -1231,10 +1176,10 @@ sage: f.diff('x', 2) 2 - sage: maxima('sin(x^2)').diff('x',4) - 16*x^4*sin(x^2)-12*sin(x^2)-48*x^2*cos(x^2) + sage: maxima('sin(x^2)').diff('x',4) + 16*x^4*sin(x^2) - 12*sin(x^2) - 48*x^2*cos(x^2) sage: f = maxima('x^2 + 17*y^2') sage: f.diff('x') - 34*y*'diff(y,x,1)+2*x + 2*x sage: f.diff('y') 34*y @@ -1305,12 +1250,12 @@ EXAMPLES: sage: maxima('x^2+1').integral() - x^3/3+x + x^3/3 + x sage: maxima('x^2+ 1 + y^2').integral('y') - y^3/3+x^2*y+y + y^3/3 + x^2*y + y sage: maxima('x / (x^2+1)').integral() - log(x^2+1)/2 + log(x^2 + 1)/2 sage: maxima('1/(x^2+1)').integral() atan(x) - sage: maxima('1/(x^2+1)').integral('x', 0, infinity) + sage.: maxima('1/(x^2+1)').integral('x', 0, infinity) %pi/2 sage: maxima('x/(x^2+1)').integral('x', -1, 1) @@ -1336,8 +1281,5 @@ def __float__(self): - try: - return float(str(self.numer())) - except ValueError: - raise TypeError, "unable to coerce '%s' to float"%repr(self) + return float(str(self.numer())) def __len__(self): @@ -1393,5 +1335,5 @@ self._check_valid() P = self.parent() - s = P._eval_line('tex(%s);'%self.name(), reformat=False) + s = maxima._eval_line('tex(%s)'%self.name(), reformat=False) if not '$$' in s: raise RuntimeError, "Error texing maxima object." @@ -1467,6 +1409,6 @@ sage: f = maxima('1/((1+x)*(x-1))') sage: f.partial_fraction_decomposition('x') - 1/(2*(x-1))-1/(2*(x+1)) - sage: print f.partial_fraction_decomposition('x') + 1/(2*(x - 1)) - 1/(2*(x + 1)) + sage: f.partial_fraction_decomposition('x').display2d() 1 1 --------- - --------- @@ -1492,7 +1434,4 @@ self.__args = args self.__latex = latex - - def __reduce__(self): - return reduce_load_Maxima_function, (self.parent(), self.__defn, self.__args, self.__latex) def __call__(self, *x): @@ -1523,5 +1462,5 @@ else: args = self.__args + ',' + var - return P.function(args, repr(f)) + return P.function(args, str(f)) @@ -1534,8 +1473,4 @@ def reduce_load_Maxima(): return maxima - -def reduce_load_Maxima_function(parent, defn, args, latex): - return parent.function(args, defn, defn, latex) - import os @@ -1549,4 +1484,2 @@ import sage.interfaces.quit sage.interfaces.quit.expect_quitall() - - Index: age/interfaces/mupad.py =================================================================== --- sage/interfaces/mupad.py (revision 3692) +++ (revision ) @@ -1,233 +1,0 @@ -r""" -Interface to MuPAD - -AUTHOR: - -- William Stein - -You must have the optional commercial MuPAD interpreter installed and -available as the command \code{mupkern} in your PATH in order to use -this interface. You do not have to install any optional \sage -packages. -""" - -############################################################################# -# Copyright (C) 2007 William Stein -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# http://www.gnu.org/licenses/ -############################################################################# - -seq = 0 -PROMPT = '___SAGE___' - -import os - -from expect import (Expect, ExpectElement, ExpectFunction, - FunctionElement, AsciiArtString) - -import pexpect - -from sage.misc.misc import verbose, DOT_SAGE -from sage.misc.pager import pager - -class Mupad(Expect): - """ - Interface to the MuPAD interpreter. - """ - def __init__(self, maxread=1000, script_subdirectory="", logfile=None): - """ - Create an instance of the MuPAD interpreter. - """ - Expect.__init__(self, - name = 'MuPAD', - prompt = '>>', - command = "mupkern -P e", - maxread = maxread, - script_subdirectory = script_subdirectory, - restart_on_ctrlc = False, - verbose_start = False, - logfile = logfile) - - def __getattr__(self, attrname): - if attrname[:1] == "_": - raise AttributeError - return MupadFunction(self, attrname) - - def _keyboard_interrupt(self): - print "Interrupting %s..."%self - self._expect.sendline(chr(3)) # send ctrl-c - self._expect.expect(PROMPT) - self._expect.expect(PROMPT) - raise RuntimeError, "Ctrl-c pressed while running %s"%self - - def __reduce__(self): - return reduce_load_mupad, tuple([]) - - def _read_in_file_command(self, filename): - return 'read "%s"'%filename - - def _start(self, alt_message=None, block_during_init=True): - Expect._start(self, alt_message=alt_message, block_during_init=block_during_init) - self._expect.sendline('Pref::promptString("%s");'%PROMPT) - self._expect.expect(PROMPT) - self._expect.send('1;') - self._expect.expect(PROMPT) - - def _quit_string(self): - return 'quit' - - def _install_hints(self): - """ - Hints for installing MuPAD on your computer. - """ - return """ -In order to use the MuPAD interface you need to have MuPAD installed -and have a script in your PATH called "mupkern" that runs the -command-line version of MuPAD. - - (1) You might have to buy MuPAD. - - (2) * LINUX: The mupkern script comes standard with your Mupad install. - - * APPLE OS X: - ??? -""" - - def expect(self): - return self._expect - - def console(self): - mupad_console() - - def eval(self, code, strip=True): - s = Expect.eval(self, code) - return AsciiArtString(s) - - def _eval_line(self, line, allow_use_file=True, wait_for_prompt=True, - need_output=True): - if self._expect is None: - self._start() - if not need_output: - E = self._expect - E.sendline(line) - return - - global seq - seq += 1 - START = '__start__(%s+1)'%seq - END = '__end__(%s+1)'%seq - line = '%s; %s; %s;'%(START, line, END) - START = '__start__(%s)'%(seq+1) - END = '__end__(%s)'%(seq+1) - - E = self._expect - E.sendline(line) - E.expect(PROMPT) - z = E.before - i = z.find(START) - if i == -1: - raise RuntimeError, "%s\nError evaluating code in MuPAD"%z - z = z[i+len(START)+2:] - z = z.rstrip().rstrip(END).rstrip('"').rstrip().strip('\n').strip('\r').strip('\n').replace('\\\r\n','') - i = z.find('Error: ') - if i != -1: - raise RuntimeError, z[i + 7:] - return z - - def cputime(self, t=None): - if t is None: - return float(self('time()')) - else: - return float(self('time() - %s'%float(t))) - - def set(self, var, value): - """ - Set the variable var to the given value. - """ - cmd = '%s:=%s:'%(var,value) - out = self.eval(cmd) - i = out.find('Error: ') - if i != -1: - raise RuntimeError, out[i + 7:] - - def get(self, var): - """ - Get the value of the variable var. - """ - s = self.eval('%s'%var) - i = s.find('=') - return s[i+1:] - - def get_using_file(self, var): - """ - Get the value of the variable var using a file. - - (I would make this the default for values that are bigger than - a few thousand characters. However, it's not at all obvious - how to figure out if the string representation of an object is - big ahead of time! We assume it is for now, if the string - used to create the object was big.) - """ - s = self.eval('save %s, "%s"'%(var, tmp)) - s = open(tmp).read().replace('\\\n','') - i = s.find('=') - return s[i+2:-2] - - def _object_class(self): - return MupadElement - - def _equality_symbol(self): - return '==' - - def _assign_symbol(self): - return ":=" - - def _help(self, str): - return os.popen('echo "?%s" | mupad -q'%str).read() - -class MupadFunction(ExpectFunction): - def _sage_doc_(self): - M = self._parent - return M._help(self._name) - -class MupadFunctionElement(FunctionElement): - def _sage_doc_(self): - return self._obj.parent()._help(self._name) - - -class MupadElement(ExpectElement): - def __getattr__(self, attrname): - if attrname[:1] == "_": - raise AttributeError - return MupadFunctionElement(self, attrname) - - def trait_names(self): - return self.parent().trait_names() - - def __repr__(self): - self._check_valid() - return self.parent().get(self._name) - - def _latex_(self): - self._check_valid() - P = self.parent() - s = P._eval_line('generate::TeX(%s)'%self.name()) - s = s.replace('\\\\','\\').strip().strip('"') - return s - -# An instance -mupad = Mupad(script_subdirectory='user') - -def reduce_load_mupad(): - return mupad - -import os -def mupad_console(): - os.system('mupkern') - - -def __doctest_cleanup(): - import sage.interfaces.quit - sage.interfaces.quit.expect_quitall() - Index: sage/interfaces/mwrank.py =================================================================== --- sage/interfaces/mwrank.py (revision 4062) +++ sage/interfaces/mwrank.py (revision 1097) @@ -68,5 +68,5 @@ def __call__(self, cmd): - return self.eval(str(cmd)) + return self.eval(cmd) def console(self): Index: sage/interfaces/quit.py =================================================================== --- sage/interfaces/quit.py (revision 4022) +++ sage/interfaces/quit.py (revision 2920) @@ -1,5 +1,5 @@ """nodoctest""" -import os, time, pexpect +import os, time expect_objects = [] @@ -11,7 +11,7 @@ try: R.quit(verbose=verbose) - pass - except RuntimeError: - pass + except RuntimeError, msg: + if verbose: + print msg kill_spawned_jobs() @@ -24,12 +24,18 @@ pid = L[:i].strip() cmd = L[i+1:].strip() - try: - #s = "Killing spawned job %s"%pid - #if len(cmd) > 0: - # s += ' (%s)'%cmd - #print s - os.killpg(int(pid), 9) - except: - pass + j = 0 + while j < 3: + j += 1 + if not is_running(pid): + break + try: + os.killpg(int(pid), 9) + except OSError, msg: + pass + else: + j += 1 + if j > 5: + os.kill(int(pid), 9) + break def is_running(pid): Index: sage/interfaces/singular.py =================================================================== --- sage/interfaces/singular.py (revision 4059) +++ sage/interfaces/singular.py (revision 3036) @@ -794,7 +794,7 @@ P.eval('%s[%s] = %s'%(self.name(), n, value.name())) - def __nonzero__(self): + def is_zero(self): P = self.parent() - return P.eval('%s == 0'%self.name()) == '0' + return P.eval('%s == 0'%self.name()) == '1' def sage_polystring(self): Index: sage/lfunctions/dokchitser.py =================================================================== --- sage/lfunctions/dokchitser.py (revision 3709) +++ sage/lfunctions/dokchitser.py (revision 3290) @@ -278,17 +278,13 @@ s = s.replace('.E','.0E').replace(' ','') return self.__CC(sage_eval(s, locals={'I':self.__CC.gen(0)})) - - def _clear_value_cache(self): - del self.__values + def __call__(self, s, c=None): - r""" + """ INPUT: s -- complex number - - NOTE: Evaluation of the function takes a long time, so each - evaluation is cached. Call \code{self._clear_value_cache()} - to clear the evaluation cache. - + c -- (optional); cutoff which should be a real number > 1 + that is chosen close to 1. + EXAMPLES: sage: E = EllipticCurve('5077a') @@ -301,10 +297,4 @@ self.__check_init() s = self.__CC(s) - try: - return self.__values[s] - except AttributeError: - self.__values = {} - except KeyError: - pass z = self.gp().eval('L(%s)'%s) if 'pole' in z: @@ -316,10 +306,6 @@ msg = z[:i].replace('digits','decimal digits') verbose(msg, level=-1) - ans = self.__to_CC(z[i+1:]) - self.__values[s] = ans - return ans - ans = self.__to_CC(z) - self.__values[s] = ans - return ans + return self.__to_CC(z[i+1:]) + return self.__to_CC(z) def derivative(self, s, k=1): Index: sage/libs/cf/cf.pyxe =================================================================== --- sage/libs/cf/cf.pyxe (revision 4059) +++ sage/libs/cf/cf.pyxe (revision 2755) @@ -873,11 +873,13 @@ return bool(CF_isOne(self.thisptr)) - def __nonzero__(CanonicalForm self): - """ - This predicate returns true if self does not represent the zero - element of the current base domain. + def is_zero(CanonicalForm self): + """ + This predicate returns true if self represents the zero + element of the current base domain. Like the predicate is_one + using the predicate f.is_zero() is also faster than a + comparison via f == 0. """ #embed{ int CF_isZero(void *e) - return not ((CanonicalForm*)e)->isZero(); + return ((CanonicalForm*)e)->isZero(); #}embed Index: sage/libs/m4ri/packedmatrix.c =================================================================== --- sage/libs/m4ri/packedmatrix.c (revision 3932) +++ sage/libs/m4ri/packedmatrix.c (revision 3498) @@ -356,10 +356,10 @@ int gaussianPackedDelayed(packedmatrix *m, int startcol, int full) { int i,j; - int start; + int start, stop=min( m->rows, m->cols); int startrow = startcol; int ii; int pivots = 0; - for (i=startcol ; icols ; i++) { + for (i=startcol ; irows; j++) { Index: sage/matrix/constructor.py =================================================================== --- sage/matrix/constructor.py (revision 3973) +++ sage/matrix/constructor.py (revision 3187) @@ -72,5 +72,4 @@ ring for all the entries (using the Sequence object): - sage: x = polygen(QQ) sage: m = matrix([[1/3,2+x],[3,4]]); m [ 1/3 x + 2] Index: sage/matrix/matrix0.pyx =================================================================== --- sage/matrix/matrix0.pyx (revision 4022) +++ sage/matrix/matrix0.pyx (revision 3543) @@ -717,5 +717,5 @@ S = [] for x in self.list(): - S.append(repr(x)) + S.append(str(x)) tmp = [] Index: sage/matrix/matrix1.pyx =================================================================== --- sage/matrix/matrix1.pyx (revision 4062) +++ sage/matrix/matrix1.pyx (revision 3477) @@ -82,5 +82,5 @@ matrix([0,1,2],[3,4,5],[6,7,8]) sage: a.charpoly('x').expand() - -x^3+12*x^2+18*x + -x^3 + 12*x^2 + 18*x sage: m.charpoly() x^3 - 12*x^2 - 18*x Index: sage/matrix/matrix2.pyx =================================================================== --- sage/matrix/matrix2.pyx (revision 4022) +++ sage/matrix/matrix2.pyx (revision 3665) @@ -390,5 +390,5 @@ # TODO: find reasonable cutoff (Field specific, but seems to be quite large for Q[x]) # if R.is_integral_domain() and R.is_exact() and algorithm == "hessenberg": - if R.is_field() and R.is_exact() and algorithm == "hessenberg": + if R.is_field() and algorithm == "hessenberg": c = self.charpoly('x')[0] if self._nrows % 2: @@ -2093,5 +2093,5 @@ if PyErr_CheckSignals(): raise KeyboardInterrupt for r from start_row <= r < nr: - if A.get_unsafe(r, c): + if A.get_unsafe(r, c) != 0: pivots.append(c) a_inverse = ~A.get_unsafe(r,c) @@ -2100,5 +2100,5 @@ for i from 0 <= i < nr: if i != start_row: - if A.get_unsafe(i,c): + if A.get_unsafe(i,c) != 0: minus_b = -A.get_unsafe(i, c) A.add_multiple_of_row(i, start_row, minus_b, c) Index: sage/matrix/matrix_complex_double_dense.pyx =================================================================== --- sage/matrix/matrix_complex_double_dense.pyx (revision 4062) +++ sage/matrix/matrix_complex_double_dense.pyx (revision 3616) @@ -328,5 +328,4 @@ EXAMPLES: - sage: I = CDF.gen() sage: m = I*Matrix(CDF, 3, range(9)) sage: vals, vecs = m.eigen_left() @@ -358,5 +357,5 @@ EXAMPLES: - sage: m = CDF.gen() * matrix(CDF, 3, range(9)) + sage: m = I*Matrix(CDF, 3, range(9)) sage: vals, vecs = m.eigen() sage: vecs*m # random lower order precision @@ -428,5 +427,4 @@ EXAMPLES: - sage: I = CDF.gen() sage: A =I*matrix(CDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]) sage: A # slightly random output @@ -473,6 +471,5 @@ EXAMPLES: - sage: I = CDF.gen() - sage: A = I*matrix(CDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]) + sage: A =I*matrix(CDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]) sage: A # slightly random output [1.0*I 2.0*I 5.0*I] @@ -547,5 +544,5 @@ [ 0 1.0] [2.0 3.0] - sage: RDF(log(abs(m.determinant()))) + sage: log(abs(m.determinant())) 0.69314718056 sage: m.log_determinant() @@ -654,5 +651,4 @@ EXAMPLES: - sage: I = CDF.gen() sage: m = matrix(CDF,[[1,2],[3,4]]) sage: m = I*m Index: sage/matrix/matrix_integer_dense.pyx =================================================================== --- sage/matrix/matrix_integer_dense.pyx (revision 4059) +++ sage/matrix/matrix_integer_dense.pyx (revision 3665) @@ -497,5 +497,5 @@ # def _dict(self): - def __nonzero__(self): + def is_zero(self): cdef mpz_t *a, *b cdef Py_ssize_t i, j @@ -503,6 +503,6 @@ for i from 0 <= i < self._nrows * self._ncols: if mpz_cmp_si(self._entries[i], 0): - return True - return False + return False + return True def _multiply_linbox(self, Matrix right): Index: sage/matrix/matrix_mod2_dense.pyx =================================================================== --- sage/matrix/matrix_mod2_dense.pyx (revision 3931) +++ sage/matrix/matrix_mod2_dense.pyx (revision 3506) @@ -58,31 +58,4 @@ [0 1 0] -TESTS: - sage: FF = FiniteField(2) - sage: V = VectorSpace(FF,2) - sage: v = V([0,1]); v - (0, 1) - sage: W = V.subspace([v]) - sage: W - Vector space of degree 2 and dimension 1 over Finite Field of size 2 - Basis matrix: - [0 1] - sage: v in W - True - - sage: M = Matrix(GF(2), [[1,1,0],[0,1,0]]) - sage: M.row_space() - Vector space of degree 3 and dimension 2 over Finite Field of size 2 - Basis matrix: - [1 0 0] - [0 1 0] - - sage: M = Matrix(GF(2), [[1,1,0],[0,0,1]]) - sage: M.row_space() - Vector space of degree 3 and dimension 2 over Finite Field of size 2 - Basis matrix: - [1 1 0] - [0 0 1] - TODO: - make linbox frontend and use it @@ -311,7 +284,4 @@ cdef int n = self._ncols cdef int k = round(min(0.75 * log(n,2), 16)) - - if k < 1: - k = 1 ## if ( self.nrows() < right.ncols() ): @@ -615,12 +585,4 @@ True - TESTS: - sage: VF2 = VectorSpace(GF(2),2) - sage: WF2 = VF2.submodule([VF2([1,1])]) - sage: WF2 - Vector space of degree 2 and dimension 1 over Finite Field of size 2 - Basis matrix: - [1 1] - ALGORITHM: Uses Gregory Bard's M4RI algorithm and implementation or LinBox. @@ -649,11 +611,9 @@ n = min(self._nrows, self._ncols) k = round(min(0.75 * log(n,2), 16)) - if k<1: - k = 1 _sig_on r = simpleFourRussiansPackedFlex(self._entries, 1, k) _sig_off - + self.cache('in_echelon_form',True) self.cache('rank', r) Index: sage/matrix/matrix_real_double_dense.pyx =================================================================== --- sage/matrix/matrix_real_double_dense.pyx (revision 4003) +++ sage/matrix/matrix_real_double_dense.pyx (revision 3616) @@ -555,5 +555,5 @@ [0.0 1.0] [2.0 3.0] - sage: RDF(log(abs(m.determinant()))) + sage: log(abs(m.determinant())) 0.69314718056 sage: m.log_determinant() Index: sage/matrix/solve.pyx =================================================================== --- sage/matrix/solve.pyx (revision 3751) +++ sage/matrix/solve.pyx (revision 3385) @@ -67,5 +67,4 @@ z=gsl_vector_complex_get(result_vector,i) list.append(sage.rings.complex_double.CDF(GSL_REAL(z),GSL_IMAG(z))) - # list.append(gsl_vector_complex_get(result_vector, i)) gsl_vector_complex_free(result_vector) return vector(sage.rings.complex_double.CDF,list) #todo: don't go through python Index: sage/misc/all.py =================================================================== --- sage/misc/all.py (revision 4063) +++ sage/misc/all.py (revision 3610) @@ -30,6 +30,4 @@ from sagedoc import search_src, search_doc -from reset import reset, restore - from getusage import top, get_memory_usage @@ -50,73 +48,10 @@ from func_persist import func_persist -from functional import (additive_order, - sqrt as numerical_sqrt, - arg, - base_ring, - base_field, - basis, - category, - charpoly, - coerce, - cyclotomic_polynomial, - decomposition, - denominator, - derivative, - det, - dimension, - dim, - discriminant, - disc, - eta, - exp, - factor, - fcp, - gens, - hecke_operator, - ideal, - image, - imag, - imaginary, - integral, - integral_closure, - interval, - xinterval, - is_commutative, - is_even, - is_integrally_closed, - is_field, - is_odd, - kernel, - krull_dimension, - lift, - minimal_polynomial, - multiplicative_order, - ngens, - norm, - numerator, - objgens, - objgen, - one, - order, - rank, - real, - regulator, - round, - quotient, - quo, - show, - isqrt, - square_free_part, - squarefree_part, - transpose, - zero, - log as log_b, - parent) - +from functional import * from latex import latex, view, lprint, jsmath # disabled -- nobody uses mathml -#from mathml ml +#from mathml import mathml from trace import trace Index: sage/misc/functional.py =================================================================== --- sage/misc/functional.py (revision 4063) +++ sage/misc/functional.py (revision 3290) @@ -52,7 +52,7 @@ EXAMPLES: - sage: z = CC(1,2) + sage: z = 1+2*I sage: theta = arg(z) - sage: cos(theta)*abs(z) + sage: cos(theta)*abs(z) # slightly random output on cygwin 1.00000000000000 sage: sin(theta)*abs(z) @@ -146,4 +146,9 @@ Return the arc cosine of x. + EXAMPLES: + sage: acos(0.5) + 1.04719755119660 + sage: acos(1 + I*1.0) + 0.904556894302381 - 1.06127506190504*I """ try: return x.acos() @@ -154,4 +159,9 @@ Return the arc sine of x. + EXAMPLES: + sage: asin(0.5) + 0.523598775598299 + sage: asin(1 + I*1.0) + 0.666239432492515 + 1.06127506190504*I """ try: return x.asin() @@ -162,4 +172,9 @@ Return the arc tangent of x. + EXAMPLES: + sage: atan(1/2) + 0.463647609001 + sage: atan(1 + I) + 1.01722196789785 + 0.402359478108525*I """ try: return x.atan() @@ -286,5 +301,5 @@ EXAMPLES: sage: eta(1+I) - 0.742048775837 + 0.19883137023*I + 0.742048775836565 + 0.198831370229911*I """ try: return x.eta() @@ -330,9 +345,9 @@ except AttributeError: return factor(charpoly(x, var)) -## def floor(x): -## try: -## return x.floor() -## except AttributeError: -## return sage.rings.all.floor(x) +def floor(x): + try: + return x.floor() + except AttributeError: + return sage.rings.all.floor(x) def gen(x): @@ -408,11 +423,11 @@ sage: z = 1+2*I sage: imaginary(z) - 2 + 2.00000000000000 sage: imag(z) - 2 + 2.00000000000000 """ return imag(x) -def integral(x, *args, **kwds): +def integral(x, var=None, algorithm='maxima'): """ Return an indefinite integral of an object x. @@ -426,18 +441,19 @@ sage: integral(f) 1/5*x^5 - 1/4*x^4 + 1/3*x^3 - 1/2*x^2 + x - sage: integral(sin(x),x) - -cos(x) - sage: integral(sin(x),y) - sin(x)*y - sage: integral(sin(x), x, 0, pi/2) - 1 - sage: sin(x).integral(x, 0,pi/2) - 1 - """ - if hasattr(x, 'integral'): - return x.integral(*args, **kwds) + """ + if var is None: + try: + return x.integral() + except AttributeError: + pass + import sage.interfaces.all as I + if var is None: + var = 'x' + if algorithm == 'maxima': + return I.maxima(x).integrate(var) + elif algorithm == 'mathematica': + return I.mathematica(x).Integrate(var) else: - from sage.calculus.calculus import SR - return SR(x).integral(*args, **kwds) + raise ValueError, 'no algorithm %s'%algorithm def integral_closure(x): @@ -588,4 +604,13 @@ argument.} + EXAMPLES: + sage: log(10,2) + 3.32192809489 + sage: log(8,2) + 3.0 + sage: log(10) + 2.30258509299 + sage: log(2.718) + 0.999896315728952 """ if b is None: @@ -631,8 +656,4 @@ sage: z = 1+2*I sage: norm(z) - 5 - sage: norm(CDF(z)) - 5.0 - sage: norm(CC(z)) 5.00000000000000 """ @@ -718,5 +739,5 @@ We compute the rank of an elliptic curve: - sage: E = EllipticCurve([0,0,1,-1,0]) + sage: E=EllipticCurve([0,0,1,-1,0]) sage: rank(E) 1 @@ -731,5 +752,5 @@ sage: z = 1+2*I sage: real(z) - 1 + 1.00000000000000 """ try: return x.real() @@ -791,5 +812,5 @@ print '
%s
'%sage.misc.latex.latex(x) return sage.misc.latex.LatexExpr('') # so not visible output - raise AttributeError, "object %s does not support show."%(x, ) + raise AttributeError, "object %s does not support show."%x def sqrt(x): @@ -804,9 +825,5 @@ """ try: return x.sqrt() - except (AttributeError, ValueError): - try: - return RDF(x).sqrt() - except TypeError: - return CDF(x).sqrt() + except (AttributeError, ValueError): return CDF(x).sqrt() def isqrt(x): @@ -862,19 +879,33 @@ squarefree_part = square_free_part -## def square_root(x): -## """ -## Return a square root of x with the same parent as x, if possible, -## otherwise raise a ValueError. -## EXAMPLES: -## sage: square_root(9) -## 3 -## sage: square_root(100) -## 10 -## """ -## try: -## return x.square_root() -## except AttributeError: -## raise NotImplementedError +def square_root(x): + """ + Return a square root of x with the same parent as x, if possible, + otherwise raise a ValueError. + + EXAMPLES: + sage: square_root(9) + 3 + sage: square_root(100) + 10 + """ + try: + return x.square_root() + except AttributeError: + raise NotImplementedError +def tan(x): + """ + Return the tangent of x. + + EXAMPLES: + sage: tan(3.1415) + -0.0000926535900581913 + sage: tan(3.1415/4) + 0.999953674278156 + """ + try: return x.tan() + except AttributeError: return RDF(x).tan() + def transpose(x): """ Index: sage/misc/hg.py =================================================================== --- sage/misc/hg.py (revision 4041) +++ sage/misc/hg.py (revision 3631) @@ -35,5 +35,4 @@ from misc import tmp_filename, branch_current_hg from remote_file import get_remote_file -from sage.server.misc import print_open_msg def embedded(): @@ -155,6 +154,5 @@ return out, err - def serve(self, port=8200, address='localhost', - open_viewer=True, options=''): + def serve(self, port=8200, open_viewer=False): """ Start a web server for this repository. @@ -166,19 +164,15 @@ INPUT: port -- port that the server will listen on - address -- (default: 'localhost') address to listen on - open_viewer -- boolean (default: True); whether to pop up the web page - options -- a string passed directly to hg's serve command. - """ + open_viewer -- boolean (default: False); whether to pop up the web page + """ + print('Now serving repository on port %s'%port) + print("Point your web browser at http://localhost:%s"%port) if open_viewer: - cmd = 'sleep 1; %s http://%s:%s 1>&2 >/dev/null'%(browser(), - address, port) + cmd = 'sleep 1; %s http://%s:%s 1>&2 >/dev/null'%(browser(), 'localhost', port) t = tmp_filename() open(t,'w').write(cmd) P = os.path.abspath(t) os.system('chmod +x %s; %s &'%(P, P)) - - print_open_msg(address, port) - self('serve --address %s --port %s %s'%(address, port, options)) - print_open_msg(address, port) + self('serve --port %s'%port) browse = serve @@ -564,43 +558,4 @@ self('%s --help | %s'%(cmd, pager())) - def outgoing(self, url=None, opts=''): - """ - Use this to find changsets that are in your branch, but not in the - specified destination repository. If no destination is specified, the - official repository is used. - - From the Mercurial documentation: - Show changesets not found in the specified destination repository or the - default push location. These are the changesets that would be pushed if - a push was requested. - - See pull() for valid destination format details. - - INPUT: - url: default: self.url() -- the official repository - * http://[user@]host[:port]/[path] - * https://[user@]host[:port]/[path] - * ssh://[user@]host[:port]/[path] - * local directory (starting with a /) - * name of a branch (for hg_sage); no /'s - options: (default: none) - -M --no-merges do not show merges - -f --force run even when remote repository is unrelated - -p --patch show patch - --style display using template map file - -r --rev a specific revision you would like to push - -n --newest-first show newest record first - --template display with template - -e --ssh specify ssh command to use - --remotecmd specify hg command to run on the remote side - """ - if url is None: - url = self.__url - - if not '/' in url: - url = '%s/devel/sage-%s'%(SAGE_ROOT, url) - - self('outgoing %s %s | %s' % (opts, url, pager())) - def pull(self, url=None, options='-u'): """ Index: sage/misc/misc.py =================================================================== --- sage/misc/misc.py (revision 4066) +++ sage/misc/misc.py (revision 3388) @@ -21,5 +21,5 @@ "assert_attribute", "LOGFILE"] -import operator, os, sys, signal, time, weakref, random, resource +import operator, os, sys, signal, time, weakref, random from banner import version, banner @@ -113,7 +113,4 @@ spent by subprocesses spawned by SAGE (e.g., Gap, Singular, etc.). - This is done via a call to resource.getrusage, so it avoids the - wraparound problems in time.clock() on Cygwin. - INPUT: t -- (optional) float, time in CPU seconds @@ -136,6 +133,5 @@ except TypeError: t = 0.0 - u,s = resource.getrusage(resource.RUSAGE_SELF)[:2] - return u+s - t + return time.clock() - t def walltime(t=0): @@ -227,4 +223,5 @@ s = s + " (time = %s)"%cputime(t) print s + sys.stdout.flush() #open(LOGFILE,"a").write(s+"\n") return cputime() Index: sage/misc/preparser.py =================================================================== --- sage/misc/preparser.py (revision 4061) +++ sage/misc/preparser.py (revision 3425) @@ -8,6 +8,4 @@ by digits of input (like mathematica). -- Joe Wetherell (2006-04-14): * added MAGMA-style constructor preparsing. - -- Bobby Moretti (2007-01-25): * added preliminary function assignment - notation EXAMPLES: @@ -51,18 +49,4 @@ SyntaxError: invalid syntax -SYMBOLIC FUNCTIONAL NOTATION: - sage: a=10; f(theta, beta) = theta + beta; b = x^2 + theta - sage: f - (theta, beta) |--> theta + beta - sage: a - 10 - sage: b - x^2 + theta - sage: f(theta,theta) - 2*theta - - sage: a = 5; f(x,y) = x*y*sqrt(a) - sage: f - (x, y) |--> sqrt(5)*x*y RAW LITERALS: @@ -130,6 +114,6 @@ # http://www.gnu.org/licenses/ ########################################################################### + import os -import pdb def isalphadigit_(s): @@ -140,18 +124,8 @@ in_double_quote = False in_triple_quote = False - def in_quote(): return in_single_quote or in_double_quote or in_triple_quote def preparse(line, reset=True, do_time=False, ignore_prompts=False): - - # find where the parens are for function assignment notation - oparen_index = -1 - cparen_index = -1 - - # for caclulus function notation: - paren_level = 0 - first_eq_index = -1 - global in_single_quote, in_double_quote, in_triple_quote line = line.rstrip() # xreadlines leaves the '\n' at end of line @@ -186,7 +160,4 @@ in_number = False is_real = False - - in_args = False - if reset: in_single_quote = False @@ -241,4 +212,5 @@ i += 1 continue + # Decide if we should wrap a particular integer or real literal @@ -269,10 +241,4 @@ continue - elif line[i] == ";" and not in_quote(): - line = line[:i+1] + preparse(line[i+1:], reset, do_time, ignore_prompts) - i = len(line) - continue - - # Support for generator construction syntax: # "obj. = objConstructor(...)" @@ -357,98 +323,4 @@ continue - # Support for calculus-like function assignment, the line - # "f(x,y,z) = sin(x^3 - 4*y) + y^x" - # gets turnd into - # "f = SR(sin(x^3 - 4*y) + y^x).function(x,y,z)" - # AUTHORS: - # - Bobby Moretti: initial version - 02/2007 - # - William Stein: make variables become defined if they aren't already defined. - - elif (line[i] == "(") and not in_quote(): - paren_level += 1 - # we need to make sure that this is the first open paren we find - if oparen_index == -1: - oparen_index = i - i += 1 - continue - - elif (line[i] == ")") and not in_quote(): - cparen_index = i - paren_level -= 1 - i += 1 - continue - - elif (line[i] == "=") and paren_level == 0 and not in_quote(): - if first_eq_index == -1: - first_eq_index = i - eq = i - - if cparen_index == -1: - i += 1 - continue - - # make sure the '=' sign is on its own, reprsenting assignment - eq_chars = ["=", "!", ">", "<", "+", "-", "*", "/", "^"] - if line[eq-1] in eq_chars or line[eq+1] in eq_chars: - i += 1 - continue - - line_before = line[:oparen_index].strip() - if line_before == "" or not line_before.isalnum(): - i += 1 - continue - - if eq != first_eq_index: - i += 1 - continue - - vars_end = cparen_index - vars_begin = oparen_index+1 - - # figure out where the line ends - line_after = line[vars_end+1:] - try: - a = line.index("#") - except ValueError: - a = len(line) - - try: - b = line.index(";") - except ValueError: - b = len(line) - - a = min(a,b) - - vars = line[vars_begin:vars_end].split(",") - vars = [v.strip() for v in vars] - b = [] - - - # construct the parsed line - k = line[:vars_begin-1].rfind(';') - if k == -1: - k = len(line) - len(line.lstrip()) - b.append(line[:k]) - b.append('_=var("%s");'%(','.join(vars))) - b.append(line[k:vars_begin-1]) - b.append('=') - b.append('symbolic_expression(') - b.append(line[eq+1:a].strip()) - b.append(').function(') - b.append(','.join(vars)) - b.append(')') - b.append(line[a:]) - - line = ''.join(b) - - # i should get set to the position of the first paren after the new - # assignment operator - n = len(line_before) - i = line.find('=', n) + 2 - - continue - # - ####### END CALCULUS ######## - # exponents can be either ^ or ** elif line[i] == "^" and not in_quote(): Index: age/misc/reset.pyx =================================================================== --- sage/misc/reset.pyx (revision 4022) +++ (revision ) @@ -1,102 +1,0 @@ -import sys - -def reset(vars=None): - """ - Delete all user defined variables, reset all globals variables - back to their default state, and reset all interfaces to other - computer algebra systems. - - If vars is specified, just restore the value of vars and leave - all other variables alone (i.e., call restore). - - INPUT: - vars -- (default: None), a list, or space or comma separated - string. - """ - if not vars is None: - restore(vars) - return - G = globals() # this is the reason the code must be in SageX. - T = type(sys) - for k in G.keys(): - if k[0] != '_' and type(k) != T: - try: - del G[k] - except KeyError: - pass - restore() - reset_interfaces() - - -def restore(vars=None): - """ - Restore predefined global variables to their default values. - - INPUT: - vars -- string or list (default: None) if not None, restores - just the given variables to the default value. - - EXAMPLES: - sage: x = 10; y = 15/3; QQ='red' - sage: QQ - 'red' - sage: restore('QQ') - sage: QQ - Rational Field - sage: x - 10 - sage: restore('x y') - sage: x - x - sage: y - y - sage: x = 10; y = 15/3; QQ='red' - sage: ww = 15 - sage: restore() - sage: x,y,QQ,ww - (x, y, Rational Field, 15) - sage: restore('ww') - sage: ww - Traceback (most recent call last): - ... - NameError: name 'ww' is not defined - """ - G = globals() # this is the reason the code must be in SageX. - import sage.all - D = sage.all.__dict__ - if vars is None: - for k, v in D.iteritems(): - G[k] = v - else: - if isinstance(vars, str): - if ',' in vars: - vars = vars.split(',') - else: - vars = vars.split() - for k in vars: - if D.has_key(k): - G[k] = D[k] - else: - try: - del G[k] # the default value was "unset" - except KeyError: - pass - - -def reset_interfaces(): - from sage.interfaces.quit import expect_quitall - expect_quitall() - -## import sys -## M = sys.modules -## for k in M.keys(): -## if 'sage.interfaces' in k: -## if not M[k] is None: -## reload(M[k]) - -## import sage.interfaces.all -## G = globals() -## for k, v in sage.interfaces.all.__dict__.iteritems(): -## G[k] = v - - Index: sage/misc/search.pyx =================================================================== --- sage/misc/search.pyx (revision 3908) +++ sage/misc/search.pyx (revision 1319) @@ -30,6 +30,5 @@ Return (True,i) where i is such that v[i] == x if there is such an i, or (False,j) otherwise, where j is the position that a should be inserted - so that v remains sorted. - + so that v remains sorted. INPUT: v -- a list, which is assumed sorted Index: sage/modular/cusps.py =================================================================== --- sage/modular/cusps.py (revision 4061) +++ sage/modular/cusps.py (revision 3311) @@ -102,6 +102,5 @@ Traceback (most recent call last): ... - TypeError: Unable to coerce I () to Rational - + TypeError: Unable to coerce 1.00000000000000*I () to Rational """ return Cusp(x, parent=self) @@ -169,6 +168,6 @@ Traceback (most recent call last): ... - TypeError: unable to convert I to a rational - + TypeError: Unable to coerce 1.00000000000000*I () to Rational + sage: a = Cusp(2,3) sage: loads(a.dumps()) == a Index: sage/modular/dirichlet.py =================================================================== --- sage/modular/dirichlet.py (revision 4003) +++ sage/modular/dirichlet.py (revision 3570) @@ -672,5 +672,5 @@ sage: abs(e.gauss_sum_numerical()) 1.73205080756888 - sage: sqrt(3.0) + sage: sqrt(3) 1.73205080756888 sage: e.gauss_sum_numerical(a=2) @@ -684,5 +684,5 @@ sage: abs(e.gauss_sum_numerical()) 3.60555127546399 - sage: sqrt(13.0) + sage: sqrt(13) 3.60555127546399 """ Index: sage/modular/modform/all.py =================================================================== --- sage/modular/modform/all.py (revision 3884) +++ sage/modular/modform/all.py (revision 3388) @@ -14,4 +14,5 @@ from hecke_operator_on_qexp import (hecke_operator_on_qexp, - hecke_operator_on_basis) + hecke_operator_on_basis) + from numerical import NumericalEigenforms as numerical_eigenforms Index: sage/modular/modform/element.py =================================================================== --- sage/modular/modform/element.py (revision 4059) +++ sage/modular/modform/element.py (revision 3616) @@ -103,6 +103,6 @@ return chi - def __nonzero__(self): - return not self.element().is_zero() + def is_zero(self): + return self.element().is_zero() def level(self): Index: sage/modular/modform/numerical.py =================================================================== --- sage/modular/modform/numerical.py (revision 3982) +++ sage/modular/modform/numerical.py (revision 3621) @@ -247,5 +247,4 @@ [28.0, 28.0, -7.92820323028, 5.92820323028] sage: m = n.modular_symbols() - sage: x = polygen(QQ, 'x') sage: m.T(2).charpoly(x).factor() (x - 9)^2 * (x^2 - 2*x - 2) Index: sage/modular/modsym/boundary.py =================================================================== --- sage/modular/modsym/boundary.py (revision 3907) +++ sage/modular/modsym/boundary.py (revision 3520) @@ -67,9 +67,5 @@ """ self.__x = x - self.__vec = parent.free_module()(x) - hecke.HeckeModuleElement.__init__(self, parent, self.__vec) - - def coordinate_vector(self): - return self.__vec + hecke.HeckeModuleElement.__init__(self, parent, parent.free_module()(x)) def _repr_(self): Index: sage/modular/modsym/space.py =================================================================== --- sage/modular/modsym/space.py (revision 4013) +++ sage/modular/modsym/space.py (revision 3569) @@ -522,5 +522,4 @@ An example that (somewhat spuriously) is over a number field: - sage: x = polygen(QQ) sage: k = NumberField(x^2+1, 'a') sage: M = ModularSymbols(11, base_ring=k, sign=1).cuspidal_submodule() @@ -1594,5 +1593,4 @@ self.__domain = modsym.ambient_module() self.__A = A - A.set_immutable() def modular_symbols_space(self): Index: sage/modules/free_module_element.pyx =================================================================== --- sage/modules/free_module_element.pyx (revision 3887) +++ sage/modules/free_module_element.pyx (revision 3544) @@ -543,5 +543,5 @@ l = self.list() if len(r) != len(l): - raise ArithmeticError, "degrees (%s and %s) must be the same"%(len(l),len(r)) + raise ArithmeticError, "degrees must be the same"%(len(l),len(r)) zero = self.parent().base_ring()(0) return sum(eval('[l[i]*r[i] for i in xrange(len(l))]', {'l':l,'r':r}), zero) Index: sage/modules/real_double_vector.pyx =================================================================== --- sage/modules/real_double_vector.pyx (revision 4021) +++ sage/modules/real_double_vector.pyx (revision 3616) @@ -333,36 +333,4 @@ memcpy(self.v.data,p,self.v.size*sizeof(double)) - ############################# - # statistics - ############################# - def mean(self): - return gsl_stats_mean(self.v.data, self.v.stride, self.v.size) - - def variance(self): - return gsl_stats_variance(self.v.data, self.v.stride, self.v.size) - - #def covariance(self): - # return gsl_stats_covariance(self.v.data, self.v.stride, self.v.size) - - def standard_deviation(self): - """ - EXAMPLES: - sage: v = vector(RDF, 5, [1,2,3,4,5]) - sage: v.standard_deviation() - 1.5811388300841898 - """ - return gsl_stats_sd(self.v.data, self.v.stride, self.v.size) - - def stats_skew(self): - return gsl_stats_skew(self.v.data, self.v.stride, self.v.size) - - def stats_kurtosis(self): - return gsl_stats_kurtosis(self.v.data, self.v.stride, self.v.size) - - def stats_lag1_autocorrelation(self): - return gsl_stats_lag1_autocorrelation(self.v.data, self.v.stride, self.v.size) - - - def unpickle_v0(parent, entries, degree): # If you think you want to change this function, don't. Index: sage/monoids/free_monoid.py =================================================================== --- sage/monoids/free_monoid.py (revision 4007) +++ sage/monoids/free_monoid.py (revision 1840) @@ -154,8 +154,6 @@ """ ## There should really some careful type checking here... - if isinstance(x, FreeMonoidElement) and x.parent() is self: - return x if isinstance(x, FreeMonoidElement) and x.parent() == self: - return FreeMonoidElement(self,x._element_list,check) + return x elif isinstance(x, (int, long, Integer)) and x == 1: return FreeMonoidElement(self, x, check) Index: sage/monoids/free_monoid_element.py =================================================================== --- sage/monoids/free_monoid_element.py (revision 4007) +++ sage/monoids/free_monoid_element.py (revision 1859) @@ -67,21 +67,21 @@ raise TypeError, "Argument x (= %s) is of the wrong type."%x -## def __cmp__(left, right): -## """ -## Compare two free monoid elements with the same parents. - -## The ordering is the one on the underlying sorted list of -## (monomial,coefficients) pairs. - -## EXAMPLES: -## sage: R. = FreeMonoid(2) -## sage: x < y -## True -## sage: x * y < y * x -## True -## sage: x * y * x^2 < x * y * x^3 -## True -## """ -## return cmp(left._element_list, right._element_list) + def __cmp__(left, right): + """ + Compare two free monoid elements with the same parents. + + The ordering is the one on the underlying sorted list of + (monomial,coefficients) pairs. + + EXAMPLES: + sage: R. = FreeMonoid(2) + sage: x < y + True + sage: x * y < y * x + True + sage: x * y * x^2 < x * y * x^3 + True + """ + return cmp(left._element_list, right._element_list) def _repr_(self): @@ -254,3 +254,4 @@ return 1 return 0 # x = self and y are equal - + + Index: sage/plot/plot.py =================================================================== --- sage/plot/plot.py (revision 4064) +++ sage/plot/plot.py (revision 3584) @@ -81,8 +81,7 @@ see the first few zeros: - sage: i = CDF.0 # define i this way for maximum speed. - sage: p1 = plot(lambda t: arg(zeta(0.5+t*i)), 1,27,rgbcolor=(0.8,0,0)) - sage: p2 = plot(lambda t: abs(zeta(0.5+t*i)), 1,27,rgbcolor=hue(0.7)) - sage: p1 + p2 + sage: p1 = plot(lambda t: arg(zeta(0.5+t*I)), 1,27,rgbcolor=(0.8,0,0)) + sage: p2 = plot(lambda t: abs(zeta(0.5+t*I)), 1,27,rgbcolor=hue(0.7)) + sage: p1+p2 Graphics object consisting of 2 graphics primitives sage: (p1+p2).save() @@ -96,11 +95,4 @@ ... sage: g.save(dpi=200, axes=False) - -Another graph: - sage: P = plot(lambda x: sin(x)/x, -4,4, rgbcolor=(0,0,1)) + \ - ... plot(lambda x: x*cos(x), -4,4, rgbcolor=(1,0,0)) + \ - ... plot(lambda x: tan(x),-4,4,rgbcolor=(0,1,0)) - ... - sage: P.save('sage.png', ymin=-pi,ymax=pi) AUTHORS: @@ -127,6 +119,4 @@ # http://www.gnu.org/licenses/ #***************************************************************************** - -import pdb from sage.structure.sage_object import SageObject @@ -471,6 +461,8 @@ EXAMPLES: - sage: g1 = plot(abs(sqrt(x^3 - 1)), 1, 5) - sage: g2 = plot(-abs(sqrt(x^3 - 1)), 1, 5) + sage: h1 = lambda x : abs(sqrt(x^3 - 1)) + sage: h2 = lambda x : -abs(sqrt(x^3 - 1)) + sage: g1 = plot(h1, 1, 5) + sage: g2 = plot(h2, 1, 5) sage: h = g1 + g2 sage: h.save() @@ -1738,23 +1730,5 @@ and plots contour lines of the function over the specified xrange and yrange as demonstrated below. - - contour_plot(f, (xmin, xmax), (ymin, ymax), ...) - - INPUT: - f -- a function of two variables - (xmin, xmax) -- 2-tuple, the range of x values - (ymin, ymax) -- 2-tuple, the range of y values - The following inputs must all be passed in as named parameters: - plot_points -- integer (default: 25); number of points to plot - in each direction of the grid - fill -- bool (default: True), whether to color in the area - between contour lines - cmap -- string (default: 'gray'), the color map to use: - autumn, bone, cool, copper, gray, hot, hsv, - jet, pink, prism, spring, summer, winter - contours -- integer (default: None), the number of contour - lines to draw. If None, determined automatically, - and usually about 5. - + contour_plot(f, (xmin, xmax), (ymin, ymax)) EXAMPLES: @@ -1895,5 +1869,6 @@ A red, blue, and green "cool cat": - sage: G = plot(-cos(x), -2, 2, thickness=5, rgbcolor=(0.5,1,0.5)) + sage: ncos = lambda x: -cos(x) + sage: G = plot(ncos, -2, 2, thickness=5, rgbcolor=(0.5,1,0.5)) sage: P = polygon([[1,2], [5,6], [5,0]], rgbcolor=(1,0,0)) sage: Q = polygon([(-x,y) for x,y in P[0]], rgbcolor=(0,0,1)) @@ -2251,5 +2226,5 @@ We can change the line style to one of '--' (dashed), '-.' (dash dot), '-' (solid), 'steps', ':' (dotted): - sage: g = plot(sin(x), 0, 10, linestyle='-.') + sage: g = plot(sin,0,10, linestyle='-.') sage: g.save('sage.png') """ @@ -2257,7 +2232,6 @@ o = self.options o['plot_points'] = 200 - o['plot_division'] = 1000 - o['max_bend'] = 0.1 - o['rgbcolor'] = (0,0,1) + o['plot_division'] = 1000 # is this a good value? + o['max_bend'] = 0.1 # is this good as well? def _repr_(self): @@ -2265,5 +2239,6 @@ def __call__(self, funcs, xmin=None, xmax=None, parametric=False, - polar=False, label='', show=None, **kwds): + polar=False, label='', + show=None, **kwds): if show is None: show = SHOW_DEFAULT @@ -2282,4 +2257,5 @@ except AttributeError: pass + if xmin is None: xmin = -1 @@ -2312,5 +2288,4 @@ data = [] dd = delta - exceptions = 0; msg='' for i in xrange(plot_points + 1): x = xmin + i*delta @@ -2321,16 +2296,10 @@ else: x = xmax # guarantee that we get the last point. - try: y = f(x) data.append((x, float(y))) - except (ZeroDivisionError, TypeError, ValueError), msg: - sage.misc.misc.verbose("%s\nUnable to compute f(%s)"%(msg, x),1) - exceptions += 1 + except (TypeError, ValueError), msg: + #raise ValueError, "%s\nUnable to compute f(%s)"%(msg, x) pass - - if (len(data) == 0 and exceptions > 0) or exceptions > 10: - print "WARNING: When plotting, failed to evaluate function at %s points."%exceptions - print "Last error message: '%s'"%msg # adaptive refinement i, j = 0, 0 @@ -2434,5 +2403,7 @@ EXAMPLE: - sage: G = parametric_plot( (sin(t), sin(2*t)), 0, 2*pi, rgbcolor=hue(0.6) ) + sage: f = lambda t: sin(t) + sage: g = lambda t: sin(2*t) + sage: G = parametric_plot((f,g),0,2*pi,rgbcolor=hue(0.6)) sage: G.save() """ @@ -2779,7 +2750,7 @@ Make some plots of $\sin$ functions: - sage: f(x) = sin(x) - sage: g(x) = sin(2*x) - sage: h(x) = sin(4*x) + sage: f = lambda x: sin(x) + sage: g = lambda x: sin(2*x) + sage: h = lambda x: sin(4*x) sage: p1 = plot(f,-2*pi,2*pi,rgbcolor=hue(0.5)) sage: p2 = plot(g,-2*pi,2*pi,rgbcolor=hue(0.9)) @@ -2820,8 +2791,8 @@ """ # TODO: figure out WTF from sage.rings.integer import Integer - from math import floor - rr = Integer(int(floor(r*255))).str(base=16) - gg = Integer(int(floor(g*255))).str(base=16) - bb = Integer(int(floor(b*255))).str(base=16) + from sage.rings.arith import floor + rr = Integer(floor(r*255)).str(base=16) + gg = Integer(floor(g*255)).str(base=16) + bb = Integer(floor(b*255)).str(base=16) rr = '0'*(2-len(rr)) + rr gg = '0'*(2-len(gg)) + gg @@ -2844,5 +2815,5 @@ ['#ff0000', '#ffda00', '#48ff00', '#00ff91', '#0091ff', '#4800ff', '#ff00da'] """ - from math import floor + from sage.rings.arith import floor R = [] for i in range(n): Index: sage/probability/random_variable.py =================================================================== --- sage/probability/random_variable.py (revision 4022) +++ sage/probability/random_variable.py (revision 2617) @@ -2,8 +2,7 @@ Random variables and probability spaces -This introduces a class of random variables, with the focus on -discrete random variables (i.e. on a discrete probability space). -This avoids the problem of defining a measure space and measurable -functions. +This introduces a class of random variables, with the focus on discrete random +variables (i.e. on a discrete probability space). This avoids the problem of +defining a measure space and measurable functions. """ Index: sage/quadratic_forms/binary_qf.py =================================================================== --- sage/quadratic_forms/binary_qf.py (revision 4063) +++ sage/quadratic_forms/binary_qf.py (revision 1894) @@ -268,5 +268,5 @@ ## Find the range of allowed b's - bmax = (-D / ZZ(3)).sqrt_approx().ceil() + bmax = (-D / ZZ(3)).sqrt().ceil() b_range = range(-bmax, bmax+1) Index: sage/rings/arith.py =================================================================== --- sage/rings/arith.py (revision 4065) +++ sage/rings/arith.py (revision 3595) @@ -62,5 +62,5 @@ This example involves a complex number. - sage: z = (1/2)*(1 + RDF(sqrt(3)) *CC.0); z + sage: z = (1/2)*(1 + sqrt(3) *CC.0); z 0.500000000000000 + 0.866025403784439*I sage: p = algdep(z, 6); p @@ -1224,5 +1224,5 @@ 1/8 """ - if bool(a == one): + if a == one: return a if m < 0: @@ -1483,5 +1483,5 @@ # primes at most a given limit. -def factor(n, proof=True, int_=False, algorithm='pari', verbose=0, **kwds): +def factor(n, proof=True, int_=False, algorithm='pari', verbose=0): """ Returns the factorization of the integer n as a sorted list of @@ -1536,5 +1536,5 @@ if not isinstance(n, (int,long, integer.Integer)): try: - return n.factor(**kwds) + return n.factor() except AttributeError: raise TypeError, "unable to factor n" @@ -1874,8 +1874,9 @@ -1 - IMPLEMENTATION: Using GMP. + IMPLEMENTATION: Using Pari. """ x = integer_ring.ZZ(x) - return integer_ring.ZZ(x.kronecker(y)) + y = integer_ring.ZZ(y) + return integer_ring.ZZ(pari(x).kronecker(y).python()) def kronecker(x,y): @@ -2260,5 +2261,5 @@ [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1] sage: continued_fraction_list(sqrt(4/19)) - [0, 2, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 18] + [0, 2, 5, 1, 1, 2, 1, 16, 1, 2, 1, 1, 5, 4, 5, 1, 1, 2, 1, 15, 2] sage: continued_fraction_list(RR(pi), partial_convergents=True) ([3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 3], @@ -2284,21 +2285,6 @@ [2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, 1, 22, 1, 1, 24, 1, 1, 26, 1, 1, 28, 1, 1, 30, 1, 1, 32, 1, 1, 34, 1, 1, 36, 1, 1, 38, 1, 1] """ - import sage.calculus.calculus - import sage.functions.constants - # if x is a SymbolicExpression, try coercing it to a real number if not bits is None: - try: - x = sage.rings.real_mpfr.RealField(bits)(x) - except TypeError: - raise TypeError, "can only find the continued fraction of a number" - elif isinstance(x, float): - from real_double import RDF - x = RDF(x) - elif isinstance(x, (sage.calculus.calculus.SymbolicExpression, - sage.functions.constants.Constant)): - try: - x = sage.rings.real_mpfr.RealField(53)(x) - except TypeError: - raise TypeError, "can only find the continued fraction of a number" + x = sage.rings.real_mpfr.RealField(bits)(x) elif not partial_convergents and \ isinstance(x, (integer.Integer, sage.rings.rational.Rational, @@ -2630,9 +2616,7 @@ 0.652965496420167 + 0.343065839816545*I sage: falling_factorial(1+I, 4) - (I - 2)*(I - 1)*I*(I + 1) - sage: expand(falling_factorial(1+I, 4)) - 4*I + 2 + 2.00000000000000 + 4.00000000000000*I sage: falling_factorial(I, 4) - (I - 3)*(I - 2)*(I - 1)*I + -10.0000000000000 sage: M = MatrixSpace(ZZ, 4, 4) @@ -2693,12 +2677,10 @@ 0.266816390637832 + 0.122783354006372*I - sage: a = rising_factorial(I, 4); a - I*(I + 1)*(I + 2)*(I + 3) - sage: expand(a) - -10 + sage: rising_factorial(I, 4) + -10.0000000000000 See falling_factorial(I, 4). - sage: x = polygen(ZZ) + sage: R = ZZ['x'] sage: rising_factorial(x, 4) x^4 + 6*x^3 + 11*x^2 + 6*x @@ -2715,11 +2697,7 @@ -def integer_ceil(x): +def ceil(x): """ Return the ceiling of x. - - EXAMPLES: - sage: integer_ceil(5.4) - 6 """ try: @@ -2730,7 +2708,9 @@ except TypeError: pass - raise NotImplementedError, "computation of floor of %s not implemented"%repr(x) - -def integer_floor(x): + raise NotImplementedError, "computation of floor of %s not implemented"%x + +ceiling = ceil + +def floor(x): r""" Return the largest integer $\leq x$. @@ -2743,11 +2723,11 @@ EXAMPLES: - sage: integer_floor(5.4) + sage: floor(5.4) 5 - sage: integer_floor(float(5.4)) + sage: floor(float(5.4)) 5 - sage: integer_floor(-5/2) + sage: floor(-5/2) -3 - sage: integer_floor(RDF(-5/2)) + sage: floor(RDF(-5/2)) -3 """ Index: sage/rings/complex_double.pyx =================================================================== --- sage/rings/complex_double.pyx (revision 4060) +++ sage/rings/complex_double.pyx (revision 3370) @@ -82,8 +82,4 @@ CC = complex_field.ComplexField() -import real_mpfr -RR = real_mpfr.RealField() - -from real_double import RealDoubleElement # PREC is the precision (in decimal digits) that all PARI computations with doubles @@ -99,9 +95,4 @@ from random import random -from sage.structure.parent_gens import ParentWithGens - -def is_ComplexDoubleField(x): - return bool(PY_TYPE_CHECK(x, ComplexDoubleField_class)) - cdef class ComplexDoubleField_class(sage.rings.ring.Field): """ @@ -110,7 +101,4 @@ ALGORITHM: Arithmetic is done using GSL (the GNU Scientific Library). """ - def __init__(self): - ParentWithGens.__init__(self, self, ('x',), normalize=False) - def is_exact(self): return False @@ -236,6 +224,4 @@ else: return t - elif hasattr(x, '_complex_double_'): - return x._complex_double_(self) else: return ComplexDoubleElement(x, 0) @@ -261,12 +247,26 @@ 3.4 - Thus the sum of a CDF and a symbolic object is symbolic: + Symbolic constants canonically coerce into the complex double field, + but CDF does not canonically coerce to symbolic constants: + sage: CDF._coerce_(pi) + 3.14159265359 + sage: R = parent(pi) + sage: R(CDF.0) + 1.0*I + sage: R._coerce_(CDF.0) + Traceback (most recent call last): + ... + TypeError: no canonical coercion of element into self. + + Thus the sum of a CDF and a symbolic constant is in CDF: sage: a = pi + CDF.0; a - 1.00000000000000*I + pi + 3.14159265359 + 1.0*I sage: parent(a) - Symbolic Ring - """ + Complex Double Field + """ + import sage.functions.constants return self._coerce_try(x, [self.real_double_field(), - CC, RR]) + sage.functions.constants.ConstantRing, + CC]) @@ -656,11 +656,11 @@ 0.0 sage: CDF(0,1).arg() - 1.57079632679 + 1.5707963267948966 sage: CDF(0,-1).arg() - -1.57079632679 + -1.5707963267948966 sage: CDF(-1,0).arg() - 3.14159265359 - """ - return RealDoubleElement(gsl_complex_arg(self._complex)) + 3.1415926535897931 + """ + return gsl_complex_arg(self._complex) def __abs__(self): @@ -670,5 +670,5 @@ EXAMPLES: sage: abs(CDF(1,2)) - 2.2360679775 + 2.2360679774997898 sage: abs(CDF(1,0)) 1.0 @@ -676,5 +676,5 @@ 3.6055512754639891 """ - return RealDoubleElement(gsl_complex_abs(self._complex)) + return gsl_complex_abs(self._complex) def abs(self): @@ -686,5 +686,5 @@ 3.6055512754639891 """ - return RealDoubleElement(gsl_complex_abs(self._complex)) + return gsl_complex_abs(self._complex) def abs2(self): @@ -697,5 +697,5 @@ 13.0 """ - return RealDoubleElement(gsl_complex_abs2(self._complex)) + return gsl_complex_abs2(self._complex) def norm(self): @@ -708,5 +708,5 @@ 13.0 """ - return RealDoubleElement(gsl_complex_abs2(self._complex)) + return gsl_complex_abs2(self._complex) def logabs(self): @@ -720,14 +720,19 @@ EXAMPLES: + We try it out. sage: CDF(1.1,0.1).logabs() - 0.0994254293726 + 0.099425429372582669 sage: log(abs(CDF(1.1,0.1))) 0.0994254293726 + Which is better? sage: log(abs(ComplexField(200)(1.1,0.1))) 0.099425429372582675602989386713555936556752871164033127857198 - """ - return RealDoubleElement(gsl_complex_logabs(self._complex)) - + + Indeed, the logabs, wins. + """ + return gsl_complex_logabs(self._complex) + + # TODO: real and imag should be elements of RealDoubleField, when that exists. def real(self): """ @@ -739,5 +744,5 @@ 3.0 """ - return RealDoubleElement(self._complex.dat[0]) + return self._complex.dat[0] def imag(self): @@ -750,5 +755,5 @@ -2.0 """ - return RealDoubleElement(self._complex.dat[1]) + return self._complex.dat[1] def parent(self): @@ -844,11 +849,5 @@ 0.5 + 0.866025403784*I sage: a^3 # slightly random-ish arch dependent output - -1.0 + 1.22460635382e-16*I - - We raise to symbolic powers: - sage: CDF(1.2)^x - 1.20000000000000^x - sage: CDF(1.2)^(x^n + n^x) - 1.20000000000000^(x^n + n^x) + -1.0 + 1.22460635382e-16*I """ try: @@ -859,12 +858,5 @@ except TypeError: # a is not a complex number - try: - return z._pow_(CDF(a)) - except TypeError: - try: - return a.parent()(z)**a - except AttributeError: - raise TypeError - + return z._pow_(CDF(a)) def exp(self): @@ -1259,5 +1251,5 @@ sage: z = CDF(1,1); z.eta() 0.742048775837 + 0.19883137023*I - sage: i = CDF(0,1); pi = CDF(pi) + sage: i = CDF(0,1) sage: exp(pi * i * z / 12) * prod([1-exp(2*pi*i*n*z) for n in range(1,10)]) 0.742048775837 + 0.19883137023*I @@ -1267,5 +1259,4 @@ sage: z.eta(omit_frac=True) 0.998129069926 - sage: pi = CDF(pi) sage: prod([1-exp(2*pi*i*n*z) for n in range(1,10)]) # slightly random-ish arch dependent output 0.998129069926 + 4.5908467128e-19*I @@ -1349,7 +1340,6 @@ EXAMPLES: - sage: i = CDF(I) - sage: (1+i).agm(2-i) - 1.62780548487 + 0.136827548397*I + sage: (1+I).agm(2-I) + 1.62780548487271 + 0.136827548397369*I """ cdef pari_sp sp @@ -1439,5 +1429,5 @@ EXAMPLE: - sage: z = (1/2)*(1 + RDF(sqrt(3)) *CDF.0); z + sage: z = (1/2)*(1 + sqrt(3) *CDF.0); z 0.5 + 0.866025403784*I sage: p = z.algdep(5); p Index: sage/rings/complex_field.py =================================================================== --- sage/rings/complex_field.py (revision 4057) +++ sage/rings/complex_field.py (revision 3290) @@ -30,5 +30,5 @@ cache = {} -def ComplexField(prec=53, names=None): +def ComplexField(prec=53): """ Return the complex field with real and imaginary parts having prec @@ -42,7 +42,4 @@ sage: ComplexField(100).base_ring() Real Field with 100 bits of precision - sage: i = ComplexField(200).gen() - sage: i^2 - -1.0000000000000000000000000000000000000000000000000000000000 """ global cache @@ -102,7 +99,4 @@ sage: loads(CC.dumps()) == CC True - sage: k = ComplexField(100) - sage: loads(dumps(k)) == k - True This illustrates basic properties of a complex field. @@ -127,7 +121,4 @@ self._prec = int(prec) ParentWithGens.__init__(self, self._real_field(), ('I',), False) - - def __reduce__(self): - return ComplexField, (self._prec, ) def is_exact(self): Index: sage/rings/complex_number.pyx =================================================================== --- sage/rings/complex_number.pyx (revision 4059) +++ sage/rings/complex_number.pyx (revision 3484) @@ -38,5 +38,5 @@ def is_ComplexNumber(x): - return bool(isinstance(x, ComplexNumber)) + return isinstance(x, ComplexNumber) cdef class ComplexNumber(sage.structure.element.FieldElement): @@ -45,5 +45,6 @@ EXAMPLES: - sage: I = CC.0 + sage: C = ComplexField() + sage: I = C.0 sage: b = 1.5 + 2.5*I sage: loads(b.dumps()) == b @@ -116,9 +117,9 @@ EXAMPLES: - sage: a = CC(1 + I) + sage: a = 1+I sage: loads(dumps(a)) == a True """ - # TODO: This is potentially slow -- make a 1 version that + # TODO: This is potentially very slow -- make a 1 version that # is native and much faster -- doesn't use .real()/.imag() return (make_ComplexNumber0, (self._parent, self._multiplicative_order, self.real(), self.imag())) @@ -260,5 +261,5 @@ """ EXAMPLES: - sage: C. = ComplexField(20) + sage: C, i = ComplexField(20).objgen() sage: a = i^2; a -1.0000 @@ -278,17 +279,9 @@ if isinstance(right, (int, long, integer.Integer)): return sage.rings.ring_element.RingElement.__pow__(self, right) - try: - P = self.parent() - right = P(right) - z = self._pari_() - w = P(right)._pari_() - m = z**w - return P(m) - except TypeError: - try: - self = right.parent()(self) - return self**right - except AttributeError: - raise TypeError + z = self._pari_() + P = (self)._parent + w = P(right)._pari_() + m = z**w + return P(m) def prec(self): @@ -355,5 +348,4 @@ EXAMPLES: - sage: I = CC.0 sage: a = ~(5+I) sage: a * (5+I) @@ -424,5 +416,5 @@ EXAMPLES: - sage: C. = ComplexField() + sage: C, i = ComplexField().objgen() sage: i.multiplicative_order() 4 @@ -437,5 +429,5 @@ sage: C(2).multiplicative_order() +Infinity - sage: w = (1+sqrt(-3.0))/2; w + sage: w = (1+sqrt(-3))/2; w 0.500000000000000 + 0.866025403784439*I sage: abs(w) @@ -470,5 +462,5 @@ """ EXAMPLES: - sage: (1+CC(I)).acos() + sage: (1+I).acos() 0.904556894302381 - 1.06127506190504*I """ @@ -478,5 +470,5 @@ """ EXAMPLES: - sage: (1+CC(I)).acosh() + sage: (1+I).acosh() 1.06127506190504 + 0.904556894302381*I """ @@ -486,5 +478,5 @@ """ EXAMPLES: - sage: (1+CC(I)).asin() + sage: (1+I).asin() 0.666239432492515 + 1.06127506190504*I """ @@ -494,5 +486,5 @@ """ EXAMPLES: - sage: (1+CC(I)).asinh() + sage: (1+I).asinh() 1.06127506190504 + 0.666239432492515*I """ @@ -502,5 +494,5 @@ """ EXAMPLES: - sage: (1+CC(I)).atan() + sage: (1+I).atan() 1.01722196789785 + 0.402359478108525*I """ @@ -510,38 +502,13 @@ """ EXAMPLES: - sage: (1+CC(I)).atanh() + sage: (1+I).atanh() 0.402359478108525 + 1.01722196789785*I """ return self._parent(self._pari_().atanh()) - def coth(self): - """ - EXAMPLES: - sage: ComplexField(100)(1,1).coth() - 0.86801414289592494863584920892 - 0.21762156185440268136513424361*I - """ - return 1/self.tanh() - - def csch(self): - """ - EXAMPLES: - sage: ComplexField(100)(1,1).csch() - 0.30393100162842645033448560451 - 0.62151801717042842123490780586*I - """ - return 1/self.sinh() - - def sech(self): - """ - EXAMPLES: - sage: ComplexField(100)(1,1).sech() - 0.49833703055518678521380589177 - 0.59108384172104504805039169297*I - """ - return 1/self.cosh() - - def cotan(self): """ EXAMPLES: - sage: (1+CC(I)).cotan() + sage: (1+I).cotan() 0.217621561854403 - 0.868014142895925*I sage: i = ComplexField(200).0 @@ -557,5 +524,5 @@ """ EXAMPLES: - sage: (1+CC(I)).cos() + sage: (1+I).cos() 0.833730025131149 - 0.988897705762865*I """ @@ -565,5 +532,5 @@ """ EXAMPLES: - sage: (1+CC(I)).cosh() + sage: (1+I).cosh() 0.833730025131149 + 0.988897705762865*I """ @@ -601,5 +568,4 @@ sage: z = 1 + i; z.eta() 0.742048775836565 + 0.198831370229911*I - sage: pi = CC(pi) # otherwise we will get a symbolic result. sage: exp(pi * i * z / 12) * prod([1-exp(2*pi*i*n*z) for n in range(1,10)]) 0.742048775836565 + 0.198831370229911*I @@ -624,5 +590,5 @@ You can also use functional notation. - sage: eta(1+CC(I)) + sage: eta(1+I) 0.742048775836565 + 0.198831370229911*I """ @@ -636,5 +602,5 @@ """ EXAMPLES: - sage: (1+CC(I)).sin() + sage: (1+I).sin() 1.29845758141598 + 0.634963914784736*I """ @@ -644,5 +610,5 @@ """ EXAMPLES: - sage: (1+CC(I)).sinh() + sage: (1+I).sinh() 0.634963914784736 + 1.29845758141598*I """ @@ -652,5 +618,5 @@ """ EXAMPLES: - sage: (1+CC(I)).tan() + sage: (1+I).tan() 0.271752585319512 + 1.08392332733869*I """ @@ -660,5 +626,5 @@ """ EXAMPLES: - sage: (1+CC(I)).tanh() + sage: (1+I).tanh() 1.08392332733869 + 0.271752585319512*I """ @@ -669,5 +635,5 @@ """ EXAMPLES: - sage: (1+CC(I)).agm(2-I) + sage: (1+I).agm(2-I) 1.62780548487271 + 0.136827548397369*I """ @@ -850,5 +816,5 @@ EXAMPLE: sage: C = ComplexField() - sage: z = (1/2)*(1 + sqrt(3.0) *C.0); z + sage: z = (1/2)*(1 + sqrt(3) *C.0); z 0.500000000000000 + 0.866025403784439*I sage: p = z.algdep(5); p Index: sage/rings/contfrac.py =================================================================== --- sage/rings/contfrac.py (revision 4059) +++ sage/rings/contfrac.py (revision 3538) @@ -626,8 +626,23 @@ return s - def sqrt(self, bits=None): + def square_root(self): + """ + Return exact square root or raise an error if self + is not a perfect square. + + EXAMPLES: + sage: a = CFF(4/25).square_root(); a + [0, 2, 2] + sage: a.value() + 2/5 + """ + return ContinuedFraction(self.parent(), + self._rational_().square_root()) + + def sqrt(self): """ Return continued fraction approximation to the - square root of the value of this continued fraction. + square root of the value of this continued fraction, if + it is positive. If self is negative raise a ValueError. EXAMPLES: @@ -640,18 +655,9 @@ sage: float(b.value()^2 - a) 4.0935373134057017e-17 - sage: a = CFF(4/25).sqrt(); a - [0, 2, 2] - sage: a.value() - 2/5 """ r = self._rational_() if r < 0: raise ValueError, "self must be positive" - if bits is None: - if r.is_square(): - return ContinuedFraction(self.parent(), r.sqrt()) - else: - bits = 53 - return ContinuedFraction(self.parent(), r.sqrt_approx(bits)) + return ContinuedFraction(self.parent(), r.sqrt()) def list(self): @@ -758,7 +764,7 @@ return self._rational_().is_one() - def __nonzero__(self): - """ - Return False if self is zero. + def is_zero(self): + """ + Return True if self is zero. EXAMPLES: @@ -768,5 +774,5 @@ False """ - return not self._rational_().is_zero() + return self._rational_().is_zero() def _pari_(self): Index: sage/rings/finite_field.py =================================================================== --- sage/rings/finite_field.py (revision 3991) +++ sage/rings/finite_field.py (revision 3125) @@ -500,5 +500,4 @@ Nonconstant polynomials do not coerce: - sage: x = polygen(QQ) sage: k(x) Traceback (most recent call last): Index: sage/rings/finite_field_givaro.pyx =================================================================== --- sage/rings/finite_field_givaro.pyx (revision 4059) +++ sage/rings/finite_field_givaro.pyx (revision 3125) @@ -1191,7 +1191,7 @@ return (self._parent) - def __nonzero__(FiniteField_givaroElement self): + def is_zero(FiniteField_givaroElement self): r""" - Return True if \code{self != k(0)}. + Return True if \code{self == k(0)}. EXAMPLES: @@ -1203,5 +1203,5 @@ True """ - return not bool((self._parent).objectptr.isZero(self.element)) + return bool((self._parent).objectptr.isZero(self.element)) def is_one(FiniteField_givaroElement self): Index: sage/rings/fraction_field.py =================================================================== --- sage/rings/fraction_field.py (revision 4057) +++ sage/rings/fraction_field.py (revision 2399) @@ -4,40 +4,4 @@ AUTHOR: William Stein (with input from David Joyner, David Kohel, and Joe Wetherell) - -EXAMPLES: -Quotienting is a constructor for an element of the fraction field: - sage: R. = QQ[] - sage: (x^2-1)/(x+1) - x - 1 - sage: parent((x^2-1)/(x+1)) - Fraction Field of Univariate Polynomial Ring in x over Rational Field - - -The GCD is not taken (since it doesn't converge sometimes) in the inexact case. - sage: Z. = CC[] - sage: I = CC.gen() - sage: (1+I+z)/(z+0.1*I) - (1.00000000000000*z + 1.00000000000000 + 1.00000000000000*I)/(1.00000000000000*z + 0.100000000000000*I) - sage: (1+I*z)/(z+1.1) - (1.00000000000000*I*z + 1.00000000000000)/(1.00000000000000*z + 1.10000000000000) - - -TESTS: - sage: F = FractionField(IntegerRing()) - sage: F == loads(dumps(F)) - True - - sage: F = FractionField(PolynomialRing(RationalField(),'x')) - sage: F == loads(dumps(F)) - True - - sage: F = FractionField(PolynomialRing(IntegerRing(),'x')) - sage: F == loads(dumps(F)) - True - - sage: F = FractionField(MPolynomialRing(RationalField(),2,'x')) - sage: F == loads(dumps(F)) - True - """ @@ -195,20 +159,5 @@ R = self.ring() x = R(x); y = R(y) - return fraction_field_element.FractionFieldElement(self, x, y, - coerce=False, reduce = self.is_exact()) - - def is_exact(self): - """ - EXAMPLES: - sage: Z.=CC[] - sage: Z.is_exact() - False - """ - try: - return self.__is_exact - except AttributeError: - r = self.ring().is_exact() - self.__is_exact = r - return r + return fraction_field_element.FractionFieldElement(self, x, y, coerce=False) def _coerce_impl(self, x): Index: sage/rings/groebner_fan.py =================================================================== --- sage/rings/groebner_fan.py (revision 4007) +++ sage/rings/groebner_fan.py (revision 2487) @@ -42,12 +42,4 @@ sage: g.reduced_groebner_bases() [[1 - y^2 + x^2], [-1 + y^2 - x^2]] - -TESTS: - sage: x,y = QQ['x,y'].gens() - sage: i = ideal(x^2 - y^2 + 1) - sage: g = i.groebner_fan() - sage: g == loads(dumps(g)) - True - """ @@ -127,7 +119,4 @@ self.__ideal = I self.__ring = S - - def __eq__(self,right): - return type(self) == type(right) and self.ideal() == right.ideal() def ideal(self): Index: sage/rings/homset.py =================================================================== --- sage/rings/homset.py (revision 4057) +++ sage/rings/homset.py (revision 2369) @@ -36,24 +36,4 @@ return "Set of Homomorphisms from %s to %s"%(self.domain(), self.codomain()) - def has_coerce_map_from(self, x): - """ - The default for coercion maps between ring homomorphism - spaces is very restrictive (until more implementation work - is done). - """ - return (x.domain() == self.domain() and x.codomain() == self.codomain()) - - def _coerce_impl(self, x): - if not isinstance(x, morphism.RingHomomorphism): - raise TypeError - if x.parent() is self: - return x - if x.parent() == self: - if isinstance(x, morphism.RingHomomorphism_im_gens): - return morphism.RingHomomorphism_im_gens(self, x.im_gens()) - elif isinstance(x, morphism.RingHomomorphism_cover): - return morphism.RingHomomorphism_cover(self) - raise TypeError - def __call__(self, im_gens, check=True): """ @@ -64,20 +44,9 @@ ... TypeError: images do not define a valid homomorphism - - TESTS: - sage: H = Hom(ZZ, QQ) - sage: H == loads(dumps(H)) - True """ - if isinstance(im_gens, (morphism.RingHomomorphism_im_gens, morphism.RingHomomorphism_cover) ): - return self._coerce_impl(im_gens) try: return morphism.RingHomomorphism_im_gens(self, im_gens, check=check) except (NotImplementedError, ValueError), err: - try: - return self._coerce_impl(im_gens) - except TypeError: - raise TypeError, "images do not define a valid homomorphism" - + raise TypeError, "images do not define a valid homomorphism" def natural_map(self): @@ -100,21 +69,6 @@ sage: phi(b) a - - TESTS: - We test pickling of a homset from a quotient. - sage: R. = PolynomialRing(QQ, 2) - sage: S. = R.quotient(x^2 + y^2) - sage: H = S.Hom(R) - sage: H == loads(dumps(H)) - True - - We test pickling of actual homomorphisms in a quotient: - sage: phi = S.hom([b,a]) - sage: phi == loads(dumps(phi)) - True """ def __call__(self, im_gens, check=True): - if isinstance(im_gens, morphism.RingHomomorphism_from_quotient): - return morphism.RingHomomorphism_from_quotient(self, im_gens._phi()) try: pi = self.domain().cover() @@ -122,15 +76,5 @@ return morphism.RingHomomorphism_from_quotient(self, phi) except (NotImplementedError, ValueError), err: - try: - return self._coerce_impl(im_gens) - except TypeError: - raise TypeError, "images do not define a valid homomorphism" - - def _coerce_impl(self, x): - if not isinstance(x, morphism.RingHomomorphism_from_quotient): - raise TypeError - if x.parent() is self: - return x - if x.parent() == self: - return morphism.RingHomomorphism_from_quotient(self, x._phi()) - raise TypeError + raise TypeError, "images do not define a valid homomorphism" + + Index: sage/rings/ideal.py =================================================================== --- sage/rings/ideal.py (revision 4059) +++ sage/rings/ideal.py (revision 3311) @@ -85,19 +85,4 @@ ... TypeError: unable to find common ring into which all ideal generators map - - TESTS: - sage: R, x = PolynomialRing(ZZ, 'x').objgen() - sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) - sage: I == loads(dumps(I)) - True - - sage: I = Ideal(R, [4 + 3*x + x^2, 1 + x^2]) - sage: I == loads(dumps(I)) - True - - sage: I = Ideal((4 + 3*x + x^2, 1 + x^2)) - sage: I == loads(dumps(I)) - True - """ if isinstance(R, Ideal_generic): @@ -138,4 +123,5 @@ gens = list(set(gens)) + if isinstance(R, sage.rings.principal_ideal_domain.PrincipalIdealDomain): # Use GCD algorithm to obtain a principal ideal @@ -144,5 +130,5 @@ g = R.gcd(g, h) return Ideal_pid(R, g) - + if len(gens) == 1: return Ideal_principal(R, gens[0]) @@ -184,13 +170,9 @@ return '(%s)'%(', '.join([str(x) for x in self.gens()])) - def __repr__(self): + def _repr_(self): return "Ideal %s of %s"%(self._repr_short(), self.ring()) def __cmp__(self, other): - S = set(self.gens()) - T = set(other.gens()) - if S == T: - return 0 - return cmp(self.gens(), other.gens()) + return cmp(set(self.gens()), set(other.gens())) def __contains__(self, x): @@ -204,6 +186,6 @@ raise NotImplementedError - def __nonzero__(self): - return self.gens() != [self.ring()(0)] + def is_zero(self): + return self.gens() == [self.ring()(0)] def base_ring(self): @@ -280,5 +262,5 @@ Ideal_generic.__init__(self, ring, [gen]) - def __repr__(self): + def _repr_(self): return "Principal ideal (%s) of %s"%(self.gen(), self.ring()) Index: sage/rings/ideal_monoid.py =================================================================== --- sage/rings/ideal_monoid.py (revision 4019) +++ sage/rings/ideal_monoid.py (revision 1851) @@ -7,5 +7,4 @@ from sage.structure.parent_gens import ParentWithGens import sage.rings.integer_ring -import ideal def IdealMonoid(R): @@ -26,13 +25,7 @@ def __call__(self, x): - if isinstance(x, ideal.Ideal_generic): - x = x.gens() return self.__R.ideal(x) def _coerce_impl(self, x): R = self.__R - if isinstance(x, ideal.Ideal_generic): - x = [R._coerce_impl(y) for y in x.gens()] - return R.ideal(x) - else: - return R.ideal(R._coerce_(x)) + return R.ideal(R._coerce_(x)) Index: sage/rings/infinity.py =================================================================== --- sage/rings/infinity.py (revision 4022) +++ sage/rings/infinity.py (revision 3335) @@ -116,14 +116,4 @@ ... SignError: cannot add positive finite value to negative finite value - -TESTS: - sage: P = InfinityRing - sage: P == loads(dumps(P)) - True - - sage: P(2) == loads(dumps(P(2))) - True - - """ @@ -271,7 +261,4 @@ def _repr_(self): return "Infinity" - - def _maxima_init_(self): - return "inf" def lcm(self, x): @@ -481,12 +468,4 @@ return "-Infinity" - def _maxima_init_(self): - """ - EXAMPLES: - sage: maxima(-oo) - minf - """ - return "minf" - def _latex_(self): return "-\\infty" @@ -558,12 +537,4 @@ return "+Infinity" - def _maxima_init_(self): - """ - EXAMPLES: - sage: maxima(oo) - inf - """ - return "inf" - def _latex_(self): return "+\\infty" @@ -626,19 +597,18 @@ infinity = InfinityRing.gen(0) Infinity = infinity -minus_infinity = InfinityRing.gen(1) - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + Index: sage/rings/integer.pyx =================================================================== --- sage/rings/integer.pyx (revision 4065) +++ sage/rings/integer.pyx (revision 3666) @@ -13,6 +13,4 @@ -- Rishikesh (2007-02-25): changed quo_rem so that the rem is positive -- David Harvey, Martin Albrecht, Robert Bradshaw (2007-03-01): optimized Integer constructor and pool - -- Robert Bradshaw (2007-04-12): is_perfect_power, Jacobi symbol (with Kronecker extension) - Convert some methods to use GMP directly rather than pari, Integer() -> PY_NEW(Integer) EXAMPLES: @@ -299,9 +297,9 @@ def _xor(Integer self, Integer other): cdef Integer x - x = PY_NEW(Integer) + x = Integer() mpz_xor(x.value, self.value, other.value) return x - def __xor__(x, y): + def xor(x, y): """ Compute the exclusive or of x and y. @@ -309,5 +307,5 @@ EXAMPLES: sage: n = ZZ(2); m = ZZ(3) - sage: n.__xor__(m) + sage: n.xor(m) 1 """ @@ -316,4 +314,7 @@ return bin_op(x, y, operator.xor) + def __xor__(self, right): + raise RuntimeError, "Use ** for exponentiation, not '^', which means xor\n"+\ + "in Python, and has the wrong precedence. Use x.xor(y) for the xor of x and y." def __richcmp__(left, right, int op): @@ -339,5 +340,5 @@ """ cdef Integer z - z = PY_NEW(Integer) + z = Integer() set_mpz(z,self.value) return z @@ -392,4 +393,5 @@ Return the string representation of \code{self} in the given base. + EXAMPLES: @@ -617,6 +619,7 @@ def __floordiv(Integer self, Integer other): cdef Integer x - x = PY_NEW(Integer) - + x = Integer() + + _sig_on mpz_fdiv_q(x.value, self.value, other.value) @@ -654,5 +657,8 @@ 1 sage: (-1)^(1/3) - -1 + Traceback (most recent call last): + ... + TypeError: exponent (=1/3) must be an integer. + Coerce your numbers to real or complex numbers first. The base need not be an integer (it can be a builtin @@ -672,22 +678,4 @@ RuntimeError: exponent must be at most 4294967294 # 32-bit RuntimeError: exponent must be at most 18446744073709551614 # 64-bit - - We raise 2 to various interesting exponents: - sage: 2^x # symbolic x - 2^x - sage: 2^1.5 # real number - 2.82842712474619 - sage: 2^I # complex number - 2^I - sage: f = 2^(sin(x)-cos(x)); f - 2^(sin(x) - cos(x)) - sage: f(3) - 2^(sin(3) - cos(3)) - sage: 2^(x+y+z) - 2^(z + y + x) - sage: 2^(1/2) - sqrt(2) - sage: 2^(-1/2) - 1/sqrt(2) """ cdef Integer _n @@ -704,9 +692,5 @@ _n = Integer(n) except TypeError: - try: - s = n.parent()(self) - return s**n - except AttributeError: - raise TypeError, "exponent (=%s) must be an integer.\nCoerce your numbers to real or complex numbers first."%n + raise TypeError, "exponent (=%s) must be an integer.\nCoerce your numbers to real or complex numbers first."%n if _n < 0: @@ -781,5 +765,5 @@ cdef Integer x cdef int is_exact - x = PY_NEW(Integer) + x = Integer() _sig_on is_exact = mpz_root(x.value, self.value, n) @@ -824,7 +808,7 @@ sage: x = 3^100000 - sage: RR(log(RR(x), 3)) + sage: log(RR(x), 3) 100000.000000000 - sage: RR(log(RR(x + 100000), 3)) + sage: log(RR(x + 100000), 3) 100000.000000000 @@ -892,5 +876,5 @@ """ cdef Integer x - x = PY_NEW(Integer) + x = Integer() mpz_abs(x.value, self.value) return x @@ -916,5 +900,5 @@ cdef Integer x - x = PY_NEW(Integer) + x = Integer() _sig_on @@ -955,6 +939,6 @@ cdef Integer q, r - q = PY_NEW(Integer) - r = PY_NEW(Integer) + q = Integer() + r = Integer() _sig_on @@ -995,6 +979,6 @@ cdef Integer q, r - q = PY_NEW(Integer) - r = PY_NEW(Integer) + q = Integer() + r = Integer() _sig_on @@ -1029,5 +1013,5 @@ raise ZeroDivisionError, "cannot raise to a power modulo 0" - x = PY_NEW(Integer) + x = Integer() _sig_on @@ -1071,5 +1055,5 @@ cdef Integer x, _mod _mod = Integer(mod) - x = PY_NEW(Integer) + x = Integer() _sig_on @@ -1084,4 +1068,7 @@ def __long__(self): return mpz_get_pylong(self.value) + + def __nonzero__(self): + return not self.is_zero() def __float__(self): @@ -1226,5 +1213,5 @@ cdef Integer z - z = PY_NEW(Integer) + z = Integer() mpz_set(z.value,x) mpz_clear(x) @@ -1294,5 +1281,5 @@ _sig_off - z = PY_NEW(Integer) + z = Integer() set_mpz(z, x) mpz_clear(x) @@ -1333,7 +1320,7 @@ return bool(mpz_cmp_si(self.value, 1) == 0) - def __nonzero__(self): + def is_zero(self): r""" - Returns \code{True} if the integers is not $0$, otherwise \code{False}. + Returns \code{True} if the integers is $0$, otherwise \code{False}. EXAMPLES: @@ -1343,5 +1330,5 @@ True """ - return bool(mpz_cmp_si(self.value, 0) != 0) + return bool(mpz_cmp_si(self.value, 0) == 0) def is_unit(self): @@ -1370,5 +1357,5 @@ False """ - return bool(mpz_perfect_square_p(self.value)) + return bool(self._pari_().issquare()) def is_prime(self): @@ -1399,85 +1386,5 @@ """ return bool(self._pari_().ispseudoprime()) - - def is_perfect_power(self): - r""" - Retuns \code{True} if self is a perfect power. - - EXAMPLES: - sage: z = 8 - sage: z.is_perfect_power() - True - sage: z = 144 - sage: z.is_perfect_power() - True - sage: z = 10 - sage: z.is_perfect_power() - False - """ - return bool(mpz_perfect_power_p(self.value)) - - def jacobi(self, b): - r""" - Calculate the Jacobi symbol $\left(\frac{self}{b}\right)$. - - EXAMPLES: - sage: z = -1 - sage: z.jacobi(17) - 1 - sage: z.jacobi(19) - -1 - sage: z.jacobi(17*19) - -1 - sage: (2).jacobi(17) - 1 - sage: (3).jacobi(19) - -1 - sage: (6).jacobi(17*19) - -1 - sage: (6).jacobi(33) - 0 - sage: a = 3; b = 7 - sage: a.jacobi(b) == -b.jacobi(a) - True - """ - cdef long tmp - if PY_TYPE_CHECK(b, int): - tmp = b - if (tmp & 1) == 0: - raise ValueError, "Jacobi symbol not defined for even b." - return mpz_kronecker_si(self.value, tmp) - if not PY_TYPE_CHECK(b, Integer): - b = Integer(b) - if mpz_even_p((b).value): - raise ValueError, "Jacobi symbol not defined for even b." - return mpz_jacobi(self.value, (b).value) - - def kronecker(self, b): - r""" - Calculate the Kronecker symbol - $\left(\frac{self}{b}\right)$ with the Kronecker extension - $(self/2)=(2/self)$ when self odd, or $(self/2)=0$ when $self$ even. - - EXAMPLES: - EXAMPLES: - sage: z = 5 - sage: z.kronecker(41) - 1 - sage: z.kronecker(43) - -1 - sage: z.kronecker(8) - -1 - sage: z.kronecker(15) - 0 - sage: a = 2; b = 5 - sage: a.kronecker(b) == b.kronecker(a) - True - """ - if PY_TYPE_CHECK(b, int): - return mpz_kronecker_si(self.value, b) - if not PY_TYPE_CHECK(b, Integer): - b = Integer(b) - return mpz_kronecker(self.value, (b).value) - + def square_free_part(self): """ @@ -1636,5 +1543,5 @@ raise ValueError, "square root of negative number not defined." cdef Integer x - x = PY_NEW(Integer) + x = Integer() _sig_on @@ -1645,5 +1552,5 @@ - def sqrt_approx(self, bits=None): + def sqrt(self, bits=None): r""" Returns the positive square root of self, possibly as a @@ -1655,5 +1562,6 @@ If bits is not specified, the number of bits of precision is at least twice the - number of bits of self. + number of bits of self (the precision + is always at least 53 bits if not specified). OUTPUT: integer, real number, or complex number. @@ -1664,28 +1572,30 @@ EXAMPLE: sage: Z = IntegerRing() - sage: Z(4).sqrt_approx(53) + sage: Z(4).sqrt() + 2 + sage: Z(4).sqrt(53) 2.00000000000000 - sage: Z(2).sqrt_approx(53) + sage: Z(2).sqrt(53) 1.41421356237310 - sage: Z(2).sqrt_approx(100) + sage: Z(2).sqrt(100) 1.4142135623730950488016887242 - sage: n = 39188072418583779289; n.sqrt() + sage: n = 39188072418583779289; n.square_root() 6260037733 - sage: (100^100).sqrt_approx() - 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - sage: (-1).sqrt_approx() + sage: (100^100).sqrt() + 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + sage: (-1).sqrt() 1.00000000000000*I - sage: (-1).sqrt() - I sage: sqrt(-2) - sqrt(2)*I - sage: sqrt(-2.0) 1.41421356237310*I sage: sqrt(97) - sqrt(97) - sage: n = 97; n.sqrt_approx(200) + 9.84885780179610 + sage: n = 97; n.sqrt(200) 9.8488578017961047217462114149176244816961362874427641717232 """ if bits is None: + try: + return self.square_root() + except ValueError: + pass bits = max(53, 2*(mpz_sizeinbase(self.value, 2)+2)) @@ -1699,5 +1609,5 @@ return R(self).sqrt() - def sqrt(self): + def square_root(self): """ Return the positive integer square root of self, or raises a ValueError @@ -1705,18 +1615,15 @@ EXAMPLES: - sage: Integer(144).sqrt() + sage: Integer(144).square_root() 12 - sage: Integer(102).sqrt() - sqrt(102) - """ - if self < 0: - from sage.calculus.calculus import sqrt - return sqrt(self) + sage: Integer(102).square_root() + Traceback (most recent call last): + ... + ValueError: self (=102) is not a perfect square + """ n = self.isqrt() if n * n == self: return n - from sage.calculus.calculus import sqrt - return sqrt(self) - #raise ValueError, "self (=%s) is not a perfect square"%self + raise ValueError, "self (=%s) is not a perfect square"%self @@ -1747,7 +1654,7 @@ _sig_off - g0 = PY_NEW(Integer) - s0 = PY_NEW(Integer) - t0 = PY_NEW(Integer) + g0 = Integer() + s0 = Integer() + t0 = Integer() set_mpz(g0,g) set_mpz(s0,s) @@ -1842,5 +1749,5 @@ cdef _and(Integer self, Integer other): cdef Integer x - x = PY_NEW(Integer) + x = Integer() mpz_and(x.value, self.value, other.value) return x @@ -1854,5 +1761,5 @@ cdef _or(Integer self, Integer other): cdef Integer x - x = PY_NEW(Integer) + x = Integer() mpz_ior(x.value, self.value, other.value) return x @@ -1934,10 +1841,10 @@ if r == 0: raise ZeroDivisionError, "Inverse does not exist." - ans = PY_NEW(Integer) + ans = Integer() set_mpz(ans,x) mpz_clear(x) return ans - def gcd(self, n): + def _gcd(self, Integer n): """ Return the greatest common divisor of self and $n$. @@ -1957,5 +1864,4 @@ cdef mpz_t g cdef object g0 - cdef Integer _n = Integer(n) mpz_init(g) @@ -1963,8 +1869,8 @@ _sig_on - mpz_gcd(g, self.value, _n.value) + mpz_gcd(g, self.value, n.value) _sig_off - g0 = PY_NEW(Integer) + g0 = Integer() set_mpz(g0,g) mpz_clear(g) @@ -2039,5 +1945,5 @@ - w = PY_NEW(Integer) + w = Integer() mpz_set(w.value, z) mpz_clear(z) @@ -2082,5 +1988,5 @@ - w = PY_NEW(Integer) + w = Integer() mpz_set(w.value, z) mpz_clear(z) @@ -2356,5 +2262,5 @@ PyObject_FREE(o) -hook_fast_tp_functions() +#hook_fast_tp_functions() def hook_fast_tp_functions(): Index: sage/rings/integer_mod.pxd =================================================================== --- sage/rings/integer_mod.pxd (revision 3924) +++ sage/rings/integer_mod.pxd (revision 3357) @@ -14,6 +14,5 @@ cdef int_fast32_t int32 cdef int_fast64_t int64 - cdef object table # a list - cdef object inverses # also a list + cdef object table # how much faster is unsafe access to a list than a c array? cdef lookup(NativeIntStruct self, Py_ssize_t value) @@ -21,11 +20,8 @@ cdef class IntegerMod_abstract(sage.structure.element.CommutativeRingElement): cdef NativeIntStruct __modulus - cdef _new_c_from_long(self, long value) - cdef void set_from_mpz(self, mpz_t value) - cdef void set_from_long(self, long value) - cdef int is_square_c(self) except -2 cdef class IntegerMod_gmp(IntegerMod_abstract): cdef mpz_t value + cdef void set_from_mpz(IntegerMod_gmp self, mpz_t value) cdef mpz_t* get_value(IntegerMod_gmp self) cdef IntegerMod_gmp _new_c(self) @@ -33,4 +29,5 @@ cdef class IntegerMod_int(IntegerMod_abstract): cdef public int_fast32_t ivalue + cdef void set_from_mpz(IntegerMod_int self, mpz_t value) cdef void set_from_int(IntegerMod_int self, int_fast32_t value) cdef int_fast32_t get_int_value(IntegerMod_int self) @@ -39,4 +36,5 @@ cdef class IntegerMod_int64(IntegerMod_abstract): cdef int_fast64_t ivalue + cdef void set_from_mpz(IntegerMod_int64 self, mpz_t value) cdef void set_from_int(IntegerMod_int64 self, int_fast64_t value) cdef int_fast64_t get_int_value(IntegerMod_int64 self) Index: sage/rings/integer_mod.pyx =================================================================== --- sage/rings/integer_mod.pyx (revision 4065) +++ sage/rings/integer_mod.pyx (revision 3598) @@ -4,22 +4,8 @@ An element of the integers modulo $n$. -There are three types of integer_mod classes, depending on the -size of the modulus. The range is capped such that a single -arithmetic operation (e.g. multiplication) will not overflow. - -- IntegerMod_int stores its value in a int_fast32_t (typically an int) -- IntegerMod_int64 stores its value in a int_fast64_t (typically a long long) -- IntegerMod_gmp stores its value in a mpz_t - -All extend IntegerMod_abstract. - -For efficency reasons, it stores the modulus (in all three forms, if possible) in a common (cdef) class NativeIntStruct rather than in the parent. - - AUTHORS: -- Robert Bradshaw (most of the work) -- Didier Deshommes (bit shifting) -- William Stein (editing and polishing; new arith architecture) - -- Robert Bradshaw (implement native is_square and square_root) TESTS: @@ -30,20 +16,6 @@ """ -################################################################################# -# Copyright (C) 2006 Robert Bradshaw -# 2006 William Stein -# -# Distributed under the terms of the GNU General Public License (GPL) -# -# http://www.gnu.org/licenses/ -#***************************************************************************** - - include "../ext/interrupt.pxi" # ctrl-c interrupt block support include "../ext/stdsage.pxi" - -cdef extern from "math.h": - double log(double) - int ceil(double) import operator @@ -135,11 +107,5 @@ cdef class NativeIntStruct: - """ - We store the various forms of the modulus here rather than in the - parent for efficiency reasons. - - We may also store a cached table of all elements of a given - ring in this class. - """ + def __init__(NativeIntStruct self, sage.rings.integer.Integer z): self.int64 = -1 @@ -155,5 +121,5 @@ return sage.rings.integer_mod.makeNativeIntStruct, (self.sageInteger, ) - def precompute_table(NativeIntStruct self, parent, inverses=True): + def precompute_table(NativeIntStruct self, parent): self.table = PyList_New(self.int64) cdef Py_ssize_t i @@ -166,13 +132,4 @@ z = IntegerMod_int64(parent, i) Py_INCREF(z); PyList_SET_ITEM(self.table, i, z) - - if inverses: - tmp = [None] * self.int64 - for i from 1 <= i < self.int64: - try: - tmp[i] = ~self.table[i] - except ZeroDivisionError: - pass - self.inverses = tmp cdef lookup(NativeIntStruct self, Py_ssize_t value): @@ -192,21 +149,4 @@ self._parent = parent self.__modulus = parent._pyx_order - - - cdef _new_c_from_long(self, long value): - cdef IntegerMod_abstract x - x = PY_NEW(PY_TYPE(self)) - if PY_TYPE_CHECK(x, IntegerMod_gmp): - mpz_init((x).value) # should be done by the new method - x._parent = self._parent - x.__modulus = self.__modulus - x.set_from_long(value) - return x - - cdef void set_from_mpz(self, mpz_t value): - raise NotImplementedError, "Must be defined in child class." - - cdef void set_from_long(self, long value): - raise NotImplementedError, "Must be defined in child class." def __abs__(self): @@ -418,4 +358,15 @@ """ return self.__modulus.sageInteger + + + def is_square(self): + """ + EXAMPLES: + sage: Mod(3,17).is_square() + False + sage: Mod(9,17).is_square() + True + """ + return bool(self.pari().issquare()) def charpoly(self, var): @@ -470,70 +421,4 @@ return self - - def is_square(self): - r""" - EXAMPLES: - sage: Mod(3,17).is_square() - False - sage: Mod(9,17).is_square() - True - sage: Mod(9,17*19^2).is_square() - True - sage: Mod(-1,17^30).is_square() - True - sage: Mod(1/9, next_prime(2^40)).is_square() - True - sage: Mod(1/25, next_prime(2^90)).is_square() - True - - TESTS: - sage: Mod(1/25, 2^8).is_square() - True - sage: Mod(1/25, 2^40).is_square() - True - - ALGORITHM: - Calculate the Jacobi symbol $(self/p)$ at each prime $p$ dividing $n$ - It must be 1 or 0 for each prime, and if it is 0 mod $p$, - where $p^k || n$, then $ord_p(self)$ must be even or greater than $k$. - - $p = 2$ handled seperatly. - - AUTHOR: - -- Robert Bradshaw - """ - return bool(self.is_square_c()) - - cdef int is_square_c(self) except -2: - if self.is_zero() or self.is_one(): - return 1 - moduli = self.parent().factored_order() - cdef int val, e - lift = self.lift() - if len(moduli) == 1: - p, e = moduli[0] - if e == 1: - return lift.jacobi(p) != -1 - elif p == 2: - return self.pari().issquare() # TODO: implement directly - elif self % p == 0: - val = lift.valuation(p) - return val >= e or (val % 2 == 0 and (lift // p**val).jacobi(p) != -1) - else: - return lift.jacobi(p) != -1 - else: - for p, e in moduli: - if p == 2: - if e > 1 and not self.pari().issquare(): # TODO: implement directly - return 0 - elif e > 1 and lift % p == 0: - val = lift.valuation(p) - if val < e and (val % 2 == 1 or (lift // p**val).jacobi(p) == -1): - return 0 - elif lift.jacobi(p) == -1: - return 0 - return 1 - - def sqrt(self): """ @@ -541,15 +426,7 @@ """ return self.square_root() - def square_root(self): """ - Calculates the square roots mod $p$ for each of the primes $p$ dividing - the order of the ring, then lifts p-adically and uses crt to - find a square root mod $n$. - - See also \code{square_root_mod_prime_power} and \code{square_root_mod_prime} - (in this module) algorithms details. - EXAMPLES: sage: mod(-1, 17).square_root() @@ -557,58 +434,9 @@ sage: mod(5, 389).square_root() 86 - sage: mod(7, 18).square_root() - 5 - sage: a = mod(14, 5^60).square_root() - sage: a*a - 14 - sage: mod(15, 389).square_root() - Traceback (most recent call last): - ... - ValueError: Self must be a square. - sage: Mod(1/9, next_prime(2^40)).square_root()^(-2) - 9 - sage: Mod(1/25, next_prime(2^90)).square_root()^(-2) - 25 - - """ - if self.is_zero() or self.is_one(): - return self - - if not self.is_square_c(): - raise ValueError, "Self must be a square." - - moduli = self._parent.factored_order() - if len(moduli) == 1: - p, e = moduli[0] - if e > 1: - x = square_root_mod_prime_power(mod(self, p**e), p, e) - else: - x = square_root_mod_prime(self, p) - - else: - # return product of square roots mod each prime power - sqrts = [square_root_mod_prime(mod(self, p), p) for p, e in moduli if e == 1] + \ - [square_root_mod_prime_power(mod(self, p**e), p, e) for p, e in moduli if e != 1] - - x = sqrts.pop() - for y in sqrts: - x = x.crt(y) - - return x._balanced_abs() - - def _balanced_abs(self): - """ - This function returns x or -x, whichever has a positive - representative in -p/2 < x < p/2. - - This is used so that the same square root is always returned, - despite the possibly probabalistic nature of the underlying - algorithm. - """ - if self.lift() > self.__modulus.sageInteger >> 1: - return -self - else: - return self - + """ + try: + return self.parent()(self.pari().sqrt()) # TODO: implement directly + except PariError: + raise ValueError, "self must be a square." def rational_reconstruction(self): @@ -746,11 +574,8 @@ return cdef sage.rings.integer.Integer z - if PY_TYPE_CHECK(value, sage.rings.integer.Integer): + if isinstance(value, sage.rings.integer.Integer): z = value - elif PY_TYPE_CHECK(value, rational.Rational): + elif isinstance(value, rational.Rational): z = value % self.__modulus.sageInteger - elif PY_TYPE_CHECK(value, int): - self.set_from_long(value) - return else: z = sage.rings.integer_ring.Z(value) @@ -768,5 +593,5 @@ mpz_clear(self.value) - cdef void set_from_mpz(self, mpz_t value): + cdef void set_from_mpz(IntegerMod_gmp self, mpz_t value): cdef sage.rings.integer.Integer modulus modulus = self.__modulus.sageInteger @@ -775,10 +600,4 @@ else: mpz_set(self.value, value) - - cdef void set_from_long(self, long value): - cdef sage.rings.integer.Integer modulus - mpz_set_si(self.value, value) - if value < 0 or mpz_cmp_si(self.__modulus.sageInteger.value, value) >= 0: - mpz_mod(self.value, self.value, self.__modulus.sageInteger.value) cdef mpz_t* get_value(IntegerMod_gmp self): @@ -825,5 +644,5 @@ def is_one(IntegerMod_gmp self): """ - Returns \code{True} if this is $1$, otherwise \code{False}. + Returns \\code{True} if this is $1$, otherwise \\code{False}. EXAMPLES: @@ -835,7 +654,7 @@ return bool(mpz_cmp_si(self.value, 1) == 0) - def __nonzero__(IntegerMod_gmp self): - """ - Returns \code{True} if this is not $0$, otherwise \code{False}. + def is_zero(IntegerMod_gmp self): + """ + Returns \\code{True} if this is $0$, otherwise \\code{False}. EXAMPLES: @@ -845,5 +664,5 @@ True """ - return bool(mpz_cmp_si(self.value, 0) != 0) + return bool(mpz_cmp_si(self.value, 0) == 0) def is_unit(self): @@ -959,7 +778,8 @@ def __mod__(self, right): + right = int(right) if self.modulus() % right != 0: raise ZeroDivisionError, "Error - reduction modulo right not defined." - return IntegerMod(integer_mod_ring.IntegerModRing(right), self) + return IntegerMod(integer_mod_ring.IntegerModRing(right, self)) def __pow__(IntegerMod_gmp self, right, m): # NOTE: m ignored, always use modulus of parent ring @@ -1095,5 +915,6 @@ if self.__modulus.table is not None: return self.__modulus.lookup(value) - cdef IntegerMod_int x = PY_NEW(IntegerMod_int) + cdef IntegerMod_int x + x = PY_NEW(IntegerMod_int) x.__modulus = self.__modulus x._parent = self._parent @@ -1101,5 +922,5 @@ return x - cdef void set_from_mpz(self, mpz_t value): + cdef void set_from_mpz(IntegerMod_int self, mpz_t value): if mpz_sgn(value) == -1 or mpz_cmp_si(value, self.__modulus.int32) >= 0: self.ivalue = mpz_fdiv_ui(value, self.__modulus.int32) @@ -1107,7 +928,4 @@ self.ivalue = mpz_get_si(value) - cdef void set_from_long(self, long value): - self.ivalue = value % self.__modulus.int32 - cdef void set_from_int(IntegerMod_int self, int_fast32_t ivalue): if ivalue < 0: @@ -1150,5 +968,5 @@ def is_one(IntegerMod_int self): """ - Returns \code{True} if this is $1$, otherwise \code{False}. + Returns \\code{True} if this is $1$, otherwise \\code{False}. EXAMPLES: @@ -1160,7 +978,7 @@ return bool(self.ivalue == 1) - def __nonzero__(IntegerMod_int self): - """ - Returns \code{True} if this is not $0$, otherwise \code{False}. + def is_zero(IntegerMod_int self): + """ + Returns \\code{True} if this is $0$, otherwise \\code{False}. EXAMPLES: @@ -1170,5 +988,5 @@ True """ - return bool(self.ivalue != 0) + return bool(self.ivalue == 0) def is_unit(IntegerMod_int self): @@ -1260,14 +1078,8 @@ 4 """ - if self.__modulus.inverses is not None: - right_inverse = self.__modulus.inverses[(right).ivalue] - if right_inverse is None: - raise ZeroDivisionError, "Inverse does not exist." - else: - return self._new_c((self.ivalue * (right_inverse).ivalue) % self.__modulus.int32) - cdef int_fast32_t x - x = self.ivalue * mod_inverse_int((right).ivalue, self.__modulus.int32) - return self._new_c(x% self.__modulus.int32) + x = (self.ivalue * mod_inverse_int( + (right).ivalue, self.__modulus.int32) ) % self.__modulus.int32 + return self._new_c(x) def __int__(IntegerMod_int self): @@ -1305,5 +1117,8 @@ 160 """ - return self._new_c((self.ivalue << right) % self.__modulus.int32) + cdef IntegerMod_int x + x = IntegerMod_int(self._parent, None, empty=True) + x.ivalue = (self.ivalue << right) % self.__modulus.int32 + return x def __rshift__(IntegerMod_int self, int right): @@ -1318,5 +1133,8 @@ 1 """ - return self._new_c(self.ivalue >> right) + cdef IntegerMod_int x + x = IntegerMod_int(self._parent, None, empty=True) + x.ivalue = (self.ivalue >> right) % self.__modulus.int32 + return x def __pow__(IntegerMod_int self, right, m): # NOTE: m ignored, always use modulus of parent ring @@ -1355,12 +1173,5 @@ 43 """ - if self.__modulus.inverses is not None: - x = self.__modulus.inverses[self.ivalue] - if x is None: - raise ZeroDivisionError, "Inverse does not exist." - else: - return x - else: - return self._new_c(mod_inverse_int(self.ivalue, self.__modulus.int32)) + return self._new_c(mod_inverse_int(self.ivalue, self.__modulus.int32)) def lift(IntegerMod_int self): @@ -1382,5 +1193,5 @@ def __float__(IntegerMod_int self): - return self.ivalue + return float(self.ivalue) def __hash__(self): @@ -1392,48 +1203,4 @@ """ return hash(self.ivalue) - - cdef int is_square_c(self) except -2: - if self.ivalue <= 1: - return 1 - moduli = self._parent.factored_order() - cdef int val, e - cdef int_fast32_t p - if len(moduli) == 1: - sage_p, e = moduli[0] - p = sage_p - if e == 1: - return jacobi_int(self.ivalue, p) != -1 - elif p == 2: - return self.pari().issquare() # TODO: implement directly - elif self.ivalue % p == 0: - val = self.lift().valuation(sage_p) - return val >= e or (val % 2 == 0 and jacobi_int(self.ivalue / int(sage_p**val), p) != -1) - else: - return jacobi_int(self.ivalue, p) != -1 - else: - for sage_p, e in moduli: - p = sage_p - if p == 2: - if e > 1 and not self.pari().issquare(): # TODO: implement directly - return 0 - elif e > 1 and self.ivalue % p == 0: - val = self.lift().valuation(sage_p) - if val < e and (val % 2 == 1 or jacobi_int(self.ivalue / int(sage_p**val), p) == -1): - return 0 - elif jacobi_int(self.ivalue, p) == -1: - return 0 - return 1 - - def _balanced_abs(self): - """ - This function returns x or -x, whichever has a positive - representative in -p/2 < x < p/2. - """ - if self.ivalue > self.__modulus.int32 / 2: - return -self - else: - return self - - ### End of class @@ -1521,41 +1288,4 @@ -cdef int jacobi_int(int_fast32_t a, int_fast32_t m) except -2: - """ - Calculates the jacobi symbol (a/n) - For use in IntegerMod_int - AUTHOR: - -- Robert Bradshaw - """ - cdef int s, jacobi = 1 - cdef int_fast32_t b - - a = a % m - - while 1: - if a == 0: - return 0 # gcd was nontrivial - elif a == 1: - return jacobi - s = 0 - while (1 << s) & a == 0: - s += 1 - b = a >> s - # Now a = 2^s * b - - # factor out (2/m)^s term - if s % 2 == 1 and (m % 8 == 3 or m % 8 == 5): - jacobi = -jacobi - - if b == 1: - return jacobi - - # quadratic reciprocity - if b % 4 == 3 and m % 4 == 3: - jacobi = -jacobi - a = m % b - m = b - - def test_gcd(a, b): return gcd_int(int(a), int(b)) @@ -1616,13 +1346,10 @@ return x - cdef void set_from_mpz(self, mpz_t value): + cdef void set_from_mpz(IntegerMod_int64 self, mpz_t value): if mpz_sgn(value) == -1 or mpz_cmp_si(value, self.__modulus.int64) >= 0: self.ivalue = mpz_fdiv_ui(value, self.__modulus.int64) else: self.ivalue = mpz_get_si(value) - - cdef void set_from_long(self, long value): - self.ivalue = value % self.__modulus.int64 - + cdef void set_from_int(IntegerMod_int64 self, int_fast64_t ivalue): if ivalue < 0: @@ -1661,5 +1388,5 @@ def is_one(IntegerMod_int64 self): """ - Returns \code{True} if this is $1$, otherwise \code{False}. + Returns \\code{True} if this is $1$, otherwise \\code{False}. EXAMPLES: @@ -1671,7 +1398,7 @@ return bool(self.ivalue == 1) - def __nonzero__(IntegerMod_int64 self): - """ - Returns \code{True} if this is not $0$, otherwise \code{False}. + def is_zero(IntegerMod_int64 self): + """ + Returns \\code{True} if this is $0$, otherwise \\code{False}. EXAMPLES: @@ -1681,5 +1408,5 @@ True """ - return bool(self.ivalue != 0) + return bool(self.ivalue == 0) def is_unit(IntegerMod_int64 self): @@ -1844,5 +1571,5 @@ 1 """ - return self._new_c(self.ivalue >> right) + return self._new_c((self.ivalue >> right) % self.__modulus.int64) def __invert__(IntegerMod_int64 self): @@ -1886,5 +1613,5 @@ 8943.0 """ - return self.ivalue + return float(self.ivalue) def __hash__(self): @@ -1902,15 +1629,4 @@ return hash(self.ivalue) - - def _balanced_abs(self): - """ - This function returns x or -x, whichever has a positive - representative in -p/2 < x < p/2. - """ - if self.ivalue > self.__modulus.int64 / 2: - return -self - else: - return self - ### End of class @@ -1987,8 +1703,8 @@ while(exp != 0): pow2 = pow2 * pow2 - if pow2 >= INTEGER_MOD_INT64_LIMIT: pow2 = pow2 % n + if pow2 >= INTEGER_MOD_INT32_LIMIT: pow2 = pow2 % n if exp % 2: prod = prod * pow2 - if prod >= INTEGER_MOD_INT64_LIMIT: prod = prod % n + if prod >= INTEGER_MOD_INT32_LIMIT: prod = prod % n exp = exp >> 1 @@ -1996,230 +1712,2 @@ prod = prod % n return prod - - -cdef int jacobi_int64(int_fast64_t a, int_fast64_t m) except -2: - """ - Calculates the jacobi symbol (a/n) - For use in IntegerMod_int64 - AUTHOR: - -- Robert Bradshaw - """ - cdef int s, jacobi = 1 - cdef int_fast64_t b - - a = a % m - - while 1: - if a == 0: - return 0 # gcd was nontrivial - elif a == 1: - return jacobi - s = 0 - while (1 << s) & a == 0: - s += 1 - b = a >> s - # Now a = 2^s * b - - # factor out (2/m)^s term - if s % 2 == 1 and (m % 8 == 3 or m % 8 == 5): - jacobi = -jacobi - - if b == 1: - return jacobi - - # quadratic reciprocity - if b % 4 == 3 and m % 4 == 3: - jacobi = -jacobi - a = m % b - m = b - - -######################## -# Square root functions -######################## - -def square_root_mod_prime_power(IntegerMod_abstract a, p, e): - r""" - Calculates the square root of $a$, where $a$ is an integer mod $p^e$. - - ALGORITHM: - Perform p-adically by stripping off even powers of $p$ to get - a unit and lifting $\sqrt{unit} mod p$ via newton's method. - - AUTHOR: - -- Robert Bradshaw - """ - if a.is_zero() or a.is_one(): - return a - - if p == 2: - return a if e == 1 else self.parent()(self.pari().sqrt()) # TODO: implement directly - - # strip off even powers of p - cdef int i, val = a.lift().valuation(p) - if val % 2 == 1: - raise ValueError, "self must be a square." - if val > 0: - unit = a._parent(a.lift() // p**val) - else: - unit = a - - # find square root of unit mod p - x = unit.parent()(square_root_mod_prime(mod(unit, p), p)) - - # lift p-adically using newton iteration - # this is done to higher precision than neccisary except at the last step - one_half = ~(a._new_c_from_long(2)) - for i from 0 <= i < ceil(log(e)/log(2)) - val/2: - x = (x+unit/x) * one_half - - # multiply in powers of p (if any) - if val > 0: - x *= p**(val // 2) - return x - -def square_root_mod_prime(IntegerMod_abstract a, p=None): - r""" - Calculates the square root of a, where a is an integer mod p. - - ALGORITHM: - Several cases based on residue class of p mod 16. - - $p$ mod 2 = 0 $\Rightarrow$ p = 2 so \sqrt{a} = a$. - $p$ mod 4 = 3 $\Rightarrow \sqrt{a} = a^{(p+1)/4}$. - $p$ mod 8 = 5 $\Rightarrow \sqrt{a} = \zeta i a$ where $\zeta = (2a)^{(p-5)/8}$, $i=\sqrt{-1}$. - $p$ mod 16 = 9$ Similar, work in a bi-quadratic extension of $\FF_p$. - $p$ mod 16 = 1$ Variant of Cipolla-Lehmer, using Lucas functions. - - REFERENCES: - Siguna M\:uller. 'On the Computation of Square Roots in Finite Fields' - Designs, Codes and Cryptography, Volume 31, Issue 3 (March 2004) - - A. Oliver L. Atkin. 'Probabilistic primality testing' (Section 4) - In P. Flajolet and P. Zimmermann, editors, Analysis of Algorithms Seminar I. INRIA Research Report XXX, 1992. - Summary by F. Morain. - \url{http://citeseer.ist.psu.edu/atkin92probabilistic.html} - - H. Postl. 'Fast evaluation of Dickson Polynomials' - Contrib. to General Algebra, Vol. 6 (1988) pp. 223--225 - - AUTHOR: - Robert Bradshaw - - TESTS: - Every case appears in the first hundred primes. - sage: all([(a*a).square_root()^2 == a*a for p in prime_range(100) for a in Integers(p)]) - True - """ - if a.is_zero() or a.is_one(): - return a - - if p is None: - p = a.parent().order() - if p < PyInt_GetMax(): - p = int(p) - - cdef int p_mod_16 = p % 16 - - if p_mod_16 % 2 == 0: # p == 2 - return a - - elif p_mod_16 % 4 == 3: - return a ** ((p+1)/4) - - elif p_mod_16 % 8 == 5: - two_a = a+a - zeta = two_a ** ((p-5)/8) - i = two_a ** ((p-1)/4) - return zeta*a*(i-1) - - elif p_mod_16 == 9: - s = (a+a) ** ((p-1)/4) - if s.is_one(): - d = a._parent.quadratic_nonresidue() - d2 = d*d - z = (2 * d2 * a) ** ((p-9)/16) - i = 2 * d2 * z*z * a - return z*d*a*(i-1) - else: - z = (a+a) ** ((p-9)/16) - i = 2 * z*z * a - return z*a*(i-1) - - else: # p_mod_16 == 1 - - four = a._new_c_from_long(4) - - if a == four: - return a._new_c_from_long(2) - - if not ((a - four)).is_square_c(): - t = 1 - P = a - 2 - return fast_lucas((p-1) // 4, P) - - else: - t = a._new_c_from_long(2) - while ((a*t*t - four)).is_square_c(): - t += 1 - P = a*t*t - 2 - return fast_lucas((p-1)//4, P)/t - - -def fast_lucas(mm, IntegerMod_abstract P): - """ - Return $V_k(P, 1)$ where $V_k$ is the Lucas function - defined by the recursive relation - - $V_k(P, Q) = PV_{k-1}(P, Q) - QV_{k-2}(P, Q)$ - - with $V_0 = 2, V_1(P_Q) = P$. - - REFERENCES: - H. Postl. 'Fast evaluation of Dickson Polynomials' - Contrib. to General Algebra, Vol. 6 (1988) pp. 223\202\304\354225 - - AUTHOR: - Robert Bradshaw - - TESTS: - sage: from sage.rings.integer_mod import fast_lucas, slow_lucas - sage: all([fast_lucas(k, a) == slow_lucas(k, a) for a in Integers(23) for k in range(13)]) - True - """ - if mm == 0: - return 2 - elif mm == 1: - return P - - cdef sage.rings.integer.Integer m - m = mm if PY_TYPE_CHECK(mm, sage.rings.integer.Integer) else sage.rings.integer.Integer(mm) - two = P._new_c_from_long(2) - d1 = P - d2 = P*P - two - - _sig_on - cdef int j - for j from mpz_sizeinbase(m.value, 2)-1 > j > 0: - if mpz_tstbit(m.value, j): - d1 = d1*d2 - P - d2 = d2*d2 - two - else: - d2 = d1*d2 - P - d1 = d1*d1 - two - _sig_off - if mpz_odd_p(m.value): - return d1*d2 - P - else: - return d1*d1 - two - -def slow_lucas(k, P, Q=1): - """ - Lucas function defined using the definition, for consitancy testing. - """ - if k == 0: - return 2 - elif k == 1: - return P - else: - return P*slow_lucas(k-1, P, Q) - Q*slow_lucas(k-2, P, Q) Index: sage/rings/integer_mod_ring.py =================================================================== --- sage/rings/integer_mod_ring.py (revision 3925) +++ sage/rings/integer_mod_ring.py (revision 3524) @@ -340,21 +340,16 @@ if arith.is_prime(n): return True - + # TODO -- the implementation below uses factoring, but it doesn't # need to; really it just needs to know if n is a prime power or not, # which is easier than factoring. - if n.is_perfect_power(): - F = arith.factor(n) - if len(F) > 1: - return False - if F[0][0] == 2: - return False - return True - - else: + F = arith.factor(n) + if len(F) > 1: return False - - + if F[0][0] == 2: + return False + return True + def multiplicative_generator(self): """ @@ -398,13 +393,4 @@ return a - def quadratic_nonresidue(self): - try: - return self._nonresidue - except AttributeError: - for a in self: - if not a.is_square(): - self._nonresidue = a - return a - def factored_order(self): """ @@ -462,5 +448,5 @@ def order(self): return self.__order - + def cardinality(self): return self.order() Index: sage/rings/integer_ring.pxd =================================================================== --- sage/rings/integer_ring.pxd (revision 4057) +++ sage/rings/integer_ring.pxd (revision 3665) @@ -8,3 +8,2 @@ cdef Integer _coerce_ZZ(self, ntl_c_ZZ *z) cdef int _randomize_mpz(self, mpz_t value, x, y, distribution) except -1 - cdef object _zero Index: sage/rings/integer_ring.pyx =================================================================== --- sage/rings/integer_ring.pyx (revision 4010) +++ sage/rings/integer_ring.pyx (revision 3665) @@ -28,10 +28,4 @@ sage: Z('94803849083985934859834583945394') 94803849083985934859834583945394 - -TESTS: - sage: Z = IntegerRing() - sage: Z == loads(dumps(Z)) - True - """ Index: sage/rings/laurent_series_ring_element.py =================================================================== --- sage/rings/laurent_series_ring_element.py (revision 4059) +++ sage/rings/laurent_series_ring_element.py (revision 3574) @@ -17,5 +17,5 @@ IndexError: Laurent series are immutable -We compute with a Laurent series over the complex mpfr numbers. +We compute with a Laurent series over a the complex mpfr numbers. sage: K. = Frac(CC[['q']]) sage: K @@ -112,5 +112,5 @@ return self.__u.is_unit() - def __nonzero__(self): + def is_zero(self): """ EXAMPLES: @@ -123,5 +123,5 @@ 1 """ - return not self.__u.is_zero() + return self.__u.is_zero() def _im_gens_(self, codomain, im_gens): @@ -748,5 +748,5 @@ return t**(self.__n) * u - def __call__(self, *x): + def __call__(self, x): """ Compute value of this Laurent series at x. @@ -762,7 +762,5 @@ 82/9 """ - if isinstance(x[0], tuple): - x = x[0] - return self.__u(x) * (x[0]**self.__n) - - + return self.__u(x) * (x**self.__n) + + Index: sage/rings/morphism.py =================================================================== --- sage/rings/morphism.py (revision 4057) +++ sage/rings/morphism.py (revision 3354) @@ -282,20 +282,4 @@ sage: i(beta^2 + 1) 2.58740105196820 - -TESTS: - sage: H = Hom(ZZ, QQ) - sage: H == loads(dumps(H)) - True - - sage: K. = CyclotomicField(7) - sage: c = K.hom([1/zeta7]) - sage: c == loads(dumps(c)) - True - - sage: R. = PowerSeriesRing(GF(5)) - sage: f = R.hom([t^5]) - sage: f == loads(dumps(f)) - True - """ @@ -348,6 +332,4 @@ To: Polynomial Ring in x, y over Rational Field Defn: Choice of lifting map - sage: S.lift() == 0 - False """ def __init__(self, R, S): @@ -360,9 +342,4 @@ raise TypeError, "No natural lift map" - def __cmp__(self, other): - if not isinstance(other, RingMap_lift): - return cmp(type(self), type(other)) - return 0 - def _repr_defn(self): return "Choice of lifting map" @@ -402,8 +379,5 @@ A *ring* homomorphism is considered to be 0 if and only if it sends the 1 element of the domain to the 0 element of the - codomain. Since rings in SAGE all have a 1 element, the - zero homomorphism is only to a ring of order 1, where 1==0, - e.g., the ring \code{Integers(1)}. - + codomain. EXAMPLES: @@ -479,48 +453,4 @@ return self.__im_gens - def __cmp__(self, other): - """ - EXAMPLES: - A single variate quotient over QQ. - sage: R. = QQ[] - sage: Q. = R.quotient(x^2 + x + 1) - sage: f1 = R.hom([a]) - sage: f2 = R.hom([a + a^2 + a + 1]) - sage: f1 == f2 - True - sage: f1 == R.hom([a^2]) - False - sage: f1(x^3 + x) - a + 1 - sage: f2(x^3 + x) - a + 1 - - TESTS: - sage: loads(dumps(f2)) == f2 - True - - EXAMPLES: - A multivariate quotient over a finite field. - sage: R. = GF(7)[] - sage: Q. = R.quotient([x^2 + x + 1, y^2 + y + 1]) - sage: f1 = R.hom([a, b]) - sage: f2 = R.hom([a + a^2 + a + 1, b + b^2 + b + 1]) - sage: f1 == f2 - True - sage: f1 == R.hom([b,a]) - False - sage: f1(x^3 + x + y^2) - 6*b + a - sage: f2(x^3 + x + y^2) - 6*b + a - - TEST: - sage: loads(dumps(f2)) == f2 - True - """ - if not isinstance(other, RingHomomorphism_im_gens): - return cmp(type(self), type(other)) - return cmp(self.__im_gens, other.__im_gens) - def _repr_defn(self): D = self.domain() @@ -547,6 +477,6 @@ b + a """ - def __init__(self, parent): - RingHomomorphism.__init__(self, parent) + def __init__(self, ring, quotient_ring): + RingHomomorphism.__init__(self, ring.Hom(quotient_ring)) def _call_(self, x): @@ -559,18 +489,4 @@ return self.codomain().defining_ideal() - def __cmp__(self, other): - """ - EXAMPLES: - sage: R. = PolynomialRing(QQ, 2) - sage: S. = R.quo(x^2 + y^2) - sage: phi = S.cover() - sage: phi == loads(dumps(phi)) - True - sage: phi == R.quo(x^2 + y^3).cover() - False - """ - if not isinstance(other, RingHomomorphism_cover): - return cmp(type(self), type(other)) - return 0 # since parents are the same, i.e., both cover maps with same domain and codomain class RingHomomorphism_from_quotient(RingHomomorphism): @@ -601,6 +517,5 @@ sage: phi(a+b+c) c + b + a - sage: loads(dumps(phi)) == phi - True + Validity of the homomorphism is determined, when possible, and a @@ -624,30 +539,6 @@ self.__phi = phi - def _phi(self): - """ - Underlying morphism used to define this quotient map (i.e., - morphism from the cover of the domain). - """ - return self.__phi - def morphism_from_cover(self): return self.__phi - - def __cmp__(self, other): - """ - EXAMPLES: - sage: R. = PolynomialRing(GF(19), 3) - sage: S. = R.quo(x^3 + y^3 + z^3) - sage: phi = S.hom([b, c, a]) - sage: psi = S.hom([c, b, a]) - sage: f = S.hom([b, c, a + a^3 + b^3 + c^3]) - sage: phi == psi - False - sage: phi == f - True - """ - if not isinstance(other, RingHomomorphism_from_quotient): - return cmp(type(self), type(other)) - return cmp(self.__phi, other.__phi) def _repr_defn(self): Index: sage/rings/mpfr.pxi =================================================================== --- sage/rings/mpfr.pxi (revision 3927) +++ sage/rings/mpfr.pxi (revision 3366) @@ -12,5 +12,4 @@ ctypedef struct __mpfr_struct: pass - #ctypedef __mpfr_struct mpfr_t[1] ctypedef __mpfr_struct* mpfr_t @@ -51,8 +50,5 @@ void mpfr_free_str (char *str) - void mpfr_get_z(mpz_t rop, mpfr_t op, mp_rnd_t rnd) mp_exp_t mpfr_get_z_exp(mpz_t rop, mpfr_t op) - - void mpfr_urandomb(mpfr_t rop, void* rnd_state) # Arithmetic @@ -149,3 +145,2 @@ int mpfr_lessequal_p (mpfr_t op1, mpfr_t op2) int mpfr_cmp (mpfr_t op1, mpfr_t op2) - int mpfr_equal_p (mpfr_t op1, mpfr_t op2) Index: sage/rings/multi_polynomial_element.py =================================================================== --- sage/rings/multi_polynomial_element.py (revision 4061) +++ sage/rings/multi_polynomial_element.py (revision 3134) @@ -69,66 +69,4 @@ return "%s"%self.__element - #################### - # Some standard conversions - #################### - def __int__(self): - if self.degree() == 0: - return int(self.constant_coefficient()) - else: - raise TypeError - - def __long__(self): - if self.degree() == 0: - return long(self.constant_coefficient()) - else: - raise TypeError - - def __float__(self): - if self.degree() == 0: - return float(self.constant_coefficient()) - else: - raise TypeError - - def _mpfr_(self, R): - if self.degree() == 0: - return R(self.constant_coefficient()) - else: - raise TypeError - - def _complex_mpfr_field_(self, R): - if self.degree() == 0: - return R(self.constant_coefficient()) - else: - raise TypeError - - def _complex_double_(self, R): - if self.degree() == 0: - return R(self.constant_coefficient()) - else: - raise TypeError - - def _real_double_(self, R): - if self.degree() == 0: - return R(self.constant_coefficient()) - else: - raise TypeError - - def _rational_(self): - if self.degree() == 0: - from rational import Rational - return Rational(repr(self)) - else: - raise TypeError - - def _integer_(self): - if self.degree() == 0: - from integer import Integer - return Integer(repr(self)) - else: - raise TypeError - - - #################### - def __call__(self, *x): """ @@ -287,5 +225,5 @@ def __pow__(self, n): if not isinstance(n, (int, long, integer.Integer)): - n = integer.Integer(n) + raise TypeError, "The exponent must be an integer." if n < 0: return 1/(self**(-n)) @@ -367,5 +305,5 @@ INPUT: - x -- multivariate polynomial (a generator of the parent of self) + x -- multivariate polynmial (a generator of the parent of self) If x is not specified (or is None), return the total degree, which is the maximum degree of any monomial. @@ -549,6 +487,6 @@ sage: c = f.coefficient(x*y); c 2 - sage: c.parent() - Polynomial Ring in x, y over Rational Field + sage: c in QQ + False sage: c in MPolynomialRing(RationalField(), 2, names = ['x','y']) True @@ -1033,11 +971,11 @@ return self._MPolynomial__element != right._MPolynomial__element - def __nonzero__(self): - """ - Returns True if self != 0 + def is_zero(self): + """ + Returns True if self == 0 \note{This is much faster than actually writing self == 0} """ - return self._MPolynomial__element.dict()!={} + return self._MPolynomial__element.dict()=={} ############################################################################ Index: sage/rings/multi_polynomial_ideal.py =================================================================== --- sage/rings/multi_polynomial_ideal.py (revision 4057) +++ sage/rings/multi_polynomial_ideal.py (revision 3645) @@ -61,11 +61,4 @@ sage: 0 in j # optional True - -TESTS: - sage: x,y,z = QQ['x,y,z'].gens() - sage: I = ideal(x^5 + y^4 + z^3 - 1, x^3 + y^3 + z^2 - 1) - sage: I == loads(dumps(I)) - True - """ @@ -337,8 +330,8 @@ return self.__dimension - def _groebner_basis_using_singular(self, algorithm="groebner"): + def _singular_groebner_basis(self, algorithm="groebner"): """ Return a Groebner basis of this ideal. If a groebner basis for - this ideal has been calculated before the cached Groebner + this ideal has been calculated before the cached groebner basis is returned regardless of the requested algorithm. @@ -364,6 +357,12 @@ sage: I = sage.rings.ideal.Cyclic(R,4); I Ideal (d + c + b + a, c*d + b*c + a*d + a*b, b*c*d + a*c*d + a*b*d + a*b*c, -1 + a*b*c*d) of Polynomial Ring in a, b, c, d over Rational Field - sage: I._groebner_basis_using_singular() + sage: I.groebner_basis() [1 - d^4 - c^2*d^2 + c^2*d^6, -1*d - c + c^2*d^3 + c^3*d^2, -1*d + d^5 - b + b*d^4, -1*d^2 - d^6 + c*d + c^2*d^4 - b*d^5 + b*c, d^2 + 2*b*d + b^2, d + c + b + a] + + \note{Some Groebner basis calculations crash on 64-bit + opterons with \SAGE's singular build, but work fine with an + official binary. If you download and install a Singular + binary from the Singular website it will not have this problem + (you can use it with \SAGE by putting it in local/bin/).} """ try: @@ -388,25 +387,4 @@ return self.__groebner_basis - def _singular_groebner_basis(self): - try: - S = self.__singular_groebner_basis - except AttributeError: - G = self.groebner_basis() - try: - return self.__singular_groebner_basis - except AttributeError: - pass - - try: - S._check_valid() - return S - except ValueError: - G = self.groebner_basis() - S = singular(G) - self.__singular_groebner_basis = S - return S - - - def genus(self): """ @@ -569,14 +547,15 @@ if self.base_ring() == sage.rings.integer_ring.ZZ: return self._reduce_using_macaulay2(f) - - try: - singular = self._singular_groebner_basis().parent() - except (AttributeError, RuntimeError): - singular = self._singular_groebner_basis().parent() + + try: + singular = self.__singular_groebner_basis.parent() + except AttributeError: + self.groebner_basis() + singular = self.__singular_groebner_basis.parent() f = self.ring()(f) g = singular(f) try: - h = g.reduce(self._singular_groebner_basis()) + h = g.reduce(self.__singular_groebner_basis) except TypeError: # This is OK, since f is in the right ring -- type error @@ -877,7 +856,7 @@ return self._macaulay2_groebner_basis() else: - return self._groebner_basis_using_singular("groebner") + return self._singular_groebner_basis("groebner") elif algorithm.startswith('singular:'): - return self._groebner_basis_using_singular(algorithm[9:]) + return self._singular_groebner_basis(algorithm[9:]) elif algorithm == 'macaulay2:gb': return self._macaulay2_groebner_basis() Index: sage/rings/multi_polynomial_ring.py =================================================================== --- sage/rings/multi_polynomial_ring.py (revision 4065) +++ sage/rings/multi_polynomial_ring.py (revision 2665) @@ -83,5 +83,4 @@ from sage.structure.parent_gens import ParentWithGens - @@ -251,7 +250,4 @@ - def is_exact(self): - return self.base_ring().is_exact() - def is_finite(self): if self.ngens() == 0: @@ -419,30 +415,5 @@ sage: f = x^2 + 2/3*y^3 sage: S(f) - 3*b^3 + a^2 - - Coercion from symbolic variables: - sage: x,y,z = var('x,y,z') - sage: R = QQ[x,y,z] - sage: type(x) - - sage: type(R(x)) - - sage: f = R(x^3 + y^3 - z^3); f - -1*z^3 + y^3 + x^3 - sage: type(f) - - sage: parent(f) - Polynomial Ring in x, y, z over Rational Field - - A more complicated symbolic and computational mix. Behind the scenes - Singular and Maxima are doing the real work. - sage: R = QQ[x,y,z] - sage: f = (x^3 + y^3 - z^3)^10; f - (-z^3 + y^3 + x^3)^10 - sage: g = R(f); parent(g) - Polynomial Ring in x, y, z over Rational Field - sage: (f - g).expand() - 0 - + 3*b^3 + a^2 """ if isinstance(x, multi_polynomial_element.MPolynomial_polydict): @@ -467,5 +438,4 @@ elif isinstance(x, polydict.PolyDict): return multi_polynomial_element.MPolynomial_polydict(self, x) - elif isinstance(x, fraction_field_element.FractionFieldElement) and x.parent().ring() == self: if x.denominator() == 1: @@ -473,5 +443,4 @@ else: raise TypeError, "unable to coerce since the denominator is not 1" - elif is_SingularElement(x) and self._has_singular: self._singular_().set_ring() @@ -480,8 +449,4 @@ except: raise TypeError, "Unable to coerce singular object" - - elif hasattr(x, '_polynomial_'): - return x._polynomial_(self) - elif isinstance(x , str) and self._has_singular: self._singular_().set_ring() @@ -490,5 +455,4 @@ except: raise TypeError,"Unable to coerce string" - elif is_Macaulay2Element(x): try: @@ -504,10 +468,6 @@ raise TypeError, "Unable to coerce macaulay2 object" return multi_polynomial_element.MPolynomial_polydict(self, x) - - if isinstance(x, dict): - return multi_polynomial_element.MPolynomial_polydict(self, x) - else: - c = self.base_ring()(x) - return multi_polynomial_element.MPolynomial_polydict(self, {self._zero_tuple:c}) + c = self.base_ring()(x) + return multi_polynomial_element.MPolynomial_polydict(self, {self._zero_tuple:c}) Index: sage/rings/number_field/number_field.py =================================================================== --- sage/rings/number_field/number_field.py (revision 4058) +++ sage/rings/number_field/number_field.py (revision 3650) @@ -98,7 +98,8 @@ EXAMPLES: Constructing a relative number field + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^2 - 2) - sage: R. = K[] - sage: L = K.extension(t^3+t+a, b); L + sage: R. = K['t'] + sage: L = K.extension(t^3+t+a, 'b'); L Extension by t^3 + t + a of the Number Field in a with defining polynomial x^2 - 2 sage: L.absolute_field() @@ -124,11 +125,4 @@ name = sage.structure.parent_gens.normalize_names(1, name) - if not isinstance(polynomial, polynomial_element.Polynomial): - try: - polynomial = polynomial.polynomial(QQ) - except (AttributeError, TypeError): - raise TypeError, "polynomial (=%s) must be a polynomial."%repr(polynomial) - - key = (polynomial, name) if _nf_cache.has_key(key): @@ -185,4 +179,5 @@ """ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^3 - 2); K Number Field in a with defining polynomial x^3 - 2 @@ -194,5 +189,5 @@ ParentWithGens.__init__(self, QQ, name) if not isinstance(polynomial, polynomial_element.Polynomial): - raise TypeError, "polynomial (=%s) must be a polynomial"%repr(polynomial) + raise TypeError, "polynomial (=%s) must be a polynomial"%polynomial if check: @@ -214,14 +209,5 @@ def __reduce__(self): - """ - TESTS: - sage: K. = NumberField(Z^3 + Z + 1) - sage: L = loads(dumps(K)) - sage: print L - Number Field in w with defining polynomial Z^3 + Z + 1 - sage: print L == K - True - """ - return NumberField_generic_v1, (self.__polynomial, self.variable_name(), self.__latex_variable_name) + return NumberField_generic, (self.__polynomial, self.variable_name(), self.__latex_variable_name) def complex_embeddings(self, prec=53): @@ -231,5 +217,4 @@ EXAMPLES: - sage: x = polygen(QQ) sage: f = x^5 + x + 17 sage: k. = NumberField(f) @@ -257,5 +242,5 @@ self.__latex_variable_name = name - def _repr_(self): + def __repr__(self): return "Number Field in %s with defining polynomial %s"%( self.variable_name(), self.polynomial()) @@ -290,8 +275,4 @@ list)): return number_field_element.NumberFieldElement(self, x) - try: - return number_field_element.NumberFieldElement(self, x._rational_()) - except (TypeError, AttributeError): - pass raise TypeError, "Cannot coerce %s into %s"%(x,self) @@ -299,7 +280,10 @@ if isinstance(x, (rational.Rational, integer.Integer, int, long)): return number_field_element.NumberFieldElement(self, x) - elif isinstance(x, number_field_element.NumberFieldElement) and x.parent() == self: - return number_field_element.NumberFieldElement(self, x.list()) raise TypeError + + def category(self): + from sage.categories.all import NumberFields + return NumberFields() + def category(self): @@ -325,4 +309,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^3-2) sage: K.ideal([a]) @@ -466,4 +451,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^2+1) sage: K.elements_of_norm(3) @@ -482,30 +468,14 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^3 - 2) - sage: R. = K[] + sage: t = K['x'].gen() sage: L. = K.extension(t^2 + a); L - Extension by t^2 + a of the Number Field in a with defining polynomial x^3 - 2 - - We create another extension. - sage: k. = NumberField(x^2 + 1); k - Number Field in a with defining polynomial x^2 + 1 - sage: m. = k.extension(y^2 + 1); m - Extension by y^2 + 1 of the Number Field in a with defining polynomial x^2 + 1 - sage: b.minpoly() - x^4 + 10*x^2 + 9 - - """ - if not isinstance(poly, polynomial_element.Polynomial): - try: - poly = poly.polynomial(self) - except (AttributeError, TypeError): - raise TypeError, "polynomial (=%s) must be a polynomial."%repr(poly) - if not names is None: - name = names - if isinstance(name, tuple): - name = name[0] + Extension by x^2 + a of the Number Field in a with defining polynomial x^3 - 2 + """ + if not names is None: name = names if name is None: raise TypeError, "the variable name must be specified." - return NumberField_extension(self, poly, repr(name)) + return NumberField_extension(self, poly, name) def factor_integer(self, n): @@ -518,4 +488,5 @@ First we form a number field defined by $x^2 + 1$: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^2 + 1); K Number Field in I with defining polynomial x^2 + 1 @@ -572,4 +543,6 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) + sage: NumberField(x^3-2, 'a').galois_group(pari_group=True) PARI group [6, -1, 2, "S3"] of degree 3 @@ -591,5 +564,6 @@ EXAMPLES: - sage: K. = NumberField(x^5 + 10*x + 1) + sage: x = polygen(QQ,'x') + sage: K. = NumberField(x^5+10*x+1) sage: K.integral_basis() [1, a, a^2, a^3, a^4] @@ -616,4 +590,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: NumberField(x^3+x+9, 'a').narrow_class_group() Multiplicative Abelian Group isomorphic to C2 @@ -662,4 +637,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K = NumberField(x^3 + 2*x - 5, 'alpha') sage: K.polynomial_quotient_ring() @@ -676,4 +652,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: NumberField(x^2-2, 'a').regulator() 0.88137358701954305 @@ -695,4 +672,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: NumberField(x^2+1, 'a').signature() (0, 1) @@ -711,4 +689,5 @@ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^2 + 3) sage: K.trace_pairing([1,zeta3]) @@ -836,4 +815,5 @@ """ EXAMPLES: + sage: R. = PolynomialRing(QQ) sage: K. = NumberField(x^3 - 2) sage: t = K['x'].gen() @@ -850,8 +830,5 @@ raise TypeError, "base (=%s) must be a number field"%base if not isinstance(polynomial, polynomial_element.Polynomial): - try: - polynomial = polynomial.polynomial(base) - except (AttributeError, TypeError), msg: - raise TypeError, "polynomial (=%s) must be a polynomial."%repr(polynomial) + raise TypeError, "polynomial (=%s) must be a polynomial"%polynomial if name == base.variable_name(): raise ValueError, "Base field and extension cannot have the same name" @@ -897,19 +874,5 @@ self.__pari_bnf_certified = False - def __reduce__(self): - """ - TESTS: - sage: K. = NumberField(Z^3 + Z + 1) - sage: L. = K.extension(Z^3 + 2) - sage: L = loads(dumps(K)) - sage: print L - Number Field in w with defining polynomial Z^3 + Z + 1 - sage: print L == K - True - """ - return NumberField_extension_v1, (self.__base_field, self.polynomial(), self.variable_name(), - self.latex_variable_name()) - - def _repr_(self): + def __repr__(self): return "Extension by %s of the Number Field in %s with defining polynomial %s"%( self.polynomial(), self.base_field().variable_name(), @@ -1060,5 +1023,5 @@ pbn = self._pari_base_nf() prp = self.pari_relative_polynomial() - pari_poly = pbn.rnfequation(prp) + pari_poly = str(pbn.rnfequation(prp)).replace('^', '**') R = self.base_field().polynomial().parent() self.__absolute_polynomial = R(pari_poly) @@ -1222,17 +1185,5 @@ self.__zeta_order = n - def __reduce__(self): - """ - TESTS: - sage: K. = CyclotomicField(7) - sage: L = loads(dumps(K)) - sage: print L - Cyclotomic Field of order 7 and degree 6 - sage: print L == K - True - """ - return NumberField_cyclotomic_v1, (self.__zeta_order, self.variable_name()) - - def _repr_(self): + def __repr__(self): return "Cyclotomic Field of order %s and degree %s"%( self.zeta_order(), self.degree()) @@ -1540,15 +1491,4 @@ NumberField_generic.__init__(self, polynomial, name=name, check=check) - def __reduce__(self): - """ - TESTS: - sage: K. = QuadraticField(7) - sage: L = loads(dumps(K)) - sage: print L - Number Field in z7 with defining polynomial x^2 - 7 - sage: print L == K - True - """ - return NumberField_quadratic_v1, (self.polynomial(), self.variable_name()) def class_number(self, proof = True): @@ -1625,19 +1565,2 @@ (arith.is_squarefree(D) or \ (d == 0 and (D//4)%4 in [2,3] and arith.is_squarefree(D//4))) - - -################### -# For pickling -################### - -def NumberField_generic_v1(poly, name, latex_name): - return NumberField_generic(poly, name, latex_name, check=False) - -def NumberField_extension_v1(base_field, poly, name, latex_name): - return NumberField_extension(base_field, poly, name, latex_name, check=False) - -def NumberField_cyclotomic_v1(zeta_order, name): - return NumberField_cyclotomic(zeta_order, name) - -def NumberField_quadratic_v1(poly, name): - return NumberField_quadratic(poly, name, check=False) Index: sage/rings/number_field/number_field_ideal.py =================================================================== --- sage/rings/number_field/number_field_ideal.py (revision 4019) +++ sage/rings/number_field/number_field_ideal.py (revision 2725) @@ -4,12 +4,4 @@ AUTHOR: -- Steven Sivek (2005-05-16) - -TESTS: - sage: K. = NumberField(x^2 - 5) - sage: I = K.ideal(2/(5+a)) - sage: I == loads(dumps(I)) - True - - """ @@ -71,5 +63,7 @@ def __cmp__(self, other): - return cmp(self.pari_hnf(), other.pari_hnf()) + if self.pari_hnf() == other.pari_hnf(): + return 0 + return -1 def _coerce_impl(self, x): Index: sage/rings/padics/extension_local_field.py =================================================================== --- sage/rings/padics/extension_local_field.py (revision 3890) +++ sage/rings/padics/extension_local_field.py (revision 3667) @@ -17,4 +17,5 @@ def has_pth_root(self): pass def has_root_of_unity(self, n): pass + def hom(self, extension): pass def inertia_degree(self): pass def inertia_subfield(self): pass Index: sage/rings/padics/extension_local_ring.py =================================================================== --- sage/rings/padics/extension_local_ring.py (revision 3890) +++ sage/rings/padics/extension_local_ring.py (revision 3667) @@ -16,4 +16,5 @@ def has_pth_root(self): pass def has_root_of_unity(self, n): pass + def hom(self, extension): pass def inertia_degree(self): pass def inertia_subring(self): pass Index: sage/rings/padics/padic_extension_generic.py =================================================================== --- sage/rings/padics/padic_extension_generic.py (revision 3890) +++ sage/rings/padics/padic_extension_generic.py (revision 3678) @@ -108,4 +108,7 @@ # raise NotImplementedError + #def hom(self, ring): + # raise NotImplementedError + def random_element(self): return reduce(lambda x,y: x+y,map(lambda a,b:a*b,[self.ground_ring().random_element() for _ in range(self.modulus().degree())],[self.gen()**i for i in range(self.modulus().degree())]),0) Index: sage/rings/padics/padic_generic_element.py =================================================================== --- sage/rings/padics/padic_generic_element.py (revision 3804) +++ sage/rings/padics/padic_generic_element.py (revision 3680) @@ -570,7 +570,8 @@ AUTHORS: + -- William Stein: initial version -- David Harvey (2006-09-13): corrected subtle precision bug (need to take denominators into account! -- see trac \#53) - -- Genya Zaytman (2007-02-14): addapted to new p-adic class + -- Genya Zaytman (2007-02-14): adapted to new p-adic class TODO: Index: sage/rings/polydict.pyx =================================================================== --- sage/rings/polydict.pyx (revision 4006) +++ sage/rings/polydict.pyx (revision 2725) @@ -570,11 +570,4 @@ def __reduce__(PolyDict self): - """ - sage: from sage.rings.polydict import PolyDict - sage: f = PolyDict({(2,3):2, (1,2):3, (2,1):4}) - sage: loads(dumps(f)) == f - True - - """ return make_PolyDict,(self.__repn,) @@ -839,12 +832,4 @@ def __reduce__(ETuple self): - """ - EXAMPLES: - sage: from sage.rings.polydict import ETuple - sage: e = ETuple([1,1,0]) - sage: bool(e == loads(dumps(e))) - True - """ - return make_ETuple,(self._data,self._length) Index: sage/rings/polynomial_element.pxd =================================================================== --- sage/rings/polynomial_element.pxd (revision 4061) +++ sage/rings/polynomial_element.pxd (revision 3650) @@ -5,8 +5,7 @@ from sage.structure.element import Element, CommutativeAlgebraElement -from sage.structure.element cimport Element, CommutativeAlgebraElement, ModuleElement +from sage.structure.element cimport Element, CommutativeAlgebraElement cdef class Polynomial(CommutativeAlgebraElement): - cdef ModuleElement _neg_c_impl(self) cdef char _is_gen Index: sage/rings/polynomial_element.pyx =================================================================== --- sage/rings/polynomial_element.pyx (revision 4061) +++ sage/rings/polynomial_element.pyx (revision 3605) @@ -5,11 +5,4 @@ -- William Stein: first version -- Martin Albrecht: Added singular coercion. - -TESTS: - sage: R. = ZZ[] - sage: f = x^5 + 2*x^2 + (-1) - sage: f == loads(dumps(f)) - True - """ @@ -102,7 +95,4 @@ self._is_gen = is_gen - cdef ModuleElement _neg_c_impl(self): - return self.polynomial([-x for x in self.list()]) - def _add_(self, right): if self.degree() >= right.degree(): @@ -152,5 +142,5 @@ return self * self.parent()(right) - def __call__(self, *x): + def __call__(self, *a): """ Evaluate polynomial at x=a using Horner's rule @@ -202,21 +192,5 @@ Full MatrixSpace of 2 by 2 dense matrices over Rational Field - Nested polynomial ring elements can be called like multi-variate polynomials. - sage: R. = QQ[] - sage: S. = R[] - sage: f = x+y*x+y^2 - sage: f.parent() - Univariate Polynomial Ring in y over Univariate Polynomial Ring in x over Rational Field - sage: f(2) - 3*x + 4 - sage: f(2,4) - 16 - sage: R. = PowerSeriesRing(QQ, 't'); S. = R[] - sage: f = 1 + x*t^2 + 3*x*t^4 - sage: f(2) - 1 + 2*t^2 + 6*t^4 - sage: f(2, 1/2) - 15/8 - + AUTHORS: -- David Joyner, 2005-04-10 @@ -224,19 +198,10 @@ is determined by the arithmetic -- William Stein, 2007-03-24: fix parent being determined in the constant case! - -- Robert Bradshaw, 2007-04-09: add support for nested calling - """ - if isinstance(x[0], tuple): - x = x[0] - a = x[0] - + """ + a = a[0] + if isinstance(a, tuple): + a = a[0] d = self.degree() result = self[d] - if len(x) > 1: - other_args = x[1:] - if hasattr(result, '__call__'): - result = result(other_args) - else: - raise TypeError, "Wrong number of arguments" - if d == 0: try: @@ -244,14 +209,8 @@ except AttributeError: return result - i = d - 1 - if len(x) > 1: - while i >= 0: - result = result * a + self[i](other_args) - i -= 1 - else: - while i >= 0: - result = result * a + self[i] - i -= 1 + while i >= 0: + result = result * a + self[i] + i -= 1 return result @@ -507,5 +466,5 @@ if n != m-1: s += " + " - x = repr(x) + x = str(x) if not atomic_repr and n > 0 and (x.find("+") != -1 or x.find("-") != -1): x = "(%s)"%x @@ -528,5 +487,4 @@ r""" EXAMPLES: - sage: x = polygen(QQ) sage: f = x^3+2/3*x^2 - 5/3 sage: f._repr_() @@ -541,5 +499,4 @@ r""" EXAMPLES: - sage: x = polygen(QQ) sage: latex(x^3+2/3*x^2 - 5/3) x^{3} + \frac{2}{3}x^{2} - \frac{5}{3} @@ -951,5 +908,5 @@ Notice that the unit factor is included when we multiply $F$ back out. - sage: expand(F) + sage: F.mul() 2*x^10 + 2*x + 2*a @@ -986,5 +943,5 @@ sage: F = factor(x^2-3); F (1.0000000000000000000000000000*x + 1.7320508075688772935274463415) * (1.0000000000000000000000000000*x - 1.7320508075688772935274463415) - sage: expand(F) + sage: F.mul() 1.0000000000000000000000000000*x^2 - 3.0000000000000000000000000000 sage: factor(x^2 + 1) @@ -994,5 +951,5 @@ sage: F = factor(x^2+3); F (1.0000000000000000000000000000*x + -1.7320508075688772935274463415*I) * (1.0000000000000000000000000000*x + 1.7320508075688772935274463415*I) - sage: expand(F) + sage: F.mul() 1.0000000000000000000000000000*x^2 + 3.0000000000000000000000000000 sage: factor(x^2+1) @@ -1000,7 +957,7 @@ sage: f = C.0 * (x^2 + 1) ; f 1.0000000000000000000000000000*I*x^2 + 1.0000000000000000000000000000*I - sage: F = factor(f); F + sage: F=factor(f); F (1.0000000000000000000000000000*I) * (1.0000000000000000000000000000*x + -1.0000000000000000000000000000*I) * (1.0000000000000000000000000000*x + 1.0000000000000000000000000000*I) - sage: expand(F) + sage: F.mul() 1.0000000000000000000000000000*I*x^2 + 1.0000000000000000000000000000*I """ @@ -1256,4 +1213,7 @@ return bool(self._is_gen) + def is_zero(self): + return bool(self.degree() == -1) + def leading_coefficient(self): return self[self.degree()] @@ -1420,5 +1380,5 @@ def _pari_init_(self): - return repr(self._pari_()) + return str(self._pari_()) def _magma_init_(self): @@ -1465,5 +1425,5 @@ def _gap_init_(self): - return repr(self) + return str(self) def _gap_(self, G): @@ -1574,14 +1534,7 @@ sage: x = CC['x'].0 - sage: i = CC.0 - sage: f = (x - 1)*(x - i) + sage: f = (x-1)*(x-I) sage: f.roots() [1.00000000000000*I, 1.00000000000000] - - A purely symbolic roots example: - sage: f = expand((X-1)*(X-I)^3*(X^2 - sqrt(2))); f - X^6 - 3*I*X^5 - X^5 + 3*I*X^4 - sqrt(2)*X^4 - 3*X^4 + 3*sqrt(2)*I*X^3 + I*X^3 + sqrt(2)*X^3 + 3*X^3 - 3*sqrt(2)*I*X^2 - I*X^2 + 3*sqrt(2)*X^2 - sqrt(2)*I*X - 3*sqrt(2)*X + sqrt(2)*I - sage: print f.roots() - [(I, 3), (-2^(1/4), 1), (2^(1/4), 1), (1, 1)] """ seq = [] Index: sage/rings/polynomial_element_generic.py =================================================================== --- sage/rings/polynomial_element_generic.py (revision 4061) +++ sage/rings/polynomial_element_generic.py (revision 3681) @@ -70,8 +70,8 @@ if fraction_field_element.is_FractionFieldElement(x): - if x.denominator().degree() >= 1: - raise TypeError, "denominator must be constant" + if x.denominator() != 1: + raise TypeError, "denominator must be 1" else: - x = x.numerator() * (~x.denominator()[0]) + x = x.numerator() if isinstance(x, Polynomial): @@ -380,5 +380,5 @@ EXAMPLES: sage: R. = PolynomialRing(CDF, sparse=True) - sage: f = CDF(1,2) + w^5 - CDF(pi)*w + CDF(e) + sage: f = CDF(1,2) + w^5 - pi*w + e sage: f._repr() '1.0*w^5 + (-3.14159265359)*w + 3.71828182846 + 2.0*I' @@ -400,5 +400,5 @@ if n != m-1: s += " + " - x = repr(x) + x = str(x) if not atomic_repr and n > 0 and (x.find("+") != -1 or x.find("-") != -1): x = "(%s)"%x @@ -434,5 +434,4 @@ EXAMPLES: sage: R. = PolynomialRing(RDF, sparse=True) - sage: e = RDF(e) sage: f = sum(e^n*w^n for n in range(4)); f 20.0855369232*w^3 + 7.38905609893*w^2 + 2.71828182846*w + 1.0 @@ -1615,5 +1614,5 @@ if n != m: s += " + " - x = repr(x) + x = str(x) if not atomic_repr and n > 0 and (x.find("+") != -1 or x.find("-") != -1): x = "(%s)"%x Index: sage/rings/polynomial_pyx.pyx =================================================================== --- sage/rings/polynomial_pyx.pyx (revision 4059) +++ sage/rings/polynomial_pyx.pyx (revision 2725) @@ -1144,6 +1144,6 @@ return self.pq.degree - def __nonzero__(self): - return self.pq.degree != -1 + def is_zero(self): + return self.pq.degree == -1 def list(self): Index: sage/rings/polynomial_quotient_ring.py =================================================================== --- sage/rings/polynomial_quotient_ring.py (revision 4003) +++ sage/rings/polynomial_quotient_ring.py (revision 3480) @@ -667,5 +667,4 @@ EXAMPLES: - sage: x = polygen(QQ) sage: f = x^5 + x + 17 sage: k = QQ['x'].quotient(f) Index: sage/rings/polynomial_ring.py =================================================================== --- sage/rings/polynomial_ring.py (revision 4059) +++ sage/rings/polynomial_ring.py (revision 3679) @@ -168,6 +168,6 @@ except: raise TypeError,"Unable to coerce string" - elif hasattr(x, '_polynomial_'): - return x._polynomial_(self) + # elif isinstance(x, multi_polynomial_element.MPolynomial_polydict): + # return x.univariate_polynomial(self) elif is_MagmaElement(x): x = list(x.Eltseq()) @@ -435,7 +435,4 @@ return True return False - - def is_exact(self): - return self.base_ring().is_exact() def is_field(self): @@ -831,6 +828,4 @@ except: raise TypeError,"Unable to coerce string" - elif hasattr(x, '_polynomial_'): - return x._polynomial_(self) return polynomial_element_generic.Polynomial_dense_mod_p(self, x, check, is_gen,construct=construct) Index: sage/rings/polynomial_ring_constructor.py =================================================================== --- sage/rings/polynomial_ring_constructor.py (revision 4022) +++ sage/rings/polynomial_ring_constructor.py (revision 3667) @@ -4,5 +4,4 @@ from sage.structure.parent_gens import normalize_names -from sage.structure.element import is_Element import ring import weakref @@ -116,10 +115,4 @@ y^2 + y - Often the quotes are not needed, because of predefined symbolic variables: - sage: R = GF(9,a)[x] - sage: R - Univariate Polynomial Ring in x over Finite Field in a of size 3^2 - - In fact, since the diamond brackets on the left determine the variable name, you can omit the variable from the square brackets: @@ -198,10 +191,4 @@ """ import polynomial_ring as m - - if is_Element(arg1) and not isinstance(arg1, (int, long, m.integer.Integer)): - arg1 = str(arg1) - if is_Element(arg2) and not isinstance(arg2, (int, long, m.integer.Integer)): - arg2 = str(arg2) - if isinstance(arg1, (int, long, m.integer.Integer)): arg1, arg2 = arg2, arg1 @@ -219,8 +206,4 @@ R = None - if isinstance(arg1, (list, tuple)): - arg1 = [repr(x) for x in arg1] - if isinstance(arg2, (list, tuple)): - arg2 = [repr(x) for x in arg2] if isinstance(arg2, (int, long, m.integer.Integer)): # 3. PolynomialRing(base_ring, names, n, order='degrevlex'): @@ -231,5 +214,5 @@ R = _multi_variate(base_ring, names, n, sparse, order) - elif isinstance(arg1, str) or (isinstance(arg1, (list,tuple)) and len(arg1) == 1): + elif isinstance(arg1, str) or len(arg1) == 1: if not ',' in arg1: # 1. PolynomialRing(base_ring, name, sparse=False): Index: sage/rings/polynomial_singular_interface.py =================================================================== --- sage/rings/polynomial_singular_interface.py (revision 4067) +++ sage/rings/polynomial_singular_interface.py (revision 2641) @@ -4,9 +4,4 @@ AUTHORS: -- Martin Albrecht (2006-04-21) - -TESTS: - sage: R = MPolynomialRing(GF(2**8,'a'),10,'x', order='revlex') - sage: R == loads(dumps(R)) - True """ @@ -35,6 +30,4 @@ from complex_field import is_ComplexField from real_mpfr import is_RealField -from complex_double import is_ComplexDoubleField -from real_double import is_RealDoubleField from integer_ring import ZZ import sage.rings.arith @@ -171,5 +164,5 @@ # size_t bits = 1 + (size_t) ((float)digits * 3.5); precision = self.base_ring().precision() - digits = sage.rings.arith.integer_ceil((2*precision - 2)/7.0) + digits = sage.rings.arith.ceil((2*precision - 2)/7.0) self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order) @@ -178,16 +171,6 @@ # size_t bits = 1 + (size_t) ((float)digits * 3.5); precision = self.base_ring().precision() - digits = sage.rings.arith.integer_ceil((2*precision - 2)/7.0) + digits = sage.rings.arith.ceil((2*precision - 2)/7.0) self.__singular = singular.ring("(complex,%d,0,I)"%digits, _vars, order=order) - - elif is_RealDoubleField(self.base_ring()): - # singular converts to bits from base_10 in mpr_complex.cc by: - # size_t bits = 1 + (size_t) ((float)digits * 3.5); - self.__singular = singular.ring("(real,15,0)", _vars, order=order) - - elif is_ComplexDoubleField(self.base_ring()): - # singular converts to bits from base_10 in mpr_complex.cc by: - # size_t bits = 1 + (size_t) ((float)digits * 3.5); - self.__singular = singular.ring("(complex,15,0,I)", _vars, order=order) elif self.base_ring().is_prime_field() or (self.base_ring() is ZZ and force): @@ -219,6 +202,4 @@ or is_RealField(base_ring) or is_ComplexField(base_ring) - or is_RealDoubleField(base_ring) - or is_ComplexDoubleField(base_ring) or base_ring is ZZ ) Index: sage/rings/power_series_ring.py =================================================================== --- sage/rings/power_series_ring.py (revision 4061) +++ sage/rings/power_series_ring.py (revision 3663) @@ -30,14 +30,5 @@ Power Series Ring in t2 over Power Series Ring in t over Integer Ring sage: S.base_ring() - Power Series Ring in t over Integer Ring - -We compute with power series over the symbolic ring. - sage: K. = PowerSeriesRing(SR, 5) - sage: f = a + b*t + c*t^2 + O(t^3) - sage: f*f - a^2 + ((b + a)^2 - b^2 - a^2)*t + ((c + b + a)^2 - (c + b)^2 - (b + a)^2 + 2*b^2)*t^2 + O(t^3) - sage: f = sqrt(2) + sqrt(3)*t + O(t^3) - sage: f^2 - 2 + ((sqrt(3) + sqrt(2))^2 - 5)*t + 3*t^2 + O(t^3) + Power Series Ring in t over Integer Ring Elements are first coerced to constants in base_ring, then coerced into the @@ -65,14 +56,4 @@ -- William Stein: the code -- Jeremy Cho (2006-05-17): some examples (above) - -TESTS: - sage: R. = PowerSeriesRing(QQ) - sage: R == loads(dumps(R)) - True - - sage: R. = PowerSeriesRing(QQ, sparse=True) - sage: R == loads(dumps(R)) - True - """ @@ -123,5 +104,5 @@ Traceback (most recent call last): ... - ValueError: first letter of variable name must be a letter + TypeError: illegal variable name sage: S = PowerSeriesRing(QQ, 'x', default_prec = 15); S @@ -130,6 +111,4 @@ 15 """ - if isinstance(name, (int,long,integer.Integer)): - default_prec = name if not names is None: name = names Index: sage/rings/power_series_ring_element.py =================================================================== --- sage/rings/power_series_ring_element.py (revision 4065) +++ sage/rings/power_series_ring_element.py (revision 3686) @@ -86,11 +86,9 @@ import sage.structure.coerce import rational_field, integer_ring -from integer import Integer -from integer_mod_ring import IntegerModRing import sage.libs.pari.all as pari import sage.misc.latex as latex from sage.libs.all import PariError from sage.misc.functional import sqrt, log -from math import ceil +from sage.rings.arith import ceil Polynomial = polynomial.Polynomial_generic_dense @@ -368,8 +366,8 @@ coeffs.sort() for (n, x) in coeffs: - if x: + if x != 0: if s != ' ': s += " + " - x = repr(x) + x = str(x) if not atomic_repr and n > 0 and (x.find("+") != -1 or x.find("-") != -1): x = "(%s)"%x @@ -387,8 +385,8 @@ for n in xrange(m): x = v[n] - if x: + if x != 0: if not first: s += " + " - x = repr(x) + x = str(x) if not atomic_repr and n > 0 and (x[1:].find("+") != -1 or x[1:].find("-") != -1): x = "(%s)"%x @@ -458,5 +456,5 @@ s += "%s|%s"%(x,var) else: - s += repr(x) + s += str(x) first = False @@ -524,5 +522,5 @@ EXAMPLES: sage: R. = CDF[[]] - sage: f = CDF(pi)^2 + m^3 + CDF(e)*m^4 + O(m^10); f + sage: f = pi^2 + m^3 + e*m^4 + O(m^10); f 9.86960440109 + 1.0*m^3 + 2.71828182846*m^4 + O(m^10) sage: f[-5] @@ -605,7 +603,7 @@ return self._mul_(right, prec) - def __nonzero__(self): - """ - Return True if this power series doesn't equal 0. + def is_zero(self): + """ + Return True if this power series equals 0. EXAMPLES: @@ -622,5 +620,5 @@ True """ - return not self.polynomial().is_zero() + return self.polynomial().is_zero() def is_unit(self): @@ -824,14 +822,10 @@ def __mod__(self, other): - """ - EXAMPLES: - sage: R. = Qp(7)[[]] - sage: f = (48*67 + 46*67^2)*T + (1 + 42*67 + 5*67^3)*T^2 + O(T^3) - sage: f % 67 - T^2 + O(T^3) - """ if isinstance(other,(int,Integer,long)): - return power_series_ring.PowerSeriesRing(IntegerModRing(other), self.variable())(self) - raise NotImplementedError, "Mod on power series ring elements not defined except modulo an integer." + try: + return power_series_ring.PowerSeriesRing(Zmod(other))(self) + except TypeError: + raise ZeroDivisionError + raise NotImplementedError, "Mod on power series ring not defined." def sqrt(self): @@ -845,5 +839,5 @@ EXAMPLES: - sage: K. = PowerSeriesRing(QQ, 5) + sage: K. = PowerSeriesRing(QQ, 't', 5) sage: sqrt(t^2) t @@ -852,13 +846,8 @@ sage: sqrt(4+t) 2 + 1/4*t - 1/64*t^2 + 1/512*t^3 - 5/16384*t^4 + O(t^5) - - If the constant term is not a square, the result maybe be defined over a different - base ring or be symbolic (potentially very very slow!): - sage: a = sqrt(2+t+O(t^2)); a - sqrt(2) + 1/(2*sqrt(2))*t + O(t^2) - sage: parent(a) - Power Series Ring in t over Symbolic Ring + sage: sqrt(2+t) + 1.41421356237309 + 0.353553390593274*t - 0.0441941738241592*t^2 + 0.0110485434560399*t^3 - 0.00345266983001233*t^4 + O(t^5) - sage: K. = PowerSeriesRing(QQ, 50) + sage: K. = PowerSeriesRing(QQ, 't', 50) sage: sqrt(1+2*t+t^2) 1 + t + O(t^50) @@ -885,14 +874,10 @@ a = self.valuation_zero_part() - try: - x = sqrt(a[0]) - x = self.base_ring()(x) - except TypeError: - self = self.change_ring(x.parent()) + x = sqrt(a[0]) newp = self.parent().base_extend(x.parent()) a = newp(a) half = ~newp.base_ring()(2) - for i in range (int(ceil(log(prec, 2)))): + for i in range (ceil(log(prec, 2))): x = half * (x + a/x) @@ -1193,5 +1178,5 @@ return self.__f - def __call__(self, *xs): + def __call__(self, x): """ EXAMPLE: @@ -1201,15 +1186,11 @@ 2 """ - if isinstance(xs[0], tuple): - xs = xs[0] - x = xs[0] try: if x.parent() is self.parent(): if not (self.prec() is infinity): x = x.add_bigoh(self.prec()*x.valuation()) - xs = list(xs); xs[0] = x; xs = tuple(xs) # tuples are immutable except AttributeError: pass - return self.__f(xs) + return self.__f(x) def __setitem__(self, n, value): @@ -1518,5 +1499,5 @@ if self.prec() is infinity: raise RuntimeError, "series precision must be finite for conversion to pari object." - return pari.pari(repr(self)) + return pari.pari(str(self)) Index: sage/rings/quotient_ring.py =================================================================== --- sage/rings/quotient_ring.py (revision 4059) +++ sage/rings/quotient_ring.py (revision 2337) @@ -4,13 +4,4 @@ AUTHOR: -- William Stein - -TESTS: - sage: R. = PolynomialRing(ZZ) - sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) - sage: S = R.quotient_ring(I); - sage: S == loads(dumps(S)) - True - - """ @@ -66,5 +57,5 @@ EXAMPLES: - sage: R. = PolynomialRing(ZZ,'x') + sage: R = PolynomialRing(ZZ,'x') sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) sage: S = R.quotient_ring(I); S @@ -145,5 +136,6 @@ except AttributeError: import morphism - pi = morphism.RingHomomorphism_cover(self.__R.Hom(self)) + pi = morphism.RingHomomorphism_cover(self.__R, self) + #pi = self.__R.homomorphism(self.__R.gens(), self) # needlessly slow (!) lift = self.lift() pi._set_lift(lift) Index: sage/rings/quotient_ring_element.py =================================================================== --- sage/rings/quotient_ring_element.py (revision 4059) +++ sage/rings/quotient_ring_element.py (revision 3134) @@ -80,6 +80,6 @@ return self.__rep - def __nonzero__(self): - return self.__rep not in self.parent().defining_ideal() + def is_zero(self): + return self.__rep in self.parent().defining_ideal() def is_unit(self): Index: sage/rings/rational.pyx =================================================================== --- sage/rings/rational.pyx (revision 4059) +++ sage/rings/rational.pyx (revision 3604) @@ -10,11 +10,4 @@ and improve behavior of sqrt. -- David Harvey (2006-09-15): added nth_root - -TESTS: - sage: a = -2/3 - sage: a == loads(dumps(a)) - True - - """ @@ -191,5 +184,13 @@ return if not base: - set_from_Rational(self, x.simplest_rational()) + v = x._pari_().contfrac().contfracpnqn() + s = '%s/%s'%(hex(v[0,0]), hex(v[1,0])) + n = mpq_set_str(self.value, s, 16) + # this mpq_denref business is to program around a bug in GMP, where + # it doesn't correctly return an error code in mpq_set_str (or canonicalalize) + # for strings with a 0 in the denominator. In fact, it crashes horribly. + if n or mpz_cmp_si(mpq_denref(self.value), 0) == 0: + raise TypeError, "unable to convert %s to a rational"%x + mpq_canonicalize(self.value) else: xstr = x.str(base) @@ -368,5 +369,5 @@ return self.numerator().valuation(p) - self.denominator().valuation(p) - def sqrt_approx(self, bits=None): + def sqrt(self, bits=None): r""" Returns the positive square root of self as a real number to @@ -385,22 +386,22 @@ EXAMPLES: sage: x = 23/2 - sage: x.sqrt_approx() + sage: x.sqrt() 3.39116499156263 sage: x = 32/5 - sage: x.sqrt_approx() + sage: x.sqrt() 2.52982212813470 sage: x = 16/9 - sage: x.sqrt_approx() + sage: x.sqrt() + 4/3 + sage: x.sqrt(53) 1.33333333333333 - sage: x.sqrt_approx(100) - 1.3333333333333333333333333333 sage: x = 9837/2 - sage: x.sqrt_approx() + sage: x.sqrt() 70.1320183653658 sage: x = 645373/45 - sage: x.sqrt_approx() + sage: x.sqrt() 119.756512233040 sage: x = -12/5 - sage: x.sqrt_approx() + sage: x.sqrt() 1.54919333848297*I @@ -409,4 +410,8 @@ """ if bits is None: + try: + return self.square_root() + except ValueError: + pass bits = max(53, 2*(mpz_sizeinbase(self.value, 2)+2)) @@ -418,5 +423,5 @@ return R(self).sqrt() - def sqrt(self): + def square_root(self): r""" Return the positive rational square root of self, or raises a @@ -425,69 +430,23 @@ EXAMPLES: sage: x = 125/5 - sage: x.sqrt() + sage: x.square_root() 5 sage: x = 64/4 - sage: x.sqrt() + sage: x.square_root() 4 sage: x = 1000/10 - sage: x.sqrt() + sage: x.square_root() 10 sage: x = 81/3 - sage: x.sqrt() - 3*sqrt(3) - sage: x = -81/3 - sage: x.sqrt() - 3*sqrt(3)*I + sage: x.square_root() + Traceback (most recent call last): + ... + ValueError: self (=27) is not a perfect square AUTHOR: - -- Naqi Jaffery (2006-03-05): some examples - """ - if self < 0: - from sage.calculus.calculus import sqrt - return sqrt(self) + -- Naqi Jaffery (2006-03-05): examples + """ # TODO -- this could be quicker, by using GMP directly. - return self.numerator().sqrt() / self.denominator().sqrt() - - def period(self): - r""" - Return the period of the repeating part of the decimal - expansion of this rational number. - - ALGORITHM: When a rational number $n/d$ with $(n,d)==1$ is - expanded, the period begins after $s$ terms and has length - $t$, where $s$ and $t$ are the smallest numbers satisfying - $10^s=10^(s+t) (mod d)$. When $d$ is coprime to 10, this - becomes a purely periodic decimal with $10^t=1 (mod d)$. - (Lehmer 1941 and Mathworld). - - EXAMPLES: - sage: (1/7).period() - 6 - sage: RR(1/7) - 0.142857142857143 - sage: (1/8).period() - 1 - sage: RR(1/8) - 0.125000000000000 - sage: RR(1/6) - 0.166666666666667 - sage: (1/6).period() - 1 - sage: x = 333/106 - sage: x.period() - 13 - sage: RealField(200)(x) - 3.1415094339622641509433962264150943396226415094339622641509 - """ - cdef unsigned int alpha, beta - d = self.denominator() - alpha = d.valuation(2) - beta = d.valuation(5) - P = d.parent() - if alpha > 0 or beta > 0: - d = d//(P(2)**alpha * P(5)**beta) - from sage.rings.integer_mod import Mod - a = Mod(P(10),d) - return a.multiplicative_order() + return self.numerator().square_root() / self.denominator().square_root() def nth_root(self, int n): @@ -694,17 +653,8 @@ 32/243 sage: (-1/1)^(1/3) - -1 - - We raise to some interesting powers: - sage: (2/3)^I - 2^I/3^I - sage: (2/3)^sqrt(2) - 2^sqrt(2)/3^sqrt(2) - sage: (2/3)^(x^n + y^n + z^n) - 3^(-z^n - y^n - x^n)*2^(z^n + y^n + x^n) - sage: (-7/11)^(tan(x)+exp(x)) - 11^(-tan(x) - e^x)*-7^(tan(x) + e^x) - sage: (2/3)^(3/4) - 2^(3/4)/3^(3/4) + Traceback (most recent call last): + ... + TypeError: exponent (=1/3) must be an integer. + Coerce your numbers to real or complex numbers first. """ cdef Rational _self, x @@ -712,23 +662,12 @@ return self.__pow__(float(n)) _self = self + if n < 0: + x = _self**(-n) + return x.__invert__() cdef unsigned int _n try: _n = integer.Integer(n) except TypeError: - if isinstance(n, Rational): - # this is the only sensible answer that avoids rounding and - # an infinite recursion. - from sage.calculus.calculus import SR - return SR(self)**SR(n) - try: - s = n.parent()(self) - return s**n - except AttributeError: - raise TypeError, "exponent (=%s) must be an integer.\nCoerce your numbers to real or complex numbers first."%n - - if n < 0: # this doesn't make sense unless n is an integer. - x = _self**(-n) - return x.__invert__() - + raise TypeError, "exponent (=%s) must be an integer.\nCoerce your numbers to real or complex numbers first."%n x = PY_NEW(Rational) cdef mpz_t num, den @@ -755,4 +694,7 @@ mpq_neg(x.value, self.value) return x + + def __nonzero__(self): + return not self.numerator().is_zero() def __abs__(self): @@ -1104,9 +1046,6 @@ return bool(mpz_cmp_si(mpq_numref(self.value), 1) == 0) - def __nonzero__(self): - return bool(mpz_cmp_si(mpq_numref(self.value), 0) != 0) - - def is_square(self): - return self.numerator().is_square() and self.denominator().is_square() + def is_zero(self): + return bool(mpz_cmp_si(mpq_numref(self.value), 0) == 0) cdef _lshift(self, long int exp): Index: sage/rings/rational_field.py =================================================================== --- sage/rings/rational_field.py (revision 4065) +++ sage/rings/rational_field.py (revision 3665) @@ -5,10 +5,4 @@ (arbitrary precision) rational numbers. Each rational number is an instance of the class \class{Rational}. - -TEST: - sage: Q = RationalField() - sage: Q == loads(dumps(Q)) - True - """ @@ -168,5 +162,5 @@ sage: t = L/O; t 0.200000000000000 - sage: QQ(RealField(45)(t)) + sage: QQ(t) 1/5 """ @@ -216,5 +210,5 @@ """ - from sage.rings.arith import integer_floor as floor + from sage.rings.arith import floor n=self(0) @@ -244,11 +238,4 @@ def ngens(self): return 1 - - def is_subring(self, K): - if K.is_field(): - return K.characteristic() == 0 - if K.characteristic() != 0: - return False - raise NotImplementedError def is_field(self): Index: sage/rings/real_double.pxd =================================================================== --- sage/rings/real_double.pxd (revision 3725) +++ sage/rings/real_double.pxd (revision 3299) @@ -5,7 +5,4 @@ from sage.rings.ring cimport Field -cdef extern from "limits.h": - int INT_MAX - double NAN cdef class RealDoubleField_class(Field): Index: sage/rings/real_double.pyx =================================================================== --- sage/rings/real_double.pyx (revision 4059) +++ sage/rings/real_double.pyx (revision 3649) @@ -22,5 +22,4 @@ include '../ext/cdefs.pxi' include '../ext/stdsage.pxi' -include '../ext/random.pxi' include '../ext/interrupt.pxi' include '../gsl/gsl.pxi' @@ -33,4 +32,6 @@ import sage.libs.pari.gen +from random import random + from sage.misc.sage_eval import sage_eval @@ -40,9 +41,4 @@ import sage.rings.integer import sage.rings.rational - -from sage.rings.integer cimport Integer - -def is_RealDoubleField(x): - return bool(PY_TYPE_CHECK(x, RealDoubleField_class)) cdef class RealDoubleField_class(Field): @@ -117,6 +113,4 @@ True """ - if hasattr(x, '_real_double_'): - return x._real_double_(self) return RealDoubleElement(x) @@ -142,6 +136,4 @@ sage: parent(CDF(5) + RDF(3)) Complex Double Field - sage: CDF.gen(0) + 5.0 - 5.0 + 1.0*I """ if isinstance(x, (int, long, sage.rings.integer.Integer, @@ -149,5 +141,6 @@ return self(x) import real_mpfr - return self._coerce_try(x, [real_mpfr.RR]) + return self._coerce_try(x, [sage.functions.constants.ConstantRing, + real_mpfr.RR]) @@ -207,5 +200,5 @@ return x - def random_element(self, double min=-1, double max=1): + def random_element(self, float min=-1, float max=1): """ Return a random element of this real double field in the interval [min, max]. @@ -217,5 +210,5 @@ 106.592535785 """ - return self._new_c((max-min)*(random())/RAND_MAX + min) + return self._new_c((max-min)*random() + min) def name(self): @@ -365,5 +358,5 @@ Real Double Field """ - return self._parent + return RDF def __repr__(self): @@ -379,16 +372,9 @@ return self.str() - def _latex_(self): - s = self.str() - parts = s.split('e') - if len(parts) > 1: - # scientific notation - if parts[1][0] == '+': - parts[1] = parts[1][1:] - s = "%s \\times 10^{%s}" % (parts[0], parts[1]) - return s + def _latex_(self): # todo -- this is terrible if sci not. + return self.str() def __hash__(self): - return hash(float(self)) + return hash(self.str()) def _im_gens_(self, codomain, im_gens): @@ -431,4 +417,7 @@ """ return self + #cdef RealDoubleElement z + #z = RealDoubleElement(self._value) + #return z def integer_part(self): @@ -460,7 +449,5 @@ -0.266666666667 """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = 1.0 / self._value - return x + return RealDoubleElement(1/self._value) cdef ModuleElement _add_c_impl(self, ModuleElement right): @@ -472,7 +459,5 @@ 1.0 """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = self._value + (right)._value - return x + return self._new_c(self._value + (right)._value) cdef ModuleElement _sub_c_impl(self, ModuleElement right): @@ -484,7 +469,5 @@ -4.0 """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = self._value - (right)._value - return x + return self._new_c(self._value - (right)._value) cdef RingElement _mul_c_impl(self, RingElement right): @@ -496,7 +479,5 @@ -3.75 """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = self._value * (right)._value - return x + return self._new_c(self._value * (right)._value) cdef RingElement _div_c_impl(self, RingElement right): @@ -508,7 +489,5 @@ inf """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = self._value / (right)._value - return x + return self._new_c(self._value / (right)._value) cdef ModuleElement _neg_c_impl(self): @@ -520,7 +499,5 @@ 1.5 """ - cdef RealDoubleElement x = PY_NEW(RealDoubleElement) - x._value = -self._value - return x + return self._new_c(-self._value) def __abs__(self): @@ -667,29 +644,9 @@ return long(self._value) - def _complex_mpfr_field_(self, CC): - """ - EXAMPLES: - sage: a = RDF(1/3) - sage: CC(a) - 0.333333333333333 - sage: a._complex_mpfr_field_(CC) - 0.333333333333333 - - If we coerce to a higher-precision field the extra bits appear - random; they are actualy 0's in base 2. - sage: a._complex_mpfr_field_(ComplexField(100)) - 0.33333333333333331482961625625 - sage: a._complex_mpfr_field_(ComplexField(100)).str(2) - '0.01010101010101010101010101010101010101010101010101010100000000000000000000000000000000000000000000000' - """ - return CC(self._value) - - def _complex_double_(self, CDF): - """ - EXAMPLES: - sage: CDF(RDF(1/3)) - 0.333333333333 - """ - return CDF(self._value) + def _complex_number_(self): + return sage.rings.complex_field.ComplexField()(self) + + def _complex_double_(self): + return sage.rings.complex_double.ComplexDoubleField()(self) def _pari_(self): @@ -748,5 +705,5 @@ sage: r.sqrt() 65.9090282131 - sage: r.sqrt()^2 - r # random low order bits + sage: r.sqrt()^2 - r 0.0 @@ -755,7 +712,7 @@ 1.41421356237*I """ - if self._value >= 0: + if self >= 0: return self.square_root() - return self._complex_double_(sage.rings.complex_double.CDF).sqrt() + return self._complex_double_().sqrt() @@ -825,5 +782,5 @@ def __pow(self, RealDoubleElement exponent): - return self._new_c(gsl_sf_exp(gsl_sf_log(self._value) * exponent._value)) + return self._new_c(self._value**exponent._value) def __pow_int(self, int exponent): @@ -846,25 +803,14 @@ sage: a^a 1.29711148178 - - Symbolic examples: - sage: RDF('-2.3')^(x+y^3+sin(x)) - -2.30000000000000^(y^3 + sin(x) + x) - sage: RDF('-2.3')^x - -2.30000000000000^x """ cdef RealDoubleElement x - if PY_TYPE_CHECK(exponent, RealDoubleElement): + if isinstance(self, RealDoubleElement): return self.__pow(RealDoubleElement(exponent)) - elif PY_TYPE_CHECK(exponent, int): - return self.__pow_int(exponent) - elif PY_TYPE_CHECK(exponent, Integer) and exponent < INT_MAX: + if isinstance(exponent, (int,Integer)): return self.__pow_int(int(exponent)) - try: - x = self.parent()(exponent) - except TypeError: - try: - return exponent.parent()(self)**exponent - except AttributeError: - raise TypeError + elif not isinstance(exponent, RealDoubleElement): + x = RealDoubleElement(exponent) + else: + x = exponent return self.__pow(x) @@ -937,5 +883,5 @@ sage: r = RDF('16.0'); r.log10() 1.20411998266 - sage: r.log() / RDF(log(10)) + sage: r.log() / log(10) 1.20411998266 sage: r = RDF('39.9'); r.log10() @@ -954,5 +900,5 @@ sage: r = RDF(16); r.logpi() 2.42204624559 - sage: r.log() / RDF(log(pi)) + sage: r.log() / log(pi) 2.42204624559 sage: r = RDF('39.9'); r.logpi() @@ -1055,7 +1001,4 @@ """ return self._new_c(gsl_sf_sin(self._value)) - - def restrict_angle(self): - return self._new_c(gsl_sf_angle_restrict_symm(self._value)) def tan(self): @@ -1071,7 +1014,7 @@ 0.57735026919 """ - cdef double denom - cos = gsl_sf_cos(self._value) - a = self._new_c(gsl_sf_sin(self._value) / cos) + _sig_on + a = self._new_c(tan(self._value)) + _sig_off return a @@ -1139,5 +1082,5 @@ 1.0344656401 """ - return self._new_c(gsl_ldexp( gsl_sf_exp(self._value) + gsl_sf_exp(-self._value), -1)) # (e^x + x^-x)/2 + return self._new_c(cosh(self._value)) def sinh(self): @@ -1148,7 +1091,8 @@ sage: q = RDF.pi()/12 sage: q.sinh() - 0.264800227602 - """ - return self._new_c(gsl_ldexp( gsl_sf_expm1(self._value) - gsl_sf_expm1(-self._value), -1)) # (e^x - x^-x)/2 + 0.264800227602 + + """ + return self._new_c(sinh(self._value)) def tanh(self): @@ -1161,5 +1105,5 @@ 0.255977789246 """ - return self.sinh() / self.cosh() + return self._new_c(tanh(self._value)) def acosh(self): @@ -1202,40 +1146,4 @@ return self._new_c(gsl_atanh(self._value)) - def sech(self): - r""" - This function returns the hyperbolic secant. - - EXAMPLES: - sage: RDF(pi).sech() - 0.0862667383341 - sage: CDF(pi).sech() - 0.0862667383341 - """ - return 1/self.cosh() - - def csch(self): - r""" - This function returns the hyperbolic cosecant. - - EXAMPLES: - sage: RDF(pi).csch() - 0.08658953753 - sage: CDF(pi).csch() - 0.08658953753 - """ - return 1/self.sinh() - - def coth(self): - r""" - This function returns the hyperbolic cotangent. - - EXAMPLES: - sage: RDF(pi).coth() - 1.0037418732 - sage: CDF(pi).coth() - 1.0037418732 - """ - return self.cosh() / self.sinh() - def agm(self, other): """ @@ -1345,207 +1253,3 @@ def is_RealDoubleElement(x): return PY_TYPE_CHECK(x, RealDoubleElement) - - - - - -################# FAST CREATION CODE ###################### -########### Based on fast integer creation code ######### -######## There is nothing to see here, move along ####### - -cdef extern from *: - - ctypedef struct RichPyObject "PyObject" - - # We need a PyTypeObject with elements so we can - # get and set tp_new, tp_dealloc, tp_flags, and tp_basicsize - ctypedef struct RichPyTypeObject "PyTypeObject": - - # We replace this one - PyObject* (* tp_new) ( RichPyTypeObject*, PyObject*, PyObject*) - - # Not used, may be useful to determine correct memory management function - RichPyObject *(* tp_alloc) ( RichPyTypeObject*, size_t ) - - # We replace this one - void (*tp_dealloc) ( PyObject*) - - # Not used, may be useful to determine correct memory management function - void (* tp_free) ( PyObject* ) - - # We set a flag here to circumvent the memory manager - long tp_flags - - cdef long Py_TPFLAGS_HAVE_GC - - # We need a PyObject where we can get/set the refcnt directly - # and access the type. - ctypedef struct RichPyObject "PyObject": - int ob_refcnt - RichPyTypeObject* ob_type - - # Allocation - RichPyObject* PyObject_MALLOC(int) - - # Useful for debugging, see below - void PyObject_INIT(RichPyObject *, RichPyTypeObject *) - - # Free - void PyObject_FREE(PyObject*) - -# We use a global element to steal all the references -# from. DO NOT INITIALIZE IT AGAIN and DO NOT REFERENCE IT! -cdef RealDoubleElement global_dummy_element -global_dummy_element = RealDoubleElement(0) - -# A global pool for performance when elements are rapidly created and destroyed. -# It operates on the following principles: -# -# - The pool starts out empty. -# - When an new element is needed, one from the pool is returned -# if available, otherwise a new Integer object is created -# - When an element is collected, it will add it to the pool -# if there is room, otherwise it will be deallocated. - -cdef enum: - element_pool_size = 50 # Pyrex has no way of defining constants - -cdef PyObject* element_pool[element_pool_size] -cdef int element_pool_count = 0 - -# used for profiling the pool -cdef int total_alloc = 0 -cdef int use_pool = 0 - -# The signature of tp_new is -# PyObject* tp_new(RichPyTypeObject *t, PyObject *a, PyObject *k). -# However we don't actually use any of it. -# -# t in this case is the RealDoubleElement TypeObject. - -cdef PyObject* fast_tp_new(RichPyTypeObject *t, PyObject *a, PyObject *k): - - global element_pool, element_pool_count, total_alloc, use_pool - - cdef RichPyObject* new - - # for profiling pool usage - # total_alloc += 1 - - # If there is a ready integer in the pool, we will - # decrement the counter and return that. - - if element_pool_count > 0: - - # for profiling pool usage - # use_pool += 1 - - element_pool_count -= 1 - new = element_pool[element_pool_count] - - # Otherwise, we have to create one. - - else: - - # allocate enough room for the Integer, sizeof_Integer is - # sizeof(Integer). The use of PyObject_MALLOC directly - # assumes that Integers are not garbage collected, i.e. - # they do not pocess references to other Python - # objects (Aas indicated by the Py_TPFLAGS_HAVE_GC flag). - # See below for a more detailed description. - - new = PyObject_MALLOC( sizeof(RealDoubleElement) ) - - # Now set every member as set in z, the global dummy Integer - # created before this tp_new started to operate. - - memcpy(new, (global_dummy_element), sizeof(RealDoubleElement) ) - - # This line is only needed if Python is compiled in debugging - # mode './configure --with-pydebug'. If that is the case a Python - # object has a bunch of debugging fields which are initialized - # with this macro. For speed reasons, we don't call it if Python - # is not compiled in debug mode. So uncomment the following line - # if you are debugging Python. - - #PyObject_INIT(new, (global_dummy_element).ob_type) - - # The global_dummy_element may have a reference count larger than - # one, but it is expected that newly created objects have a - # reference count of one. This is potentially unneeded if - # everybody plays nice, because the gobal_dummy_Integer has only - # one reference in that case. - - # Objects from the pool have reference count zero, so this - # needs to be set in this case. - - new.ob_refcnt = 1 - - return new - -cdef void fast_tp_dealloc(PyObject* o): - - # If there is room in the pool for a used integer object, - # then put it in rather than deallocating it. - - global element_pool, element_pool_count - - if element_pool_count < element_pool_size: - - # And add it to the pool. - element_pool[element_pool_count] = o - element_pool_count += 1 - return - - # Free the object. This assumes that Py_TPFLAGS_HAVE_GC is not - # set. If it was set another free function would need to be - # called. - - PyObject_FREE(o) - -hook_fast_tp_functions() - -def hook_fast_tp_functions(): - """ - """ - global global_dummy_element - - cdef long flag - - cdef RichPyObject* o - o = global_dummy_element - - # By default every object created in Pyrex is garbage - # collected. This means it may have references to other objects - # the Garbage collector has to look out for. We remove this flag - # as the only reference an Integer has is to the global Integer - # ring. As this object is unique we don't need to garbage collect - # it as we always have a module level reference to it. If another - # attribute is added to the Integer class this flag removal so as - # the alloc and free functions may not be used anymore. - # This object will still be reference counted. - flag = Py_TPFLAGS_HAVE_GC - o.ob_type.tp_flags = (o.ob_type.tp_flags & (~flag)) - - # Finally replace the functions called when an Integer needs - # to be constructed/destructed. - o.ob_type.tp_new = &fast_tp_new - o.ob_type.tp_dealloc = &fast_tp_dealloc - -def time_alloc_list(n): - cdef int i - l = [] - for i from 0 <= i < n: - l.append(PY_NEW(RealDoubleElement)) - - return l - -def time_alloc(n): - cdef int i - for i from 0 <= i < n: - z = PY_NEW(RealDoubleElement) - -def pool_stats(): - print "Used pool %s / %s times" % (use_pool, total_alloc) - print "Pool contains %s / %s items" % (integer_pool_count, integer_pool_size) Index: sage/rings/real_mpfi.pxd =================================================================== --- sage/rings/real_mpfi.pxd (revision 3716) +++ sage/rings/real_mpfi.pxd (revision 2633) @@ -10,7 +10,4 @@ cimport sage.structure.element from sage.structure.element cimport RingElement - -from rational import Rational -from rational cimport Rational cimport real_mpfr @@ -46,3 +43,3 @@ cdef RealIntervalFieldElement abs(RealIntervalFieldElement self) - cdef Rational _simplest_rational_helper(self) + Index: sage/rings/real_mpfi.pyx =================================================================== --- sage/rings/real_mpfi.pyx (revision 4059) +++ sage/rings/real_mpfi.pyx (revision 3478) @@ -140,4 +140,7 @@ from integer import Integer from integer cimport Integer + +from rational import Rational +from rational cimport Rational from real_double import RealDoubleElement @@ -1492,106 +1495,4 @@ # return sage.libs.pari.all.pari.new_with_bits_prec(str(self), (self._parent).__prec) - def simplest_rational(self, low_open=False, high_open=False): - """ - Returns the simplest rational in this interval. - Given rationals a/b and c/d (both in lowest terms), the former - is simpler if b= low", SAGE converts try1 to a - # floating-point number rounding down, and "try1 <= high" - # rounds up (since "low" and "high" are in downward-rounding - # and upward-rounding fields, respectively). - if try1 >= low and try1 <= high: - ok = True - if low_open and (try1 == low.exact_rational()): - ok = False - if high_open and (try1 == high.exact_rational()): - ok = False - if ok: - return try1 - - # We could try again with higher precision; instead, we - # go directly to using exact arithmetic. - return _simplest_rational_exact(low.exact_rational(), - high.exact_rational(), - low_open, - high_open) - - cdef Rational _simplest_rational_helper(self): - """ - Returns the simplest rational in an interval which is - either equal to or slightly larger than self. We assume - that both endpoints of self are nonnegative. - """ - - low = self.lower() - - cdef RealIntervalFieldElement new_elt - - if low <= 1: - if low == 0: - return Rational(0) - if self.upper() >= 1: - return Rational(1) - new_elt = ~self - return ~(new_elt._simplest_rational_helper()) - - fl = low.floor() - new_elt = self - fl - return fl + new_elt._simplest_rational_helper() ########################################### @@ -1859,5 +1760,5 @@ return bool(mpfi_is_inside_fr( other_rn.value, self.value)) try: - other_intv = self._parent(other) + other_intv = self._parent._coerce_(other) return bool(mpfi_is_inside(other_intv.value, self.value)) except TypeError, msg: @@ -1886,5 +1787,5 @@ else: # Let type errors from _coerce_ propagate... - other_intv = self._parent(other) + other_intv = self._parent._coerce_(other) mpfi_intersect(x.value, self.value, other_intv.value) @@ -1922,5 +1823,5 @@ else: # Let type errors from _coerce_ propagate... - other_intv = self._parent(other) + other_intv = self._parent._coerce_(other) mpfi_union(x.value, self.value, other_intv.value) return x @@ -2105,5 +2006,5 @@ sage: r = RIF(16.0); r.log10() [1.2041199826559245 ... 1.2041199826559248] - sage: r.log() / log(10.0) + sage: r.log() / log(10) [1.2041199826559245 ... 1.2041199826559251] @@ -2520,5 +2421,5 @@ we're much more likely to get the right answer, even if the interval is very imprecise. - sage: r = r.union(sqrt(2.0)) + sage: r = r.union(sqrt(2)) sage: r.algdep(5) x^2 - 2 @@ -2641,75 +2542,6 @@ -def _simplest_rational_test_helper(low, high, low_open=False, high_open=False): - """ - Call _simplest_rational_exact(). Only used to allow doctests - on that function. - """ - return _simplest_rational_exact(low, high, low_open, high_open) - -cdef _simplest_rational_exact(Rational low, Rational high, int low_open, int high_open): - """ - Return the simplest rational between low and high. May return low - or high unless low_open or high_open (respectively) are true (non-zero). - We assume that low and high are both nonnegative, and that high>low. - - This is a helper function for simplest_rational() on RealIntervalField, - and should not be called directly. - - EXAMPLES: - sage: test = sage.rings.real_mpfi._simplest_rational_test_helper - sage: test(1/4, 1/3, 0, 0) - 1/3 - sage: test(1/4, 1/3, 0, 1) - 1/4 - sage: test(1/4, 1/3, 1, 1) - 2/7 - sage: test(QQ(0), QQ(2), 0, 0) - 0 - sage: test(QQ(0), QQ(2), 1, 0) - 1 - sage: test(QQ(0), QQ(1), 1, 0) - 1 - sage: test(QQ(0), QQ(1), 1, 1) - 1/2 - sage: test(1233/1234, QQ(1), 0, 0) - 1 - sage: test(1233/1234, QQ(1), 0, 1) - 1233/1234 - sage: test(10000/32007, 10001/32007, 0, 0) - 289/925 - sage: test(QQ(0), 1/3, 1, 0) - 1/3 - sage: test(QQ(0), 1/3, 1, 1) - 1/4 - sage: test(QQ(0), 2/5, 1, 0) - 1/3 - sage: test(QQ(0), 2/5, 1, 1) - 1/3 - """ - cdef Rational r - - if low < 1: - if low == 0: - if low_open: - if high > 1: - return Rational(1) - inv_high = ~high - if high_open: - return ~Rational(inv_high.floor() + 1) - else: - return ~Rational(inv_high.ceil()) - else: - return Rational(0) - - if high > 1: - return Rational(1) - - r = _simplest_rational_exact(~high, ~low, high_open, low_open) - return ~r - - fl = low.floor() - return fl + _simplest_rational_exact(low - fl, high - fl, low_open, high_open) - +RR = RealIntervalField() + def RealInterval(s, upper=None, int base=10, int pad=0, min_prec=53): Index: sage/rings/real_mpfr.pyx =================================================================== --- sage/rings/real_mpfr.pyx (revision 4059) +++ sage/rings/real_mpfr.pyx (revision 3649) @@ -48,5 +48,4 @@ include '../ext/interrupt.pxi' include "../ext/stdsage.pxi" -include "../ext/random.pxi" cimport sage.rings.ring @@ -217,4 +216,8 @@ """ if hasattr(x, '_mpfr_'): + # This design with the hasattr is very annoying. + # The only thing that uses it right now is symbolic constants + # and symbolic function evaluation. + # Getting rid of this would speed things up. return x._mpfr_(self) cdef RealNumber z @@ -243,7 +246,6 @@ elif self.__prec <= 53 and is_RealDoubleElement(x): return self(x) - raise TypeError - #import sage.functions.constants - #return self._coerce_try(x, [sage.functions.constants.ConstantRing]) + import sage.functions.constants + return self._coerce_try(x, [sage.functions.constants.ConstantRing]) def __cmp__(self, other): @@ -409,25 +411,8 @@ 0.69314718055994530941723212146 """ - cdef RealNumber x = self._new() + cdef RealNumber x + x = self._new() mpfr_const_log2(x.value, self.rnd) return x - - def random_element(self, min=-1, max=1, distribution=None): - """ - Returns a uniformly distributed random number between - min and max (default -1 to 1). - - EXAMPLES: - sage: RealField(100).random_element(-5, 10) - 4.2682457657074627882421620493 - sage: RealField(10).random_element() - .27 - """ - cdef RealNumber x = self._new() - mpfr_urandomb(x.value, state) - if min == 0 and max == 1: - return x - else: - return (max-min)*x + min def factorial(self, int n): @@ -678,12 +663,5 @@ def _latex_(self): - s = self.str() - parts = s.split('e') - if len(parts) > 1: - # scientific notation - if parts[1][0] == '+': - parts[1] = parts[1][1:] - s = "%s \\times 10^{%s}" % (parts[0], parts[1]) - return s + return str(self) def _interface_init_(self): @@ -893,7 +871,10 @@ 100000000000000000 """ - cdef Integer z = Integer() - mpfr_get_z(z.value, self.value, GMP_RNDZ) - return z + s = self.str(base=32, no_sci=True) + i = s.find(".") + if i != -1: + return Integer(s[:i], base=32) + else: + return Integer(s, base=32) ######################## @@ -1390,193 +1371,4 @@ return gen - def exact_rational(self): - """ - Returns the exact rational representation of this floating-point - number. - - EXAMPLES: - sage: RR(0).exact_rational() - 0 - sage: RR(1/3).exact_rational() - 6004799503160661/18014398509481984 - sage: RR(37/16).exact_rational() - 37/16 - sage: RR(3^60).exact_rational() - 42391158275216203520420085760 - sage: RR(3^60).exact_rational() - 3^60 - 6125652559 - sage: RealField(5)(-pi).exact_rational() - -25/8 - """ - cdef Integer mantissa = Integer() - cdef mp_exp_t exponent - - if not mpfr_number_p(self.value): - raise ValueError, 'Calling exact_rational() on infinity or NaN' - - exponent = mpfr_get_z_exp(mantissa.value, self.value) - - return Rational(mantissa) * Integer(2) ** exponent - - def simplest_rational(self): - """ - Returns the simplest rational which is equal to self (in the SAGE - sense). Recall that SAGE defines the equality operator by - coercing both sides to a single type and then comparing; - thus, this finds the simplest rational which (when coerced to - this RealField) is equal to self. - - Given rationals a/b and c/d (both in lowest terms), the former - is simpler if bself._parent).rnd - cdef int prec = (self._parent).__prec - - cdef RealNumber low, high - cdef int odd - - if rnd == GMP_RNDN: - # hp == "high precision" - hp_field = RealField(prec + 1) - hp_val = hp_field(self) - hp_intv_field = RealIntervalField(prec + 1) - low = hp_val.nextbelow() - high = hp_val.nextabove() - hp_intv = hp_intv_field(low, high) - # In GMP_RNDN mode, we round to nearest, preferring even mantissas - # if we are exactly halfway between representable floats. - # Thus, the values low and high will round to self iff the - # mantissa of self is even. (Note that this only matters - # if low or high is an integer; if they are not integers, - # then self is simpler than either low or high.) - # Is there a better (faster) way to check this? - odd = self._parent(low) != self - return hp_intv.simplest_rational(low_open=odd, high_open=odd) - - if rnd == GMP_RNDZ: - if mpfr_sgn(self.value) > 0: - rnd = GMP_RNDD - else: - rnd = GMP_RNDU - - intv_field = RealIntervalField(prec) - - if rnd == GMP_RNDD: - intv = intv_field(self, self.nextabove()) - return intv.simplest_rational(high_open = True) - if rnd == GMP_RNDU: - intv = intv_field(self.nextbelow(), self) - return intv.simplest_rational(low_open = True) - - ########################################### # Comparisons: ==, !=, <, <=, >, >= @@ -1662,12 +1454,11 @@ def sqrt(self): - r""" + """ Return a square root of self. If self is negative a complex number is returned. - If you use \code{self.sqrt_approx()} then a real number will - always be returned (though it will be NaN if self is - negative). + If you use self.square_root() then a real number will always + be returned (though it will be NaN if self is negative). EXAMPLES: @@ -1680,11 +1471,9 @@ sage: r = 4344 sage: r.sqrt() - 2*sqrt(1086) - - sage: r = 4344.0 + 65.9090282131363 sage: r.sqrt()^2 == r True sage: r.sqrt()^2 - r - 0.000000000000000 + 0.000000000000000 sage: r = -2.0 @@ -1693,8 +1482,9 @@ """ if self >= 0: - return self.sqrt_approx() + return self.square_root() return self._complex_number_().sqrt() - - def sqrt_approx(self): + + + def square_root(self): """ Return a square root of self. A real number will always be @@ -1705,5 +1495,5 @@ EXAMPLES: sage: r = -2.0 - sage: r.sqrt_approx() + sage: r.square_root() NaN sage: r.sqrt() @@ -1766,10 +1556,4 @@ 1.0000000*I # 32-bit -1.0842022e-19 + 1.0000000*I # 64-bit - - We raise a real number to a symbolic object: - sage: 1.5^x - 1.50000000000000^x - sage: -2.3^(x+y^3+sin(x)) - -2.30000000000000^(y^3 + sin(x) + x) """ cdef RealNumber x @@ -1777,12 +1561,6 @@ return self.__pow__(float(exponent)) if not PY_TYPE_CHECK(exponent, RealNumber): - try: - x = self - exponent = x._parent(exponent) - except TypeError: - try: - return exponent.parent()(self)**exponent - except AttributeError: - raise TypeError + x = self + exponent = x._parent(exponent) return self.__pow(exponent) @@ -2119,28 +1897,4 @@ return x - def coth(self): - """ - EXAMPLES: - sage: RealField(100)(2).coth() - 1.0373147207275480958778097648 - """ - return 1/self.tanh() - - def csch(self): - """ - EXAMPLES: - sage: RealField(100)(2).csch() - 0.27572056477178320775835148216 - """ - return 1/self.sinh() - - def sech(self): - """ - EXAMPLES: - sage: RealField(100)(2).sech() - 0.26580222883407969212086273982 - """ - return 1/self.cosh() - def acosh(self): """ @@ -2303,5 +2057,5 @@ EXAMPLE: - sage: r = sqrt(2.0); r + sage: r = sqrt(2); r 1.41421356237310 sage: r.algdep(5) @@ -2320,5 +2074,5 @@ EXAMPLE: - sage: r = sqrt(2.0); r + sage: r = sqrt(2); r 1.41421356237310 sage: r.algdep(5) @@ -2420,8 +2174,8 @@ def is_RealField(x): - return bool(PY_TYPE_CHECK(x, RealField)) + return PY_TYPE_CHECK(x, RealField) def is_RealNumber(x): - return bool(PY_TYPE_CHECK(x, RealNumber)) + return PY_TYPE_CHECK(x, RealNumber) def __create__RealField_version0(prec, sci_not, rnd): Index: sage/rings/ring.pxd =================================================================== --- sage/rings/ring.pxd (revision 4057) +++ sage/rings/ring.pxd (revision 3443) @@ -5,5 +5,4 @@ cdef public object _zero_ideal cdef public object _unit_ideal - cdef _an_element_c_impl(self) cdef class CommutativeRing(Ring): Index: sage/rings/ring.pyx =================================================================== --- sage/rings/ring.pyx (revision 4057) +++ sage/rings/ring.pyx (revision 3649) @@ -129,7 +129,4 @@ "in Python, and has the wrong precedence." - cdef _an_element_c_impl(self): # override this in SageX - return self.zero_element() - def base_extend(self, R): """ Index: sage/rings/sparse_poly.pyx =================================================================== --- sage/rings/sparse_poly.pyx (revision 4059) +++ sage/rings/sparse_poly.pyx (revision 1793) @@ -131,5 +131,5 @@ raise NotImplementedError - def __nonzero__(self): + def is_zero(self): raise NotImplementedError Index: sage/schemes/elliptic_curves/ell_generic.py =================================================================== --- sage/schemes/elliptic_curves/ell_generic.py (revision 4058) +++ sage/schemes/elliptic_curves/ell_generic.py (revision 3390) @@ -204,83 +204,5 @@ def _magma_init_(self): - return 'EllipticCurve([%s])'%(','.join([x._magma_init_() for x in self.ainvs()])) - - def _symbolic_(self, SR): - r""" - Many elliptic curves can be converted into a symbolic expression - using the \code{symbolic_expression} command. - - EXAMPLES: - We find a torsion point on 11a. - sage: E = EllipticCurve('11a') - sage: E.torsion_subgroup().gens() - ((5 : 5 : 1),) - - We find the corresponding symbolic equality: - sage: eqn = symbolic_expression(E); eqn - (y^2 + y) == (x^3 - x^2 - 10*x - 20) - sage: print eqn - 2 3 2 - y + y == x - x - 10 x - 20 - - We verify that the given point is on the curve: - sage: eqn(x=5,y=5) - (30) == (30) - sage: bool(eqn(x=5,y=5)) - True - - We create a single expression: - sage: F = eqn.lhs() - eqn.rhs(); print F - 2 3 2 - y + y - x + x + 10 x + 20 - sage: print F.solve(y) - [ - 3 2 - - sqrt(4 x - 4 x - 40 x - 79) - 1 - y == ----------------------------------- - 2, - 3 2 - sqrt(4 x - 4 x - 40 x - 79) - 1 - y == --------------------------------- - 2 - ] - - You can also solve for x in terms of y, but the result is horrendous. - Continuing with the above example, we can explicitly find points - over random fields by substituting in values for x: - - sage: v = F.solve(y)[0].rhs() - sage: print v - 3 2 - - sqrt(4 x - 4 x - 40 x - 79) - 1 - ----------------------------------- - 2 - sage: v(3) - (-sqrt(127)*I - 1)/2 - sage: v(7) - (-sqrt(817) - 1)/2 - sage: v(-7) - (-sqrt(1367)*I - 1)/2 - sage: v(sqrt(2)) - (-sqrt(-32*sqrt(2) - 87) - 1)/2 - - We can even do arithmetic with them, as follows: - sage: E2 = E.change_ring(SR); E2 - Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Symbolic Ring - sage: P = E2(3, v(3)) - sage: P - (3 : (-sqrt(127)*I - 1)/2 : 1) - sage: P + P - (-756/127 : (sqrt(127)*I + 1)/2 + 12507*I/(127*sqrt(127)) - 1 : 1) - - We can even throw in a transcendental: - sage: w = E2(pi,v(pi)); w - (pi : (-sqrt(4*pi^3 - 4*pi^2 - 40*pi - 79) - 1)/2 : 1) - sage: 2*w - ((3*pi^2 - 2*pi - 10)^2/(4*pi^3 - 4*pi^2 - 40*pi - 79) - 2*pi + 1 : (sqrt(4*pi^3 - 4*pi^2 - 40*pi - 79) + 1)/2 - ((3*pi^2 - 2*pi - 10)*((-(3*pi^2 - 2*pi - 10)^2)/(4*pi^3 - 4*pi^2 - 40*pi - 79) + 3*pi - 1)/(sqrt(4*pi^3 - 4*pi^2 - 40*pi - 79))) - 1 : 1) - """ - a = [SR(x) for x in self.a_invariants()] - x, y = SR.var('x, y') - return y**2 + a[0]*x*y + a[2]*y == x**3 + a[1]*x**2 + a[3]*x + a[4] + return 'EllipticCurve([%s])'%(','.join([x._magma_init_() for x in self.ainvs()])) def __cmp__(self, other): @@ -322,5 +244,5 @@ return y**2 + a[0]*x*y + a[2]*y == x**3 + a[1]*x**2 + a[3]*x + a[4] - def __call__(self, *args, **kwds): + def __call__(self, *args): """ EXAMPLES: @@ -374,9 +296,18 @@ sage: P+P (0 : 1 : 0) + + We can create points that aren't really on the curve (but we + must use the point command): + sage: E = EllipticCurve('37a').change_ring(Qp(5)) + sage: P = E.point([1,2,3],check=False) + sage: P + (1 : 2 : 3) + sage: P+P + (4*5^-2 + 3 + 4*5 + 4*5^2 + 4*5^3 + 4*5^4 + 4*5^5 + 4*5^6 + 4*5^7 + 4*5^8 + 4*5^9 + 4*5^10 + 4*5^11 + 4*5^12 + 4*5^13 + 4*5^14 + 4*5^15 + 4*5^16 + O(5^17) : 2*5^-3 + 3*5^-2 + 3 + 4*5 + 4*5^2 + 4*5^3 + 4*5^4 + 4*5^5 + 4*5^6 + 4*5^7 + 4*5^8 + 4*5^9 + 4*5^10 + 4*5^11 + 4*5^12 + 4*5^13 + 4*5^14 + 4*5^15 + O(5^16) : 1) """ if len(args) == 1 and args[0] == 0: R = self.base_ring() return self.point([R(0),R(1),R(0)], check=False) - return plane_curve.ProjectiveCurve_generic.__call__(self, *args, **kwds) + return plane_curve.ProjectiveCurve_generic.__call__(self, *args) def _homset_class(self, *args, **kwds): Index: sage/schemes/elliptic_curves/ell_modular_symbols.py =================================================================== --- sage/schemes/elliptic_curves/ell_modular_symbols.py (revision 3907) +++ sage/schemes/elliptic_curves/ell_modular_symbols.py (revision 3521) @@ -24,5 +24,4 @@ from sage.modular.modsym.all import ModularSymbols from sage.rings.arith import next_prime -from sage.rings.infinity import unsigned_infinity as infinity def modular_symbol_space(E, sign, base_ring, bound=None): @@ -38,7 +37,4 @@ OUTPUT: a space of modular symbols - - EXAMPLES: - """ _sign = int(sign) @@ -62,31 +58,10 @@ class ModularSymbol(SageObject): - r""" - A modular symbol attached to an elliptic curve, which is the map - from $\QQ\to \QQ$ obtained by sending $r$ to the normalized - symmetrized (or anti-symmetrized) integral from r to infinity. - - This is as defined in Mazur-Tate-Teitelbaum. It's possible the - map could be off from what you expect by -1 or +/- 2, but - otherwise it is definitely normalized correctly. - - EXAMPLES: - - """ - def __init__(self, E, sign, normalize=True): + def __init__(self, E, sign, base_ring): """ INPUT: E -- an elliptic curve sign -- an integer, -1 or 1 - normalize -- (default: True); if True, the modular symbol - is correctly normalized (up to possibly a factor of - -1 or 2). If False, the modular symbol is almost certainly - not correctly normalized, i.e., all values will be a - fixed scalar multiple of what they should be. But - the initial computation of the modular symbol is - much faster, though evaluation of it after computing - it won't be any faster. - - EXAMPLES: + base_ring -- a ring """ _sign = int(sign) @@ -96,28 +71,13 @@ raise TypeError, 'sign must -1 or 1' self._E = E - self._modsym = E.modular_symbol_space(sign=_sign) + self._modsym = E.modular_symbol_space(sign=_sign, base_ring=base_ring) self._ambient_modsym = self._modsym.ambient_module() - if normalize: - P = self._modsym.integral_period_mapping() - e = P.matrix().transpose()[0] - e /= 2 - else: - e = self._modsym.dual_eigenvector() - self._e = e + self._e = self._modsym.dual_eigenvector() + # todo -- here must rescale self._e def sign(self): - """ - Return the sign of this elliptic curve modular symbol. - - EXAMPLES: - """ - return self._modsym.sign() def base_ring(self): - """ - Return the base ring for this modular symbol. - EXAMPLES: - """ return self._modsym.base_ring() @@ -125,6 +85,6 @@ return self._E - def __call__(self, r): - w = self._ambient_modsym([infinity,r]).element() + def __call__(self, x): + w = self._ambient_modsym([0,x]).element() return (self._e).dot_product(w) Index: sage/schemes/elliptic_curves/ell_padic_field.py =================================================================== --- sage/schemes/elliptic_curves/ell_padic_field.py (revision 3890) +++ sage/schemes/elliptic_curves/ell_padic_field.py (revision 3664) @@ -160,19 +160,17 @@ def coleman_integrals_on_basis(self, P, Q): """ - Return the coleman integral of dx/y and x dx/y from P to Q. - - EXAMPLES: - sage: K = pAdicField(13, 7) - sage: E = EllipticCurve(K, [-31/3, -2501/108]) # 11a - sage: P = E(K(14/3), K(11/2)) - sage: res = E.coleman_integrals_on_basis(P, 2*P); res - (7*13^6 + O(13^7), 2 + 7*13 + 2*13^2 + 5*13^3 + 10*13^4 + 7*13^5 + 8*13^6 + O(13^7)) - - As the Coleman integral of dx/y is in invariant under - translation, it should evaluate to zero between a torsion - point and its multiples. - - sage: res[0].valuation() >= 6 - True + Return the coleman integral of dx/y and x dx/y from P to Q + + sage: K = pAdicField(13, 7) + sage: E = EllipticCurve(K, [-31/3, -2501/108]) # 11a + sage: P = E(K(14/3), K(11/2)) + sage: res = E.coleman_integrals_on_basis(P, 2*P); res + (7*13^6 + O(13^7), 2 + 7*13 + 2*13^2 + 5*13^3 + 10*13^4 + 7*13^5 + 8*13^6 + O(13^7)) + + As the Coleman integral of dx/y is in invariant under translation, it should + evaluate to zero between a torsion point and its multiples. + + sage: res[0].valuation() >= 6 + True """ K = self.base_field() Index: sage/schemes/elliptic_curves/ell_point.py =================================================================== --- sage/schemes/elliptic_curves/ell_point.py (revision 4059) +++ sage/schemes/elliptic_curves/ell_point.py (revision 3374) @@ -143,5 +143,5 @@ return self.scheme() - def __nonzero__(self): + def is_zero(self): """ Return True if this is the zero point on the curve. @@ -157,5 +157,5 @@ False """ - return bool(self[2]) + return self[2] == 0 def is_finite_order(self): Index: sage/schemes/elliptic_curves/ell_rational_field.py =================================================================== --- sage/schemes/elliptic_curves/ell_rational_field.py (revision 4065) +++ sage/schemes/elliptic_curves/ell_rational_field.py (revision 3686) @@ -546,5 +546,5 @@ return f - def modular_symbol_space(self, sign=1, base_ring=Q, bound=None): + def modular_symbol_space(self, sign=1, base_ring=Q): r""" Return the space of cuspidal modular symbols associated to @@ -556,12 +556,5 @@ EXAMPLES: - sage: f = EllipticCurve('37b') - sage: f.modular_symbol_space() - Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 3 for Gamma_0(37) of weight 2 with sign 1 over Rational Field - sage: f.modular_symbol_space(-1) - Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(37) of weight 2 with sign -1 over Rational Field - sage: f.modular_symbol_space(0, bound=3) - Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 5 for Gamma_0(37) of weight 2 with sign 0 over Rational Field - + NOTE: If you just want the $q$-expansion, use \code{self.q_expansion(prec)}. @@ -574,9 +567,9 @@ except KeyError: pass - M = ell_modular_symbols.modular_symbol_space(self, sign, base_ring, bound=bound) + M = ell_modular_symbols.modular_symbol_space(self, sign, base_ring) self.__modular_symbol_space[typ] = M return M - def modular_symbol(self, sign=1, normalize=True): + def modular_symbol(self, sign=1, base_ring=Q): r""" Return the modular symbol associated to this elliptic curve, @@ -585,25 +578,15 @@ normalized so that all values of this map take values in QQ. - If sign=1, the normalization is such that the p-adic - L-function associated to this modular symbol is correct. - I.e., the normalization is the same as for the integral period - mapping divided by 2. + NOTE: Currently there is no guarantee about how this map is + normalized. This will be added. INPUT: sign -- -1, or 1 base_ring -- a ring - normalize -- (default: True); if True, the modular symbol - is correctly normalized (up to possibly a factor of - -1 or 2). If False, the modular symbol is almost certainly - not correctly normalized, i.e., all values will be a - fixed scalar multiple of what they should be. But - the initial computation of the modular symbol is - much faster, though evaluation of it after computing - it won't be any faster. - - EXAMPLES: - - """ - typ = (sign, normalize) + + NOTE: If you just want the $q$-expansion, use + \code{self.q_expansion(prec)}. + """ + typ = (sign, base_ring) try: return self.__modular_symbol[typ] @@ -612,20 +595,15 @@ except KeyError: pass - M = ell_modular_symbols.ModularSymbol(self, sign, normalize) + M = ell_modular_symbols.ModularSymbol(self, sign, base_ring) self.__modular_symbol[typ] = M return M - def padic_lseries(self, p, normalize=True): - r""" - Return the $p$-adic $L$-series of self at $p$, which is an object - whose approx method computes approximation to the true $p$-adic - $L$-series to any deesired precision. + def padic_lseries(self, p, prec=20): + """ + Return the p-adic Lseries of self at p with given p-adic precision. INPUT: p -- prime - normalize -- (default: True); if True the p-adic L-series - is normalized correctly (up to multiplication by -1 and - 2); otherwise it isn't, but computation of the series is - quicker. + prec -- precision of p-adic computations EXAMPLES: @@ -634,46 +612,7 @@ 5-adic L-series of Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field sage: type(L) - - - We compute the $3$-adic $L$-series of two curves of rank $0$ - and in each case verify the interpolation property for their - leading coefficient (i.e., value at 0): - sage: e = EllipticCurve('11a') - sage: ms = e.modular_symbol() - sage: [ms(1/11), ms(1/3), ms(0), ms(oo)] - [0, -3/10, 1/5, 0] - sage: ms(0) - 1/5 - sage: L = e.padic_lseries(3) - sage: P = L.series(5) - sage: P(0) - 2 + 3 + 3^2 + 2*3^3 + 2*3^5 + 3^6 + O(3^7) - sage: alpha = L.alpha(9); alpha - 2 + 3^2 + 2*3^3 + 2*3^4 + 2*3^6 + 3^8 + O(3^9) - sage: R. = QQ[] - sage: f = x^2 - e.ap(3)*x + 3 - sage: f(alpha) - O(3^9) - sage: r = e.L_ratio(); r - 1/5 - sage: (1 - alpha^(-1))^2 * r - 2 + 3 + 3^2 + 2*3^3 + 2*3^5 + 3^6 + 3^7 + O(3^9) - sage: P(0) - 2 + 3 + 3^2 + 2*3^3 + 2*3^5 + 3^6 + O(3^7) - - Next consider the curve 37b: - sage: e = EllipticCurve('37b') - sage: L = e.padic_lseries(3) - sage: P = L.series(5) - sage: alpha = L.alpha(9); alpha - 1 + 2*3 + 3^2 + 2*3^5 + 2*3^7 + 3^8 + O(3^9) - sage: r = e.L_ratio(); r - 1/3 - sage: (1 - alpha^(-1))^2 * r - 3 + 3^2 + 2*3^4 + 2*3^5 + 2*3^6 + 3^7 + O(3^9) - sage: P(0) - 3 + 3^2 + 2*3^4 + 2*3^5 + 2*3^6 + O(3^7) - """ - key = (p, normalize) + + """ + key = (p,prec) try: return self._padic_lseries[key] @@ -683,14 +622,12 @@ pass if self.ap(p) % p != 0: - Lp = padic_lseries.pAdicLseriesOrdinary(self, p, - normalize = normalize) + Lp = padic_lseries.pAdicLseriesOrdinary(self, p, prec) else: - Lp = padic_lseries.pAdicLseriesSupersingular(self, p, - normalize = normalize) + Lp = padic_lseries.pAdicLseriesSupersingular(self, p, prec) self._padic_lseries[key] = Lp return Lp def newform(self): - r""" + """ Same as \code{self.modular_form()}. """ @@ -698,6 +635,6 @@ def q_eigenform(self, prec): - r""" - Synonym for \code{self.q_expansion(prec)}. + """ + Synonym for self.q_expansion(prec). """ return self.q_expansion(prec) @@ -1506,29 +1443,4 @@ return tuple(self.pari_curve().omega().python()) - def period_lattice_is_rectangular(self): - r""" - Return True precisely if the period lattice of self - is rectangular. - - EXAMPLES: - sage: f = EllipticCurve('11a') - sage: f.period_lattice() - (1.269209304279553421688794616754547305219492241830608667967136921230408338613, 0.6346046521397767108443973083772736526097461209153043339835684606152041693064 + 1.458816616938495229330889612903675257159243428952665161469618762450537896609*I) # 32-bit - (1.26920930427955342168879461675454730521949224183060866796713692123040833861277772269036230592151260731164529627832128743728170032847684397649271401057075, 0.634604652139776710844397308377273652609746120915304333983568460615204169306388861345181152960756303655822648139160643718640850164238421988246357005285375 + 1.45881661693849522933088961290367525715924342895266516146961876245053789660902872639765673368315820172095257526042401249237362183079269125313009041993832*I) # 64-bit - sage: f.period_lattice_is_rectangular() - False - sage: f = EllipticCurve('37b') - sage: f.period_lattice() - (1.088521592904229173504308311539594823105140504301377799086597419750048367573, 1.767610670233789475881323144497815233734289378984139837146363810096739201810*I) # 32-bit - (1.08852159290422917350430831153959482310514050430137779908659741975004836757281196724615591294512604175793056433512324867543024134734839104934760089947025, 1.76761067023378947588132314449781523373428937898413983714636381009673920180953691706599273805495417094215579677634900614786897226142483706622542207437740*I) # 64-bit - sage: f.period_lattice_is_rectangular() - True - - ALGORITHM: - The period lattice is rectangular precisely if the - discriminant of the Weierstrass equation is positive. - """ - return self.discriminant() > 0 - def omega(self): """ @@ -2403,46 +2315,4 @@ raise ValueError, "unknown algorithm '%s'%"%algorithm - def isogeny_graph(self): - r""" - Returns a graph representing the isogeny class of this elliptic curve, - where the vertices are isogenous curves over $\Q$ and the edges are - prime degree isogenies labeled by their degree. - - EXAMPLES: - sage: LL = [] - sage: for e in cremona_optimal_curves(range(1, 38)): - ... G = e.isogeny_graph() - ... already = False - ... for H in LL: - ... if G.is_isomorphic(H): - ... already = True - ... break - ... if not already: - ... LL.append(G) - ... - sage.: graphs_list.show_graphs(LL) - - sage: E = EllipticCurve('195a') - sage: G = E.isogeny_graph() - sage: for v in G: print v, G.obj(v) - ... - 0 Elliptic Curve defined by y^2 + x*y = x^3 - 110*x + 435 over Rational Field - 1 Elliptic Curve defined by y^2 + x*y = x^3 - 115*x + 392 over Rational Field - 2 Elliptic Curve defined by y^2 + x*y = x^3 + 210*x + 2277 over Rational Field - 3 Elliptic Curve defined by y^2 + x*y = x^3 - 520*x - 4225 over Rational Field - 4 Elliptic Curve defined by y^2 + x*y = x^3 + 605*x - 19750 over Rational Field - 5 Elliptic Curve defined by y^2 + x*y = x^3 - 8125*x - 282568 over Rational Field - 6 Elliptic Curve defined by y^2 + x*y = x^3 - 7930*x - 296725 over Rational Field - 7 Elliptic Curve defined by y^2 + x*y = x^3 - 130000*x - 18051943 over Rational Field - sage: G.plot(edge_labels=True).save('isogeny_graph.png') - """ - from sage.graphs.graph import Graph - L, M = self.isogeny_class() - G = Graph(M, format='weighted_adjacency_matrix') - d = {} - for v in G.vertices(): - d[v] = L[v] - G.associate(d) - return G ########################################################## @@ -2454,9 +2324,4 @@ Return True if the mod-p representation attached to E is reducible. - - INPUT: - p -- a prime number - - NOTE: The answer is cached. EXAMPLES: @@ -2475,18 +2340,8 @@ 1 """ - try: - return self.__is_reducible[p] - except AttributeError: - self.__is_reducible = {} - except KeyError: - pass - - if not arith.is_prime(p): - raise ValueError, 'p (=%s) must be prime'%p # we do is_surjective first, since this is # much easier than computing isogeny_class t, why = self.is_surjective(p) if t == True: - self.__is_reducible[p] = False return False # definitely not reducible isogeny_matrix = self.isogeny_class()[ 1 ] @@ -2494,7 +2349,5 @@ for a in v: if a != 0 and a % p == 0: - self.__is_reducible[p] = True return True - self.__is_reducible[p] = False return False @@ -2502,17 +2355,6 @@ """ Return True if the mod p represenation is irreducible. - - EXAMPLES: - sage: e = EllipticCurve('37b') - sage: e.is_irreducible(2) - True - sage: e.is_irreducible(3) - False - sage: e.is_reducible(2) - False - sage: e.is_reducible(3) - True - """ - return not self.is_reducible(p) + """ + return not self.is_reducible() def is_surjective(self, p, A=1000): @@ -2520,7 +2362,5 @@ Return True if the mod-p representation attached to E is surjective, False if it is not, or None if we were - unable to determine whether it is or not. - - NOTE: The answer is cached. + unable to determine whether it is or not. INPUT: @@ -2534,10 +2374,4 @@ EXAMPLES: - sage: e = EllipticCurve('37b') - sage: e.is_surjective(2) - (True, None) - sage: e.is_surjective(3) - (False, '3-torsion') - REMARKS: @@ -2556,18 +2390,5 @@ if not arith.is_prime(p): raise TypeError, "p (=%s) must be prime."%p - A = int(A) - key = (p, A) - try: - return self.__is_surjective[key] - except KeyError: - pass - except AttributeError: - self.__is_surjective = {} - - ans = self._is_surjective(p, A) - self.__is_surjective[key] = ans - return ans - - def _is_surjective(self, p, A): + T = self.torsion_subgroup().order() if T % p == 0: Index: sage/schemes/elliptic_curves/monsky_washnitzer.py =================================================================== --- sage/schemes/elliptic_curves/monsky_washnitzer.py (revision 4065) +++ sage/schemes/elliptic_curves/monsky_washnitzer.py (revision 3665) @@ -46,7 +46,6 @@ from sage.matrix.matrix_space import MatrixSpace -from sage.rings.arith import binomial, integer_ceil as ceil, integer_floor as floor -from math import floor -from sage.misc.functional import log, sqrt +from sage.rings.arith import binomial, floor +from sage.misc.functional import log, ceil, sqrt Index: sage/schemes/elliptic_curves/padic_lseries.py =================================================================== --- sage/schemes/elliptic_curves/padic_lseries.py (revision 3913) +++ sage/schemes/elliptic_curves/padic_lseries.py (revision 3451) @@ -23,122 +23,29 @@ from sage.rings.integer_ring import ZZ -from sage.rings.rational_field import QQ from sage.rings.padics.qp import Qp -from sage.rings.infinity import infinity from sage.rings.integer import Integer -from sage.rings.arith import valuation, binomial from sage.structure.sage_object import SageObject -from sage.misc.all import verbose - class pAdicLseries(SageObject): - """ - The p-adic L-series of an elliptic curve. - - EXAMPLES: - A superingular example: - sage: e = EllipticCurve('37a') - sage: L = e.padic_lseries(3); L - 3-adic L-series of Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field - sage: L.series(2) - WARNING: supersingular prime -- answer is *not* to as high of precision as claimed. - ((3^-1 + O(3^3))*alpha + 2*3^-1 + O(3^3))*T + ((3^-1 + O(3^3))*alpha + 2*3^-1 + O(3^3))*T^2 + O(T^3) - - An ordinary example: - sage: e = EllipticCurve('389a') - sage: L = e.padic_lseries(5) - sage: L.series(0) - Traceback (most recent call last): - ... - ValueError: n (=0) must be a positive integer - sage: L.series(1) - O(T^1) - sage: L.series(2) - (4 + O(5))*T^2 + (2 + O(5))*T^3 + (3 + O(5))*T^4 + O(T^5) - sage: L.series(3) - (4 + 4*5 + O(5^2))*T^2 + (2 + 4*5 + O(5^2))*T^3 + (3 + O(5^2))*T^4 + (1 + O(5))*T^5 + (3*5 + O(5^2))*T^6 + (4 + 5 + O(5^2))*T^7 + (2 + 5 + O(5^2))*T^8 + (5 + O(5^2))*T^11 + (2 + O(5^2))*T^12 + (1 + 3*5 + O(5^2))*T^13 + (4 + 4*5 + O(5^2))*T^14 + (3 + O(5))*T^15 + (3*5 + O(5^2))*T^16 + (3*5 + O(5^2))*T^17 + (1 + 4*5 + O(5^2))*T^19 + (3 + O(5))*T^20 + (4 + 3*5 + O(5^2))*T^21 + (2 + O(5^2))*T^22 + (2 + O(5^2))*T^23 + (2 + O(5^2))*T^24 + O(T^25) - - A prime p such that E[p] is reducible: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.series(1) - 5 + 4*5^2 + O(5^3) + O(T) - sage: L.series(2) - 5 + 4*5^2 + 4*5^3 + O(5^4) + O(T^5) - sage: L.series(3) - 5 + 4*5^2 + 4*5^3 + O(5^5) + (4*5 + O(5^2))*T + (5 + O(5^2))*T^2 + (4*5 + O(5^2))*T^3 + (3*5 + O(5^2))*T^4 + (3*5 + O(5^2))*T^6 + (4*5 + O(5^2))*T^8 + (5 + O(5^2))*T^9 + (5 + O(5^2))*T^11 + (3*5 + O(5^2))*T^13 + (3*5 + O(5^2))*T^14 + (3*5 + O(5^2))*T^16 + (4*5 + O(5^2))*T^18 + (2*5 + O(5^2))*T^21 + (3*5 + O(5^2))*T^22 + (2*5 + O(5^2))*T^23 + (2*5 + O(5^2))*T^24 + O(T^25) - - """ - def __init__(self, E, p, normalize): - """ - INPUT: - E -- an elliptic curve - p -- a prime of good reduction - normalize -- (bool, default: True); whether or not to correctly - normalize the L-series, up to a power of -1 and 2. - If False computations may be faster. - """ + def __init__(self, E, p, prec): self._E = E self._p = ZZ(p) - self._normalize = normalize if not self._p.is_prime(): raise ValueError, "p (=%s) must be a prime"%p #if E.conductor() % self._p == 0: # raise NotImplementedError, "p (=%s) must be a prime of good reduction"%p - self._modular_symbol = E.modular_symbol(sign=1, normalize=normalize) - - def elliptic_curve(self): - """ - Return the elliptic curve to which this p-adic L-series is associated. - - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.elliptic_curve() - Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field - """ - return self._E - - def prime(self): - """ - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.prime() - 5 - """ - return self._p + self._prec = prec + self._modular_symbol = E.modular_symbol() + self._Qp = Qp(p, self._prec, print_mode='series') def _repr_(self): - """ - Return print representation. + return "%s-adic L-series of %s"%(self._p, self._E) - sage: e = EllipticCurve('37a') - sage: e.padic_lseries(3) - 3-adic L-series of Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field - sage: e.padic_lseries(3,normalize=False) - 3-adic L-series of Elliptic Curve defined by y^2 + y = x^3 - x over Rational Field (not normalized) - sage: L = e.padic_lseries(3,normalize=False) - sage: L.rename('(factor)*L_3(T)') - sage: L - (factor)*L_3(T) - """ - s = "%s-adic L-series of %s"%(self._p, self._E) - if not self._normalize: - s += ' (not normalized)' - return s + def modular_symbol(self, x): + return self._modular_symbol(x) - def modular_symbol(self, r): - """ - Return the modular symbol used to compute this p-adic - L-series evaluated at r. - - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: [L.modular_symbol(r) for r in [0,1/5,oo,1/11]] - [1/5, 6/5, 0, 0] - """ - return self._modular_symbol(r) - - def measure(self, a, n, prec): + def measure(self, a, n): r""" Return the measure on $\ZZ_p^*$ defined by @@ -149,17 +56,11 @@ that is used to define this $p$-adic $L$-function. - INPUT: - a -- an integer - n -- a non-negative integer - prec -- an integer - - EXAMPLES: sage: E = EllipticCurve('37a') - sage: L = E.padic_lseries(5) - sage: L.measure(1,2, prec=9) - 1 + 4*5 + 2*5^2 + 4*5^3 + 3*5^4 + 5^5 + 4*5^6 + 4*5^7 + 4*5^8 + O(5^9) + sage: L = E.padic_lseries(5, prec=9) + sage: L.measure(1,2) + 2 + 3*5 + 4*5^3 + 2*5^4 + 3*5^5 + 3*5^6 + 4*5^7 + 4*5^8 + O(5^9) """ p = self._p - alpha = self.alpha(prec) + alpha = self.alpha() z = 1/(alpha**n) w = p**(n-1) @@ -167,185 +68,59 @@ return z * f(a/(p*w)) - (z/alpha) * f(a/w) - def alpha(self, prec): + def alpha(self): r""" - Return a p-adic root $\alpha$ of the polynomial $x^2 - a_p x - + p$ with $\ord_p(\alpha) < 1$. In the ordinary case this is - just the unit root. - - INPUT: - prec -- positive integer, the p-adic precision of the root. + Return the p-adic root $\alpha$ of the polynomial $x^2 - a_p x + + p$ with $\ord_p(\alpha) < 1$. EXAMPLES: - Consider the elliptic curve 37a: sage: E = EllipticCurve('37a') - - An ordinary prime: - sage: L = E.padic_lseries(5) - sage: alpha = L.alpha(10); alpha - 3 + 2*5 + 4*5^2 + 2*5^3 + 5^4 + 4*5^5 + 2*5^7 + 5^8 + 5^9 + O(5^10) - sage: alpha^2 - E.ap(5)*alpha + 5 - O(5^10) - - A supersingular prime. - sage: L = E.padic_lseries(3) - sage: alpha = L.alpha(10); alpha - (1 + O(3^10))*alpha - sage: alpha^2 - E.ap(3)*alpha + 3 - 0 - - A reducible prime: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.alpha(5) - 1 + 4*5 + 3*5^2 + 2*5^3 + 4*5^4 + O(5^5) + sage: L = E.padic_lseries(5, prec=10) + sage: L.alpha() + 3 + 2*5 + 4*5^2 + 2*5^3 + 5^4 + 4*5^5 + 2*5^7 + 5^8 + 5^9 + O(5^10) """ try: - return self._alpha[prec] + return self._alpha except AttributeError: - self._alpha = {} - except KeyError: pass E = self._E p = self._p a_p = E.ap(p) - K = Qp(p, prec, print_mode='series') R = ZZ['x'] f = R([p, -a_p, 1]) if E.is_ordinary(p): - G = f.factor_padic(p, prec+5) + G = f.factor_padic(p, self._prec) for pr, e in G: a = -pr[0] if a.valuation() < 1: - self._alpha[prec] = K(a) - return K(a) + self._alpha = self._Qp(a) + return self._Qp(a) raise ValueError, "bug in p-adic L-function alpha" else: # supersingular case - f = f.change_ring(Qp(p, prec, print_mode='series')) + f = f.change_ring(Qp(p, self._prec, print_mode='series')) a = f.root_field('alpha', check_irreducible=False).gen() - self._alpha[prec] = a + self._alpha = a return a - def order_of_vanishing(self, proof=True): + def approx(self, n): """ - Return the order of vanishing of this p-adic L-series. + Return the n-th approximation to the p-adic L-series as a + power series in T. - The output of this function is provably correct, due to a - theorem of Kato. This function will terminate if and only if - the Mazur-Tate-Teitelbaum analogue of the BSD conjecture about - the rank of the curve is true and the subgroup of elements of - p-power order in the Shafarevich-Tate group of this curve is - finite. I.e., if this function terminates (with no errors!), - then you may conclude that the p-adic BSD rank conjecture is - true and that the p-part of Sha is finite. - - NOTE: currently p must be a prime of good ordinary reduction. + INPUT: + n -- an integer EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(3) - sage: L.order_of_vanishing() - 0 - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.order_of_vanishing() - 0 - sage: L = EllipticCurve('37a').padic_lseries(5) - sage: L.order_of_vanishing() - 1 - sage: L = EllipticCurve('43a').padic_lseries(3) - sage: L.order_of_vanishing() - 1 - sage: L = EllipticCurve('37b').padic_lseries(3) - sage: L.order_of_vanishing() - 0 - - We verify that Sha(E)(p) is finite for p=3,5,7 for the - first curve of rank 2: - sage: e = EllipticCurve('389a') - sage: for p in primes(3,10): - ... print p, e.padic_lseries(p).order_of_vanishing() - 3 2 - 5 2 - 7 2 - """ - try: - return self.__ord - except AttributeError: - pass - - if not self.is_ordinary(): - raise NotImplementedError - E = self.elliptic_curve() - if not E.is_good(self.prime()): - raise ValueError, "prime must be of good reduction" - r = E.rank() - n = 1 - while True: - f = self.series(n) - v = f.valuation() - if v < r: - raise RuntimeError, "while computing p-adic order of vanishing, got a contradiction: the curve is %s, the curve has rank %s, but the p-adic L-series vanishes to order <= %s"%(E, r, v) - if v == r: - self.__ord = v - return v - n += 1 - - - def _c_bounds(self, n): - raise NotImplementedError - - def _prec_bounds(self, n): - raise NotImplementedError - - def teichmuller(self, prec): - r""" - Return Teichmuller lifts to the given precision. - - INPUT: - prec -- a positive integer. - - OUTPUT: - the cached Teichmuller lifts - - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(7) - sage: L.teichmuller(1) - [0, 1, 2, 3, 4, 5, 6] - sage: L.teichmuller(2) - [0, 1, 30, 31, 18, 19, 48] - """ - p = self._p - K = Qp(p, prec, print_mode='series') - return [Integer(0)] + \ - [a.residue(prec).lift() for a in K.teichmuller_system()] - - def _e_bounds(self, n): - p = self._p - T = (ZZ['T']).gen() - w = (1+T)**(p**n) - 1 - return [infinity] + [valuation(w[j],p) for j in range(1,w.degree()+1)] - - -class pAdicLseriesOrdinary(pAdicLseries): - def series(self, n): - """ - Return the n-th approximation to the p-adic L-series as a - power series in T. Each coefficient is a p-adic number whose - precision is provably correct (as long as p is a prime of - ordinary reduction). - - INPUT: - n -- a positive integer - - EXAMPLES: - We compute some $p$-adic $L$-functions associated to the elliptic - curve 11a. - + We compute some $p$-adic $L$-functions associated to the elliptic curve 11a. sage: E = EllipticCurve('11a') sage: p = 3 sage: E.is_ordinary(p) True - sage: L = E.padic_lseries(p) - sage: L.series(3) - 2 + 3 + 3^2 + 2*3^3 + O(3^5) + (1 + 3 + O(3^2))*T + (1 + 2*3 + O(3^2))*T^2 + (2*3 + O(3^2))*T^4 + (2 + O(3^2))*T^5 + (1 + O(3))*T^6 + (2 + O(3^2))*T^7 + (2 + O(3^2))*T^8 + O(T^9) + sage: L = E.padic_lseries(p, prec=10) + #sage: L.approx(4) + #1 + 2*3 + 3^2 + 2*3^3 + 2*3^4 + 2*3^5 + 3^6 + 3^8 + 3^9 + O(3^10) + (2 + 3^3 + 3^5 + 2*3^7 + 3^9 + O(3^10))*T + (2 + 2*3 + 2*3^2 + 3^3 + 2*3^4 + 2*3^5 + 2*3^7 + 3^8 + O(3^10))*T^2 + (2*3 + 3^2 + 3^5 + 2*3^6 + 3^8 + 2*3^9 + O(3^10))*T^3 + (3 + 2*3^2 + 3^5 + 2*3^6 + 2*3^7 + 3^8 + O(3^10))*T^4 + O(T^5) + #sage: L.approx(5) + #1 + 2*3 + 3^2 + 2*3^4 + 3^5 + 2*3^6 + O(3^10) + (2 + 3^5 + 3^6 + 2*3^7 + 3^9 + O(3^10))*T + (2 + 2*3 + 2*3^3 + 2*3^4 + 2*3^6 + 3^7 + 3^9 + O(3^10))*T^2 + (2*3 + 2*3^2 + 2*3^3 + 2*3^5 + 3^6 + 2*3^8 + 2*3^9 + O(3^10))*T^3 + (3 + 2*3^2 + 2*3^5 + 2*3^6 + 3^8 + 2*3^9 + O(3^10))*T^4 + (1 + 3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^6 + 3^7 + 3^8 + O(3^10))*T^5 + O(T^6) Another example at a prime of bad reduction, where the @@ -357,7 +132,8 @@ sage: E.is_ordinary(p) True - sage: L = E.padic_lseries(p) - sage: L.series(2) - (10 + O(11))*T + (6 + O(11))*T^2 + (2 + O(11))*T^3 + (5 + O(11))*T^4 + (4 + O(11))*T^5 + (1 + O(11))*T^6 + (5 + O(11))*T^8 + (6 + O(11))*T^9 + (5 + O(11))*T^10 + O(T^11) + sage: L = E.padic_lseries(p, prec=10) + + #sage: L.approx(2) + #10*11^2 + 7*11^3 + 9*11^5 + 6*11^8 + 10*11^9 + O(11^10) + (6 + 8*11 + 9*11^2 + 11^3 + 11^4 + 5*11^5 + 5*11^6 + 5*11^7 + 4*11^8 + 3*11^9 + O(11^10))*T + (8 + 9*11 + 3*11^2 + 7*11^3 + 9*11^4 + 8*11^6 + 4*11^7 + 6*11^8 + 10*11^9 + O(11^10))*T^2 + O(T^3) We compute a $p$-adic $L$-function that vanishes to order $2$. @@ -366,171 +142,58 @@ sage: E.is_ordinary(p) True - sage: L = E.padic_lseries(p) - sage: L.series(1) - O(T^1) - sage: L.series(2) - (2 + O(3))*T^2 + O(T^3) - sage: L.series(3) - (2 + 2*3 + O(3^2))*T^2 + (2 + O(3))*T^3 + (1 + 3 + O(3^2))*T^4 + (1 + O(3^2))*T^5 + (2 + O(3))*T^6 + (1 + 3 + O(3^2))*T^7 + (1 + 3 + O(3^2))*T^8 + O(T^9) + sage: L = E.padic_lseries(p,prec=10) + + #sage: L.approx(1) + #0 + #sage: L.approx(2) + #(3 + 3^2 + 2*3^3 + 3^4 + 3^5 + 2*3^7 + 2*3^8 + 2*3^9 + O(3^10))*T + (2 + 2*3 + 3^2 + 3^5 + 3^6 + 2*3^7 + 2*3^8 + O(3^10))*T^2 + O(T^3) + #sage: L.approx(3) + #(2*3^2 + 3^5 + 3^6 + 2*3^7 + 2*3^8 + O(3^10))*T + (2 + 2*3 + 2*3^4 + 2*3^5 + 3^6 + 3^7 + 2*3^8 + O(3^10))*T^2 + (2 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 3^5 + O(3^10))*T^3 + O(T^4) + #sage: L.approx(4) + #(2*3^3 + 3^6 + 3^7 + 2*3^8 + 2*3^9 + O(3^10))*T + (2 + 2*3 + 2*3^2 + 3^3 + 3^4 + 2*3^5 + 2*3^6 + 2*3^7 + O(3^10))*T^2 + (2 + 2*3^2 + 3^6 + 3^8 + O(3^10))*T^3 + (1 + 2*3 + 3^3 + 2*3^4 + 2*3^5 + 3^7 + 3^8 + O(3^10))*T^4 + O(T^5) + """ - n = ZZ(n) - if n < 1: - raise ValueError, "n (=%s) must be a positive integer"%n - try: - return self.__series[n] + return self.__approx[n] except AttributeError: - self.__series = {} + self.__approx = {} except KeyError: pass - bounds = self._prec_bounds(n) - prec = max(bounds[1:]) + 5 - p = self._p - - K = QQ - gamma = K(1 + p) - R = K[['T']] - T = R(R.gen(), p**(n-1)) + gamma = 1 + p + R = self._Qp[['T']] + T = R(R.gen(), n+1) L = R(0) one_plus_T_factor = R(1) gamma_power = 1 - teich = self.teichmuller(prec) + teich = self.teichmuller(n) for j in range(p**(n-1)): - s = K(0) + s = 0 for a in range(1,p): b = teich[a] * gamma_power - s += self.measure(b, n, prec).lift() + s += self.measure(b, n) L += s * one_plus_T_factor one_plus_T_factor *= 1+T gamma_power *= gamma - - # Now create series but with each coefficient truncated - # so it is proven correct: - K = Qp(p, prec, print_mode='series') - R = K[['T']] - L = R(L) - aj = L.list() - if len(aj) > 0: - aj = [aj[0].add_bigoh(prec-2)] + [aj[j].add_bigoh(bounds[j]) for j in range(1,len(aj))] - L = R(aj, p**(n-1)) - self.__series[n] = L + self.__approx[n] = L return L - def is_ordinary(self): + def teichmuller(self, n): """ - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.is_ordinary() - True + INPUT: + n -- a positive integer. + + OUTPUT: + the Teichmuller lifts to precision p^n as integers. """ - return True - - def is_supersingular(self): - """ - EXAMPLES: - sage: L = EllipticCurve('11a').padic_lseries(5) - sage: L.is_supersingular() - False - """ - return False - - def _c_bound(self): - try: - return self.__c_bound - except AttributeError: - pass - E = self._E - p = self._p - if E.is_irreducible(p): - ans = 0 - else: - m = E.modular_symbol_space(sign=1) - b = m.boundary_map().codomain() - C = b._known_cusps() # all known, since computed the boundary map - ans = max([valuation(self.modular_symbol(a).denominator(), p) for a in C], [0]) - if ans > 0: - ans = 0 - self.__c_bound = ans - return ans - - def _prec_bounds(self, n): - p = self._p - e = self._e_bounds(n-1) - c = self._c_bound() - return [e[j] - c for j in range(len(e))] + K = self._Qp + return [Integer(0)] + \ + [a.residue(n).lift() for a in K.teichmuller_system()] +class pAdicLseriesOrdinary(pAdicLseries): + pass + class pAdicLseriesSupersingular(pAdicLseries): - def series(self, n): - """ - Return the n-th approximation to the p-adic L-series as a - power series in T. Each coefficient is a p-adic number whose - precision is provably correct (as long as p is a prime of - ordinary reduction). - - INPUT: - n -- a positive integer - - EXAMPLES: - sage: L = EllipticCurve('37a').padic_lseries(3) - sage: L.series(2) - WARNING: supersingular prime -- answer is *not* to as high of precision as claimed. - ((3^-1 + O(3^3))*alpha + 2*3^-1 + O(3^3))*T + ((3^-1 + O(3^3))*alpha + 2*3^-1 + O(3^3))*T^2 + O(T^3) - sage: L.alpha(2).parent() - Univariate Quotient Polynomial Ring in alpha over 3-adic Field with capped relative precision 2 with modulus (1 + O(3^2))*x^2 + (3 + O(3^3))*x + 3 + O(3^3) - """ - n = ZZ(n) - if n < 1: - raise ValueError, "n (=%s) must be a positive integer"%n - - try: - return self.__series[n] - except AttributeError: - self.__series = {} - except KeyError: - pass - - bounds = self._prec_bounds(n) - prec = max(bounds[1:]) + 5 - - p = self._p - - alpha = self.alpha(prec) - K = alpha.parent() - gamma = 1 + p - R = K[['T']] - T = R(R.gen(), p**(n-1)) - L = R(0) - one_plus_T_factor = R(1) - gamma_power = 1 - teich = self.teichmuller(prec) - for j in range(p**(n-1)): - s = K(0) - for a in range(1,p): - b = teich[a] * gamma_power - s += self.measure(b, n, prec) - L += s * one_plus_T_factor - one_plus_T_factor *= 1+T - gamma_power *= gamma - - # To fix this, just need to use p-adic extension rings, which - # David Roe has probably not quite finished yet. - print 'WARNING: supersingular prime -- answer is *not* to as high of precision as claimed.' - self.__series[n] = L - return L - - def is_ordinary(self): - return False - - def is_supersingular(self): - return True - - def _prec_bounds(self, n): - p = self._p - e = self._e_bounds(n-1) - c = ZZ(n+2)/2 - return [infinity] + [(e[j] - c).floor() for j in range(1,len(e))] - - + pass Index: sage/schemes/generic/algebraic_scheme.py =================================================================== --- sage/schemes/generic/algebraic_scheme.py (revision 4058) +++ sage/schemes/generic/algebraic_scheme.py (revision 4068) @@ -141,5 +141,5 @@ def _error_bad_coords(self, v): - raise TypeError, "coordinates %s do not define a point on %s"%(v,self) + raise TypeError, "Coordinates %s do not define a point on %s"%(v,self) def _check_satisfies_equations(self, v): @@ -155,35 +155,16 @@ self._error_bad_coords(v) - def rational_points(self, F=None, B=0): + def rational_points(self, F=None, bound=0): """ Return the set of rational points over its base ring. - - EXAMPLES: - sage: E = EllipticCurve('37a') - sage: Etilde = E.base_extend(GF(3)) - sage: Etilde.rational_points() - [(0 : 0 : 1), - (0 : 0 : 1), - (1 : 0 : 1), - (2 : 0 : 1), - (0 : 0 : 1), - (1 : 0 : 1), - (2 : 0 : 1), - (0 : 2 : 1), - (1 : 2 : 1), - (2 : 2 : 1), - (0 : 1 : 0), - (0 : 1 : 0)] """ if F is None: F = self.base_ring() - if B == 0: + if bound == 0: if is_RationalField(F): - raise TypeError, \ - "A positive bound B (= %s) must be specified."%B + raise TypeError, "A positive bound (= %s) must be specified."%bound if not is_FiniteField(F): - raise TypeError, \ - "Argument F (= %s) must be a finite field."%F + raise TypeError, "Argument F (= %s) must be a finite field."%F pts = [] polys = self.__X.defining_polynomials() @@ -234,5 +215,5 @@ def _error_bad_coords(self, v): - raise TypeError, "coordinates %s do not define a point on %s"%(list(v),self) + raise TypeError, "coordinates %s do not define a point on %s"%(v,self) def _check_satisfies_equations(self, v): @@ -290,6 +271,6 @@ We define what is clearly a union of four hypersurfaces in $\P^4_{\Q}$ then find the irreducible components. - sage: P. = ProjectiveSpace(4,QQ) - sage: V = P.subscheme( (x^2 - y^2 - z^2)*(w^5 - 2*v^2*z^3)* w * (v^3 - x^2*z) ) + sage: PP. = ProjectiveSpace(4,QQ) + sage: V = PP.subscheme( (x^2 - y^2 - z^2)*(w^5 - 2*v^2*z^3)* w * (v^3 - x^2*z) ) sage: V.irreducible_components() [ @@ -431,13 +412,56 @@ self.defining_ideal(), self.defining_ideal() + other.defining_ideal()) - def rational_points(self, F=None, B=0): + def rational_points(self, F=None, bound=0): + """ + EXAMPLES: + + One can enumerate points up to a given bound on a projective scheme + over the rationals. + + sage: E = EllipticCurve('37a') + sage: E.rational_points(bound=8) + [(0 : 0 : 1), + (1 : 0 : 1), + (-1 : 0 : 1), + (0 : -1 : 1), + (1 : -1 : 1), + (-1 : -1 : 1), + (2 : 2 : 1), + (2 : -3 : 1), + (1/4 : -3/8 : 1), + (1/4 : -5/8 : 1), + (0 : 1 : 0)] + + For a small finite field, the complete set of points can be enumerated. + + sage: Etilde = E.base_extend(GF(3)) + sage: Etilde.rational_points() + [(0 : 0 : 1), (1 : 0 : 1), (2 : 0 : 1), (0 : 2 : 1), (1 : 2 : 1), (2 : 2 : 1), (0 : 1 : 0)] + + The class of hyperelliptic curves does not (yet) support desingularization + of the places at infinity into two points. + + sage: FF = FiniteField(7) + sage: P. = PolynomialRing(FiniteField(7)) + sage: C = HyperellipticCurve(x^8+x+1) + sage: C.rational_points() + [(2 : 0 : 1), (4 : 0 : 1), (0 : 1 : 1), (6 : 1 : 1), (0 : 6 : 1), (6 : 6 : 1), (0 : 1 : 0)] + + TODO: + + 1. The above algorithms enumerate all projective points and test whethr they + lie on the scheme; Implement a more naive sieve at least for covers of \P^1. + + 2. Implement Stoll's model in weighted projective space to resolve singularities + and find two points (1 : 1 : 0) and (-1 : 1 : 0) at infinity. + """ if F == None: F = self.base_ring() X = self(F) if is_RationalField(F) or F == ZZ: - if not B > 0: - raise TypeError, "A positive bound B (= %s) must be specified."%B + if not bound > 0: + raise TypeError, "A positive bound (= %s) must be specified."%bound try: - return X.points(B) + return X.points(bound) except TypeError: raise TypeError, "Unable to enumerate points over %s."%F Index: sage/schemes/generic/homset.py =================================================================== --- sage/schemes/generic/homset.py (revision 3482) +++ sage/schemes/generic/homset.py (revision 4068) @@ -4,4 +4,5 @@ import sage.rings.integer_ring +from sage.rings.arith import gcd # Some naive point enumeration routines for default. @@ -9,12 +10,11 @@ def enum_projective_rational_field(X,B): - n = X.codomain().ngens() - R = [ k-B for k in range(2*B+1) ] + n = X.codomain().ambient_space().ngens() Q = [ k+1 for k in range(B) ] + R = [ 0 ] + [ s*k for k in Q for s in [1,-1] ] pts = [] i = int(n-1) while not i < 0: P = [ 0 for _ in range(n) ]; P[i] = 1 - m = Z(0) try: pts.append(X(P)) @@ -22,13 +22,13 @@ pass iters = [ iter(R) for _ in range(i) ] + [ iters[j].next() for j in range(i) ] j = 0 while j < i: try: - aj = Z(iters[j].next()) - m = m.gcd(aj) + aj = ZZ(iters[j].next()) P[j] = aj for ai in Q: P[i] = ai - if m.gcd(ai) == 1: + if gcd(P) == 1: try: pts.append(X(P)) @@ -36,9 +36,8 @@ pass j = 0 - m = Z(0) except StopIteration: iters[j] = iter(R) # reset - iters[j].next() # put at zero P[j] = 0 + P[j] = iters[j].next() # reset P[j] to 0 and increment j += 1 i -= 1 @@ -46,13 +45,13 @@ def enum_affine_rational_field(X,B): - n = X.codomain().ngens() - R = [ k-B for k in range(2*B+1) ] - if X.value_ring() is Z: + n = X.codomain().ambient_space().ngens() + if X.value_ring() is ZZ: Q = [ 1 ] else: # rational field Q = [ k+1 for k in range(B) ] + R = [ 0 ] + [ s*k for k in range(1,B+1) for s in [1,-1] ] pts = [] P = [ 0 for _ in range(n) ] - m = Z(0) + m = ZZ(0) try: pts.append(X(P)) @@ -60,8 +59,9 @@ pass iters = [ iter(R) for _ in range(n) ] + [ iters[j].next() for j in range(n) ] i = 0 while i < n: try: - a = Z(iters[i].next()) + a = ZZ(iters[i].next()) m = m.gcd(a) P[i] = a @@ -73,14 +73,13 @@ pass i = 0 - m = Z(0) + m = ZZ(0) except StopIteration: - iters[i] = iter(R) # reset - iters[i].next() # put at zero - P[i] = 0 + iters[i] = iter(R) # reset + P[i] = iters[i].next() # reset P[i] to 0 and increment i += 1 return pts def enum_projective_finite_field(X): - n = X.codomain().ngens() + n = X.codomain().ambient_space().ngens() R = X.value_ring() pts = [] @@ -92,5 +91,7 @@ except: pass + # define some iterators and increment them: iters = [ iter(R) for _ in range(i) ] + [ iters[j].next() for j in range(i) ] j = 0 while j < i: @@ -102,9 +103,7 @@ pass j = 0 - m = sage.rings.integer_ring.ZZ(0) except StopIteration: - iters[j] = iter(R) # reset - iters[j].next() # put at zero - P[j] = 0 + iters[j] = iter(R) # reset iterator at j + P[j] = iters[j].next() # reset P[j] to 0 and increment j += 1 i -= 1 @@ -112,5 +111,5 @@ def enum_affine_finite_field(X): - n = X.codomain().ngens() + n = X.codomain().ambient_space().ngens() R = X.value_ring() pts = [] Index: sage/schemes/generic/morphism.py =================================================================== --- sage/schemes/generic/morphism.py (revision 4065) +++ sage/schemes/generic/morphism.py (revision 4068) @@ -170,5 +170,5 @@ def _repr_defn(self): - return repr(self.ring_homomorphism()) + return str(self.ring_homomorphism()) @@ -235,6 +235,6 @@ raise TypeError, "polys (=%s) must be a list or tuple"%polys polys = Sequence(polys) - if len(polys) != parent.codomain().ngens(): - raise ValueError, "there must be %s polynomials"%parent.codomain().ngens() + if len(polys) != parent.codomain().ambient_space().ngens(): + raise ValueError, "there must be %s polynomials"%parent.codomain().ambient_space().ngens() polys.set_immutable() self.__polys = polys @@ -361,5 +361,5 @@ all_zero = True for i in range(n): - if v[n-1-i]: + if v[n-1-i] != 0: all_zero = False c = v[n-1-i] @@ -370,5 +370,5 @@ break if all_zero: - raise ValueError, "%s does not define a valid point since all entries are 0"%repr(v) + raise ValueError, "%s does not define a valid point since all entries are 0"%v X.codomain()._check_satisfies_equations(v) @@ -381,5 +381,5 @@ if isinstance(n, (RingElement, int, long)): # [n]*P - multiplication by n. - return AdditiveGroupElement._rmul_(self, Integer(n)) + return AdditiveGroupElement._lmul_(self, Integer(n)) else: # Function composition Index: sage/schemes/generic/projective_space.py =================================================================== --- sage/schemes/generic/projective_space.py (revision 4058) +++ sage/schemes/generic/projective_space.py (revision 2047) @@ -215,5 +215,5 @@ if v is None: v = self.gens() - return '(%s)'%(" : ".join([repr(f) for f in v])) + return '(%s)'%(" : ".join([str(f) for f in v])) def _latex_generic_point(self, v=None): Index: sage/schemes/hyperelliptic_curves/jacobian_morphism.py =================================================================== --- sage/schemes/hyperelliptic_curves/jacobian_morphism.py (revision 4059) +++ sage/schemes/hyperelliptic_curves/jacobian_morphism.py (revision 2047) @@ -178,4 +178,4 @@ return self.__mul__(n) - def __nonzero__(self): - return self.__polys[0] != 1 + def is_zero(self): + return self.__polys[0] == 1 Index: age/server/misc.py =================================================================== --- sage/server/misc.py (revision 3889) +++ (revision ) @@ -1,14 +1,0 @@ -def print_open_msg(address, port): - s = "Open your web browser to http://%s:%s"%(address, port) - t = len(s) - if t%2: - t += 1 - s += ' ' - n = max(t+4, 50) - k = n - t - 1 - j = k/2 - print '*'*n - print '*'+ ' '*(n-2) + '*' - print '*' + ' '*j + s + ' '*j + '*' - print '*'+ ' '*(n-2) + '*' - print '*'*n Index: sage/server/notebook/cell.py =================================================================== --- sage/server/notebook/cell.py (revision 3700) +++ sage/server/notebook/cell.py (revision 3566) @@ -482,5 +482,5 @@ s += """ -