diff -r 02bd6ab343a2 sage/rings/polynomial/plural.pxd --- a/sage/rings/polynomial/plural.pxd Wed Jul 21 12:21:55 2010 +0200 +++ b/sage/rings/polynomial/plural.pxd Wed Jul 21 17:34:06 2010 +0200 @@ -1,16 +1,21 @@ include "../../libs/singular/singular-cdefs.pxi" from sage.rings.ring cimport Ring -from sage.structure.element cimport RingElement +from sage.structure.element cimport RingElement, Element +from sage.structure.parent cimport Parent from sage.libs.singular.function cimport RingWrap from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular cdef class NCPolynomialRing_plural(Ring): cdef object __ngens + cdef object _c + cdef object _d cdef object __term_order cdef public object _has_singular cdef public object _magma_gens, _magma_cache +# cdef _richcmp_c_impl(left, Parent right, int op) + cdef int _cmp_c_impl(left, Parent right) except -2 cdef ring *_ring # cdef NCPolynomial_plural _one_element diff -r 02bd6ab343a2 sage/rings/polynomial/plural.pyx --- a/sage/rings/polynomial/plural.pyx Wed Jul 21 12:21:55 2010 +0200 +++ b/sage/rings/polynomial/plural.pyx Wed Jul 21 17:34:06 2010 +0200 @@ -33,6 +33,7 @@ cdef class NCPolynomialRing_plural(Ring): def __init__(self, base_ring, n, names, c, d, order='degrevlex', check = True): order = TermOrder(order,n) + self._relations = None n = int(n) if n < 0: raise ValueError, "Multivariate Polynomial Rings must " + \ @@ -42,20 +43,21 @@ PolynomialRing P = PolynomialRing(base_ring, n, names, order) - c = c.change_ring(P) - d = d.change_ring(P) + self._c = c.change_ring(P) + self._d = d.change_ring(P) - #print "c:",c - #print "c.parent()",c.parent() + + #print "c:",self._c + #print "c.parent()",self._c.parent() #print "type(c):",type(c) - #print "d:",d - #print "d.parent()",d.parent() + #print "d:",self._d + #print "d.parent()",self._d.parent() #print "type(d):",type(d) from sage.libs.singular.function import singular_function ncalgebra = singular_function('nc_algebra') - cdef RingWrap rw = ncalgebra(c, d, ring = P) + cdef RingWrap rw = ncalgebra(self._c, self._d, ring = P) self._ring = rw._ring self._ring.ShortOut = 0 @@ -72,7 +74,6 @@ self._one_element = new_NCP(self, p_ISet(1, self._ring)) self._zero_element = new_NCP(self, NULL) - self._relations = self.relations() if check: import sage.libs.singular @@ -183,7 +184,7 @@ sage: P(0) 0 """ - + if element == 0: return self._zero_element if element == 1: @@ -198,7 +199,13 @@ base_ring = self.base_ring() if(_ring != currRing): rChangeCurrRing(_ring) - + + if PY_TYPE_CHECK(element, NCPolynomial_plural): + if element.parent() is self: + return element + elif element.parent() == self: + # is this safe? + _p = p_Copy((element)._poly, _ring) if PY_TYPE_CHECK(element, CommutativeRingElement): # base ring elements @@ -289,147 +296,55 @@ """ return hash(self.__repr__()) -## def _richcmp_(self, right, int op): -## return (self)._richcmp_helper(right, op) - + + def __cmp__(self, right): + r""" + Multivariate polynomial rings are said to be equal if: -## ## cdef int _cmp_c_impl(left, Parent right) except -2: -## ## return 0#cmp(type(left),type(right)) + - their base rings match, + - their generator names match, + - their term orderings match, and + - their relations match. -## def __cmp__(self, x): -## """ -## EXAMPLES:: -## """ -## if PY_TYPE_CHECK(x, NCPolynomialRing_plural): -## print "huhu" -## return 0 -## print "hihi" -## return 0# return cmp(type(self), type(x)) - -## def __richcmp__(self, right, int op): -## print "CMP" -## print "base", self.base_ring() -## print "gens" -## for elt in self.gens(): -## print elt -## print self.term_order() -## for elt in self.relations(): -## print elt -## print PY_TYPE_CHECK(right, NCPolynomialRing_plural), "huhu" + EXAMPLES:: + sage: A. = FreeAlgebra(QQ, 3) + sage: P = A.g_algebra(relations={y*x:-x*y}, order = 'lex') -## print "base", right.base_ring() -## print "gens" -## for elt in right.gens(): -## print elt -## print right.term_order() -## for elt in right.relations(): -## print elt -## return False - -## print cmp(self.base_ring(), right.base_ring()) -## print cmp( map(str, self.gens()), map(str, right.gens())) -## print cmp( map(str, self.relations()), map(str, right.relations())) + sage: P == P + True + sage: Q = A.g_algebra(relations={y*x:-x*y}, order = 'lex') + sage: Q == P + True + + sage: from sage.matrix.constructor import Matrix + sage: c = Matrix(3) + sage: c[0,1] = -1 + sage: c[0,2] = 1 + sage: c[1,2] = 1 + sage: from sage.rings.polynomial.plural import NCPolynomialRing_plural + sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') + sage: R == P + True + + sage: c[0,1] = -2 + sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') + sage: P == R + False + """ -## return False -## if PY_TYPE_CHECK(right, NCPolynomialRing_plural): -## return cmp( (self.base_ring(), map(str, self.gens()), -## self.term_order(), map(str, self.relations())), -## (right.base_ring(), map(str, right.gens()), -## right.term_order(), map(str, right.relations())) -## ) -## else: -## return cmp(type(self),type(right)) + if PY_TYPE_CHECK(right, NCPolynomialRing_plural): -## # return False - - # def __richcmp__(left, right, int op): - # return (left)._richcmp(right, op) - # return False -## r""" -## Multivariate polynomial rings are said to be equal if: - -## - their base rings match, -## - their generator names match, -## - their term orderings match, and -## - their relations match. + return cmp( (self.base_ring(), map(str, self.gens()), + self.term_order(), self._c, self._d), + (right.base_ring(), map(str, right.gens()), + right.term_order(), + (right)._c, + (right)._d) + ) + else: + return cmp(type(self),type(right)) - -## EXAMPLES:: -## sage: A. = FreeAlgebra(QQ, 3) -## sage: P = A.g_algebra(relations={y*x:-x*y}, order = 'lex') - -## sage: P == P -## True -## sage: Q = copy(P) -## sage: Q == P -## True - -## sage: from sage.matrix.constructor import Matrix -## sage: c = Matrix(3) -## sage: c[0,1] = -1 -## sage: c[0,2] = 1 -## sage: c[1,2] = 1 -## sage: from sage.rings.polynomial.plural import NCPolynomialRing_plural -## sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') -## sage: R == P -## True - -## sage: c[0,1] = -2 -## sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') -## sage: P == R -## False -## """ -### return (left)._richcmp(right, op) - ##return (left)._richcmp(right, op) -## cdef int _cmp_c_impl(left, Parent right) except -2: -## r""" -## Multivariate polynomial rings are said to be equal if: - -## - their base rings match, -## - their generator names match, -## - their term orderings match, and -## - their relations match. - - -## EXAMPLES:: -## sage: A. = FreeAlgebra(QQ, 3) -## sage: P = A.g_algebra(relations={y*x:-x*y}, order = 'lex') - -## sage: P == P -## True -## sage: Q = copy(P) -## sage: Q == P -## True - -## sage: from sage.matrix.constructor import Matrix -## sage: c = Matrix(3) -## sage: c[0,1] = -1 -## sage: c[0,2] = 1 -## sage: c[1,2] = 1 -## sage: from sage.rings.polynomial.plural import NCPolynomialRing_plural -## sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') -## sage: R == P -## True - -## sage: c[0,1] = -2 -## sage: R. = NCPolynomialRing_plural(QQ, 3, c = c, d = Matrix(3), order='lex') -## sage: P == R -## False -## """ -## print "huhu", PY_TYPE_CHECK(right, NCPolynomialRing_plural) -## if PY_TYPE_CHECK(right, NCPolynomialRing_plural): -## return True -## return cmp( (left.base_ring(), map(str, left.gens()), -## left.term_order(), map(str, left.relations())), -## (right.base_ring(), map(str, right.gens()), -## right.term_order(), map(str, right.relations())) -## ) -## else: -## return cmp(type(left),type(right)) - - - def __pow__(self, n, _): """ Return the free module of rank `n` over this ring. @@ -466,7 +381,7 @@ """ #TODO: print the relations varstr = ", ".join([ rRingVar(i,self._ring) for i in range(self.__ngens) ]) - return "Noncommutative Multivariate Polynomial Ring in %s over %s, nc-relations: %s"%(varstr,self.base_ring(),self._relations) + return "Noncommutative Multivariate Polynomial Ring in %s over %s, nc-relations: %s"%(varstr,self.base_ring(), self.relations()) def _ringlist(self): @@ -486,13 +401,8 @@ sage: P # indirect doctest Noncommutative Multivariate Polynomial Ring in x, y over Rational Field, nc-relations: ... """ -#TODO: get the relations - L = self._ringlist() - - assert( len(L) == 6 ) - - C = L[4] - D = L[5] + if self._relations is not None: + return self._relations from sage.algebras.free_algebra import FreeAlgebra A = FreeAlgebra( self.base_ring(), self.ngens(), self.gens() ) @@ -501,12 +411,12 @@ n = self.ngens() for r in range(0, n-1, 1): for c in range(r+1, n, 1): - if ((C[r, c] * self.gen(r) * self.gen(c) + D[r, c]) != self.gen(r) * self.gen(c)) or add_commutative: - res[ A.gen(c) * A.gen(r) ] = C[r, c] * self.gen(r) * self.gen(c) + D[r, c] + if (self.gen(c) * self.gen(r) != self.gen(r) * self.gen(c)) or add_commutative: + res[ A.gen(c) * A.gen(r) ] = self.gen(c) * self.gen(r) # C[r, c] * P.gen(r) * P.gen(c) + D[r, c] - return res - - + + self._relations = res + return self._relations def ngens(self): """