# HG changeset patch # User Alexandru Ghitza # Date 1239430054 -36000 # Node ID d8b83a10963a68d8f9b1d4c054740d5e250f3395 # Parent 470a0a0e9a2c89bdace62f0d5e2051c43f6b0747 trac 5747: improve doctest coverage for schemes/generic/ambient_space.py diff -r 470a0a0e9a2c -r d8b83a10963a sage/schemes/generic/affine_space.py --- a/sage/schemes/generic/affine_space.py Sun Apr 05 23:49:53 2009 -0700 +++ b/sage/schemes/generic/affine_space.py Sat Apr 11 16:07:34 2009 +1000 @@ -265,6 +265,44 @@ v = self.gens() return '\\left(%s\\right)'%(", ".join([str(latex(f)) for f in v])) + def _check_satisfies_equations(self, v): + """ + Return True if `v` defines a point on the scheme self; raise a + TypeError otherwise. + + EXAMPLES:: + + sage: A = AffineSpace(3, ZZ) + sage: A._check_satisfies_equations([1, 1, 0]) + True + sage: A._check_satisfies_equations((0, 1, 0)) + True + sage: A._check_satisfies_equations([0, 0, 0]) + True + sage: A._check_satisfies_equations([1, 2, 3, 4, 5]) + Traceback (most recent call last): + ... + TypeError: The list v=[1, 2, 3, 4, 5] must have 3 components + sage: A._check_satisfies_equations([1/2, 1, 1]) + Traceback (most recent call last): + ... + TypeError: The components of v=[1/2, 1, 1] must be elements of Integer Ring + sage: A._check_satisfies_equations(5) + Traceback (most recent call last): + ... + TypeError: The argument v=5 must be a list or tuple + """ + if not isinstance(v, (list, tuple)): + raise TypeError, 'The argument v=%s must be a list or tuple'%v + n = self.ngens() + if not len(v) == n: + raise TypeError, 'The list v=%s must have %s components'%(v, n) + R = self.base_ring() + from sage.structure.sequence import Sequence + if not Sequence(v).universe() == R: + raise TypeError, 'The components of v=%s must be elements of %s'%(v, R) + return True + def __pow__(self, m): """ EXAMPLES:: diff -r 470a0a0e9a2c -r d8b83a10963a sage/schemes/generic/ambient_space.py --- a/sage/schemes/generic/ambient_space.py Sun Apr 05 23:49:53 2009 -0700 +++ b/sage/schemes/generic/ambient_space.py Sat Apr 11 16:07:34 2009 +1000 @@ -18,6 +18,20 @@ import scheme def is_AmbientSpace(x): + """ + Return True if `x` is an ambient space. + + EXAMPLES:: + + sage: from sage.schemes.generic.ambient_space import is_AmbientSpace + sage: is_AmbientSpace(ProjectiveSpace(3, ZZ)) + True + sage: is_AmbientSpace(AffineSpace(2, QQ)) + True + sage: P. = ProjectiveSpace(2, ZZ) + sage: is_AmbientSpace(P.subscheme([x+y+z])) + False + """ return isinstance(x, AmbientSpace) class AmbientSpace(scheme.Scheme, ParentWithGens): @@ -32,6 +46,12 @@ - ``R`` - ring """ def __init__(self, n, R=ZZ): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + """ if not is_CommutativeRing(R): raise TypeError, "R (=%s) must be a commutative ring"%R n = Integer(n) @@ -44,29 +64,98 @@ # Derived classes must overload all of the following functions ####################################################################### def __cmp__(self, right): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A.__cmp__(ProjectiveSpace(2, QQ)) + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _constructor(self): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._constructor() + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _latex_(self): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._latex_() + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _repr_(self): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._repr_() + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _repr_generic_point(self, coords=None): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._repr_generic_point([1, 2, 3, 4, 5]) + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _latex_generic_point(self, coords=None): + """ + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._latex_generic_point([1, 2, 3, 4, 5]) + Traceback (most recent call last): + ... + NotImplementedError + """ raise NotImplementedError def _check_satisfies_equations(self, v): """ Verify that the coordinates of v define a point on this scheme, or raise a TypeError. + + TEST:: + + sage: from sage.schemes.generic.ambient_space import AmbientSpace + sage: A = AmbientSpace(5, ZZ) + sage: A._check_satisfies_equations([1, 2, 3, 4, 5]) + Traceback (most recent call last): + ... + NotImplementedError """ - return True + raise NotImplementedError ####################################################################### # End overloads @@ -74,6 +163,23 @@ def base_extend(self, S, check=True): + """ + Return the base change of self to the ring `S`, via the natural + map from the base ring of self to `S`. + + A ValueError is raised if there is no natural map between the + two rings. + + EXAMPLES:: + + sage: P. = ProjectiveSpace(2, ZZ) + sage: PQ = P.base_extend(QQ); PQ + Projective Space of dimension 2 over Rational Field + sage: PQ.base_extend(GF(5)) + Traceback (most recent call last): + ... + ValueError: No natural map from the base ring (=Rational Field) to S (=Finite Field of size 5) + """ if is_CommutativeRing(S): R = self.base_ring() if S == R: @@ -86,9 +192,34 @@ raise NotImplementedError def ambient_space(self): + """ + Return the ambient space of the scheme self, in this case self + itself. + + EXAMPLES:: + + sage: P = ProjectiveSpace(4, ZZ) + sage: P.ambient_space() is P + True + + sage: A = AffineSpace(2, GF(3)) + sage: A.ambient_space() + Affine Space of dimension 2 over Finite Field of size 3 + """ return self def defining_polynomials(self): + """ + Return the defining polynomials of the scheme self. Since + self is an ambient space, this is an empty list. + + EXAMPLES:: + + sage: ProjectiveSpace(2, QQ).defining_polynomials() + () + sage: AffineSpace(0, ZZ).defining_polynomials() + () + """ return () ###################################################################### @@ -96,13 +227,48 @@ ###################################################################### def gen(self, n=0): + """ + Return the `n`-th generator of the coordinate ring of the + scheme self. + + EXAMPLES:: + + sage: P. = ProjectiveSpace(2, ZZ) + sage: P.gen(1) + y + """ return self.coordinate_ring().gen(n) def gens(self): + """ + Return the generators of the coordinate ring of the scheme + self. + + EXAMPLES:: + + sage: AffineSpace(0, QQ).gens() + () + + sage: P. = ProjectiveSpace(2, GF(5)) + sage: P.gens() + (x, y, z) + """ return self.coordinate_ring().gens() def ngens(self): - raise NotImplementedError + """ + Return the number of generators of the coordinate ring of the + scheme self. + + EXAMPLES:: + + sage: AffineSpace(0, QQ).ngens() + 0 + + sage: ProjectiveSpace(50, ZZ).ngens() + 51 + """ + return len(self.gens()) ## def assign_names(self, names=None): ## """