For schemes and
, this module implements the set of morphisms
. This is done by SchemeHomset_generic.
As a special case, the Hom-sets can also represent the points of a
scheme. Recall that the -rational points of a scheme
over
can be identified with the set of morphisms
. In Sage
the rational points are implemented by such scheme morphisms. This is
done by SchemeHomset_points and its subclasses.
Note
You should not create the Hom-sets manually. Instead, use the Hom() method that is inherited by all schemes.
AUTHORS:
Bases: sage.schemes.generic.homset.SchemeHomset_points
Set of rational points of an affine variety.
INPUT:
See SchemeHomset_generic.
EXAMPLES:
sage: from sage.schemes.affine.affine_homset import SchemeHomset_points_affine
sage: SchemeHomset_points_affine(Spec(QQ), AffineSpace(ZZ,2))
Set of rational points of Affine Space of dimension 2 over Rational Field
Return some or all rational points of an affine scheme.
INPUT:
OUTPUT:
EXAMPLES: The bug reported at #11526 is fixed:
sage: A2 = AffineSpace(ZZ,2)
sage: F = GF(3)
sage: A2(F).points()
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
sage: R = ZZ
sage: A.<x,y> = R[]
sage: I = A.ideal(x^2-y^2-1)
sage: V = AffineSpace(R,2)
sage: X = V.subscheme(I)
sage: M = X(R)
sage: M.points(1)
[(-1, 0), (1, 0)]
Bases: sage.schemes.generic.homset.SchemeHomset_generic
Set of rational points of an affine variety.
INPUT:
See SchemeHomset_generic.
EXAMPLES:
sage: from sage.schemes.affine.affine_homset import SchemeHomset_points_spec
sage: SchemeHomset_points_spec(Spec(QQ), Spec(QQ))
Set of rational points of Spectrum of Rational Field