Base class for old-style parent objects with a base ring
Base class for old-style parent objects with a base ring
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class sage.structure.parent_base.ParentWithBase
Bases: sage.structure.parent_old.Parent
This class is being deprecated, see parent.Parent for the new model.
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Hom(codomain, category=None)
self.Hom(codomain, category = None):
Returns the homspace code{Hom(self, codomain, category)} of all
homomorphisms from self to codomain in the category cat. The
default category is code{self.category()}.
- EXAMPLES:
- sage: R.<x,y> = PolynomialRing(QQ, 2)
sage: R.Hom(QQ)
Set of Homomorphisms from Multivariate Polynomial Ring in x, y over Rational Field to Rational Field
- Homspaces are defined for very general sage objects, even elements of familiar rings.
- sage: n = 5; Hom(n,7)
Set of Morphisms from 5 to 7 in Category of elements of Integer Ring
sage: z=(2/3); Hom(z,8/1)
Set of Morphisms from 2/3 to 8 in Category of elements of Rational Field
- This example illustrates the optional third argument:
- sage: QQ.Hom(ZZ, Sets())
Set of Morphisms from Rational Field to Integer Ring in Category of sets
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base_extend(X)
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sage.structure.parent_base.is_ParentWithBase(x)
Return True if x is a parent object with base.