Morphisms

AUTHORS:

• William Stein: initial version
• David Joyner (12-17-2005): added examples
• Robert Bradshaw (2007-06-25) Pyrexification

class sage.categories.morphism.CallMorphism

Bases: sage.categories.morphism.Morphism

class sage.categories.morphism.FormalCoercionMorphism

Bases: sage.categories.morphism.Morphism

class sage.categories.morphism.IdentityMorphism

Bases: sage.categories.morphism.Morphism

class sage.categories.morphism.Morphism

Bases: sage.categories.map.Map

category()

is_endomorphism()

pushforward(I)

register_as_coercion()

Register this morphism as a coercion to Sage’s coercion model (see sage.structure.coerce).

EXAMPLES:

By default, adding polynomials over different variables triggers an error:

sage: X.<x> = ZZ[]
sage: Y.<y> = ZZ[]
sage: x^2 + y
...
TypeError: unsupported operand parent(s) for '+': 'Univariate Polynomial Ring in x over Integer Ring' and 'Univariate Polynomial Ring in y over Integer Ring'

Let us declare a coercion from to :

sage: Z.<z> = ZZ[]
sage: phi = Hom(X, Z)(z)
sage: phi(x^2+1)
z^2 + 1
sage: phi.register_as_coercion()

Now we can add elements from and , because the elements of the former are allowed to be implicitly coerced into the later:

sage: x^2 + z
z^2 + z

Caveat: the registration of the coercion must be done before any other coercion is registered or discovered:

sage: phi = Hom(X, Y)(y)
sage: phi.register_as_coercion()
...
AssertionError: coercion from Univariate Polynomial Ring in x over Integer Ring to Univariate Polynomial Ring in y over Integer Ring already registered or discovered

class sage.categories.morphism.SetMorphism

Bases: sage.categories.morphism.Morphism

sage.categories.morphism.is_Morphism(x)

sage.categories.morphism.make_morphism(_class, parent, _dict, _slots)