20.3 Morphisms

Module: sage.categories.morphism

Morphisms

Author Log:

Module-level Functions

is_Morphism( )

make_morphism( )

Class: CallMorphism

class CallMorphism

Special Functions: _repr_type

_repr_type( )

Class: FormalCoercionMorphism

class FormalCoercionMorphism

Special Functions: __init__,$ \,$ _repr_type

_repr_type( )

Class: FormalCompositeMorphism

class FormalCompositeMorphism

Functions: first,$ \,$ second

first( )

The first morphism in the formal composition, where the composition is x|-> second(first(x)).

second( )

The second morphism in the formal composition, where the composition is x|-> second(first(x)).

Special Functions: __init__,$ \,$ _repr_defn,$ \,$ _repr_type

_repr_defn( )

_repr_type( )

Class: IdentityMorphism

class IdentityMorphism

Special Functions: __init__,$ \,$ __invert__,$ \,$ __mul__,$ \,$ __pow__,$ \,$ __rmul__,$ \,$ __rpow__,$ \,$ _repr_type

__invert__( )

__mul__( )

_repr_type( )

Class: Morphism

class Morphism

Functions: category,$ \,$ codomain,$ \,$ domain,$ \,$ is_endomorphism,$ \,$ pushforward

Special Functions: __call__,$ \,$ __init__,$ \,$ __invert__,$ \,$ __mul__,$ \,$ __pow__,$ \,$ __reduce__,$ \,$ __rmul__,$ \,$ __rpow__,$ \,$ _call_,$ \,$ _composition_,$ \,$ _repr_,$ \,$ _repr_defn,$ \,$ _repr_type,$ \,$ _test_extra_slots,$ \,$ _test_update_slots

__call__( )

Apply this morphism to x.

Input:

x
- an element coercible to self; also objects like ideals are supported in some cases

Output: an element (or ideal, etc.)

sage: R.<x,y> = QQ[]; phi=R.hom([y,x])
sage: phi(y)
x

We take the image of an ideal:

sage: I = ideal(x,y); I
Ideal (x, y) of Multivariate Polynomial Ring in x, y over Rational Field
sage: phi(I)
Ideal (y, x) of Multivariate Polynomial Ring in x, y over Rational Field

__invert__( )

__mul__( )

The multiplication * operator is operator composition.

Input:

self
- Morphism
right
- Morphism

Output: The morphism $ x \mapsto self(right(x))$ .

__reduce__( )

_call_( )

_composition_( )

_repr_( )

_repr_defn( )

_repr_type( )

_test_extra_slots( )

_test_update_slots( )

Class: Section

class Section

Special Functions: __init__,$ \,$ _repr_type

_repr_type( )

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