Module: sage.categories.morphism
Morphisms
Author Log:
Module-level Functions
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Class: CallMorphism
Special Functions: _repr_type
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Class: FormalCoercionMorphism
Special Functions: __init__,
_repr_type
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Class: FormalCompositeMorphism
Functions: first,
second
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The first morphism in the formal composition, where the composition is x|-> second(first(x)).
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The second morphism in the formal composition, where the composition is x|-> second(first(x)).
Special Functions: __init__,
_repr_defn,
_repr_type
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Class: IdentityMorphism
Special Functions: __init__,
__invert__,
__mul__,
__pow__,
__rmul__,
__rpow__,
_repr_type
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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
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Apply this morphism to x.
Input:
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
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The multiplication * operator is operator composition.
Input:
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Class: Section
Special Functions: __init__,
_repr_type
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