Package sage :: Package categories :: Module morphism :: Class Morphism

Class Morphism

                      object --+        
                               |        
structure.sage_object.SageObject --+    
                                   |    
           structure.element.Element --+
                                       |
                                      Morphism

Known Subclasses:: schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism, groups.matrix_gps.matrix_group_morphism.MatrixGroupMap, groups.perm_gps.permgroup_morphism.PermutationGroupMap, groups.abelian_gps.abelian_group_morphism.AbelianGroupMap, rings.morphism.RingMap, rings.integer_mod.IntegerMod_hom, rings.extended_rational_field.Q_to_ExtendedQ, rings.rational.Z_to_Q, rings.rational.int_to_Q, rings.integer.int_to_Z, rings.integer.long_to_Z, rings.complex_double.FloatToCDF, rings.real_double.ToRDF, rings.number_field.number_field_element_quadratic.Q_to_quadratic_field_element, structure.wrapper_parent.StealMorphism, modules.matrix_morphism.MatrixMorphism_abstract, CallMorphism, FormalCoercionMorphism, FormalCompositeMorphism, IdentityMorphism, Section, action.ActionEndomorphism, modular.hecke.morphism.HeckeModuleMorphism

Instance Methods

[hide private]

__call__(...)
File: sage/categories/morphism.pyx (starting at line 108) Apply this morphism to x.

__init__(...)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature

__invert__(...)
File: sage/categories/morphism.pyx (starting at line 105)

__mul__(...)
File: sage/categories/morphism.pyx (starting at line 160) The multiplication * operator is operator composition.

__new__(T, S, ...)

__pow__(x, y, z=...)
pow(x, y[, z])

__reduce__(...)
File: sage/categories/morphism.pyx (starting at line 68)

__rmul__(x, y)
y*x

__rpow__(y, x, z=...)
pow(x, y[, z])

_call_(...)
File: sage/categories/morphism.pyx (starting at line 145)

_composition_(...)
File: sage/categories/morphism.pyx (starting at line 178)

_repr_(...)
File: sage/categories/morphism.pyx (starting at line 81)

_repr_defn(...)
File: sage/categories/morphism.pyx (starting at line 78)

_repr_type(...)
File: sage/categories/morphism.pyx (starting at line 75)

_test_extra_slots(...)
File: sage/categories/morphism.pyx (starting at line 65)

_test_update_slots(...)
File: sage/categories/morphism.pyx (starting at line 57)

category(...)
File: sage/categories/morphism.pyx (starting at line 99)

codomain(...)
File: sage/categories/morphism.pyx (starting at line 96)

domain(...)
File: sage/categories/morphism.pyx (starting at line 93)

is_endomorphism(...)
File: sage/categories/morphism.pyx (starting at line 102)

pushforward(...)
File: sage/categories/morphism.pyx (starting at line 157)

Inherited from structure.element.Element: __cmp__, __eq__, __ge__, __gt__, __hash__, __le__, __lt__, __ne__, __nonzero__, __rxor__, __xor__, _cmp_, _im_gens_, _richcmp_, base_base_extend, base_base_extend_canonical_sym, base_extend, base_extend_canonical, base_extend_canonical_sym, base_extend_recursive, base_ring, is_zero, n, parent, subs, substitute

Inherited from structure.element.Element (private): _coeff_repr, _is_atomic, _latex_coeff_repr, _make_new_with_parent_c, _set_parent

Inherited from structure.sage_object.SageObject: __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce_ex__, __setattr__, __str__

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

call(...)
(Call operator)

File: sage/categories/morphism.pyx (starting at line 108)

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.)

EXAMPLES:
    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

init(...)
(Constructor)

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: structure.element.Element.__init__

mul(...)

File: sage/categories/morphism.pyx (starting at line 160)

The multiplication * operator is operator composition. 

INPUT:
    self -- Morphism
    right -- Morphism

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

new(T, S, ...)

Returns:

a new object with type S, a subtype of T

Overrides: structure.element.Element.__new__

reduce(...)

File: sage/categories/morphism.pyx (starting at line 68)

Overrides: structure.element.Element.__reduce__

_repr_(...)

File: sage/categories/morphism.pyx (starting at line 81)

Overrides: structure.element.Element._repr_

category(...)

File: sage/categories/morphism.pyx (starting at line 99)

Overrides: structure.element.Element.category

Class Morphism

__call__(...) (Call operator)

__init__(...) (Constructor)

__mul__(...)

__new__(T, S, ...)

__reduce__(...)

_repr_(...)

category(...)

call(...)
(Call operator)

init(...)
(Constructor)

mul(...)

new(T, S, ...)

reduce(...)