Package sage :: Package structure :: Module parent :: Class Parent

Class Parent

            object --+    
                     |    
sage_object.SageObject --+
                         |
                        Parent

Known Subclasses:: parent_base.ParentWithBase, Set_generic, combinat.crystals.crystals.Crystal

File: sage/structure/parent.pyx (starting at line 61)

Parents are the SAGE/mathematical analogues of container objects
in computer science.

Instance Methods

[hide private]

Hom(...)
File: sage/structure/parent.pyx (starting at line 588) self.Hom(codomain, cat=None): Return the homspace \code{Hom(self, codomain, cat)} of all homomorphisms from self to codomain in the category cat.

__contains__(x, y)
y in x

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

__new__(T, S, ...)

_an_element(...)
File: sage/structure/parent.pyx (starting at line 495)

_an_element_impl(...)
File: sage/structure/parent.pyx (starting at line 459) Implementation of a function that returns an element (often non-trivial) of a parent object.

_coerce_(...)
File: sage/structure/parent.pyx (starting at line 351)

_coerce_impl(...)
File: sage/structure/parent.pyx (starting at line 373) Canonically coerce x in assuming that the parent of x is not equal to self.

_coerce_self(...)
File: sage/structure/parent.pyx (starting at line 402)

_coerce_try(...)
File: sage/structure/parent.pyx (starting at line 380) Given a list v of rings, try to coerce x canonically into each one in turn.

coerce_map_from(...)
File: sage/structure/parent.pyx (starting at line 133)

coerce_map_from_impl(...)
File: sage/structure/parent.pyx (starting at line 170)

construction(...)
File: sage/structure/parent.pyx (starting at line 340) Returns a pair (functor, parent) such that functor(parent) return self.

get_action(...)
File: sage/structure/parent.pyx (starting at line 202)

get_action_impl(...)
File: sage/structure/parent.pyx (starting at line 223)

has_coerce_map_from(...)
File: sage/structure/parent.pyx (starting at line 421)

has_coerce_map_from_impl(...)
File: sage/structure/parent.pyx (starting at line 445)

init_coerce(...)
File: sage/structure/parent.pyx (starting at line 87)

Inherited from sage_object.SageObject: __hash__, __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_, category, db, dump, dumps, plot, rename, reset_name, save, version

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

Properties

[hide private]

__an_element

_has_coerce_map_from

Inherited from object: __class__

Method Details

[hide private]

Hom(...)

File: sage/structure/parent.pyx (starting at line 588)

self.Hom(codomain, cat=None):

Return the homspace \code{Hom(self, codomain, cat)} 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

init(...)
(Constructor)

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

Overrides: object.__init__

new(T, S, ...)

Returns:

a new object with type S, a subtype of T

Overrides: sage_object.SageObject.__new__

_an_element_impl(...)

File: sage/structure/parent.pyx (starting at line 459)

Implementation of a function that returns an element (often non-trivial)
of a parent object.  Every parent object should implement it,
unless the default implementation works.

NOTE: Parent structures that are implemented in SageX should
implement \code{_an_element_c_impl} instead.

_coerce_try(...)

File: sage/structure/parent.pyx (starting at line 380)

Given a list v of rings, try to coerce x canonically into each
one in turn.  Return the __call__ coercion of the result into
self of the first canonical coercion that succeeds.  Raise a
TypeError if none of them succeed.

INPUT:
     x -- Python object
     v -- parent object or list (iterator) of parent objects

construction(...)

File: sage/structure/parent.pyx (starting at line 340)

Returns a pair (functor, parent) such that functor(parent) return self. 
If this ring does not have a functorial construction, return None.

Class Parent

Hom(...)

__init__(...) (Constructor)

__new__(T, S, ...)

_an_element_impl(...)

_coerce_try(...)

construction(...)

init(...)
(Constructor)

new(T, S, ...)