Bases: sage.structure.parent.Parent
Generic module class.
EXAMPLES:
sage: from sage.modules.module import Module
sage: M = Module(ZZ)
sage: M.category()
Category of modules over Integer Ring
sage: M.category().required_methods()
{'parent': {'required': ['__contains__'],
'optional': []},
'element': {'required': [],
'optional': ['_add_']}}
sage: M_QQ = Module(QQ)
sage: M_QQ.category()
Category of vector spaces over Rational Field
Return the endomorphism ring of this module in its category.
EXAMPLES:
sage: from sage.modules.module import Module
sage: M = Module(ZZ); M
<type 'sage.modules.module.Module'>
sage: M.endomorphism_ring()
Set of Morphisms from <type 'sage.modules.module.Module'> to
<type 'sage.modules.module.Module'> in Category of
modules over Integer Ring
Whether the elements have atomic string representations.
OUTPUT:
Boolean. True if the elements have atomic string representations, in the sense that they print if they print s, then -s means the negative of s. For example, integers are atomic but polynomials are not.
EXAMPLES:
sage: from sage.modules.module import Module
sage: M = Module(ZZ)
sage: M.is_atomic_repr()
False
sage: ZZ.is_atomic_repr()
True
Bases: sage.structure.parent_gens.ParentWithAdditiveAbelianGens
Generic module class.
Return the category to which this module belongs.
Return the endomorphism ring of this module in its category.
True if the elements have atomic string representations, in the sense that they print if they print at s, then -s means the negative of s. For example, integers are atomic but polynomials are not.
Return True if x is a module.
INPUT:
OUTPUT:
Boolean.
EXAMPLES:
sage: from sage.modules.module import is_Module
sage: M = FreeModule(RationalField(),30)
sage: is_Module(M)
True
sage: is_Module(10)
False
Return True if x is a vector space.
INPUT:
OUTPUT:
Boolean.
EXAMPLES:
sage: from sage.modules.module import is_Module, is_VectorSpace
sage: M = FreeModule(RationalField(),30)
sage: is_VectorSpace(M)
True
sage: M = FreeModule(IntegerRing(),30)
sage: is_Module(M)
True
sage: is_VectorSpace(M)
False