Abstract base class for modules

class sage.modules.module.Module

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
endomorphism_ring()

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
is_atomic_repr()

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
class sage.modules.module.Module_old

Bases: sage.structure.parent_gens.ParentWithAdditiveAbelianGens

Generic module class.

category()

Return the category to which this module belongs.

endomorphism_ring()

Return the endomorphism ring of this module in its category.

is_atomic_repr()

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.

sage.modules.module.is_Module(x)

Return True if x is a module.

INPUT:

  • x – anything.

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
sage.modules.module.is_VectorSpace(x)

Return True if x is a vector space.

INPUT:

  • x – anything.

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

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