Graded Algebras#

class sage.categories.graded_algebras.GradedAlgebras(base_category)[source]#

Bases: GradedModulesCategory

The category of graded algebras

EXAMPLES:

sage: GradedAlgebras(ZZ)
Category of graded algebras over Integer Ring
sage: GradedAlgebras(ZZ).super_categories()
[Category of filtered algebras over Integer Ring,
 Category of graded modules over Integer Ring]

>>> from sage.all import *
>>> GradedAlgebras(ZZ)
Category of graded algebras over Integer Ring
>>> GradedAlgebras(ZZ).super_categories()
[Category of filtered algebras over Integer Ring,
 Category of graded modules over Integer Ring]
class ElementMethods[source]#

Bases: object

class ParentMethods[source]#

Bases: object

graded_algebra()[source]#

Return the associated graded algebra to self.

Since self is already graded, this just returns self.

EXAMPLES:

sage: m = SymmetricFunctions(QQ).m()                                    # needs sage.combinat sage.modules
sage: m.graded_algebra() is m                                           # needs sage.combinat sage.modules
True

>>> from sage.all import *
>>> m = SymmetricFunctions(QQ).m()                                    # needs sage.combinat sage.modules
>>> m.graded_algebra() is m                                           # needs sage.combinat sage.modules
True
class SignedTensorProducts(category, *args)[source]#

Bases: SignedTensorProductsCategory

extra_super_categories()[source]#

EXAMPLES:

sage: Algebras(QQ).Graded().SignedTensorProducts().extra_super_categories()
[Category of graded algebras over Rational Field]
sage: Algebras(QQ).Graded().SignedTensorProducts().super_categories()
[Category of graded algebras over Rational Field]

>>> from sage.all import *
>>> Algebras(QQ).Graded().SignedTensorProducts().extra_super_categories()
[Category of graded algebras over Rational Field]
>>> Algebras(QQ).Graded().SignedTensorProducts().super_categories()
[Category of graded algebras over Rational Field]

Meaning: a signed tensor product of algebras is an algebra

class SubcategoryMethods[source]#

Bases: object

SignedTensorProducts()[source]#

Return the full subcategory of objects of self constructed as signed tensor products.

See also

EXAMPLES:

sage: AlgebrasWithBasis(QQ).Graded().SignedTensorProducts()
Category of signed tensor products of graded algebras with basis
 over Rational Field

>>> from sage.all import *
>>> AlgebrasWithBasis(QQ).Graded().SignedTensorProducts()
Category of signed tensor products of graded algebras with basis
 over Rational Field