Graded Algebras

class sage.categories.graded_algebras.GradedAlgebras(base_category)

Bases: sage.categories.graded_modules.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]

class ElementMethods

Bases: object

class ParentMethods

Bases: object

graded_algebra()

Return the associated graded algebra to self.

Since self is already graded, this just returns self.

EXAMPLES:

sage: m = SymmetricFunctions(QQ).m()
sage: m.graded_algebra() is m
True

class SignedTensorProducts(category, *args)

Bases: sage.categories.signed_tensor.SignedTensorProductsCategory

extra_super_categories()

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]

Meaning: a signed tensor product of algebras is an algebra

class SubcategoryMethods

Bases: object

SignedTensorProducts()

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

See also

• SignedTensorProductsCategory

• CovariantFunctorialConstruction

EXAMPLES:

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