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


class