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