Graded algebras with basis

class sage.categories.graded_algebras_with_basis.GradedAlgebrasWithBasis(base_category)

Bases: sage.categories.graded_modules.GradedModulesCategory

The category of graded algebras with a distinguished basis

EXAMPLES:

sage: C = GradedAlgebrasWithBasis(ZZ); C
Category of graded algebras with basis over Integer Ring
sage: sorted(C.super_categories(), key=str)
[Category of filtered algebras with basis over Integer Ring,
 Category of graded algebras over Integer Ring,
 Category of graded modules with basis over Integer Ring]
class ElementMethods
class ParentMethods
graded_algebra()

Return the associated graded algebra to self.

This is self, because self is already graded. See graded_algebra() for the general behavior of this method, and see AssociatedGradedAlgebra for the definition and properties of associated graded algebras.

EXAMPLES:

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