Lambda Bracket Algebras With Basis¶
AUTHORS:
- Reimundo Heluani (2020-08-21): Initial implementation. 
- class sage.categories.lambda_bracket_algebras_with_basis.LambdaBracketAlgebrasWithBasis(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of Lambda bracket algebras with basis. - EXAMPLES: - sage: LieConformalAlgebras(QQbar).WithBasis() # needs sage.rings.number_field Category of Lie conformal algebras with basis over Algebraic Field - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).WithBasis() # needs sage.rings.number_field Category of Lie conformal algebras with basis over Algebraic Field - class ElementMethods[source]¶
- Bases: - object- index()[source]¶
- The index of this basis element. - EXAMPLES: - sage: # needs sage.combinat sage.modules sage: V = lie_conformal_algebras.NeveuSchwarz(QQ) sage: V.inject_variables() Defining L, G, C sage: G.T(3).index() ('G', 3) sage: v = V.an_element(); v L + G + C sage: v.index() Traceback (most recent call last): ... ValueError: index can only be computed for monomials, got L + G + C - >>> from sage.all import * >>> # needs sage.combinat sage.modules >>> V = lie_conformal_algebras.NeveuSchwarz(QQ) >>> V.inject_variables() Defining L, G, C >>> G.T(Integer(3)).index() ('G', 3) >>> v = V.an_element(); v L + G + C >>> v.index() Traceback (most recent call last): ... ValueError: index can only be computed for monomials, got L + G + C 
 
 - class FinitelyGeneratedAsLambdaBracketAlgebra(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of finitely generated lambda bracket algebras with basis. - EXAMPLES: - sage: # needs sage.rings.number_field sage: C = LieConformalAlgebras(QQbar) sage: C1 = C.WithBasis().FinitelyGenerated(); C1 Category of finitely generated Lie conformal algebras with basis over Algebraic Field sage: C2 = C.FinitelyGenerated().WithBasis(); C2 Category of finitely generated Lie conformal algebras with basis over Algebraic Field sage: C1 is C2 True - >>> from sage.all import * >>> # needs sage.rings.number_field >>> C = LieConformalAlgebras(QQbar) >>> C1 = C.WithBasis().FinitelyGenerated(); C1 Category of finitely generated Lie conformal algebras with basis over Algebraic Field >>> C2 = C.FinitelyGenerated().WithBasis(); C2 Category of finitely generated Lie conformal algebras with basis over Algebraic Field >>> C1 is C2 True - class Graded(base_category)[source]¶
- Bases: - GradedModulesCategory- The category of H-graded finitely generated lambda bracket algebras with basis. - EXAMPLES: - sage: C = LieConformalAlgebras(QQbar) # needs sage.rings.number_field sage: C.WithBasis().FinitelyGenerated().Graded() # needs sage.rings.number_field Category of H-graded finitely generated Lie conformal algebras with basis over Algebraic Field - >>> from sage.all import * >>> C = LieConformalAlgebras(QQbar) # needs sage.rings.number_field >>> C.WithBasis().FinitelyGenerated().Graded() # needs sage.rings.number_field Category of H-graded finitely generated Lie conformal algebras with basis over Algebraic Field - class ParentMethods[source]¶
- Bases: - object- degree_on_basis(m)[source]¶
- Return the degree of the basis element indexed by - min- self.- EXAMPLES: - sage: V = lie_conformal_algebras.Virasoro(QQ) # needs sage.combinat sage.modules sage: V.degree_on_basis(('L', 2)) # needs sage.combinat sage.modules 4 - >>> from sage.all import * >>> V = lie_conformal_algebras.Virasoro(QQ) # needs sage.combinat sage.modules >>> V.degree_on_basis(('L', Integer(2))) # needs sage.combinat sage.modules 4