Finitely Generated Lambda bracket Algebras¶
AUTHORS:
- Reimundo Heluani (2020-08-21): Initial implementation. 
- class sage.categories.finitely_generated_lambda_bracket_algebras.FinitelyGeneratedLambdaBracketAlgebras(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of finitely generated lambda bracket algebras. - EXAMPLES: - sage: from sage.categories.lambda_bracket_algebras import LambdaBracketAlgebras sage: LambdaBracketAlgebras(QQbar).FinitelyGenerated() # needs sage.rings.number_field Category of finitely generated lambda bracket algebras over Algebraic Field - >>> from sage.all import * >>> from sage.categories.lambda_bracket_algebras import LambdaBracketAlgebras >>> LambdaBracketAlgebras(QQbar).FinitelyGenerated() # needs sage.rings.number_field Category of finitely generated lambda bracket algebras over Algebraic Field - class Graded(base_category)[source]¶
- Bases: - GradedModulesCategory- The category of H-graded finitely generated Lie conformal algebras. - EXAMPLES: - sage: LieConformalAlgebras(QQbar).FinitelyGenerated().Graded() # needs sage.rings.number_field Category of H-graded finitely generated Lie conformal algebras over Algebraic Field - >>> from sage.all import * >>> LieConformalAlgebras(QQbar).FinitelyGenerated().Graded() # needs sage.rings.number_field Category of H-graded finitely generated Lie conformal algebras over Algebraic Field 
 - class ParentMethods[source]¶
- Bases: - object- gen(i)[source]¶
- The - i-th generator of this Lie conformal algebra.- EXAMPLES: - sage: # needs sage.combinat sage.modules sage: V = lie_conformal_algebras.Affine(QQ, 'A1') sage: V.gens() (B[alpha[1]], B[alphacheck[1]], B[-alpha[1]], B['K']) sage: V.gen(0) B[alpha[1]] sage: V.1 B[alphacheck[1]] - >>> from sage.all import * >>> # needs sage.combinat sage.modules >>> V = lie_conformal_algebras.Affine(QQ, 'A1') >>> V.gens() (B[alpha[1]], B[alphacheck[1]], B[-alpha[1]], B['K']) >>> V.gen(Integer(0)) B[alpha[1]] >>> V.gen(1) B[alphacheck[1]] 
 - ngens()[source]¶
- The number of generators of this Lie conformal algebra. - EXAMPLES: - sage: Vir = lie_conformal_algebras.Virasoro(QQ) # needs sage.combinat sage.modules sage: Vir.ngens() # needs sage.combinat sage.modules 2 sage: V = lie_conformal_algebras.Affine(QQ, 'A2') # needs sage.combinat sage.modules sage: V.ngens() # needs sage.combinat sage.modules 9 - >>> from sage.all import * >>> Vir = lie_conformal_algebras.Virasoro(QQ) # needs sage.combinat sage.modules >>> Vir.ngens() # needs sage.combinat sage.modules 2 >>> V = lie_conformal_algebras.Affine(QQ, 'A2') # needs sage.combinat sage.modules >>> V.ngens() # needs sage.combinat sage.modules 9 
 - some_elements()[source]¶
- Some elements of this Lie conformal algebra. - This method returns a list with elements containing at least the generators. - EXAMPLES: - sage: V = lie_conformal_algebras.Affine(QQ, 'A1', # needs sage.combinat sage.modules ....: names=('e', 'h', 'f')) sage: V.some_elements() # needs sage.combinat sage.modules [e, h, f, K, ...] sage: all(v.parent() is V for v in V.some_elements()) # needs sage.combinat sage.modules True - >>> from sage.all import * >>> V = lie_conformal_algebras.Affine(QQ, 'A1', # needs sage.combinat sage.modules ... names=('e', 'h', 'f')) >>> V.some_elements() # needs sage.combinat sage.modules [e, h, f, K, ...] >>> all(v.parent() is V for v in V.some_elements()) # needs sage.combinat sage.modules True