Lie Conformal Algebra Element¶
AUTHORS:
- Reimundo Heluani (2019-08-09): Initial implementation. 
- class sage.algebras.lie_conformal_algebras.lie_conformal_algebra_element.LCAStructureCoefficientsElement[source]¶
- Bases: - LCAWithGeneratorsElement- An element of a Lie conformal algebra given by structure coefficients. 
- class sage.algebras.lie_conformal_algebras.lie_conformal_algebra_element.LCAWithGeneratorsElement[source]¶
- Bases: - IndexedFreeModuleElement- The element class of a Lie conformal algebra with a preferred set of generators. - T(n=1)[source]¶
- The \(n\)-th derivative of this element. - INPUT: - n– nonnegative integer (default: \(1\)); how many times to apply \(T\) to this element
 - We use the divided powers notation \(T^{(j)} = \frac{T^j}{j!}\). - EXAMPLES: - sage: Vir = lie_conformal_algebras.Virasoro(QQ) sage: Vir.inject_variables() Defining L, C sage: L.T() TL sage: L.T(3) 6*T^(3)L sage: C.T() 0 sage: R = lie_conformal_algebras.NeveuSchwarz(QQbar); R.inject_variables() Defining L, G, C sage: (L + 2*G.T() + 4*C).T(2) 2*T^(2)L + 12*T^(3)G - >>> from sage.all import * >>> Vir = lie_conformal_algebras.Virasoro(QQ) >>> Vir.inject_variables() Defining L, C >>> L.T() TL >>> L.T(Integer(3)) 6*T^(3)L >>> C.T() 0 >>> R = lie_conformal_algebras.NeveuSchwarz(QQbar); R.inject_variables() Defining L, G, C >>> (L + Integer(2)*G.T() + Integer(4)*C).T(Integer(2)) 2*T^(2)L + 12*T^(3)G 
 - is_monomial()[source]¶
- Whether this element is a monomial. - EXAMPLES: - sage: Vir = lie_conformal_algebras.Virasoro(QQ); L = Vir.0 sage: (L + L.T()).is_monomial() False sage: L.T().is_monomial() True - >>> from sage.all import * >>> Vir = lie_conformal_algebras.Virasoro(QQ); L = Vir.gen(0) >>> (L + L.T()).is_monomial() False >>> L.T().is_monomial() True