Lie Conformal Algebra Element

AUTHORS:

• Reimundo Heluani (2019-08-09): Initial implementation.

class sage.algebras.lie_conformal_algebras.lie_conformal_algebra_element.LCAStructureCoefficientsElement

Bases: LCAWithGeneratorsElement

An element of a Lie conformal algebra given by structure coefficients.

class sage.algebras.lie_conformal_algebras.lie_conformal_algebra_element.LCAWithGeneratorsElement

Bases: IndexedFreeModuleElement

The element class of a Lie conformal algebra with a preferred set of generators.

T(n=1)

The n-th derivative of this element.

INPUT:

• n – a non-negative 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

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

Python

>>> 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()

Whether this element is a monomial.

EXAMPLES:

Sage

sage: Vir = lie_conformal_algebras.Virasoro(QQ); L = Vir.0
sage: (L + L.T()).is_monomial()
False
sage: L.T().is_monomial()
True

Python

>>> 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