LieElement -- the class of all Lie algebra elements

i1 : L = lieAlgebra{a,b,c}

o1 = L

o1 : LieAlgebra

i2 : showStructure L

o2 = Thing : BasicList : LieElement : L

o2 : Descent

i3 : x = a a b - 3 c b a

o3 =  - (a b a) - 3 (c b a)

o3 : L

i4 : x#0

o4 = BasicList{-1, -3}

o4 : BasicList

i5 : x#1

o5 = BasicList{BasicList{0, 1, 0}, BasicList{2, 1, 0}}

o5 : BasicList

Functions and methods returning an object of class LieElement :

• ZZ _ LieAlgebra -- get the zero element

Methods that use an object of class LieElement :

• - LieElement -- unary negation
• coefficients(LieElement) -- get the coefficients and monomials of a Lie element
• "firstDegree(LieElement)" -- see firstDegree -- get the degree of an element
• "indexForm(LieElement)" -- see indexForm -- get a Lie element in the polynomial ring representation
• "innerDerivation(LieElement)" -- see innerDerivation -- make the derivation defined by right Lie multiplication by a Lie element
• LieAlgebraMap @ LieElement -- formal application of a Lie map to a Lie element
• LieAlgebraMap LieElement -- apply a Lie homomorphism
• LieDerivation @ LieElement -- formal application of a derivation to a Lie element
• LieDerivation LieElement -- apply a derivation
• LieElement + LieElement -- addition of Lie elements
• LieElement ++ LieElement -- formal addition of Lie elements
• LieElement - LieElement -- subtraction of Lie elements
• LieElement / LieElement -- formal subtraction of Lie elements
• LieElement @ LieElement -- formal multiplication of Lie elements
• LieElement LieElement -- multiplication of Lie elements
• member(LieElement,LieSubSpace) -- whether a Lie element belongs to a Lie subspace
• monomials(LieElement) -- get the monomials of a Lie element
• "normalForm(LieElement)" -- see normalForm -- compute the normal form of a LieElement
• Number @ LieElement -- formal multiplication of a number and a Lie element
• Number LieElement -- multiplication of a number and a Lie element
• RingElement @ LieElement -- formal multiplication of a ring element and a Lie element
• RingElement LieElement -- multiplication of a field element and a Lie element
• "sign(LieElement)" -- see sign -- get the sign of a homogeneous element
• "weight(LieElement)" -- see weight -- get the weight of a homogeneous element

For the programmer

The object LieElement is a type, with ancestor classes BasicList < Thing.