coefficients(LieElement) -- get the coefficients and monomials of a Lie element

Synopsis

Function: coefficients
Usage:

c = coefficients(x)
Inputs:
- x, an instance of the type LieElement, $x$ is of type $L$, where $L$ is of type LieAlgebra
Optional inputs:
- Monomials => ..., default value null,
- Variables => ..., default value null,
Outputs:
- c, a list, the lists of coefficients and monomials in $x$

Description

The optional inputs given above are not relevant for Lie algebras. A Lie element $x$ has a normal form in a Lie algebra $L$, which is a linear combination of basis elements in a certain order; coefficients(x) gives the lists of coefficients and monomials in this representation. If the Lie element has been obtained using the "formal" operators, then coefficients(x) gives the coefficients and monomials for all the iterated Lie products used in the expression.

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

o1 = L

o1 : LieAlgebra

i2 : x = a b c - 3 c b a +(1/3) b a c

o2 =  - (4/3)(b c a) - 2 (c b a)

o2 : L

i3 : coefficients x

         4
o3 = {{- -, -2}, {(b c a), (c b a)}}
         3

o3 : List

i4 : y = a@b@c/3@c@b@a++(1/3)@b@a@c

o4 = (a b c) - 3 (c b a) + (1/3)(b a c)

o4 : L

i5 : coefficients y

              1
o5 = {{1, -3, -}, {(a b c), (c b a), (b a c)}}
              3

o5 : List

Ways to use this method: