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GradedLieAlgebras :: toMonomialLie

toMonomialLie -- expresses an arbitrary Lie product as a general Lie expression

Synopsis

Description

Given input (p,G,S), where p is an arbitrary Lie product of symbols from the set G with signs given by S, the output is a generalExpressionLie, which is equal to p in the free Lie algebra. Given as input only a Lie product p from a Lie algebra L, then the output is a basicExpressionLie which is equal to p in L. Instead of just one product p, one may give as input a linear combination of Lie products of the form {{coefs},{prods}}.

i1 : r1=toMonomialLie([[[a,b],a],c],{a,b,c},{1,1,0})

o1 = {{1, 1, -1, -1}, {[a, b, a, c], [b, a, a, c], [a, a, b, c], [a, b, a,
     ------------------------------------------------------------------------
     c]}}

o1 : List
i2 : L=lieAlgebra({a,b,c},{},genSigns=>{1,1,0})

o2 = L

o2 : LieAlgebra
i3 : r2=toMonomialLie([[[a,b],a],c])

         1
o3 = {{- -}, {[c, b, a, a]}}
         2

o3 : List
i4 : normalFormLie r1

         1
o4 = {{- -}, {[c, b, a, a]}}
         2

o4 : List
i5 : r3=toMonomialLie{{2,1},{[[[a,b],a],c],[c,[b,[a,a]]]}}

o5 = []

o5 : Array

Ways to use toMonomialLie :