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7.10.4.9 lieBracket

Procedure from library freegb.lib (see freegb_lib).

Usage:
lieBracket(a,b[,N]); a,b letterplace polynomials, N an optional integer

Return:
poly

Assume:
basering has a letterplace ring structure

Purpose:
compute the Lie bracket [a,b] = ab - ba between letterplace polynomials

Note:
if N>1 is specified, then the left normed bracket [a,[...[a,b]]]] is computed.

Example:
 
LIB "freegb.lib";
ring r = 0,(x,y),dp;
def R = freeAlgebra(r, 4); // R with letterplace structure
setring R;
poly a = x*y; poly b = y;
lieBracket(a,b);
==> -y*x*y+x*y*y
lieBracket(x,y,2);
==> y*x*x-2*x*y*x+x*x*y