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7.7.9.0. 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(1),y(1),x(2),y(2),x(3),y(3),x(4),y(4)),dp;
def R = setLetterplaceAttributes(r,4,2); // supply R with letterplace structure
setring R;
poly a = x(1)*y(2); poly b = y(1);
lieBracket(a,b);
==> -y(1)*x(2)*y(3)+x(1)*y(2)*y(3)
lieBracket(x(1),y(1),2);
==> -y(1)*x(2)*x(3)*x(4)+3*x(1)*y(2)*x(3)*x(4)-3*x(1)*x(2)*y(3)*x(4)+x(1)*x(2\
)*x(3)*y(4)
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