FUNCTION: NcaNormal - normalize an element of the nilCoxeter algebra

CALLING SEQUENCE:

NcaNormal(e)

NcaNormal(e, m)

NCA[NcaNormal](e)

NCA[NcaNormal](e, m)

PARAMETERS:

e = any element of the nilCoxeter algebra

m = any positive integer denoting the degree of a symmetric group

SYNOPSIS:

• The NcaNormal function reduces each permutation inside an expression to the minimum symmetric group containing it (Sn is contained in Sn+1 by addition of the fixed point n+1).

• If a parameter m has been specified, the minimum is choosen to be m.

• Whenever there is a conflict between the function name NcaNormal and another name used in the same session, use the long form NCA['NcaNormal'].

EXAMPLES:

> with(NCA):
> NcaNormal(a*A[3,1,2] - b^2*A[2,1,3,4]);
 
                              2
                           - b  A[2, 1] + a A[3, 1, 2]
 
> NcaNormal(a*A[3,1,2] - b^2*A[2,1,3,4], 3);
 
                             2
                          - b  A[2, 1, 3] + a A[3, 1, 2]