FUNCTION: Table2Nca - convert a table into an element of the nilCoxeter algebra

CALLING SEQUENCE:

Table2Nca(t)

NCA[Table2Nca](t)

PARAMETERS:

t = any table denoting an element of the nilCoxeter algebra

SYNOPSIS:

• The Table2Nca function converts a table into an element of the nilCoxeter algebra. The table should be indexed by permutations and each entry corresponding to a permutation perm is interpreted as the coefficient of perm in the expression of the element e in the basis of permutations.

• Whenever there is a conflict between the function name Table2Nca and another name used in the same session, use the long form NCA['Table2Nca'].

EXAMPLES:

> with(NCA):
> t:=table([[2,3,1]=x1+x2, [1,3,2]=x1^2, [1,2,3]=1]);
 
                          t := table([
                                 [2, 3, 1] = x1 + x2
                                               2
                                 [1, 3, 2] = x1
                                 [1, 2, 3] = 1
                               ])
 
> Table2Nca(t);
 
                                      2
             (x1 + x2) A[2, 3, 1] + x1  A[1, 3, 2] + A[1, 2, 3]