FUNCTION: Sga2Table - convert an element of the symmetric group algebra into a table

CALLING SEQUENCE:

Sga2Table(e)

SGA[Sga2Table](e)

PARAMETERS:

e = any element of the symmetric group algebra

SYNOPSIS:

• The Sga2Table function converts an element of the symmetric group algebra into a table. The table is indexed by permutations and each entry corresponding to a permutation is the coefficient of this permutation in the element e.

• Note that all permutations in the indices of the table are adjusted to belong to the same minimal symmetric group.

• This function can be useful if one wants to act either on coefficients or on permutations. For instance, one can use the map function to act on coefficients.

• Whenever there is a conflict between the function name Sga2Table and another name used in the same session, use the long form SGA['Sga2Table'].

EXAMPLES:

> with(SGA):
> t := Sga2Table((x1+x2)*A[2,3,1] + x1^2*A[1,3,2] + A[1,2]);
 
                       t := table(sparse,[
                              [2, 3, 1] = x1 + x2
                                            2
                              [1, 3, 2] = x1
                              [1, 2, 3] = 1
                            ])
 
> t := map(SP['ToX'], t);
 
                      t := table(sparse,[
                             [2, 3, 1] = X[1, 3, 2]
                             [1, 3, 2] = X[3, 1, 2]
                             [1, 2, 3] = X[1]
                           ])
 
> Table2Sga(t);
 
    X[1, 3, 2] A[2, 3, 1] + X[3, 1, 2] A[1, 3, 2] + X[1] A[1, 2, 3]