FUNCTION: Sf2TableVar - variable set of a symmetric function

CALLING SEQUENCE:

Sf2TableVar(sf)

SYMF[Sf2TableVar](sf)

PARAMETERS:

sf = any symmetric function

SYNOPSIS:

• The Sf2TableVar function returns a table whose entries describe the set of all symmetric functions that appear in a given expression sf. The indices of the table are taken into the global variable SYMFBases.

• For all bases of type 'indexed' (SYMFBasesIndexed), the entry consists of the set of all partitions that index the corresponding symmetric function in sf.

• For all bases of type 'string' (SYMFBasesString), the entry consists of the set of all integers that index the corresponding symmetric function in sf.

• An entry equal to an empty set means that the symmetric function does not appear in sf.

• One can add a second argument to select some symmetric functions among those in SYMFBases. If the second argument is a set of names, then the restriction to this set of indices of the table is returned. In case the second argument is the name of a basis, then the corresponding entry in the table is returned instead of the table.

• Whenever there is a conflict between the function name Sf2TableVar and another name used in the same session, use the long form SYMF['Sf2TableVar'].

EXAMPLES:

> with(SYMF):
> Sf2TableVar(s[5]*s[4]*h3 + q*m[3]*p4*p6);
 
                              table([
                                  p = {4, 6}
                                  s = {[5], [4]}
                                  m = {[3]}
                                  c = {}
                                  e = {}
                                  h = {3}
                              ])
 
> Sf2TableVar(s[5]*s[4]*h3 + q*m[3]*p4*p6, {'p', 'm'});
 
                                table([
                                    p = {4, 6}
                                    m = {[3]}
                                ])
 
> Sf2TableVar(s[5]*s[4]*h3 + q*m[3]*p4*p6, 's');
 
                                  {[5], [4]}