FUNCTION: Sp2TableVar - variable set for the SP package

CALLING SEQUENCE:

Sp2TableVar(expr)

SP[Sp2TableVar](expr)

PARAMETERS:

expr = any expression

SYNOPSIS:

• The Sp2TableVar function returns a table whose entries describe the set of all Schubert polynomials and variables that appear in a given expression expr. The indices of the table are taken into the global variable SPBases.

• For all bases of type 'indexed' (SPBasesIndexed), the entry consists of the set of all permutations that index the corresponding Schubert polynomials in expr.

• For all bases of type 'string' (SPBasesString), the entry consists of the set of all integers that index the corresponding variable in expr.

• An entry equal to an empty set means that the element does not appear in expr.

• One can add a second argument to select some elements among those in SPBases. 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 a single name, then the corresponding entry in the table is returned instead of the table.

• Whenever there is a conflict between the function name Sp2TableVar and another name used in the same session, use the long form SP['Sp2TableVar'].

EXAMPLES:

> with(SP):
> Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1]);
 
                      table([
                          x = {1, 4}
                          YY = {}
                          XX = {}
                          X = {[4, 1, 3, 2], [2, 3, 1]}
                          Y = {}
                          y = {4, 6}
                      ])
 
> Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], {'X', 'x'});
 
                      table([
                          x = {1, 4}
                          X = {[4, 1, 3, 2], [2, 3, 1]}
                      ])
 
> Sp2TableVar(x1^3*x4*y4 + q*y6*X[4,1,3,2]*X[2,3,1], 'y');
 
                                  {4, 6}