FUNCTION: Xfix2x - from X Schubert basis with symmetric functions as coefficients to the basis of monomials

CALLING SEQUENCE:

Xfix2x(schub)

FM[Xfix2x](schub)

PARAMETERS:

schub = any expression in X Schubert basis

SYNOPSIS:

• The Xfix2x function converts an expression from X Schubert basis of the ring of polynomials as a free module over symmetric polynomials to the basis of monomials. Symmetric functions are also converted.

• The result is not expanded.

• Whenever there is a conflict between the function name Xfix2x and another name used in the same session, use the long form FM['Xfix2x'].

EXAMPLES:

> with(FM):
> FM_n(3);
 
                                     3
 
> Xfix2x(h2*X[1,3,2] + a*X[3,1,2]);
 
            2                     2             2                  2
         (x3  + x3 x2 + x3 x1 + x2  + x2 x1 + x1 ) (x2 + x1) + a x1