FUNCTION: Xfix2X - from X Schubert basis with symmetric functions as coefficients to X Schubert basis

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 X Schubert basis. Symmetric polynomials are also converted.

• The result is not expanded.

• One may add 'noexpand' just after the argument schub to choose not to expand the expression schub before treating it.

• One may add 'collect' just after the argument schub or just after the argument 'noexpand' to collect the result.

• We recommend to use the collect option to have the result simplified.

• 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]);
 
                     X[1, 3, 5, 2, 4] + X[1, 5, 2, 3, 4]