FUNCTION: x2X - from the basis of monomials to X Schubert basis

CALLING SEQUENCE:

x2X(pol)

SP[x2X](pol)

PARAMETERS:

pol = any expression in the basis of monomials

SYNOPSIS:

• The x2X function converts any expression from the basis of monomials to X Schubert basis. It uses a different algorithm than ToX (taking the leading monomials successively).

• The result is not expanded.

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

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

• Whenever there is a conflict between the function name x2X and another name used in the same session, use the long form SP['x2X'].

EXAMPLES:

> with(SP):
> Flag(-1):
> x2X((1+q)^5*x1*x2^2):                          # expands the input
> x2X((1+q)^5*x1*x2^2,noexpand):                 # does not expand (1+q)^5
> x2X((1+q)^5*x1*x2^2,collect):                  # collects the result
> x2X((1+q)^5*x1*x2^2,noexpand,collect):
> x2X(2*x1^3 + 4*q^2*x1^2);
 
                                           2
                      2 X[4, 1, 2, 3] + 4 q  X[3, 1, 2]