FUNCTION: x2XX - from the basis of monomials to XX Schubert basis

CALLING SEQUENCE:

x2XX(pol)

SP[x2XX](pol)

PARAMETERS:

pol = any expression on monomial basis

SYNOPSIS:

• The x2XX function converts any expression from the basis of monomials to XX Schubert basis. It uses a different algorithm than ToXX (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 x2XX and another name used in the same session, use the long form SP['x2XX'].

EXAMPLES:

> with(SP):
> Flag(-1):
> x2XX((1+q)^5*x1*x2^2):                         # expands the input
> x2XX((1+q)^5*x1*x2^2,noexpand):                # does not expand (1+q)^5
> x2XX((1+q)^5*x1*x2^2,collect):                 # collects the result
> x2XX((1+q)^5*x1*x2^2,noexpand,collect):
> r := x2XX(2*x1^3 + 4*q^2*x1^2, collect);
 
             3      2   2
   r := (2 y1  + 4 q  y1 ) XX[1]
 
                       2       2      2         2
      + (2 y2 y1 + 2 y1  + 2 y2  + 4 q  y2 + 4 q  y1) XX[2, 1]
 
                                 2
      + (2 y1 + 2 y3 + 2 y2 + 4 q ) XX[3, 1, 2] + 2 XX[4, 1, 2, 3]
 
> Tox(r);
 
                                   3      2   2
                               2 x1  + 4 q  x1