FUNCTION: Sf2Qsf - expand a symmetric function on F-basis (dual basis of noncommutative ribbon Schur function)

CALLING SEQUENCE:

Sf2Qsf(sf)

NCSF[Sf2Qsf](sf)

PARAMETERS:

sf = any symmetric function

SYNOPSIS:

• The Sf2Qsf function computes the expansion of sf on F basis ( dual basis of noncommutative ribbon Schur function ).

• The result is expressed on F basis.

• The input is any expression in terms of the basic symmetric functions.

• The symmetric function sf is expanded and the result is not collected.

• One may add 'noexpand' just after sf to choose not to expand the symmetric function sf before treating it.

• One may collect the result by adding a third argument: this is done by Sf2Qsf(sf,'collect').

• Whenever there is a conflict between the function name Sf2Qsf and another name used in the same session, use the long form NCSF['Sf2Qsf'].

EXAMPLES:

> with(NCSF):
> Sf2Qsf((1-q)^3*s[2,1]):                  # expand the input
> Sf2Qsf((1-q)^3*s[2,1],noexpand):         # does not expand the input
> Sf2Qsf((1-q)^3*s[2,1],collect):          # collect the result
> Sf2Qsf((1-q)^3*s[2,1]+s[3],noexpand,collect);
 
                         3                   3
                  (1 - q)   F[2, 1] + (1 - q)   F[1, 2] + F[3]