FUNCTION: ToF - express any quasi-symmetric function in the F-basis (dual basis of Ribbon Schur basis)

CALLING SEQUENCE:

ToF(qsf)

ToF(qsf, b)

NCSF[ToF](qsf)

NCSF[ToF](qsf, b)

PARAMETERS:

qsf = any quasi-symmetric function

b = any name of a known basis

SYNOPSIS:

• The ToF function computes the expansion of qsf in the F-basis.

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

• The quasi-symmetric function qsf is expanded and the result is not collected.

• One may specify by a second argument, say b, that qsf is solely expressed in terms of the known basis b.

• The call ToF(qsf, 'F') does not affect the argument qsf.

• One may add 'noexpand' just after the argument qsf to choose not to expand the quasi-symmetric function qsf before treating it.

• One may collect the result by adding a third argument: this is done by ToF(qsf, b, 'collect'). For instance, ToF(qsf, 'F', 'collect') may be used to collect the argument qsf.

• The noncommutative multiplication is denoted by the &* operator.

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

EXAMPLES:

> with(NCSF):
> ToF((1+q)^5*QPh[2,1]+t*M[3],noexpand,collect);
 
                       5                              5
         (- 1/2 (1 + q)  - t) F[1, 2] + (- 1/2 (1 + q)  + t) F[1, 1, 1]
 
                          5                         5
            + (1/2 (1 + q)  + t) F[3] + (1/2 (1 + q)  - t) F[2, 1]