FUNCTION: ToQPs - express any quasi-symmetric function in the QPs-basis (dual basis of noncommutative power sums symmetric functions of the first kind)

CALLING SEQUENCE:

ToQPs(qsf)

ToQPs(qsf, b)

NCSF[ToQPs](qsf)

NCSF[ToQPs](qsf, b)

PARAMETERS:

qsf = any quasi-symmetric function

b = any name of a known basis

SYNOPSIS:

• The ToQPs function computes the expansion of qsf in the QPs-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 ToQPs(qsf, 'QPs') 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 ToQPs(qsf, b, 'collect'). For instance, ToQPs(qsf, 'QPs', '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 ToQPs and another name used in the same session, use the long form NCSF['ToQPs'].

EXAMPLES:

> with(NCSF):
> ToQPs((1+q)^5*QPh[2,2]+M[4]+t^3*M[3,1],noexpand,collect);
 
               3                    3                        5
       (- 1/4 t  + 1) QPs[4] + 1/4 t  QPs[3, 1] + 1/2 (1 + q)  QPs[2, 2]