FUNCTION: ToPs - express any noncommutative symmetric function in the Ps-basis (noncommutative power sums symmetric function of the first kind)

CALLING SEQUENCE:

ToPs(ncsf)

ToPs(ncsf, b)

NCSF[ToPs](ncsf)

NCSF[ToPs](ncsf, b)

PARAMETERS:

ncsf = any noncommutative symmetric function

b = any name of a known basis

SYNOPSIS:

• The ToPs function computes the expansion of ncsf in the Ps-basis.

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

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

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

• The call ToPs(ncsf, 'Ps') does not affect the argument ncsf.

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

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

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

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

EXAMPLES:

> with(NCSF):
> ToPs((1-q)^3*S[3]+R[1,2],noexpand,collect);
 
               3                               3
   (1/3 (1 - q)  + 1/6) Ps[1, 2] + (1/3 (1 - q)  - 1/3) Ps[3]
 
                    3                               3
      + (1/6 (1 - q)  - 1/6) Ps[2, 1] + (1/6 (1 - q)  + 1/3) Ps[1, 1, 1]