FUNCTION: ToPh - express any noncommutative symmetric function in the Ph-basis (noncommutative power sums symmetric function of the second kind)

CALLING SEQUENCE:

ToPh(ncsf)

ToPh(ncsf, b)

NCSF[ToPh](ncsf)

NCSF[ToPh](ncsf, b)

PARAMETERS:

ncsf = any noncommutative symmetric function

b = any name of a known basis

SYNOPSIS:

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

EXAMPLES:

> with(NCSF):
> ToPh((1-q)^3*S[3]+Ps[1,2],noexpand,collect);
 
                 3                    3
      1/3 (1 - q)  Ph[3] + 1/4 (1 - q)  Ph[2, 1]
 
                      3                            3
        + (1/4 (1 - q)  + 1) Ph[1, 2] + 1/6 (1 - q)  Ph[1, 1, 1]