FUNCTION: ToS - express any noncommutative symmetric function in the S-basis (noncommutative complete symmetric function)

CALLING SEQUENCE:

ToS(ncsf)

ToS(ncsf, b)

NCSF[ToS](ncsf)

NCSF[ToS](ncsf, b)

PARAMETERS:

ncsf = any noncommutative symmetric function

b = any name of a known basis

SYNOPSIS:

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

EXAMPLES:

> with(NCSF):
> ToS((1-q)^3*Ps[3]+L[1,2],noexpand,collect);
 
                3                   3                            3
       - (1 - q)  S[2, 1] + ((1 - q)  + 1) S[1, 1, 1] + 3 (1 - q)  S[3]
 
                         3
           + (- 2 (1 - q)  - 1) S[1, 2]