FUNCTION: ToR - express any noncommutative symmetric function in the R-basis (ribbon Schur function)

CALLING SEQUENCE:

ToR(ncsf)

ToR(ncsf, b)

NCSF[ToR](ncsf)

NCSF[ToR](ncsf, b)

PARAMETERS:

ncsf = any noncommutative symmetric function

b = any name of a known basis

SYNOPSIS:

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

EXAMPLES:

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