FUNCTION: ToM - express any quasi-symmetric function in the M-basis (quasi-monomial symmetric functions)

CALLING SEQUENCE:

ToM(qsf)

ToM(qsf, b)

NCSF[ToM](qsf)

NCSF[ToM](qsf, b)

PARAMETERS:

qsf = any quasi-symmetric function

b = any name of a known basis

SYNOPSIS:

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

EXAMPLES:

> with(NCSF):
> ToM((1+q)^5*QPh[2,1,2]+t^3*M[3,2],noexpand,collect);
 
                    5                   5                  5
         1/6 (1 + q)  M[5] + 1/2 (1 + q)  M[2, 3] + (1 + q)  M[2, 1, 2]
 
                          5    3
            + (1/2 (1 + q)  + t ) M[3, 2]