FUNCTION: NcsfTransAlpha - specialization A/(1-q) --> A or A --> A/(1-q)

CALLING SEQUENCE:

NcsfTransAlpha(ncsf, specialize, q)

NCSF[NcsfTransAlpha](ncsf, specialize, q)

PARAMETERS:

ncsf = any noncommutative symmetric function

specialize = indicate the type of specialization

q = any formal parameter

SYNOPSIS:

• The NcsfTransAlpha function computes the direct transformation A/(1-q) --> A or the inverse transformation A --> A/(1-q). A is a set of variables on the noncommutative symmetric function ncsf.

• The NcsfTransAlpha function computes the direct transformation A/(1-q) --> A when the second argument matches 'direct'.

• The NcsfTransAlpha function computes the inverse transformation A --> A/(1-q) when the second argument matches 'inverse'.

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

• One may collect the result by adding a fourth argument: this is done by NcsfTransAlpha(ncsf, specialize, q, 'collect').

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

EXAMPLES:

> with(NCSF):
> NcsfTransAlpha((1-q)^3*S[2,1],direct,'q'):          # expand the input
> NcsfTransAlpha((1-q)^3*S[2,1],direct,'q',noexpand): # does not expand
                                                      # the input
> NcsfTransAlpha((1-q)^3*S[2,1],direct,'q',collect):  # collect the result
> NcsfTransAlpha((1-q)^3*S[2,1],direct,'q',noexpand): # the most efficient
> NcsfTransAlpha((1-q)^3*S[2,1],direct,'q',noexpand,collect);
 
                          S[2, 1] (q - 1)   S[1, 1, 1] q
                        - --------------- + ------------
                               q + 1            q + 1
 
> NcsfTransAlpha((1-q)^3*S[2,1],inverse,'q',noexpand,collect);
 
                    5
             (q - 1)  (- R[3] - R[2, 1] + q R[1, 2] + q R[1, 1, 1])