FUNCTION: Tox_n - express any symmetric function in the basis of monomials

CALLING SEQUENCE:

Tox_n(sf)

Tox_n(sf, b)

CLG[Tox_n](sf)

CLG[Tox_n](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Tox_n function expresses any symmetric function in the basis of monomials in x1, x2, ...

• The input is any expression in terms of the basic symmetric functions.

• The symmetric function sf is expanded and the result is not collected.

• One may specify by a second argument, say b, that sf is solely expressed in terms of the known basis b.

• One may add 'noexpand' just after the argument sf to choose not to expand the symmetric function sf before treating it.

• One may collect the result by adding a third argument: this is done by Tox_n(sf, b, 'collect').

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

EXAMPLES:

> with(CLG):
> CLG_n(3);
                                      3
 
> Tox_n((1+q)^3*e3*e2):                          # expands the input
> Tox_n((1+q)^3*e3*e2,noexpand):                 # does not expand (1+q)^3
> Tox_n((1+q)^3*e3*e2,collect):                  # collects the result
> Tox_n((1+q)^3*e3*e2,noexpand,'e'):             # the most efficient
> Tox_n((1+q)^3*e3*e2,'e',collect):              # specifies a basis
> Tox_n((1+q)^3*e3*e2,noexpand,'e',collect):
> Tox_n(p2^3);
 
   6       4   2       4   2       2   4       2   2   2       2   4     6
 x1  + 3 x1  x2  + 3 x1  x3  + 3 x1  x2  + 6 x1  x2  x3  + 3 x1  x3  + x2
 
           4   2       2   4     6
     + 3 x2  x3  + 3 x2  x3  + x3