FUNCTION: Toe - convert any symmetric function to a e-polynomial

CALLING SEQUENCE:

Toe(sf)

Toe(sf, b)

SYMF[Toe](sf)

SYMF[Toe](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Toe function converts any symmetric function to a e-polynomial.

• 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 Toe(sf, b, 'collect'). For instance, Toe(sf, 'e', 'collect') may be used to collect the argument sf.

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

EXAMPLES:

> with(SYMF):
> Toe((1+q)^5*h3*h4):                            # expands the input
> Toe((1+q)^5*h3*h4,noexpand):                   # does not expand (1+q)^5
> Toe((1+q)^5*h3*h4,collect):                    # collects the result
> Toe((1+q)^5*h3*h4,noexpand,'h'):               # the most efficient
> Toe((1+q)^5*h3*h4,'h',collect):                # specifies a basis
> Toe((1+q)^5*h3*h4,noexpand,'h',collect):
> Toe(s[2,1]*h4 - 2*q*p3);
 
                             2          2        3        2          2   3
 - e4 e2 e1 + e4 e3 + 5 e3 e1  e2 - 2 e3  e1 + e2  e1 - e2  e3 - 3 e2  e1
 
               5        4                                 3
           + e1  e2 - e1  e3 - 6 q e3 + 6 q e2 e1 - 2 q e1