FUNCTION: Toh_n - convert any symmetric function to a h-polynomial

CALLING SEQUENCE:

Toh_n(sf)

Toh_n(sf, b)

CLG[Toh_n](sf)

CLG[Toh_n](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Toh_n function converts any symmetric function to a h-polynomial. It uses the relations e.k = 0 for k>_CLGn.

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

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

EXAMPLES:

> with(CLG):
> _CLGn;
 
                                   5
 
> Toh_n((1+q)^5*s[3,2,2,1]):                     # expands the input
> Toh_n((1+q)^5*s[3,2,2,1],noexpand):            # does not expand (1+q)^5
> Toh_n((1+q)^5*s[3,2,2,1],collect):             # collects the result
> Toh_n((1+q)^5*s[3,2,2,1],noexpand,'s'):        # the most efficient
> Toh_n((1+q)^5*s[3,2,2,1],'s',collect):         # specifies a basis
> Toh_n((1+q)^5*s[3,2,2,1],noexpand,'s',collect):
> Toh_n(s[2,1]*h4 - 2*q*p3 + aa*e6);
 
                                                             3
               h4 h2 h1 - h4 h3 - 6 q h3 + 6 q h2 h1 - 2 q h1