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

CALLING SEQUENCE:

Toh(sf)

Toh(sf, b)

SYMF[Toh](sf)

SYMF[Toh](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Toh function converts any symmetric function to a h-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 Toh(sf, b, 'collect'). For instance, Toh(sf, 'h', 'collect') may be used to collect the argument sf.

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

EXAMPLES:

> with(SYMF):
> Toh((1+q)^5*e3*e4):                            # expands the input
> Toh((1+q)^5*e3*e4,noexpand):                   # does not expand (1+q)^5
> Toh((1+q)^5*e3*e4,collect):                    # collects the result
> Toh((1+q)^5*e3*e4,noexpand,'e'):               # the most efficient
> Toh((1+q)^5*e3*e4,'e',collect):                # specifies a basis
> Toh((1+q)^5*e3*e4,noexpand,'e',collect):
> Toh(s[2,1]*e4 - 2*q*p3);
 
                            2          2        3        2          2   3
- h4 h2 h1 + h4 h3 + 5 h3 h1  h2 - 2 h3  h1 + h2  h1 - h2  h3 - 3 h2  h1
 
                 5        4                                 3
             + h1  h2 - h1  h3 - 6 q h3 + 6 q h2 h1 - 2 q h1