FUNCTION: Top - convert any symmetric function to a p-polynomial

CALLING SEQUENCE:

Top(sf)

Top(sf, b)

SYMF[Top](sf)

SYMF[Top](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

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

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

EXAMPLES:

> with(SYMF):
> Top((1+q)^5*e3*e4):                            # expands the input
> Top((1+q)^5*e3*e4,noexpand):                   # does not expand (1+q)^5
> Top((1+q)^5*e3*e4,collect):                    # collects the result
> Top((1+q)^5*e3*e4,noexpand,'p'):               # the most efficient
> Top((1+q)^5*e3*e4,'p',collect):                # specifies a basis
> Top((1+q)^5*e3*e4,noexpand,'p',collect):
> Top(s[2,1]*h3 - 2*q*e3);
 
           3         2            4                         6           3
 1/18 p3 p1  - 1/9 p3  + 1/6 p2 p1  - 1/6 p2 p1 p3 + 1/18 p1  - 1/3 q p1
 
                         + q p2 p1 - 2/3 q p3