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

CALLING SEQUENCE:

Toe_n(sf)

Toe_n(sf, b)

CLG[Toe_n](sf)

CLG[Toe_n](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Toe_n function converts any symmetric function to a e-polynomial. The e.k, for k>_CLGn, are sent to 0.

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

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

EXAMPLES:

> with(CLG):
> _CLGn;
 
                                   5
 
> Toe_n((1+q)^5*s[3,2,2,1]):                     # expands the input
> Toe_n((1+q)^5*s[3,2,2,1],noexpand):            # does not expand (1+q)^5
> Toe_n((1+q)^5*s[3,2,2,1],collect):             # collects the result
> Toe_n((1+q)^5*s[3,2,2,1],noexpand,'s'):        # the most efficient
> Toe_n((1+q)^5*s[3,2,2,1],'s',collect):         # specifies a basis
> Toe_n((1+q)^5*s[3,2,2,1],noexpand,'s',collect):
> Toe_n(s[2,1]*h4 - 2*q*p3 + aa*e6);
 
                                    2          2        3        2
        - e4 e2 e1 + e4 e3 + 5 e3 e1  e2 - 2 e3  e1 + e2  e1 - e2  e3
 
              2   3      5        4                                 3
        - 3 e2  e1   + e1  e2 - e1  e3 - 6 q e3 + 6 q e2 e1 - 2 q e1