FUNCTION: Tos_n - express any symmetric function in the basis of Schur functions

CALLING SEQUENCE:

Tos_n(sf)

Tos_n(sf, b)

CLG[Tos_n](sf)

CLG[Tos_n](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Tos_n function expresses any symmetric function in the basis of Schur functions, i.e. as a linear combination of Schur functions. It sends to 0 all Schur functions indexed by partitions with more than _CLGn parts.

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

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

EXAMPLES:

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