FUNCTION: Tom_n - express any symmetric function in the basis of monomial symmetric functions

CALLING SEQUENCE:

Tom_n(sf)

Tom_n(sf, b)

CLG[Tom_n](sf)

CLG[Tom_n](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Tom_n function expresses any symmetric function in the basis of monomial symmetric functions. It sends to 0 all those which are 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 Tom_n(sf, b, 'collect'). For instance, Tom_n(sf, 'm', 'collect') may be used to collect the argument sf.

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

EXAMPLES:

> with(CLG):
> _CLGn;
 
                                   5
 
> Tom_n((1+q)^5*e3*e4):                          # expands the input
> Tom_n((1+q)^5*e3*e4,noexpand):                 # does not expand (1+q)^5
> Tom_n((1+q)^5*e3*e4,collect):                  # collects the result
> Tom_n((1+q)^5*e3*e4,noexpand,'e'):             # the most efficient
> Tom_n((1+q)^5*e3*e4,'e',collect):              # specifies a basis
> Tom_n((1+q)^5*e3*e4,noexpand,'e',collect):
> Tom_n(s[2,1]*h4 - 2*q*p3 + aa*m[1,1,1,1,1,1]);
 
 m[6, 1] + 2 m[5, 2] + 4 m[5, 1, 1] + 2 m[4, 3] + 6 m[4, 2, 1]
 
 + 11 m[4, 1, 1, 1] + 6 m[3, 3, 1] + 8 m[3, 2, 2] + 14 m[3, 2, 1, 1]
 
 + 24 m[3, 1, 1, 1, 1] + 17 m[2, 2, 2, 1] + 28 m[2, 2, 1, 1, 1] - 2 q m[3]