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

CALLING SEQUENCE:

Tom(sf)

Tom(sf, b)

SYMF[Tom](sf)

SYMF[Tom](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The Tom function expresses any symmetric function in the basis of monomial symmetric functions.

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

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

EXAMPLES:

> with(SYMF):
> Tom((1+q)^5*e3*e4):                            # expands the input
> Tom((1+q)^5*e3*e4,noexpand):                   # does not expand (1+q)^5
> Tom((1+q)^5*e3*e4,collect):                    # collects the result
> Tom((1+q)^5*e3*e4,noexpand,'e'):               # the most efficient
> Tom((1+q)^5*e3*e4,'e',collect):                # specifies a basis
> Tom((1+q)^5*e3*e4,noexpand,'e',collect):
> Tom(s[2,1]*h4 - 2*q*p3);
 
    8 m[3, 2, 2] + 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] + 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]
 
  + 45 m[2, 1, 1, 1, 1, 1] + 70 m[1, 1, 1, 1, 1, 1, 1] - 2 q m[3]