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

CALLING SEQUENCE:

ToO(sf)

ToO(sf, b)

CG[ToO](sf)

CG[ToO](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

• The ToO function expresses any symmetric function in the basis of orthogonal Schur functions, i.e. as a linear combination of orthogonal Schur 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 ToO(sf, b, 'collect'). For instance, ToO(sf, 'O', 'collect') may be used to collect the argument sf.

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

EXAMPLES:

> with(CG):
> ToO(h4+2*e2*s[3,1]);
 
     3 O[4] + 7 O[2] + 3 O[] + 2 O[3, 1, 1, 1] + 2 O[1, 1, 1, 1]
 
   + 6 O[2, 1, 1] + 2 O[3, 2, 1] + 4 O[2, 2] + 6 O[3, 1] + 4 O[1, 1]
 
   + 2 O[4, 2] + 2 O[4, 1, 1]