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

CALLING SEQUENCE:

ToSp(sf)

ToSp(sf, b)

CG[ToSp](sf)

CG[ToSp](sf, b)

PARAMETERS:

sf = any symmetric function

b = any name of a known basis

SYNOPSIS:

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

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

EXAMPLES:

> with(CG):
> ToSp(e3*s[3,2]);
 
   2 Sp[2, 2, 1, 1] + Sp[2, 1, 1, 1, 1] + 2 Sp[3, 1, 1, 1] + 4 Sp[3, 2, 1]
 
 + 5 Sp[2, 1, 1] + 4 Sp[2, 2] + 4 Sp[3, 1] + 2 Sp[1, 1, 1, 1] + 4 Sp[1, 1]
 
 + 3 Sp[2] + Sp[3, 2, 1, 1, 1] + 2 Sp[3, 3] + Sp[] + Sp[3, 3, 1, 1]
 
 + Sp[4, 1, 1] + 2 Sp[4, 2] + Sp[4, 2, 1, 1] + Sp[4, 3, 1]