FUNCTION: SfDiff - differential operator

CALLING SEQUENCE:

SfDiff(sf_1, sf_2)

SYMF[SfDiff](sf_1, sf_2)

PARAMETERS:

sf_1, sf_2 = any symmetric functions

SYNOPSIS:

• The SfDiff function computes D_{sf_1}(sf_2) in which D_{sf_1} stands for the differential operator corresponding to the symmetric function sf_1. Both symmetric functions sf_1 and sf_2 can be expressed in terms of any known basis since both expressions are converted in terms of Schur functions.

• The result is a linear combination of Schur functions, and not collected.

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

EXAMPLES:

> with(SYMF):
> SfDiff(s[3,1] + q*s[3], 2*e2*p2);
 
                               2 s[] + 2 q s[1]
 
> Tos(2*e2*p2);
 
                   2 s[3, 1] - 2 s[1, 1, 1, 1] - 2 s[2, 2]
 
> SfDiff(s[4,3,2,1,1], s[4,3,2,1,1]);
 
                                     s[]