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SYMF::SfDiff -- differential operator

Call(s)


SYMF::SfDiff(sf1,sf2)

Parameters

sf1, sf2- any symmetric functions

Introduction

The SYMF::SfDiff function computes D_sf1(sf2) in which D_sf1 stands for the differential operator corresponding to the symmetric function sf1. Both symmetric functions sf1 and sf2 can be expressed in terms of any known basis since both expressions are converted in terms of Schur functions. One has D_s[part1](s[part2]) = s[part2/part1], and the operation is extended by linearity to any pair sf1, sf2.

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

Example 1

>> muEC::SYMF::SfDiff( s[3,1] + q*s[3], 2*e[2]*p[2] );
                             2 s[] + 2 q s[1]
>> muEC::SYMF::Tos( 2*e[2]*p[2] );
                  2 s[3, 1] - 2 s[2, 2] - 2 s[1, 1, 1, 1]
>> muEC::SYMF::SfDiff( s[4,3,2,1,1], s[4,3,2,1,1] );
                                    s[]

Related Functions

Tos

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MuPAD Combinat, an open source algebraic combinatorics package