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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