SYMF::SfDiff --
differential operator
Call(s)
SYMF::SfDiff(sf1,sf2)
Parameterssf1, 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 FunctionsMuPAD Combinat, an open source algebraic combinatorics package