SYMF::SfDiff
--
differential operator
SYMF::SfDiff(sf1,sf2)
sf1, sf2 | - | any symmetric functions |
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.
>> 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[]
MuPAD Combinat, an open source algebraic combinatorics package