SYMF::SfScalar
--
scalar product of symmetric functions
SYMF::SfScalar(sf1,sf2 <,sfp>)
sf1, sf2 | - | any symmetric functions |
sfp | - | any procedure accepting a partition as input |
The SYMF::SfScalar
function computes the scalar product between the
symmetric functions sf1
and sf2.
This scalar product is such that Schur functions constitute an orthonormal basis.
The p
-basis is an orthogonal basis:
.
SYMF::SfScalar
(p[part],
p[part]) = SfZee([part])
One can choose another scalar product, for which the
p
-basis will still remain orthogonal by replacing
SfZee
with any procedure sfp
accepting partitions.
>> muEC::SYMF::SfScalar( p[3,3,1], p[3,3,1] );
18
>> muEC::SYMF::SfZee( [3,3,1] );
18
MuPAD Combinat, an open source algebraic combinatorics package