muEC::SYMF::SfScalar( p[3,3,1], p[3,3,1] );
muEC::SYMF::SfZee( [3,3,1] );
muEC::SYMF::SfScalar – scalar product of symmetric functions
computes the scalar product of symmetric functions
Call:
muEC::SYMF::SfScalar(sf1, sf2, <sfp>)
Parameters:
|
sf1, sf2: |
any symmetric functions |
|
sfp: |
any procedure accepting a partition as input |
Related Functions:
Details:
The muEC::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: muEC::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] );
muEC::SYMF::SfZee( [3,3,1] );