SYMF::SfScalar --
scalar product of symmetric functions
Call(s)
SYMF::SfScalar(sf1,sf2 <,sfp>)
Parameterssf1, sf2 | - | any symmetric functions |
sfp | - | any procedure accepting a partition as input |
IntroductionThe 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.
Example 1>> muEC::SYMF::SfScalar( p[3,3,1], p[3,3,1] );
18
>> muEC::SYMF::SfZee( [3,3,1] );
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Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package