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SYMF::SfScalar -- scalar product of symmetric functions

Call(s)


SYMF::SfScalar(sf1,sf2 <,sfp>)

Parameters

sf1, sf2- any symmetric functions
sfp- any procedure accepting a partition as input

Introduction

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.

Example 1

>> muEC::SYMF::SfScalar( p[3,3,1], p[3,3,1] );
                                    18
>> muEC::SYMF::SfZee( [3,3,1] );
                                    18

Related Functions

SfZee

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MuPAD Combinat, an open source algebraic combinatorics package