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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