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## `SYMF::Sf2TableVar` -- variable set of a symmetric function

#### Call(s)

`SYMF::Sf2TableVar(sf <,b,bset>)`

#### Parameters

`sf` | - | any symmetric function
`b` | - | a known basis
`bset` | - | a set of known bases

#### Introduction

The `SYMF::Sf2TableVar` function returns a table whose entries describe the set of all symmetric functions that appear in a given expression `sf`. The indices of the table are taken into the global variable `SYMFBases`.

For each basis, the entry consists of the set of all partitions that index the corresponding symmetric function in `sf`.

An entry equal to an empty set means that the symmetric function does not appear in `sf`.

One can add a second argument to select some symmetric functions among those in `SYMFBases`.

If the second argument is a set of names, then the restriction to this set of indices of the table is returned.

In case the second argument is the name of a basis, then the corresponding entry in the table is returned instead of the table.

#### Example 1

    >> muEC::SYMF::Sf2TableVar( s[5]*s[4]*h[3] + q*m[3]*p[6,4] );

                                 table(
                                   s = {[4], [5]},
                                   m = {[3]},
                                   p = {[6, 4]},
                                   h = {[3]},
                                   e = {}
                                 )

    >> muEC::SYMF::Sf2TableVar( s[5]*s[4]*h[3] + q*m[3]*p[6,4], {p, m} );

                                  table(
                                    m = {[3]},
                                    p = {[6, 4]}
                                  )

    >> muEC::SYMF::Sf2TableVar( s[5]*s[4]*h[3] + q*m[3]*p[6,4], s );

                                    {[4], [5]}

#### Related Functions

`Sf2Table`

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MuPAD Combinat, an open source algebraic combinatorics package