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## `SYMF::Sf2Table` -- converts a symmetric function into a table

#### Call(s)

`SYMF::Sf2Table(sf,b)`

#### Parameters

`sf` | - | any symmetric function
`b` | - | any name of known basis

#### Introduction

The `SYMF::Sf2Table` function converts a symmetric function into a table. The table is indexed by partitions (possibly empty) and each entry that corresponds to a partition `part` is interpreted as the coefficient of `b[part]` in the expression of the symmetric function in the basis `b`.

This function can be useful if one wants to act either on coefficients or on partitions. For instance, one can use the `map` function to act on coefficients.

#### Example 1

    >> muEC::SYMF::Sf2Table( q^2*s[3,1,1] + q*s[4,2] + q + s[4,2], s );

                                 table(
                                   [] = q,
                                                2
                                   [3, 1, 1] = q ,
                                   [4, 2] = q + 1
                                 )

    >> map( %, coefficient -> coefficient - 1 );

                               table(
                                 [] = q - 1,
                                              2
                                 [3, 1, 1] = q  - 1,
                                 [4, 2] = q
                               )

    >> muEC::SYMF::Table2Sf( %, s );

                     2
                   (q  - 1) s[3, 1, 1] + q s[4, 2] + s[] (q - 1)

#### Related Functions

`Sf2TableVar`, `Table2Sf`

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MuPAD Combinat, an open source algebraic combinatorics package