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## `SYMF::Tos` -- converts any symmetric function into a `s`-polynomial

#### Call(s)

`SYMF::Tos(sf <,b> <,Collect> <,NoExpand>)`

#### Parameters

`sf` | - | any symmetric function
`b` | - | converts only `b`-polynomials appearing in `sf`

#### Options

`NoExpand` | - | keeps the recursive structure of `sf`
`Collect` | - | expresses the result on the `s`-basis

#### Introduction

The `SYMF::Tos` function converts any symmetric function into a `s`-polynomial.

The symmetric function sf is expanded and the result is not collected.

One may convert only `b`-polynomials of `sf` by adding the base `b` in the arguments.

One may preserve the recursive structure of `sf` by adding the argument `NoExpand`.

One may collect the result by adding the argument `Collect`. The result will be collected in all `s`-polynomials appearing in `sf`.

#### Example 1

    >> muEC::SYMF::Tos( (e[1,1] - k*h[1,1])^2 * q - p[1]^3 );

          q s[4] + 2 q s[2, 2] + 3 q s[3, 1] + 3 q s[2, 1, 1] +

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

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

                                                             2
             2 k q (s[2, 2] + s[2, 1, 1] + s[1, 1, 1, 1]) + k  q s[4] +

                2                2                2
             2 k  q s[2, 2] + 3 k  q s[3, 1] + 3 k  q s[2, 1, 1] +

              2
             k  q s[1, 1, 1, 1] - 2 s[2, 1] - s[1, 1, 1]

    >> muEC::SYMF::Tos( (e[1,1] - k*h[1,1])^2 * q - p[1]^3, Collect );

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

                       2
             (2 q + 2 k  q - 4 k q) s[2, 2] +

                       2
             (3 q + 3 k  q - 6 k q) s[3, 1] +

                       2
             (3 q + 3 k  q - 6 k q) s[2, 1, 1] - s[3] - 2 s[2, 1] -

             s[1, 1, 1]

    >> muEC::SYMF::Tos( (e[1,1] - k*h[1,1])^2 * q - p[1]^3, Collect,
            NoExpand );

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

    >> muEC::SYMF::Tos( (e[1,1] - k*h[1,1])^2 * q - p[1]^3, NoExpand, h );

                                                     2       3
                     q (k (s[2] + s[1, 1]) - e[1, 1])  - p[1]

#### Related Functions

`Toe`, `Toh`, `Tom`, `Top`, `SfAddBasis`, `Sf`

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MuPAD Combinat, an open source algebraic combinatorics package