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## `SYMF::Tom` -- converts any symmetric function into a `m`-polynomial

#### Call(s)

`SYMF::Tom(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 `m`-basis

#### Introduction

The `SYMF::Tom` function converts any symmetric function into a `m`-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 `m`-polynomials appearing in `sf`.

#### Example 1

    >> muEC::SYMF::Tom( (s[2] - k*e[2])^2 * q - p[1]^3 );

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

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

             2 k q (m[2, 2] + 2 m[2, 1, 1] + 6 m[1, 1, 1, 1]) +

              2                2                   2
             k  q m[2, 2] + 2 k  q m[2, 1, 1] + 6 k  q m[1, 1, 1, 1] -

             3 m[2, 1] - 6 m[1, 1, 1]

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

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

                       2
             (4 q + 2 k  q - 6 k q) m[2, 1, 1] +

                       2
             (6 q + 6 k  q - 12 k q) m[1, 1, 1, 1] +

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

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

                                                  2       3
                        q ((k - 1) m[1, 1] - m[2])  - m[1]

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

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

#### Related Functions

`Toe`, `Toh`, `Top`, `Tos`, `SfAddBasis`, `Sf`

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MuPAD Combinat, an open source algebraic combinatorics package