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## `SYMF::Top` -- converts any symmetric function into a `p`-polynomial

#### Call(s)

`SYMF::Top(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 `p`-basis

#### Introduction

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

#### Example 1

    >> muEC::SYMF::Top( (m[2] - k*h[2])^2 * q - e[1]^3 );

                                                      2
                                                     k  q p[2, 2]
          q p[2, 2] - k q p[2, 2] - k q p[2, 1, 1] + ------------ +
                                                           4

              2                 2
             k  q p[2, 1, 1]   k  q p[1, 1, 1, 1]
             --------------- + ------------------ - p[1, 1, 1]
                    2                   4

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

          /      2         \           /        2   \
          |     k  q       |           |       k  q |
          | q + ---- - k q | p[2, 2] - | k q - ---- | p[2, 1, 1] +
          \       4        /           \         2  /

              2
             k  q p[1, 1, 1, 1]
             ------------------ - p[1, 1, 1]
                      4

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

                       / / k     \        k p[1, 1] \2       3
                     q | | - - 1 | p[2] + --------- |  - p[1]
                       \ \ 2     /            2     /

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

                      /   / p[2]   p[1, 1] \        \2       3
                    q | k | ---- + ------- | - m[2] |  - e[1]
                      \   \   2       2    /        /

#### Related Functions

`Toe`, `Toh`, `Tom`, `Tos`, `SfAddBasis`, `Sf`

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MuPAD Combinat, an open source algebraic combinatorics package