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## `SYMF::Toh` -- converts any symmetric function into a `h`-polynomial

#### Call(s)

`SYMF::Toh(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 `h`-basis

#### Introduction

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

#### Example 1

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

          q h[3, 3] - 2 q h[3, 2, 1] + q h[2, 2, 1, 1] -

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

             2 k q h[3, 1, 1, 1] - 2 k q h[2, 1, 1, 1, 1] +

              2                      2
             k  q h[2, 2, 1, 1] - 2 k  q h[2, 1, 1, 1, 1] +

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

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

                2
          (q + k  q + 2 k q) h[2, 2, 1, 1] -

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

             (2 q + 2 k q) h[3, 2, 1] + 2 k q h[3, 1, 1, 1] +

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

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

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

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

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

#### Related Functions

`Toe`, `Tom`, `Top`, `Tos`, `SfAddBasis`, `Sf`

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MuPAD Combinat, an open source algebraic combinatorics package