## `detools::hilbert` -- Hilbert polynomial of a differential equation

#### Introduction

`detools::hilbert``(alpha,r)` computes the Hilbert polynomial of a differential equation with Cartan characters `alpha`. The identifier `r` is used as variable of the polynomial.

#### Call(s)

`detools::hilbert(alpha, r)`

#### Parameters

`alpha` | - | the Cartan characters: a list of nonnegative integers.
`r` | - | variable for the polynomial: an identifier.

#### Returns

a univariate polynomial (of type `DOM_POLY`) in the variable `r` with rational coefficients.

#### Related Functions

`detools::cartan`

#### Details

- `detools::hilbert``(alpha,r)` determines the Hilbert polynomial of a differential equation with Cartan characters `alpha`. The result is a univariate polynomial in the variable `r`. The Hilbert polynomial should always be interpreted relative to the order of the differential equation. If the Cartan characters have been computed at order q, the arising polynomial is H(q+r).

#### Example 1

The Cartan characters of Maxwell's equations of electrodynamics are `[6,6,4,0]`. The corresponding Hilbert polynomial is

    >> detools::hilbert([6, 6, 4, 0], r)

                            2
                    poly(2 r  + 12 r + 16, [r], Dom::Rational)

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