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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

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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