detools::hilbert -- Hilbert
polynomial of a differential equation
Introductiondetools::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)
Parametersalpha |
- | the Cartan characters: a list of nonnegative integers. |
r |
- | variable for the polynomial: an identifier. |
Returnsa univariate polynomial (of type DOM_POLY) in the variable r with
rational coefficients.
Related
Functions
Detailsdetools::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
1The 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)