detools::hilbert
-- Hilbert
polynomial of a differential equationdetools::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.
detools::hilbert(alpha, r)
alpha |
- | the Cartan characters: a list of nonnegative integers. |
r |
- | variable for the polynomial: an identifier. |
a univariate polynomial (of type DOM_POLY
) in the variable r
with
rational coefficients.
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).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)