detools::cartan
-- Cartan
characters of a differential equationdetools::cartan
determines the Cartan characters of a
differential equation either from the indices of the symbol or from the
Hilbert polynomial.
detools::cartan(n, m, q, beta)
detools::cartan(n, hp)
n |
- | number of independent variables: a positive integer. |
m |
- | number of dependent variables: a positive integer. |
q |
- | order of the equation: a positive integer. |
beta |
- | indices of symbol: a list of nonnegative integer. |
hp |
- | Hilbert polynomial: a univariate polynomial (type
DOM_POLY ) with rational
coefficients. |
a list of nonnegative integers.
detools::arbFuns
,
detools::hilbert
detools::cartan
determines the Cartan characters of a
differential equation from either the indices of the symbol or the
Hilbert polynomial. In the first case, the number of independent and
dependent variables, respectively, of the equation and its order must
be given.detools::cartan
the number
of independent variables suffices, as detools::cartan
assumes that the Hilbert polynomial is given relative to the order of
the differential equation, i.e. as a function of q+r.The indices of the symbol of Maxwell's equations of
electrodynamics (a first order system in four independent and six
dependent variables) are [0,0,2,6]
. They can be converted
into Cartan characters with the following command.
>> detools::cartan(4, 6, 1, [0, 0, 2, 6])
[6, 6, 4, 0]
Alternatively, we may start with the Hilbert polynomial of Maxwell's equations: H(1+r)=2r^2+12r+16.
>> detools::cartan(4, poly(2*r^2 + 12*r + 16, [r], Dom::Rational))
[6, 6, 4, 0]