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detools::cartan -- Cartan characters of a differential equation

Introduction

detools::cartan determines the Cartan characters of a differential equation either from the indices of the symbol or from the Hilbert polynomial.

Call(s)

detools::cartan(n, m, q, beta)
detools::cartan(n, hp)

Parameters

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.

Returns

a list of nonnegative integers.

Related Functions

detools::arbFuns, detools::hilbert

Details

Example 1

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]

Background




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