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ode::ratSys

Rational solutions of a first order homogeneous linear differential system

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Syntax

ode::ratSys(M, x)

Description

ode::ratSys(M, x) computes a fundamental set of rational solutions of the first order homogeneous linear differential system Y'=MY. This method uses a cyclic vector and therefore is not optimal.

Examples

Example 1

We compute the rational solutions of the following differential system:

A := matrix([ [2*(x+x^2-9)/x/(x-2),2*(x^2-6)/x/(x-2)], 
     [-3*(2*x+x^2-12)/x/(x-2),-(2*x+3*x^2-24)/x/(x-2)] ])

v := ode::ratSys(A, x)

And we can check the result:

diff(v[1], x) = normal(A*v[1])

Parameters

M

A square matrix of type Dom::Matrix with coefficients in the field (x) of rational functions over the rationals.

x

The independent function.

Return Values

set, possibly empty, of objects of type Dom::Matrix.

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