Transforms a linear differential system to an equivalent linear differential system with a companion matrix.
This functionality does not run in MATLAB.
ode::cyclicVector(A, x, <v>)
ode::cyclicVector(A, x, v) converts a first order homogeneous differential system into a corresponding first order homogeneous differential system , where B is a companion matrix, by substituting Z = PY using the potential cyclic vector v. If v is not cyclic then an empty list is returned otherwise a list is returned whose first element is a list corresponding to the last row of B and second element is the invertible matrix P.
When the optional argument v is not given then the vector [1,0,...,0] is tested. If it is not cyclic then a suitable one is determined randomly by the procedure.
We compute a differential system equivalent to the following differential system:
A := matrix( [ [x^2-1,1,0], [0,x^2+5*x+1/3,1], [0,0,2]])
So [1,0,0] is a cyclic vector; [x,0,0] is also a cyclic vector:
l := ode::cyclicVector(A, x, [x,0,0])
And we can build easily a linear homogeneous differential equation associated to it (c.f. ode::mkODE):
-ode::mkODE(l.[-1], y, x)
A square matrix of type Dom::Matrix.
The independent variable.
A list of size the dimension of A, default is [1,0,...,0].