Transforms a linear differential system to an equivalent linear differential system with a companion matrix.
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ode::cyclicVector(A, x, v) converts a first
order homogeneous differential system
into a corresponding
first order homogeneous differential system
a companion matrix, by substituting Z = PY using
the potential cyclic vector
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
second element is the invertible matrix
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]])
[1,0,0] is a cyclic vector;
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(l.[-1], y, x)
A square matrix of type
The independent variable.
A list of size the dimension of
List, possibly empty, of two lists.