Is it possible to improve it for the work on field R, not on C?
I am writing a function to the asymptotic expansion of solutions of
linear ODE in the neighborhood of a regular singular point, and I really
need this functionality.
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As is well known, for the real matrix A there exists a real matrix T
(det(T)#0):
A=T^(-1)JT,
where J is real block-diagonal matrix with blocks j1,j2,...
corresponding to the eigenvalues t1,t2,... ??of the matrix A.
If t1=a1+%i*b1 is complex number, then
j1=matrix(
[k1,e,0,...],
[0,k1,e,0,...],
[0,0,k1,e,0,...],
...)
k1=matrix(
[a1,b1],
[-b1,a1]
)
e=ident(2)
If t1 is real then
j1=matrix(
[t1,1,0,...],
[0,t1,1,0,...],
[0,0,t1,1,0,...],
...)