On Sat, Dec 10, 2011 at 10:37 AM, pedda <notforyou...@hmamail.com> wrote:
> I have tried to do it non-symbolically, but I think it is rather
> inelegant. I am also trying to promote the use of python/sage over the
> use of Mathematica with my fellow students and it is somewhat
> important to show that they can do the same thing for free with other
> advantages. Since Mathematica is able to calculate the eigenvalues
> without any problem or delay, it is hard to convince someone to switch
> to a system that takes so much longer and is not as reliable.

Mathematica is old and well tested and polished system, so it's
currently more reliable.
SymPy is improved by people like you or me, who have a problem, and want to
solve it using opensource tools (because we believe in opensource),
as opposed to just feed it to Mathematica and
be done with it.

All you need are just eigenvalues of this matrix? Or also eigenvectors?

What is the algorithm that Mathematica uses? In particular, what
is the best algorithm for this type of matrix to get the eigenvalues?

Let's get it implemented in SymPy so that we can solve these kind of matrices.
I would be very interested in that myself. I do my PhD in atomic
electronic structure,
I do things numerically using LAPACK or other libraries, but I would love
to be able to solve simpler physical systems symbolically in sympy.
With Brian, we want to be able to do such things in the sympy.quantum module.

Would you be willing to contribute some example of how you generate
the matrices?

Anyway, if you know the right algorithm for your matrix, I would help
you implement it
in SymPy.

Ondrej

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