Comment #15 on issue 2172 by [email protected]: diagonalize method to Matrix
http://code.google.com/p/sympy/issues/detail?id=2172
Yes, but I'll add some reservations to clarify the current situation.
Jordan from is calculated now without appropriated transformation yielding
(in other words it's not implemented now indeed). It is due to the some
reasons. For one method generalization eigenvectors needed (issue 2194).
Also modern methods are exists specially for symbolic computation (division
free and others).
In some there are involved: Frobenius form of matrix, Rational form of
matrix, direct methods for Jordan form, accessory minimal polynomial of
matrix and so on. I investigate some algorithms now to be in system. In
medium priority though.
Also, during the while reviewing of pull
https://github.com/sympy/sympy/pull/115 , some enhancement issued are
shaped.
First of all, it is sorting of eigenvalues in resulted diagonal form. (It
is concerned Jordan form too) (there no mathematical definition what order
is right, just standards are). But it is needed to think, what is the right
way. I think to connect the sorting of eigenvalues with `roots` procedure.
(either directly in this procedure through option of sorting roots kind
which is needed, or with _compare_pretty as it is now, or somehow with more
professional design).
Another enchantment is the rational simplification (see pull 115 too).
I working with it in medium-priority (one may say low), but something from
this can be formed as separate issues, so one can feel free to realize it
independently.
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