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#3243 eigenvectors() extremely slow to output an unusable answer
Not unrelated to bugs:#3239.
build_info(version="5.38.1",timestamp="2016-11-01 13:12:23",host=
"x86_64-pc-linux-gnu",lisp_name="GNU Common Lisp (GCL)",lisp_version="GCL 2.6.12")
Given :
Mx:matrix([1,0,0],[0,cos(theta),-sin(theta)],[0,sin(theta),cos(theta)]);
My:matrix([cos(phi),0,-sin(phi)],[0,1,0],[sin(phi),0,cos(phi)]);
The following :
~~~
eigenvectors(My.Mx);
~~~
1. Needs about 10 minutes, to
2. output tens of pages of trig giberrish.
According to a bit of research in Sage's Maxima (5.35.1, ECL), this is not the same as a recently fixed bug in eigenvalues(). See bugs:#3239's discussion.
When I try the example with a current build (post-5.46, tried it with SBCL and with GCL), I get the 10 pages of gibberish, but it only take about 10 seconds.
I didn't try to verify the gibberish output, but if it's only messy, then that's okay. Maybe someone can try to verify the output.
I also got a result in 2.5 secs (Maxima 5.45.1 SBCL 2.0.0).
Is there any reason to believe that the result is incorrect? In general, the eigenvalues of a symbolic 3x3 matrix involve the solutions of a cubic polynomial, which are usually messy.