Hello,
I noticed that none of the included eigenvalue routines (that I am
aware of at least) work in a reasonable way with bfloat and irrational
numbers.
The problem with 'eigenvectors' seems to be 'algsys'. It is a bit
embarrassing that there are no routines to handle even 2x2 matrices
automatically, since the algebra is at the (maybe junior) high school
level.
Of course, this can be overcome by writing one's own routines for 2x2,
maybe 3x3, and/or 4x4 matrices directly, but I think they should be a
part of the standard maxima tools.
Here are some examples:
Since my command line output always has lines shifted, I will suppress
output, so only the errors show up.
(%i30) build_info();
Maxima version: 5.14.0
Maxima build date: 13:44 2/10/2008
host type: i686-pc-linux-gnu
lisp-implementation-type: CLISP
lisp-implementation-version: 2.41 (2006-10-13) (built on gumbie
[192.168.1.109])
(%o30)
(%i31) A: matrix([sqrt(2),1],[1,1]);
(%i32) eigenvectors(A)$
(%i33)
so this is fine.
Now, look at this:
(%i33) B: matrix([bfloat(sqrt(2)),1],[1,1]);
%i34) eigenvectors(B)$
`rat' replaced 1.414213562373095B0 by 8119/5741 = 1.414213551646055B0
algsys failure: the eigenvector(s) for the 1 th eigenvalue will be missing.
algsys failure: the eigenvector(s) for the 2 th eigenvalue will be missing.
There are no eigenvectors. The eigenvalues are computed, however.
Also, maybe it does not come as a surprise, but the lapack routine
'dgeev' does not work with bfloats.
-sen