Conrad Schiff wrote:
> I hope that this helps and I hope ?might be able to contribute to Maxima.
>
>
> Thanks,
> Conrad
Let me throw some ideas about things i have been interested in recently
related to maxima.
Something which has been discussed several times here and could be worked on
is adding the ability to do integrals resulting in elliptic functions. Code in
partially working state has been shown in the mailing list by Prof. Fateman
and R. Toy, if i remember well. The mathematics of this game are completely
straightforward, very easily accesssible, and i suppose it is a good problem
to learn the maxima insides.
Another subject which is more related to numerical analysis is to investigate
if one could devise something systematic to directly compile the Fortran
programs used in maxima (lapack, etc.) and link them into maxima. Apparently
this is somewhat lisp specific, but it seems that most free systems use
sbcl nowadays, so this should be a good starting point. The problem is that
the conversion of fortran to lisp followed by lisp compilation produces poor
performance, and one gets better experience with scientific python, for
example.
On the same theme, all these fortran programs are very old and assume that
"double precision" is the ultimate end of scientific computation precision.
However in many computations nowadays, double precision is dramatically
insufficient. Fortunately maxima has "big floats" so that computations
entirely done in maxima can bypass the precision problems. But this rules away
all the converted fortran code. For example you can diagonalize big matrices
with the help of the fortran routines, but the result is essentially random,
however it is obtained rapidly. If the matrix is symmetric you can use
eigens_by_jacobi, written in lisp, which i think supports bigfloats, and
get correct results but at great length of time. Finally a well known
algorithm which is not implemented at all in maxima for the computation of
eigenvalues of big matrices is Arnoldi with restart. The Fortran program is
available.
Another approach to these questions is to export the computation to external
programs in fortran or C. To this aim there exists the program gentran
in share/contrib. It was broken in modern maxima, but it has been partially
repaired recently. I think it still needs work, for example i think the
conversion to fortran works but the conversion to C doesn't. It should be
rather easy to locate the correction which have been applied to the fortran
producing code, and do the same in the C producing code. The problem is that
gentran is written in some old dialect of lisp which needs to be modernized.
Then it would be nice and useful to play a bit with gentran and produce some
good documentation.
--
Michel Talon