Hi,

I would like to discuss how to improve calculus in SAGE.

I know, that currently, most of the developers need other things more
urgently, but I think calculus will be the most frequently used part
in SAGE. For example all my friends and colleagues cannot really use
SAGE at the moment, because it cannot yet compete with Mathematica in
calculus. I would like this to be changed.

Ways to progress that come to my mind:

1) Expose as much Maxima functionality as possible (one example is
substitution of other things besides symbols).
2) It's important to allow users to create their own functions and the
calculus package should be able to work with them. Maybe it will by
possible to hack the Maxima interface even more to allow this somehow.

However, I think that in the long run, the main engine of calculus
should be in Python + Cython (maybe also in C/C++), not in LISP.
Because that will allow SAGE to extend it with new features and make
it play nicely with the rest of SAGE.

So my idea is to

3) Integrate SymPy and make it play nicely with the rest of SAGE. I
made a some progress on SD6, will send patches soon, together with a
new release of SymPy, but more work needs to be done.

Unfortunately, 3) will not solve all problems, at least not for now,
because first, there are still much more bugs in SymPy than in Maxima
(this should improve in time), and second, SymPy is slower (this could
be handled by Cython, or rewriting some parts to C/C++).


So I think the best way is to do 1), 2) and 3) in parallel and see. Is
there any other approach that I missed?

I would like to clear this out, so that I am working on something that
makes sense and is good for SAGE.

Ondrej

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