Dear Michael,

just a short recap, whether I have understood things correctly:

   the problem you currently face with external symbolic calculus is that the
   representation of the objects is not identical in SAGE and in the external
   progam (Maxima).

   you are using something called "pexpect" which does the parsing.

I do not see how the problem of differing representations can be resolved.  Up
to now I thought that Sage simply doesn't have an "internal" representation,
and just uses the one from the external program - that's how my polymake
interface for FriCAS/Axiom works.

If this is correct and if Sage insists on having an internal representation,
then it probably only makes sense to have external programs for "large" jobs,
where the time spent in parsing is not an issue.  Either, because the result is
not processed much further anyway, or because obtaining the result is much more
costly than the parsing.

Thus, the obvious candidates for using FriCAS are integration (it beats the
commercial CAS in the elementary case, by the way) and related stuff like
solving ODE's, and guessing (ditto).

Please correct me, if I'm wrong.

-------------------------------------------------------------------------------

Apart from that, I would like to clarify a point, that might become a
misunderstanding otherwise:

FriCAS (as far as I can control it) has a pragmatic approach what concerns the
"target language" of it's compiler and the language it's interpreter is written
in.  Currently, it's lisp, because that works, works well, seems to be
reasonably fast and works on many platforms, including MS Windows.  FriCAS
builds on quite a few lisps, sbcl seems to be fastest.

HOWEVER: FriCAS has (almost) no mathematics written in lisp, not even for
bootstrapping.  We use bignums, arrays, floats, strings, symbols from lisp, but
that's about it.

The goals of FriCAS and open-axiom are quite similar, as far as I can tell.  I
truly hope that the collaboration of the two will continue.

-------------------------------------------------------------------------------

Finally, concerning lisp: is it correct that Sage would not mind (for the
moment) a default lisp, that builds the Sage way, but would use a "better
suited" lisp, if available and installed on the target machine?  (in fact,
that's how FriCAS and, as far as I know, open-axiom work currently, anyway.)

Martin


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