I think that some of the suggestions here pretty much miss the mark.

If you want to have Maxima do the same thing as Mathematica's Reduce
program
(and, by the way I think this would be good, especially since
Mathematica's Reduce
program seems to have been improved substantially so it is a store-
house of neat things, in current Mma), then you should write a program
that implements Reduce. Probably most easily done by adding to the
Maxima code.

Patching together something that answers questions from Maxima, either
in
python, pexpect, or for that matter, lisp, doesn't seem to me to be as
worthwhile.

As for the CAD (cylindrical algebraic decomposition) stuff,  Reduce
has gone far beyond that.  Having a program that does only CAD is not
very useful in the general world of "solve" unless you are only
interested in polynomials  and in particular, CAD.
So no trig, log, exp, etc.

Implementing CAD and a good geometry data-base for assume, and writing
a version of Reduce for Maxima and/or Sage -- sure. Someone should go
ahead and design it in detail. Write a nice paper about it, perhaps.
Then decide how to implement it, in Python/Sage or "Maxima language"
or Lisp.  One nice thing about the latter two choices is that it would
improve "standalone" Maxima too.




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