Re: Axiom or Maxima?

Martin Rubey wrote:
....

I'm afraid, a direct comparison Maxima vs FriCAS is rather difficult,
since they are very different systems. One of the very big differences
is -- as I understand them -- that Maxima is essentially untyped (i.e.,
it is probably difficult to distinguish between 0 the polynomial and 0
the integer, or, put differently, there are very few types, namely:
expressions, matrices, probably polynomials),

yes, although there are different ways of storing 0, e.g. as a taylor series, a polynomial, or an expression, the expression 0 itself is generally not tagged with information that might indicate that it is (say) an element in a finite field {0,1,2,3,4} of size 5 or ...

whereas in FriCAS
maintains a rather huge hierarchy of types, and functions producing
types: "Polynomial" is a function that takes an argument of type "Ring",
which could be Integer, Float, Matrix Integer, PrimeField 1783, etc.

This has potential advantages. Most users of systems like Mathematica do not know the difference between a finite field and a corn field, and so the advantages are somewhat muted in practice.

.....


2) SPAD/Aldor is geared towards mapping mathematical dependencies, as
indicated with the function "Polynomial" above. Very likeyl one
could do that in lisp, too, but sometimes a framework (for "bad"
programmers) can be very helpful.

Initial work on SPAD predated the refinement of the common lisp object system design. which might be a suitable framework. There has been at least one attempt to do the "right thing" more specifically in CLOS (by Rich Zippel when he was at Cornell), but it was not funded. So whether one could/should write a new CAS in Lisp using CLOS has not been examined fully. (I've defined a package for "more generic" arithmetic that pushes that envelope a bit.)


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