Hi,
having worked with some CA systems I want to add that
not only the collection of algorithms is important but also the
data base of algebraic objects.
For instance the group theoretic package Magma (formerly Caley) comes
with as much information on finite groups as the the libraries of algorithms.
This data base represents condensed information from hundrets of papers
and an incredible large amount of computation.
> 1. A huge, huge library of algorithms. Rewriting Maple is a horrendal
> task. Making some toy system with limited functionality is aimless.
One option would be interfacing or translating a FPL into the CA system.
For instance Axion uses an own language (strongly typed, very powerful)
which is translated into lisp, than to C, assembler and finally machine language
(at least these are the steps done on IBM mainframes).
I could imagine that a second front end, Haskell could translated in compatible
Lisp code easily. This would allow using the libraries (data base and
algorithms) of Axiom.
I once wrote an interface between Magma and a theorem prover.
Andreas
