Re: Steps towards writing a computer algebra system

parisse_at_domain.invalid
Date: 01/19/05 

Date: Wed, 19 Jan 2005 08:06:49 +0100

Richard J. Fateman wrote:
> These books would definitely not tell you how to write
> a computer algebra system.
>

I would rather say that they describe some mathematical
algorithms. Then you must add data structures to hold symbolics,
implement long integers and polynomials, a parser and write a (G)UI.

> They have some interesting material, but a careful reading
> of some of these will give you reliably bad advice on
> what makes sense to include in an actual program.
>
> In fact it might make an interesting chart to fill out
>
> recommendations implemented by
> as "best" algorithm Macsyma/Reduce/Mma/Maple/NTL/GiNAC/.
>
>
> Then we would have to admit that most of the "optimal" algorithms
> are not used by some of the most intensively developed systems.
>
> Because they are not useful enough (slow on practical sizes, not general
> enough) and sometimes difficult to write out in full detail and debug.
>

I agree. For example, an algorithm on symbolic matrices
that is faster for e.g. N>1000, is likely not to be implemented...