Re: [Axiom-mail] A question about Axiom capabilities, Fwd: [fricas-devel] Abstract Vector Algebra

[Ralf Hemmecke]

On 04/05/2013 10:51 AM, Martin Baker wrote:
> It seems a sight irony that Axiom(the program) does not do much about
> axioms.

Of course, AXIOM can deal with axioms, but the SPAD language does not
include any way to specify axiom (not even Aldor can do this).

>> Looks like you aim at a general term rewriting system.

> Yes, but again I recognise that there are no resources, so I was 
> wondering if it would be possible to start with a very simple domain 

For a term rewriting system you basically have to start with the
implementation of a term algebra. The signature would basically tell,
what symbols are allowed. Since LISP is so fitting for a representation
of such a term algebra, it is no surprise that quite a lot of computer
algebra systems were written in LISP.

Then you can add equations (axioms) and a mechanism to reduce a given
term modulo such equations. But there is no general algorithm to
transform a given term modulo such equation into a canonical form. A
"canonical form" does not even exist for every given term rewriting
system. The non-existence of the "eierlegende Wollmilchsau"
(http://de.wikipedia.org/wiki/Eierlegende_Wollmilchsau
http://en.wiktionary.org/wiki/eierlegende_Wollmilchsau) is the reason
why people work on specialized solvers and use special representations
of the respective term algebra to make things fast.

Ralf