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

[Ralf Hemmecke]

On 03/30/2013 06:25 PM, Martin Baker wrote:
> On 30/03/13 12:01, Ralf Hemmecke wrote:
>> Unless you specify what solver you intend to write, it's probably an
>> unsolvable task to write a general solver that works for all types of
>> algebras.

> Agreed, but I was thinking more about doing it on a per-domain basis and
> building up gradually.
> 
> So we start with a very simple algebra that we want to create a equation
> solver for, for example we might want to create an algebra domain based
> on this category:
> 
> MyAlgebra() : Category with
>   myOp1 : ($,$) -> $
>   myOp2 : ($) -> $

I don't quite understand. If you assume myOp1 to be commutative, then
solving equations is quite a different task from when it is
non-commutative. Where would you store all these axioms?

If you mean "equations solver" then that includes also solving for (x,y)
in x + y = 0.

Or suppose your algebra is a ring. Do you want to write a solver for

  7*x^5+y^3*x^4+2 = 0

i.e. finding all pairs (x,y) that fulfil this equation?

Looks like you aim at a general term rewriting system.

Ralf