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

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.
 >
 > Ralf

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 : ($) -> $

Then create an expression holder that is specific to that algebra:

MyAlgebraExpression() : Exports == Implementation where
   Implementation == add
   Rep := Union(_
          literalTerm : MyAlgebra, _
          variableTerm : Symbol, _
          myOp1Term : Record(left: $, right: $), _
          myOp2Term : $_
          )
   bind : (Symbol,MyAlgebra,$) -> $
   canonicalForm : $ -> $
   decomposeMyOp1 : $ -> ($,$)
   decomposeMyOp2 : $ -> ($)

Then create an equation solver that is also specific to that algebra:

MyAlgebraEquation() : Exports == Implementation where
   Implementation == add
   Rep := Record(left: MyAlgebraExpression, right: MyAlgebraExpression)
   solveFor : (Symbol,$) -> MyAlgebraExpression

This would require 3 domains for every algebra that we wanted to be able 
to solve but why not have some separate common rule interpreter code. So 
MyAlgebraEquation domain would consist mostly of a set of substitution 
rules for that particular algebra?

Martin