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Re: [Axiom-developer] Am I posing this solve problem wrong?

From: Bill Page
Subject: Re: [Axiom-developer] Am I posing this solve problem wrong?
Date: Mon, 5 May 2008 10:03:05 -0400

On Mon, May 5, 2008 at 3:43 AM, Ralf Hemmecke wrote:
> ...
> Having types, Axiom should actually allow you to specify what you want.
>  R:=MPOLY([C1,D1,y1,x],Integer)
>  P:=MPOLY([y],R)
>  E1: P := x^2*D1^2+(y-y1)^2*C1^2 - C1^2*D1^2
>  solve(E1=0,y)@List(R))
> Unfortunately, that doesn't work (yet), but I would expect it to work in an
> ideal AXIOM.

I do not think this can work exactly like this since the solution
cannot be expressed in R. You need Expression in order to include
kernels involving 'sqrt'. Or did you have something else in mind?

Inspite of that, could you explain a little more about how you think
the ideal AXIOM should work? It seems to me that the way it works now
is rather complex and is a consequence of several interacting factors
such a coercion rules that heuristically start with the most specify
type (i.e. a polynomial type) using coercion to expand the range of
possibilities.  This is affected in a non-trivial and not so easily
predicted manner by the exports exports from the underlying types.
This is built into the Axiom interpreter in a rather deep way. Is
there a different way this could work that might produce less surprise
(and frustration) on the part of the user?

Bill Page.

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