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Re: [Axiom-developer] Lisp

From: Waldek Hebisch
Subject: Re: [Axiom-developer] Lisp
Date: Wed, 5 Mar 2008 16:14:03 +0100 (CET)

Martin Rubey wrote:
> "Bill Page" <address@hidden> writes:
> > Personally I really wish that that were true, but all of my experience with
> > Axiom over the last few years demonstrates to me that using Axiom is still
> > really rather difficult - too difficult for most people. 
> I don't think that this is the reason. I believe rather the problem is that
> axiom just can't do many things mathematicians want to do.  As a recent
> example, the solver seems to be especially week.  How come that Mathematica
> spits out the solutions to Rainer Gluege's problem without any tricks, while
> axiom cannot do it at all?

I agree to the general statement: there are many problems that Axiom can
not do -- most beginers will probably give up concluding "Axiom is too hard
to use" and not realize that what they want to do in not doable using Axiom.

However, I do not understand statement about Rainer Gluege's problem: can
Mathematica really solve it?  I admit that what Rainer wrote is not entiriely
clear for me, but my understanding is: Rainer has a bunch of conditions.
Ignoring integrality condition we have solution set of dimension 4.  It
should be possible to use Groebner bases to give explicit equations for
this set.  But then we are left with problem of finding integral points
on an algebraic surface.  I would be surprised if Mathematica really can
solve this problem (that is give correct solutions and prove that there are
no others).

                              Waldek Hebisch

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