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Re: [Axiom-developer] Cylindrical Algebraic Decomposition added

From: Renaud Rioboo
Subject: Re: [Axiom-developer] Cylindrical Algebraic Decomposition added
Date: Wed, 10 Sep 2014 08:35:46 +0200


> Well, since Tim (and actually me too) want to see the description of the
> algorithm, it would be rather interesting if you could point out which
> paper(s) you used when you implemented CAD in AXIOM.
> Nowadays, it's certainly not hard to find a good description about CAD,
> but what is most interesting, is what paper(s) *you* followed when
> implementing it. That would make this particular implementation easier
> to understand/maintain.

Well, that is a hard question since it's been almost 25 years... As far
as I remember I had the papers of Arnon, Collins and Mc Callum, the book
by Davenport, Siret and Tournier, the book by Buchberger, Collins and
Loos. There was no web by the time.

Furthermore I had a colleague working with the SAC2 implementation of
quantifier elimination and benefited from numerous discussions with
Michel Coste, Marie Fran├žoise Roy and Jean Jacques Risler.

But I am not sure I ever understood CAD, the package produces lists of
cells :-)

All the best

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