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[Axiom-math] Re: [Axiom-mail] Solving inequalities

From: Martin Rubey
Subject: [Axiom-math] Re: [Axiom-mail] Solving inequalities
Date: 12 Nov 2006 19:56:08 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

address@hidden (Ludovic Courtès) writes:

> Hello,
> I'm trying to solve an inequality of the following form:
>   find all values of x such that f(x) > 1,
>     where f(x) is an `Expression Integer'
> `solve' and `radicalSolve' are apparently not helpful here.  Any idea on
> how to achieve this?

For polynomial f this can be done using "cylindrical algebraic decompositions"
(CADs). Quite a bit of this is actually implemented by Renaud Rioboo, see
AxiomContributions on MathAction. Unfortunately, some pieces are missing in
order to solve inequalities.

If you were able to fill the gaps, this would be really great. The algorithm is
described in Renaud Rioboos thesis. Maybe Renaud could give some instructions
on how to proceed from his packages. Another way to help would be to provide
explanations for Renaud's stuff, although I guess for you it would make more
sense to read up on CAD and provide the missing pieces to make it into a
inequality solver. This would be a really nice thing to have for Axiom!!! Maybe
Renaud would be able to help you there?

By the way: an implementation exists in Mathematica (it's called
InequalitySolve there), and in fact, it was able to prove a theorem for me

> Thanks, and sorry for bothering you,

why exactly should you be sorry? If I wouldn't love to work on axiom/aldor, I
wouldn't do it.


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