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

 From: Ralf Hemmecke Subject: [Axiom-math] Re: [Axiom-mail] Solving inequalities Date: Thu, 16 Nov 2006 09:52:26 +0100 User-agent: Thunderbird 1.5.0.8 (X11/20061025)

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'

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.

Actually, I'm not a mathematician and I'm afraid I wouldn't be able to
contribute to it without attending tens of hours of classes on that
topic.  ;-)

The problem is, as Martin has already pointed out, that your problem is undecidable if you do not restrict f to a certain class of functions (like for example polynomial functions). So nobody will be able to write a general solver for your problem.

Could you specify they type of functions more clearly, ie, replace "Expression Integer" to some smaller class of functions?

Ralf