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

[Ralf Hemmecke]

> > > 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.
>
> (Sorry for the late reply.)
>
> 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