fourier_elim does not always return empty set as emptyset



> Does this mean that Maxima is unable to handle arbitrary sets of polynomial inequations?

I'm unaware of a Maxima package for that will handle polynomial inequations.

> Is there software that can handle that?

Yes; see, for example, http://reference.wolfram.com/mathematica/ref/CylindricalDecomposition.html

--Barton