Solving Algebraic Inequalities
Adam Strzeboński · The Mathematica Journal · 2000
We study the problem of solving, possibly quantified, systems of real algebraic equations and inequalities. We propose a way of representing solution sets in a computer algebra system and present an algorithm for computing the representation. We also discuss specialized algorithms for solving several important special cases, including finding “generic solutions”, deciding existence of solutions, global optimization of algebraic functions subject to algebraic constraints, and solving linear equation and inequality systems. Finally, we give some examples and present results of some experiments with our implementation of the algorithms within Mathematica.