Let's say I have two sets $S_1,S_2 \subseteq \mathbb{R}^n$ each defined by a number of polynomial inequalities. Is there a computationally feasible way to find whether $S_1 = S_2$? In particular, is there software available that will test this? I don't need a provably correct algorithm - a probabilistic/empirical test would be fine. If $S_1 \neq S_2$ I would like to be able to produce a specific counterexample.
2026-03-25 04:39:37.1774413577
Determining equality of sets defined by polynomial inequalities in several variables
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I think one should be able to do this using Cylindrical Algebraic Decomposition (CAD). You can find an introduction in "Algorithms in real algebraic geometry" by Basu, Pollack and Roy. This algorithm is also implemented in Mathematica.