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Expressing the cone radius in the relational calculus with real polynomial constraints

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Abstract:

We show that there is a query expressible in first-order logic over the reals that returns, on any given semi-algebraic set A, for every point a radius around which A is conical. We obtain this result by combining famous results from calculus and real algebraic geometry, notably Sard's theorem and Thom's first isotopy lemma, with recent algorithmic results by Rannou.

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