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 in every small enough box. We obtain this result by combining results from differential topology and real algebraic geometry, with recent algorithmic results by Rannou.
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Geerts, F. Expressing the box cone radius in the relational calculus with real polynomial constraints. Discrete Comput Geom 30, 607–622 (2003). https://doi.org/10.1007/s00454-003-0770-2
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DOI: https://doi.org/10.1007/s00454-003-0770-2