Expressing the cone radius in the relational calculus with real polynomial constraints
<|reference_start|>Expressing the cone radius in the relational calculus with real polynomial constraints: 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.<|reference_end|>
@article{geerts2001expressing,
    title={Expressing the cone radius in the relational calculus with real
  polynomial constraints},
    author={Floris Geerts},
    journal={arXiv preprint arXiv:cs/0106046},
    year={2001},
    archivePrefix={arXiv},
    eprint={cs/0106046},
    primaryClass={cs.DB cs.LO}
}