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

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

2001-06-21

arxiv.org/abs/cs/0106046v1

Computer Science

Databases

9 pages

Scientific paper

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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