Separation of Semialgebraic Sets

Details Separation of Semialgebraic Sets Separation of Semialgebraic Sets

1996-11-19

arxiv.org/abs/alg-geom/9611023v1

Mathematics

Algebraic Geometry

postscript only, 29 pages with figures

Scientific paper

In this paper we study the problem of deciding whether two disjoint semialgebraic sets of an algebraic variety over R are separable by a polynomial. For that we isolate a dense subfamily of Spaces of Orderings, named Geometric, which suffice to test separation and that reduce the problem to the study of the behaviour of the semialgebraic sets in their boundary. Then we derive several characterizations for the generic separation, among which there is a Geometric Criterion that can be tested algorithmically. Finally we show how to check recursively whether we can pass from the generic separation to the separation of the two sets, yielding a decision procedure to solve the problem.

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