1996/11/19 by Francesca Acquistapace, F. Acquistapace, Carlos Andradas +6
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Polynomial and algebraic computation #alg-geom #math.AG #msc:14P
paper · pdf · doi:10.48550/arxiv.alg-geom/9611023
postscript only, 29 pages with figures
arxiv created 1996/11/19 · arxiv updated 2009/11/30
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.