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Separation of semialgebraic sets


Acquistapace, Francesca and Andradas Heranz, Carlos and Broglia, Fabrizio (1999) Separation of semialgebraic sets. Journal of the American Mathematical Society, 12 (3). pp. 703-728. ISSN 0894-0347

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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 generic separation to separation,
obtaining a decision procedure for solving the problem.

Item Type:Article
Uncontrolled Keywords:decidability of separation problem of semialgebraic sets; algorithm
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:14799

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Deposited On:18 Apr 2012 08:32
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