Computation with semialgebraic sets represented by cylindrical algebraic formulas

Authors:
Adam Strzeboński
Affiliations:
Wolfram Research Inc., Champaign, IL
Venue:
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Year:
2010

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Abstract

Cylindrical algebraic formulas are an explicit representation of semialgebraic sets as finite unions of cylindrically arranged disjoint cells bounded by graphs of algebraic functions. We present a version of the Cylindrical Algebraic Decomposition (CAD) algorithm customized for efficient computation of arbitrary combinations of unions, intersections and complements of semialgebraic sets given in this representation. The algorithm can also be used to eliminate quantifiers from Boolean combinations of cylindrical algebraic formulas. We show application examples and an empirical comparison with direct CAD computation for unions and intersections of semialgebraic sets.