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Recent Progress on Consistency Testing for Polynomial Systems

  • Scott McCallum
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 325)

Abstract

We survey recent progress on determining consistency over the real numbers of a system of integral polynomial equations and inequalities. We briefly state some recent results on the computational complexity of this problem. We describe how the cylindrical algebraic decomposition (cad) algorithm [2] can be used to solve this problem. We describe improvements to the efficiency of the cad-based approach to the consistency problem, some being applicable also to cad-based approaches to more general quantifier elimination problems. We present a version of the cad algorithm which solves the consistency problem for conjunctions of strict inequalities, and which runs faster than the original method applied to this problem.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Scott McCallum
    • 1
  1. 1.Department of Computing School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversitySydneyAustralia

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