Computational Algebra and Number Theory pp 243-253 | Cite as

# Recent Progress on Consistency Testing for Polynomial Systems

## 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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