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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McCallum, S. (1995). Recent Progress on Consistency Testing for Polynomial Systems. In: Bosma, W., van der Poorten, A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1108-1_17
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DOI: https://doi.org/10.1007/978-94-017-1108-1_17
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