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Computer Science > Symbolic Computation

arXiv:1805.10136 (cs)
[Submitted on 24 May 2018]

Title:Towards Incremental Cylindrical Algebraic Decomposition in Maple

Authors:Alexander Imani Cowen-Rivers, Matthew England
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Abstract:Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation community and has found recent interest in the Satisfiability Checking community. The present report describes a proof of concept implementation of an Incremental CAD algorithm in Maple, where CADs are built and then refined as additional polynomial constraints are added. The aim is to make CAD suitable for use as a theory solver for SMT tools who search for solutions by continually reformulating logical formula and querying whether a logical solution is admissible. We describe experiments for the proof of concept, which clearly display the computational advantages compared to iterated re-computation. In addition, the project implemented this work under the recently verified Lazard projection scheme (with corresponding Lazard valuation).
Comments: FLoC 2018. arXiv admin note: substantial text overlap with arXiv:1804.08564
Subjects: Symbolic Computation (cs.SC); Computational Geometry (cs.CG); Algebraic Geometry (math.AG)
Cite as: arXiv:1805.10136 [cs.SC]
  (or arXiv:1805.10136v1 [cs.SC] for this version)
  https://doi.org/10.48550/arXiv.1805.10136
Journal reference: In: A. Bigatti and M. Brain eds. Proceedings of the 3rd Workshop on Satisfiability Checking and Symbolic Computation (SC2 '18), pp. 3-18. CEUR Workshop Proceedings 2189, 2018

Submission history

From: Alexander Cowen-Rivers [view email]
[v1] Thu, 24 May 2018 10:57:18 UTC (724 KB)
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