Towards Incremental Cylindrical Algebraic Decomposition in Maple

Alexander Cowen-Rivers; Matthew England

Towards Incremental Cylindrical Algebraic Decomposition in Maple

Alexander Cowen-Rivers, Matthew England

School of Computing, Electronics and Maths

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding

1 Citation (Scopus)

14 Downloads (Pure)

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).

Original language	English
Title of host publication	Proceedings of the 3rd International Workshop on Satisfiability Checking and Symbolic Computation
Subtitle of host publication	SC-Square 2018
Publisher	CEUR Workshop Proceedings
Pages	3-18
Number of pages	16
Volume	2189
Publication status	Published - 1 Sep 2018
Event	3rd International Workshop on Satisfiability Checking and Symbolic Computation - University of Oxford, Oxford, United Kingdom Duration: 11 Jul 2018 → 11 Jul 2018 Conference number: 3 http://www.sc-square.org/CSA/workshop3.html

Workshop

Workshop	3rd International Workshop on Satisfiability Checking and Symbolic Computation
Abbreviated title	SC-Square 2018
Country	United Kingdom
City	Oxford
Period	11/07/18 → 11/07/18
Internet address	http://www.sc-square.org/CSA/workshop3.html

Bibliographical note

CEUR Workshop Proceedings (CEUR-WS.org) is a free open-access publication service at Sun SITE Central Europe operated under the umbrella of RWTH Aachen University. CEUR-WS.org is a recognized ISSN publication series, ISSN 1613-0073.

Access to Document

PublishedFinal published version, 1.17 MBLicence: CC BY

http://ceur-ws.org/Vol-2189/

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Cite this

Cowen-Rivers, A., & England, M. (2018). Towards Incremental Cylindrical Algebraic Decomposition in Maple. In Proceedings of the 3rd International Workshop on Satisfiability Checking and Symbolic Computation: SC-Square 2018 (Vol. 2189, pp. 3-18). CEUR Workshop Proceedings.

Cowen-Rivers, A & England, M 2018, Towards Incremental Cylindrical Algebraic Decomposition in Maple. in Proceedings of the 3rd International Workshop on Satisfiability Checking and Symbolic Computation: SC-Square 2018. vol. 2189, CEUR Workshop Proceedings, pp. 3-18, 3rd International Workshop on Satisfiability Checking and Symbolic Computation, Oxford, United Kingdom, 11/07/18.

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