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 |
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| 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 Sept 2018 |
| Event | Third International Workshop on Satisfiability Checking and Symbolic Computation 2018 - University of Oxford, Oxford, United Kingdom Duration: 7 Jul 2018 → 9 Jul 2018 Conference number: 3 http://www.sc-square.org/CSA/workshop3.html |
Conference
| Conference | Third International Workshop on Satisfiability Checking and Symbolic Computation 2018 |
|---|---|
| Abbreviated title | SC 2018 |
| Country/Territory | United Kingdom |
| City | Oxford |
| Period | 7/07/18 → 9/07/18 |
| Internet address |