Experience with Heuristics, Benchmarks & Standards for Cylindrical Algebraic Decomposition

TL;DR

This paper shares experiences with heuristics, standards, and benchmarks in Cylindrical Algebraic Decomposition, aiming to enhance symbolic computation by adopting strategies from satisfiability checking community.

Contribution

It introduces heuristics developed for Cylindrical Algebraic Decomposition and advocates for standards and benchmarks to improve symbolic computation practices.

Findings

Heuristics from satisfiability checking can benefit symbolic computation.

Standards and benchmarks are crucial for advancing the field.

Cross-community learning enhances algorithm development.

Abstract

In the paper which inspired the SC-Square project, [E. Abraham, Building Bridges between Symbolic Computation and Satisfiability Checking, Proc. ISSAC '15, pp. 1-6, ACM, 2015] the author identified the use of sophisticated heuristics as a technique that the Satisfiability Checking community excels in and from which it is likely the Symbolic Computation community could learn and prosper. To start this learning process we summarise our experience with heuristic development for the computer algebra algorithm Cylindrical Algebraic Decomposition. We also propose and discuss standards and benchmarks as another area where Symbolic Computation could prosper from Satisfiability Checking expertise, noting that these have been identified as initial actions for the new SC-Square community in the CSA project, as described in [E.~Abraham et al., SC$^2$: Satisfiability Checking meets Symbolic Computation (Project Paper)}, Intelligent Computer Mathematics (LNCS 9761), pp. 28--43, Springer, 2015].