Improving the use of equational constraints in cylindrical algebraic decomposition

Matthew England, R. Bradford, J.H. Davenport

Research output: Contribution to conferencePaper

19 Citations (Scopus)
19 Downloads (Pure)

Abstract

When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs, propagating those in the input throughout the projection set. We improve on the approach of McCallum in ISSAC 2001 by using the reduced projection theory to make savings in the lifting phase (both to the polynomials we lift with and the cells lifted over). We demonstrate the benefits with worked examples and a complexity analysis.
Original languageEnglish
Pages165-172
DOIs
Publication statusPublished - 2015
Event40th International Symposium on Symbolic and Algebraic Computation (ISSAC) - The University of Bath, Bath, United Kingdom
Duration: 6 Jul 20159 Jul 2015

Conference

Conference40th International Symposium on Symbolic and Algebraic Computation (ISSAC)
CountryUnited Kingdom
CityBath
Period6/07/159/07/15

Keywords

  • cylindrical algebraic decomposition
  • equational constraint

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    England, M., Bradford, R., & Davenport, J. H. (2015). Improving the use of equational constraints in cylindrical algebraic decomposition. 165-172. Paper presented at 40th International Symposium on Symbolic and Algebraic Computation (ISSAC), Bath, United Kingdom. https://doi.org/10.1145/2755996.2756678