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Improving the use of equational constraints in cylindrical algebraic decomposition

2015/01/31 by Matthew England, Russell Bradford, James H. Davenport · 1 citation
Computer Science · #cs.SC #msc:68W30 #msc:03C10 #acm:68W30 #acm:03C10

paper · pdf · doi:10.1145/2755996.2756678

published as Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation (ISSAC '15), pp. 165--172. ACM, 2015

arxiv created 2015/05/07 · arxiv updated 2015/07/20

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.

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