An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

Changbo Chen; Marc Moreno Maza

An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions

Symbolic Computation 2012-10-23 v1

Authors: Changbo Chen , Marc Moreno Maza

Abstract

In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real space. The incrementality comes from the first part of the algorithm, where a complex cylindrical tree is constructed by refining a previous complex cylindrical tree with a polynomial constraint. We have implemented our algorithm in Maple. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.

Keywords

computer algebra matrix multiplication decision tree

Cite

@article{arxiv.1210.5543,
  title  = {An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions},
  author = {Changbo Chen and Marc Moreno Maza},
  journal= {arXiv preprint arXiv:1210.5543},
  year   = {2012}
}

Related papers

View all related →