Projects per year

### Abstract

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm.

Original language | English |
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Title of host publication | Mathematical Software – ICMS 2014 |

Subtitle of host publication | 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings |

Publisher | Springer |

Pages | 450-457 |

Number of pages | 8 |

Volume | 8592 |

ISBN (Print) | 978-3-662-44198-5 |

DOIs | |

Publication status | Published - 2014 |

## Fingerprint Dive into the research topics of 'Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Real Geometry and Connectedness via Triangular Description

Davenport, J., Bradford, R., England, M. & Wilson, D.

Engineering and Physical Sciences Research Council

1/10/11 → 31/12/15

Project: Research council

## Cite this

England, M., Bradford, R. J., Davenport, J. H., & Wilson, D. (2014). Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition. In

*Mathematical Software – ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings*(Vol. 8592, pp. 450-457). Springer. https://doi.org/10.1007/978-3-662-44199-2_68