Projects per year

### Abstract

Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of variables in the worst case, but the actual computation time can vary greatly. It is possible to offer different formulations for a given problem leading to great differences in tractability. In this paper we suggest a new measure for CAD complexity which takes into account the real geometry of the problem. This leads to new heuristics for choosing the variable ordering for a CAD problem, choosing a designated equational constraint and choosing clause formulation for truth-table invariant CADs (TTICADs). We then consider the possibility of using Groebner bases to precondition TTICAD and when such formulations constitute the creation of a new problem.

Original language | English |
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Title of host publication | Intelligent Computer Mathematics |

Subtitle of host publication | MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings |

Editors | Jacques Carette, David Aspinall, Christoph Lange, Petr Sojka, Wolfgang Windsteiger |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 19-34 |

Number of pages | 15 |

ISBN (Electronic) | 9783642393204 |

ISBN (Print) | 9783642393198 |

DOIs | |

Publication status | Published - 2013 |

Event | Conferences on Intelligent Computer Mathematics: CICM 2013 - Bath, UK United Kingdom Duration: 7 Jul 2013 → 11 Jul 2013 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 7961 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | Conferences on Intelligent Computer Mathematics: CICM 2013 |
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Country | UK United Kingdom |

City | Bath |

Period | 7/07/13 → 11/07/13 |

### Keywords

- cylindrical algebraic decomposition
- Groebner bases
- problem formulation
- symbolic computation
- equational constraint

## Fingerprint Dive into the research topics of 'Optimising problem formulation for cylindrical algebraic 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

Bradford, R., Davenport, J. H., England, M., & Wilson, D. (2013). Optimising problem formulation for cylindrical algebraic decomposition. In J. Carette, D. Aspinall, C. Lange, P. Sojka, & W. Windsteiger (Eds.),

*Intelligent Computer Mathematics: MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings*(pp. 19-34). (Lecture Notes in Computer Science; Vol. 7961). Springer. https://doi.org/10.1007/978-3-642-39320-4_2