Projects per year

### Abstract

Gröebner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a mixed system of equalities and inequalities, it is possible to apply Gröebner basesto the (conjoined) equalities before invoking CAD. We see that this is,
quite often but not always, a beneficial preconditioning of the CAD problem.
It is also possible to precondition the (conjoined) inequalities with respect to the equalities, and this can also be useful in many cases.

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

Editors | Johan Jeuring, John A Campbell, Jacques Carette, Gabriel Dos Reis, Petr Sojka, Makarius Wenzel, Volker Sorge |

Place of Publication | Heidelberg |

Pages | 280-294 |

Number of pages | 15 |

Volume | 7362 |

ISBN (Electronic) | 9783642313745 |

DOIs | |

Publication status | Published - 2012 |

Event | 11th International Conference, AISC 2012, 19th Symposium, Calculemus 2012, 5th International Workshop, DML 2012, 11th International Conference, MKM 2012, Systems and Projects, held as part of CICM 2012 - Bremen, Germany Duration: 8 Jul 2012 → 13 Jul 2012 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 7362 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 11th International Conference, AISC 2012, 19th Symposium, Calculemus 2012, 5th International Workshop, DML 2012, 11th International Conference, MKM 2012, Systems and Projects, held as part of CICM 2012 |
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Abbreviated title | CICM 2012 |

Country | Germany |

City | Bremen |

Period | 8/07/12 → 13/07/12 |

### Keywords

- Groebner basis
- Cylindrical Algebraic Decomposition

## Fingerprint Dive into the research topics of 'Speeding up cylindrical algebraic decomposition by Gröebner Bases'. 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

## Datasets

### Real Geometry and Connectedness via Triangular Description: CAD Example Bank

Wilson, D. (Creator), University of Bath, Apr 2012

DOI: 10.15125/BATH-00069, http://www.cs.bath.ac.uk/~djw42/triangular/examplebank.html

Dataset

## Cite this

Wilson, D. J., Bradford, R. J., & Davenport, J. H. (2012). Speeding up cylindrical algebraic decomposition by Gröebner Bases. In J. Jeuring, J. A. Campbell, J. Carette, G. Dos Reis, P. Sojka, M. Wenzel, & V. Sorge (Eds.),

*Intelligent Computer Mathematics*(Vol. 7362, pp. 280-294). (Lecture Notes in Computer Science; Vol. 7362).. https://doi.org/10.1007/978-3-642-31374-5_19