### Abstract

Original language | English |
---|---|

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 |
---|---|

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 |
---|---|

Abbreviated title | CICM 2012 |

Country | Germany |

City | Bremen |

Period | 8/07/12 → 13/07/12 |

### Fingerprint

### Keywords

- Groebner basis
- Cylindrical Algebraic Decomposition

### Cite this

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

**Speeding up cylindrical algebraic decomposition by Gröebner Bases.** / Wilson, David J; Bradford, Russell J; Davenport, James H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Intelligent Computer Mathematics.*vol. 7362, Lecture Notes in Computer Science, vol. 7362, Heidelberg, pp. 280-294, 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, 8/07/12. https://doi.org/10.1007/978-3-642-31374-5_19

}

TY - GEN

T1 - Speeding up cylindrical algebraic decomposition by Gröebner Bases

AU - Wilson, David J

AU - Bradford, Russell J

AU - Davenport, James H

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Groebner basis

KW - Cylindrical Algebraic Decomposition

UR - http://www.scopus.com/inward/record.url?scp=84864958030&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/978-3-642-31374-5_19

U2 - 10.1007/978-3-642-31374-5_19

DO - 10.1007/978-3-642-31374-5_19

M3 - Conference contribution

SN - 9783642313738

VL - 7362

T3 - Lecture Notes in Computer Science

SP - 280

EP - 294

BT - Intelligent Computer Mathematics

A2 - Jeuring, Johan

A2 - Campbell, John A

A2 - Carette, Jacques

A2 - Dos Reis, Gabriel

A2 - Sojka, Petr

A2 - Wenzel, Makarius

A2 - Sorge, Volker

CY - Heidelberg

ER -