### Abstract

Original language | English |
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Title of host publication | Automated Deduction in Geometry |

Subtitle of host publication | 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers |

Editors | F. Botana, P. Quaresma |

Publisher | Springer |

Pages | 37-52 |

Number of pages | 16 |

ISBN (Print) | 9783319213613 |

DOIs | |

Publication status | Published - 31 Aug 2015 |

Event | 10th International Workshop on Automated Deduction in Geometry (ADG), 2014 - University of Coimbra , Coimbra, Portugal Duration: 9 Jul 2011 → 11 Jul 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9201 |

### Workshop

Workshop | 10th International Workshop on Automated Deduction in Geometry (ADG), 2014 |
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Country | Portugal |

City | Coimbra |

Period | 9/07/11 → 11/07/11 |

### Fingerprint

### Cite this

*Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers*(pp. 37-52). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9201). Springer. https://doi.org/10.1007/978-3-319-21362-0_3

**Recent advances in real geometric reasoning.** / Davenport, James H.; England, Matthew.

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

*Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9201, Springer, pp. 37-52, 10th International Workshop on Automated Deduction in Geometry (ADG), 2014 , Coimbra, Portugal, 9/07/11. https://doi.org/10.1007/978-3-319-21362-0_3

}

TY - CHAP

T1 - Recent advances in real geometric reasoning

AU - Davenport, James H.

AU - England, Matthew

PY - 2015/8/31

Y1 - 2015/8/31

N2 - In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be inherent. We discuss some of the recent major advances in Collins' method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems to do with these polynomials".

AB - In the 1930s Tarski showed that real quantifier elimination was possible, and in 1975 Collins gave a remotely practicable method, albeit with doubly-exponential complexity, which was later shown to be inherent. We discuss some of the recent major advances in Collins' method: such as an alternative approach based on passing via the complexes, and advances which come closer to "solving the question asked" rather than "solving all problems to do with these polynomials".

UR - http://www.scopus.com/inward/record.url?scp=84947235024&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/978-3-319-21362-0_3

U2 - 10.1007/978-3-319-21362-0_3

DO - 10.1007/978-3-319-21362-0_3

M3 - Chapter

SN - 9783319213613

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 37

EP - 52

BT - Automated Deduction in Geometry

A2 - Botana, F.

A2 - Quaresma, P.

PB - Springer

ER -