Recent advances in real geometric reasoning

James H. Davenport, Matthew England

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

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".
LanguageEnglish
Title of host publicationAutomated Deduction in Geometry
Subtitle of host publication10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers
EditorsF. Botana, P. Quaresma
PublisherSpringer
Pages37-52
Number of pages16
ISBN (Print)9783319213613
DOIs
StatusPublished - 31 Aug 2015
Event10th International Workshop on Automated Deduction in Geometry (ADG), 2014 - University of Coimbra , Coimbra, Portugal
Duration: 9 Jul 201111 Jul 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9201

Workshop

Workshop10th International Workshop on Automated Deduction in Geometry (ADG), 2014
CountryPortugal
CityCoimbra
Period9/07/1111/07/11

Fingerprint

Polynomials

Cite this

Davenport, J. H., & England, M. (2015). Recent advances in real geometric reasoning. In F. Botana, & P. Quaresma (Eds.), 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.

Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers. ed. / F. Botana; P. Quaresma. Springer, 2015. p. 37-52 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9201).

Research output: Chapter in Book/Report/Conference proceedingChapter

Davenport, JH & England, M 2015, Recent advances in real geometric reasoning. in F Botana & P Quaresma (eds), 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
Davenport JH, England M. Recent advances in real geometric reasoning. In Botana F, Quaresma P, editors, Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers. Springer. 2015. p. 37-52. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-21362-0_3
Davenport, James H. ; England, Matthew. / Recent advances in real geometric reasoning. Automated Deduction in Geometry: 10th International Workshop, ADG 2014, Coimbra, Portugal, July 9-11, 2014, Revised Selected Papers. editor / F. Botana ; P. Quaresma. Springer, 2015. pp. 37-52 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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