Recent advances in real geometric reasoning

James H. Davenport; Matthew England

doi:10.1007/978-3-319-21362-0_3

Recent advances in real geometric reasoning

James H. Davenport, Matthew England

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

2 Citations (SciVal)

145 Downloads (Pure)

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".

Original language	English
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	https://doi.org/10.1007/978-3-319-21362-0_3
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)
Volume	9201

Workshop

Workshop	10th International Workshop on Automated Deduction in Geometry (ADG), 2014
Country/Territory	Portugal
City	Coimbra
Period	9/07/11 → 11/07/11

Access to Document

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

DE15Submitted manuscript, 485 KBLicence: CC BY-NC-ND

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 or section in a book/report/conference proceeding › Chapter or section

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)). doi: 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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Recent advances in real geometric reasoning

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Real Geometry and Connectedness via Triangular Description

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Recent advances in real geometric reasoning

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Real Geometry and Connectedness via Triangular Description

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