Recent advances in real geometric reasoning

J. Davenport; Matthew England

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

Recent advances in real geometric reasoning

J. Davenport, Matthew England

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2 Citations (Scopus)

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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
Pages	37-52
DOIs	https://doi.org/10.1007/978-3-319-21362-0_3
Publication status	Published - 2015

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-21362-0_3.

Keywords

computing
geometric reasoning

Access to Document

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

Post-PrintAccepted author manuscript, 541 KBLicence: CC BY

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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”. ",

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PY - 2015

Y1 - 2015

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”.

KW - computing

KW - geometric reasoning

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

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

M3 - Paper

SP - 37

EP - 52

ER -

Recent advances in real geometric reasoning

Abstract

Bibliographical note

Keywords

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Cite this