Výsledky vyhledávání - "Pascal Schreck"

Two New Ways to Formally Prove Dandelin-Gallucci's Theorem

Autor: Nicolas Magaud, Pascal Schreck, David Braun

Publikováno v: ISSAC 2021 : International Symposium on Symbolic and Algebraic Computation
ISSAC 2021 : International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint Petersburg (virtual event), Russia. ⟨10.1145/3452143.3465550⟩
ISSAC

International audience; Mechanizing proofs of geometric theorems in 3D is significantly more challenging than in 2D. As a first noteworthy case study, we consider an iconic theorem of 3D geometry: Dandelin-Gallucci's theorem. We work in the very simp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6024b6558d6b643d56ad6ce933f572c6
https://hal.archives-ouvertes.fr/hal-03225987/file/paper-issac-21.pdf

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On the Mechanization of Straightedge and Compass Constructions

Autor: Pascal Schreck

Publikováno v: Journal of Systems Science and Complexity. 32:124-149

The geometric constructions obtained with only straightedge and compass are famous and play a special role in the development of geometry. On the one hand, the constructibility of figures is a key ingredient in Euclid geometry and, on the other hand,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::484c1604c3c4766c3afdd339c5de6a57
https://doi.org/10.1007/s11424-019-8347-1

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Two cryptomorphic formalizations of projective incidence geometry

Autor: Pascal Schreck, David Braun, Nicolas Magaud

Publikováno v: Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence, Springer Verlag, In press
Annals of Mathematics and Artificial Intelligence, In press

International audience; Incidence geometry is a well-established theory which captures the very basic properties of all geometries in terms of points belonging to lines, planes, etc. Moreover, projective incidence geometry leads to a simple framework

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ed657f135f5a7a05d96df73bf16abaf
https://doi.org/10.1007/s10472-018-9604-z

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Parallel postulates and continuity axioms: a mechanized study in intuitionistic logic using Coq

Autor: Charly Gries, Pascal Schreck, Pierre Boutry, Julien Narboux

Publikováno v: Journal of Automated Reasoning
Journal of Automated Reasoning, Springer Verlag, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
Journal of Automated Reasoning, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩

online first; International audience; In this paper we focus on the formalization of the proofs of equivalence between different versions of Euclid's 5 th postulate. Our study is performed in the context of Tarski's neutral geometry, or equivalently

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5295cfedebbea0e5f43a1d51340f29ca
https://hal.inria.fr/hal-01178236v2/document

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Automatic Constructibility Checking of a Corpus of Geometric Construction Problems

Autor: Pascal Schreck, Pascal Mathis

Publikováno v: Mathematics in Computer Science. 10:41-56

Straightedge and compass constructions play a special role in geometry. First, for a very long time, they were used in practice by land surveyors or architects in order to solve concrete problems. Second, they are an inexhaustible source of exercises

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::bab457f616d3ad6fd89b7bb6f678cfec
https://doi.org/10.1007/s11786-016-0247-3

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Constructibility Classes for Triangle Location Problems

Autor: Vesna Marinković, Predrag Janičić, Pascal Schreck

Publikováno v: Mathematics in Computer Science. 10:27-39

Straightedge-and-compass construction problems are well known for different reasons. One of them is the difficulty to prove that a problem is not constructible: it took about two millennia to prove that it is not possible in general to cut an angle i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::580483dd660b59eb3af99d70021c2a70
https://doi.org/10.1007/s11786-016-0255-3

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Formalizing Some ' Small ' Finite Models of Projective Geometry in Coq

Autor: Nicolas Magaud, Pascal Schreck, David Braun

Publikováno v: Proceedings of the 13th International Conference on Artificial Intelligence and Symbolic Computation (AISC'2018)
Proceedings of the 13th International Conference on Artificial Intelligence and Symbolic Computation (AISC'2018), Sep 2018, Suzhou, China
Artificial Intelligence and Symbolic Computation
13th International Conference Artificial Intelligence and Symbolic Computation ( AISC 2018 )
13th International Conference Artificial Intelligence and Symbolic Computation ( AISC 2018 ), Sep 2018, Suzhou, China. ⟨10.1007/978-3-319-99957-9⟩
Artificial Intelligence and Symbolic Computation ISBN: 9783319999562
AISC

International audience; We study two different descriptions of incidence projective geometry: a synthetic, mathematics-oriented one and a more practical, computation-oriented one, based on the combinatorial concept of rank of a set of points. Using b

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8cfbc80c470cea233921a4f8b17c47ff
https://hal.archives-ouvertes.fr/hal-01835493/file/bms.pdf

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Determining automatically compass and straightedge unconstructibility in triangles

Autor: Pascal Mathis, Pascal Schreck

Publikováno v: SCSS

In many areas, some geometry problems can not be solved using only geometry and are treated by the means of algebraic tools. However, geometric properties can be still employed to simplify the system of equations. This allows either to speed up the t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c9b4242219082e783dda495ecad9f94c
https://doi.org/10.29007/b28w

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