[图书][B] Handbook of geometric constraint systems principles
M Sitharam, AS John, J Sidman - 2018 - taylorfrancis.com
The Handbook of Geometric Constraint Systems Principles is an entry point to the currently
used principal mathematical and computational tools and techniques of the geometric …
used principal mathematical and computational tools and techniques of the geometric …
Computer-assisted theorem proving in synthetic geometry
Computer-assisted theorem proving in synthetic geometry Page 56 Chapter 2 Computer-Assisted
Theorem Proving in Synthetic Geometry Julien Narboux University of Strasbourg Predrag …
Theorem Proving in Synthetic Geometry Julien Narboux University of Strasbourg Predrag …
Formalization of the Poincaré disc model of hyperbolic geometry
We describe formalization of the Poincaré disc model of hyperbolic geometry within the
Isabelle/HOL proof assistant. The model is defined within the complex projective line CP^ 1 …
Isabelle/HOL proof assistant. The model is defined within the complex projective line CP^ 1 …
On the formalization of foundations of geometry
P Boutry - 2018 - theses.hal.science
In this thesis, we investigate how a proof assistant can be used to study the foundations of
geometry. We start by focusing on ways to axiomatize Euclidean geometry and their …
geometry. We start by focusing on ways to axiomatize Euclidean geometry and their …
Multi-scale arithmetization of linear transformations
L Mazo - Journal of Mathematical Imaging and Vision, 2019 - Springer
A constructive nonstandard interpretation of a multiscale affine transformation scheme is
presented. It is based on the Ω Ω-numbers of Laugwitz and Schmieden and on the discrete …
presented. It is based on the Ω Ω-numbers of Laugwitz and Schmieden and on the discrete …
Transferring arithmetic decision procedures (on Z) to alternative representations
N Magaud - CoqPL 2017: The Third International Workshop on …, 2017 - inria.hal.science
We propose a generic approach to make arithmetic decision procedures designed for the
concrete data-type Z of Coq available for alternative representations of integers. It is based …
concrete data-type Z of Coq available for alternative representations of integers. It is based …
Some representations of real numbers using integer sequences
L Mazo, MA Da Col-Jacob, L Fuchs… - … Structures in Computer …, 2022 - cambridge.org
The paper describes three models of the real field based on subsets of the integer
sequences. The three models are compared to the Harthong–Reeb line. Two of the new …
sequences. The three models are compared to the Harthong–Reeb line. Two of the new …
Non-standard Analysis in Projective Geometry
M Strobel - 2018 - mediatum.ub.tum.de
In this thesis we will integrate concepts of non-standard analysis into projective geometry.
Especially, we will analyze the properties of a projective space over a non-Archimedean …
Especially, we will analyze the properties of a projective space over a non-Archimedean …
Contributions au développement des méthodes formelles de preuves et applications à la géométrie
N Magaud - 2020 - hal.science
L'utilisation des assistants de preuve comme Coq prend de plus en plus d'ampleur. De tels
outils permettent de démontrer formellement aussi bien des résultats mathématiques que …
outils permettent de démontrer formellement aussi bien des résultats mathématiques que …
[PDF][PDF] Proving and Computing with the Harthong-Reeb line using Ω-integers
In TYPES 2011, we presented a formal description of the Harthong-Reeb line based on
axiomatic non-standard integers (intuitively they correspond to Z where we introduce a-new …
axiomatic non-standard integers (intuitively they correspond to Z where we introduce a-new …