Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices
An analogue of the Euclidean algorithm for square matrices of size $2$ with integral non-negative entries and positive determinant $n$ defines a finite set $\mathcal{R}(n)$ of Euclid-reduced matrices corresponding to elements of $\lbrace (a,b,c,d)\in \mathbb{N}^4\ \vert \ n=ab-cd,\ 0\le c,d
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-07-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.451/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206215948369920 |
|---|---|
| author | Bacher, Roland |
| author_facet | Bacher, Roland |
| author_sort | Bacher, Roland |
| collection | DOAJ |
| description | An analogue of the Euclidean algorithm for square matrices of size $2$ with integral non-negative entries and positive determinant $n$ defines a finite set $\mathcal{R}(n)$ of Euclid-reduced matrices corresponding to elements of $\lbrace (a,b,c,d)\in \mathbb{N}^4\ \vert \ n=ab-cd,\ 0\le c,d |
| format | Article |
| id | doaj-art-2892ad5ff7b94c7487572549d5aec865 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-2892ad5ff7b94c7487572549d5aec8652025-02-07T11:08:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-07-01361G588989510.5802/crmath.45110.5802/crmath.451Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ MatricesBacher, Roland0Univ. Grenoble Alpes, Institut Fourier, 38000 Grenoble, FranceAn analogue of the Euclidean algorithm for square matrices of size $2$ with integral non-negative entries and positive determinant $n$ defines a finite set $\mathcal{R}(n)$ of Euclid-reduced matrices corresponding to elements of $\lbrace (a,b,c,d)\in \mathbb{N}^4\ \vert \ n=ab-cd,\ 0\le c,dhttps://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.451/ |
| spellingShingle | Bacher, Roland Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices Comptes Rendus. Mathématique |
| title | Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices |
| title_full | Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices |
| title_fullStr | Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices |
| title_full_unstemmed | Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices |
| title_short | Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices |
| title_sort | euclid meets popeye the euclidean algorithm for 2 times 2 matrices |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.451/ |
| work_keys_str_mv | AT bacherroland euclidmeetspopeyetheeuclideanalgorithmfor2times2matrices |