An analogue of the Euclidean algorithm for square matrices of size with integral non-negative entries and positive determinant defines a finite set of Euclid-reduced matrices corresponding to elements of . With Popeye’s help (acknowledged by his appearance in the title; he refused co-authorship on the flimsy pretext of a weak contribution due to a poor spinach-harvest) on the use of sails of lattices we show that contains elements.
Accepted:
Revised after acceptance:
Published online:
Roland Bacher 1
@article{CRMATH_2023__361_G5_889_0, author = {Roland Bacher}, title = {Euclid meets {Popeye:} {The} {Euclidean} {Algorithm} for $2\times 2$ {Matrices}}, journal = {Comptes Rendus. Math\'ematique}, pages = {889--895}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.451}, language = {en}, }
Roland Bacher. Euclid meets Popeye: The Euclidean Algorithm for $2\times 2$ Matrices. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 889-895. doi : 10.5802/crmath.451. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.451/
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