{"paper":{"title":"$3$-dimensional Continued Fraction Algorithms Cheat Sheets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.DS","authors_text":"S\\'ebastien Labb\\'e","submitted_at":"2015-11-26T14:34:50Z","abstract_excerpt":"Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\\mathbb{R}^d$. We consider multidimensional continued fraction algorithms that acts symmetrically on the positive cone $\\mathbb{R}^d_+$ for $d=3$. We include well-known and old ones (Poincar\\'e, Brun, Selmer, Fully Subtractive) and new ones (Arnoux-Rauzy-Poincar\\'e, Reverse, Cassaigne).\n  For each algorithm, one page (called cheat sheet) gathers a handful of informations most of them generated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08399","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}