{"paper":{"title":"On Affine Tropical F5 Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Kazuhiro Yokoyama, Thibaut Verron, Tristan Vaccon (XLIM-MATHIS)","submitted_at":"2018-05-16T08:13:25Z","abstract_excerpt":"Let $K$ be a field equipped with a valuation. Tropical varieties over $K$ can be defined with a theory of Gr{\\\"o}bner bases taking into account the valuation of $K$.Because of the use of the valuation, the theory of tropical Gr{\\\"o}bner bases has proved to provide settings for computations over polynomial rings over a $p$-adic field that are more stable than that of classical Gr{\\\"o}bner bases.Beforehand, these strategies were only available for homogeneous polynomials. In this article, we extend the F5 strategy to a new definition of tropical Gr{\\\"o}bner bases in an affine setting.We provide "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06183","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"}