{"paper":{"title":"Matrix-F5 algorithms over finite-precision complete discrete valuation fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Tristan Vaccon (IRMAR)","submitted_at":"2014-03-20T12:37:01Z","abstract_excerpt":"Let $(f\\_1,\\dots, f\\_s) \\in \\mathbb{Q}\\_p [X\\_1,\\dots, X\\_n]^s$ be a sequence of homogeneous polynomials with $p$-adic coefficients. Such system may happen, for example, in arithmetic geometry. Yet, since $\\mathbb{Q}\\_p$ is not an effective field, classical algorithm does not apply.We provide a definition for an approximate Gr{\\\"o}bner basis with respect to a monomial order $w.$ We design a strategy to compute such a basis, when precision is enough and under the assumption that the input sequence is regular and the ideals $\\langle f\\_1,\\dots,f\\_i \\rangle$ are weakly-$w$-ideals. The conjecture "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5464","kind":"arxiv","version":2},"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"}