{"paper":{"title":"On modular computation of Groebner bases with integer coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"S. Yu. Orevkov","submitted_at":"2013-12-22T02:35:07Z","abstract_excerpt":"Let $I_1\\subset I_2\\subset\\dots$ be an increasing sequence of ideals of the ring $\\Bbb Z[X]$, $X=(x_1,\\dots,x_n)$ and let $I$ be their union. We propose an algorithm to compute the Gr\\\"obner base of $I$ under the assumption that the Gr\\\"obner bases of the ideal $\\Bbb Q I$ of the ring $\\Bbb Q[X]$ and the the ideals $I\\otimes(\\Bbb Z/m\\Bbb Z)$ of the rings $(\\Bbb Z/m\\Bbb Z)[X]$ are known.\n  Such an algorithmic problem arises, for example, in the construction of Markov and semi-Markov traces on cubic Hecke algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6331","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1312.6331/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}