{"paper":{"title":"An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Shinichi Tajima, Takafumi Shibuta","submitted_at":"2017-10-04T01:40:43Z","abstract_excerpt":"In this paper, we present an algorithm for computing the minimal reductions of $\\mathfrak{m}$-primary ideals of Cohen--Macaulay local rings. Using this algorithm, we are able to compute the Hilbert--Samuel multiplicities and solve the membership problem for the integral closure of $\\mathfrak{m}$-primary ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01435","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"}