{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:2HEZ3RVEJKYRN6AQUTXA6AD2N7","short_pith_number":"pith:2HEZ3RVE","schema_version":"1.0","canonical_sha256":"d1c99dc6a44ab116f810a4ee0f007a6fd1674d48a384f5a5b808bf711e15a998","source":{"kind":"arxiv","id":"1601.01067","version":2},"attestation_state":"computed","paper":{"title":"A Polynomial-time Algorithm to Compute Generalized Hermite Normal Form of Matrices over Z[x]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.SC","authors_text":"Chun-Ming Yuan, Rui-Juan Jing, Xiao-Shan Gao","submitted_at":"2016-01-06T03:32:37Z","abstract_excerpt":"In this paper, a polynomial-time algorithm is given to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Groebner basis of the Z[x]-module generated by the column vectors of F. The algorithm is also shown to be practically more efficient than existing algorithms. The algorithm is based on three key ingredients. First, an F4 style algorithm to compute the Groebner basis is adopted, where a novel prolongation is designed such that the coefficient matrices under consideration have polynomial sizes. Second, fast algorithms to compute Hermite normal "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1601.01067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-01-06T03:32:37Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"defb5ce2ad1b19abac7318c4096766d070c5e572dc6384b9a3cb81a0bd8806b6","abstract_canon_sha256":"8c0689b94426a92b52b3523b02b1e37a60406b571624f1bf6d2cda0e92dc66ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:42.877771Z","signature_b64":"hiUEeRvoOaXAubeTQ/tAEMjZA6/5Wiwk8H97MClex3k8hX5KLR+UTt5ArZZPtI7R//LZZtyMMuh3oY8AlX8wAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1c99dc6a44ab116f810a4ee0f007a6fd1674d48a384f5a5b808bf711e15a998","last_reissued_at":"2026-05-18T01:10:42.877349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:42.877349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Polynomial-time Algorithm to Compute Generalized Hermite Normal Form of Matrices over Z[x]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.SC","authors_text":"Chun-Ming Yuan, Rui-Juan Jing, Xiao-Shan Gao","submitted_at":"2016-01-06T03:32:37Z","abstract_excerpt":"In this paper, a polynomial-time algorithm is given to compute the generalized Hermite normal form for a matrix F over Z[x], or equivalently, the reduced Groebner basis of the Z[x]-module generated by the column vectors of F. The algorithm is also shown to be practically more efficient than existing algorithms. The algorithm is based on three key ingredients. First, an F4 style algorithm to compute the Groebner basis is adopted, where a novel prolongation is designed such that the coefficient matrices under consideration have polynomial sizes. Second, fast algorithms to compute Hermite normal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01067","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.01067","created_at":"2026-05-18T01:10:42.877413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01067v2","created_at":"2026-05-18T01:10:42.877413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01067","created_at":"2026-05-18T01:10:42.877413+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HEZ3RVEJKYR","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HEZ3RVEJKYRN6AQ","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HEZ3RVE","created_at":"2026-05-18T12:29:55.572404+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7","json":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7.json","graph_json":"https://pith.science/api/pith-number/2HEZ3RVEJKYRN6AQUTXA6AD2N7/graph.json","events_json":"https://pith.science/api/pith-number/2HEZ3RVEJKYRN6AQUTXA6AD2N7/events.json","paper":"https://pith.science/paper/2HEZ3RVE"},"agent_actions":{"view_html":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7","download_json":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7.json","view_paper":"https://pith.science/paper/2HEZ3RVE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01067&json=true","fetch_graph":"https://pith.science/api/pith-number/2HEZ3RVEJKYRN6AQUTXA6AD2N7/graph.json","fetch_events":"https://pith.science/api/pith-number/2HEZ3RVEJKYRN6AQUTXA6AD2N7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7/action/storage_attestation","attest_author":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7/action/author_attestation","sign_citation":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7/action/citation_signature","submit_replication":"https://pith.science/pith/2HEZ3RVEJKYRN6AQUTXA6AD2N7/action/replication_record"}},"created_at":"2026-05-18T01:10:42.877413+00:00","updated_at":"2026-05-18T01:10:42.877413+00:00"}