{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JL5IDQUS2IC6KYKK5SHUMW65X2","short_pith_number":"pith:JL5IDQUS","schema_version":"1.0","canonical_sha256":"4afa81c292d205e5614aec8f465bddbea769c175128d8640e5813902b5362b6b","source":{"kind":"arxiv","id":"1008.3596","version":1},"attestation_state":"computed","paper":{"title":"Exact Bivariate Polynomial Factorization in Q by Approximation of Roots","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.NA","cs.SC"],"primary_cat":"math.AG","authors_text":"Jingzhong Zhang, Wenyuan Wu, Yong Feng","submitted_at":"2010-08-21T03:28:20Z","abstract_excerpt":"Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, we present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. Our method can be directly implemented in efficient programming language such C++ together with t"},"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":"1008.3596","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2010-08-21T03:28:20Z","cross_cats_sorted":["cs.NA","cs.SC"],"title_canon_sha256":"ef5ace6fd315808f936657e37404c1f9bbbe55f5cab9e758ec1a36d91c96f06e","abstract_canon_sha256":"9434bc22c04b940669867d828cb2dc1ab2b48e2c9bcf56aae76f0fdce46ecfe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:55.565200Z","signature_b64":"Wxa7zvuWtgkER775Med7HRjocpROdWSXLNkHHomBgWTip8UFnl+vQkpzE9sg2pLxFHSvFitZ6cpBRVGpX0+XDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4afa81c292d205e5614aec8f465bddbea769c175128d8640e5813902b5362b6b","last_reissued_at":"2026-05-18T04:41:55.564562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:55.564562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Bivariate Polynomial Factorization in Q by Approximation of Roots","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.NA","cs.SC"],"primary_cat":"math.AG","authors_text":"Jingzhong Zhang, Wenyuan Wu, Yong Feng","submitted_at":"2010-08-21T03:28:20Z","abstract_excerpt":"Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not support symbolic computation directly. Hence, it leads to difficulties in applying factorization in engineering fields. In this paper, we present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational coefficients. Our method can be directly implemented in efficient programming language such C++ together with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3596","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.3596","created_at":"2026-05-18T04:41:55.564656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.3596v1","created_at":"2026-05-18T04:41:55.564656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3596","created_at":"2026-05-18T04:41:55.564656+00:00"},{"alias_kind":"pith_short_12","alias_value":"JL5IDQUS2IC6","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JL5IDQUS2IC6KYKK","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JL5IDQUS","created_at":"2026-05-18T12:26:09.077623+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/JL5IDQUS2IC6KYKK5SHUMW65X2","json":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2.json","graph_json":"https://pith.science/api/pith-number/JL5IDQUS2IC6KYKK5SHUMW65X2/graph.json","events_json":"https://pith.science/api/pith-number/JL5IDQUS2IC6KYKK5SHUMW65X2/events.json","paper":"https://pith.science/paper/JL5IDQUS"},"agent_actions":{"view_html":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2","download_json":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2.json","view_paper":"https://pith.science/paper/JL5IDQUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.3596&json=true","fetch_graph":"https://pith.science/api/pith-number/JL5IDQUS2IC6KYKK5SHUMW65X2/graph.json","fetch_events":"https://pith.science/api/pith-number/JL5IDQUS2IC6KYKK5SHUMW65X2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2/action/storage_attestation","attest_author":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2/action/author_attestation","sign_citation":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2/action/citation_signature","submit_replication":"https://pith.science/pith/JL5IDQUS2IC6KYKK5SHUMW65X2/action/replication_record"}},"created_at":"2026-05-18T04:41:55.564656+00:00","updated_at":"2026-05-18T04:41:55.564656+00:00"}