{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QA4FD2UW5HXD2XJACNLJOKIGXB","short_pith_number":"pith:QA4FD2UW","schema_version":"1.0","canonical_sha256":"803851ea96e9ee3d5d201356972906b842107f211f4a4b7441c2ab3b11d995a6","source":{"kind":"arxiv","id":"1109.4323","version":1},"attestation_state":"computed","paper":{"title":"On the complexity of computing with zero-dimensional triangular sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Adrien Poteaux, \\'Eric Schost","submitted_at":"2011-09-20T15:34:04Z","abstract_excerpt":"We study the complexity of some fundamental operations for triangular sets in dimension zero. Using Las-Vegas algorithms, we prove that one can perform such operations as change of order, equiprojectable decomposition, or quasi-inverse computation with a cost that is essentially that of modular composition. Over an abstract field, this leads to a subquadratic cost (with respect to the degree of the underlying algebraic set). Over a finite field, in a boolean RAM model, we obtain a quasi-linear running time using Kedlaya and Umans' algorithm for modular composition. Conversely, we also show how"},"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":"1109.4323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2011-09-20T15:34:04Z","cross_cats_sorted":[],"title_canon_sha256":"d324dd3aaabbbb17bb6d40c90cd77104a80735f809e8cc7729f00e1fab9e5def","abstract_canon_sha256":"059f8df1847c62779092b2e50a9858084732de167bfcd29e9733aa507d8cfbd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:43.552728Z","signature_b64":"azag6dT5Uotp1IySWMx3gJFvTZhcSTKE94YqnjEquvhCIALmmodY6sJv0k5ukP0eJre99lFa9WHixf8csRWyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"803851ea96e9ee3d5d201356972906b842107f211f4a4b7441c2ab3b11d995a6","last_reissued_at":"2026-05-18T04:12:43.552056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:43.552056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the complexity of computing with zero-dimensional triangular sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Adrien Poteaux, \\'Eric Schost","submitted_at":"2011-09-20T15:34:04Z","abstract_excerpt":"We study the complexity of some fundamental operations for triangular sets in dimension zero. Using Las-Vegas algorithms, we prove that one can perform such operations as change of order, equiprojectable decomposition, or quasi-inverse computation with a cost that is essentially that of modular composition. Over an abstract field, this leads to a subquadratic cost (with respect to the degree of the underlying algebraic set). Over a finite field, in a boolean RAM model, we obtain a quasi-linear running time using Kedlaya and Umans' algorithm for modular composition. Conversely, we also show how"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4323","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":"1109.4323","created_at":"2026-05-18T04:12:43.552152+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4323v1","created_at":"2026-05-18T04:12:43.552152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4323","created_at":"2026-05-18T04:12:43.552152+00:00"},{"alias_kind":"pith_short_12","alias_value":"QA4FD2UW5HXD","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QA4FD2UW5HXD2XJA","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QA4FD2UW","created_at":"2026-05-18T12:26:39.201973+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/QA4FD2UW5HXD2XJACNLJOKIGXB","json":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB.json","graph_json":"https://pith.science/api/pith-number/QA4FD2UW5HXD2XJACNLJOKIGXB/graph.json","events_json":"https://pith.science/api/pith-number/QA4FD2UW5HXD2XJACNLJOKIGXB/events.json","paper":"https://pith.science/paper/QA4FD2UW"},"agent_actions":{"view_html":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB","download_json":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB.json","view_paper":"https://pith.science/paper/QA4FD2UW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4323&json=true","fetch_graph":"https://pith.science/api/pith-number/QA4FD2UW5HXD2XJACNLJOKIGXB/graph.json","fetch_events":"https://pith.science/api/pith-number/QA4FD2UW5HXD2XJACNLJOKIGXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB/action/storage_attestation","attest_author":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB/action/author_attestation","sign_citation":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB/action/citation_signature","submit_replication":"https://pith.science/pith/QA4FD2UW5HXD2XJACNLJOKIGXB/action/replication_record"}},"created_at":"2026-05-18T04:12:43.552152+00:00","updated_at":"2026-05-18T04:12:43.552152+00:00"}