{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VGBVUAFL5HRVGAWJ5S6EKSYT5Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4343e570043c573fb6d32b04f3dde17154f2ff671e91b9a2d0d45f1ea9948389","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-16T10:20:19Z","title_canon_sha256":"454eeb2048c6b09eaa0681d0a0f6c7f6029f55e21be2f140b4317e37e42addd7"},"schema_version":"1.0","source":{"id":"1201.3198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3198","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3198v1","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3198","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"VGBVUAFL5HRV","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VGBVUAFL5HRVGAWJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VGBVUAFL","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1d6b277621535a1c2038a6cce9d19b47ef80e4643456554b42aa310a91a9d9ff","target":"graph","created_at":"2026-05-18T01:17:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present an algorithm to compute the annihilator of (i.e., the linear differential equations for) the logarithm of a polynomial in the ring of differential operators with polynomial coefficients. The algorithm consists of differentiation with respect to the parameter s of the annihilator of f^s for a polynomial f and quotient computation. More generally, the annihilator of f^s(log f)^m for a complex number s and a positive integer m can be computed, which constitutes what is called a holonomic system in D-module theory. This enables us to compute a holonomic system for the integral of a func","authors_text":"Toshinori Oaku","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-16T10:20:19Z","title":"An algorithm to compute the differential equations for the logarithm of a polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3198","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b619753690d631c99e97bf8306a3b2701923337d0de1633ddf82ddd8ccf99594","target":"record","created_at":"2026-05-18T01:17:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4343e570043c573fb6d32b04f3dde17154f2ff671e91b9a2d0d45f1ea9948389","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-16T10:20:19Z","title_canon_sha256":"454eeb2048c6b09eaa0681d0a0f6c7f6029f55e21be2f140b4317e37e42addd7"},"schema_version":"1.0","source":{"id":"1201.3198","kind":"arxiv","version":1}},"canonical_sha256":"a9835a00abe9e35302c9ecbc454b13ec0fef5b4477577bd55e2b28bd8bfe00de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9835a00abe9e35302c9ecbc454b13ec0fef5b4477577bd55e2b28bd8bfe00de","first_computed_at":"2026-05-18T01:17:53.646239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.646239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uZLZRfuL+s0mEP2x5zp2cUGZTL/f4nIkH4G0NfPW+rtBap+N701QZ0rbyud1x385Mt9X+pPYpBgH1q1YBySVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.646949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b619753690d631c99e97bf8306a3b2701923337d0de1633ddf82ddd8ccf99594","sha256:1d6b277621535a1c2038a6cce9d19b47ef80e4643456554b42aa310a91a9d9ff"],"state_sha256":"7c6c278d6715392a64f6fba3abdf9debdea8b2b8c746b9ba0e6cb21f90232bd5"}