{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:8c5e05bd-6774-4afe-aae0-27aa273bad37",
  "labels": {
    "zh-CN": "普法夫方程组",
    "en": "Pfaffian system"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "7a0bf4df57f57cb5f9fd7627e739e7d87b0158c8d4800824be60d713ed184dc6",
  "occurrences": [
    {
      "concept_id": "urn:uuid:8c5e05bd-6774-4afe-aae0-27aa273bad37",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-16/03-frobenius-theorem-dual-form",
      "anchor": "first-8d5abeaa322326ce650d-zh",
      "chapter": "16",
      "section": "16.3",
      "offset": 7073,
      "range": [
        10900,
        11142
      ],
      "source_revision": "cdfe45869ae5f7e8e68239781754b9128a5f357949874a0e171bb7cab3177c78",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "普法夫方程组(Pfaffian system)",
      "context": {
        "range": [
          10382,
          11142
        ],
        "quote": "开集$U _ { \\textrm { \\scriptsize : } }$上线性无关的一组1-形式$\\omega ^ { 1 } , \\ldots , \\omega ^ { r }$，若满足本定理的条件$( \\mathrm { i } ) { - } ( \\mathrm { v } )$中的任意一条，则称其为<u class=\"concept-term\" data-concept-identity=\"urn:uuid:e710238e-7313-48c6-806b-126872e4579a\" data-concept-route=\"/concept-identities#concept-e710238e-7313-48c6-806b-126872e4579a\" id=\"first-43695f3536ee91f7379b-zh\">完全可积的(completely integrable)</u>。消去这些$\\omega ^ { a }$的分布$D ^ { k } \\left( k = n - r \\right)$由方程$\\langle \\omega ^ { a } , X \\rangle = 0$给出，通常写成一个方程组的<u class=\"concept-term\" data-concept-identity=\"urn:uuid:8c5e05bd-6774-4afe-aae0-27aa273bad37\" data-concept-route=\"/concept-identities#concept-8c5e05bd-6774-4afe-aae0-27aa273bad37\" id=\"first-8d5abeaa322326ce650d-zh\">普法夫方程组(Pfaffian system)</u>",
        "quote_sha256": "8c89e39e41c247dfec4af7ed0f180903d56ea006381edcf37208b7bffbf5f141",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-16/03-frobenius-theorem-dual-form",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-6952e95d0da3f2b339bc397a"
    },
    {
      "concept_id": "urn:uuid:8c5e05bd-6774-4afe-aae0-27aa273bad37",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-16/03-frobenius-theorem-dual-form",
      "anchor": "first-8d5abeaa322326ce650d-en",
      "chapter": "16",
      "section": "16.3",
      "offset": 9125,
      "range": [
        12473,
        12707
      ],
      "source_revision": "ec0904a49c35a99336fd665b2d0f0b3a671e5d9768c37f2a27deafb3c2ec7566",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "Pfaffian system",
      "context": {
        "range": [
          11781,
          12720
        ],
        "quote": "A system of linearly independent 1-forms $\\omega ^ { 1 } , \\ldots , \\omega ^ { r }$ on an open set $U _ { \\textrm { \\scriptsize : } }$ , satisfying any of the conditions $( \\mathrm { i } ) { - } ( \\mathrm { v } )$ of this theorem is said to be <u class=\"concept-term\" data-concept-identity=\"urn:uuid:e710238e-7313-48c6-806b-126872e4579a\" data-concept-route=\"/concept-identities#concept-e710238e-7313-48c6-806b-126872e4579a\" id=\"first-43695f3536ee91f7379b-en\">completely integrable</u> . The equations defining the distribution $D ^ { k } \\left( k = n - r \\right)$ that annihilates these $\\omega ^ { a }$ is given by the equations $\\langle \\omega ^ { a } , X \\rangle = 0$ , often written as a <u class=\"concept-term\" data-concept-identity=\"urn:uuid:8c5e05bd-6774-4afe-aae0-27aa273bad37\" data-concept-route=\"/concept-identities#concept-8c5e05bd-6774-4afe-aae0-27aa273bad37\" id=\"first-8d5abeaa322326ce650d-en\">Pfaffian system</u> of equations",
        "quote_sha256": "679f8a3db1e9c4ee64c6d0efa360c31fdc710016802aafcdf7a27605ba3b2348",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-16/03-frobenius-theorem-dual-form",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-3a67da8fa77d419382223afc"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-16/03-frobenius-theorem-dual-form",
      "lang": "en",
      "section": "16.3",
      "signal": "term-mark",
      "label": "Pfaffian system",
      "english": "Pfaffian system",
      "offset": 8863
    },
    {
      "route": "zh/chapter-16/03-frobenius-theorem-dual-form",
      "lang": "zh-CN",
      "section": "16.3",
      "signal": "term-mark",
      "label": "普法夫方程组",
      "english": "Pfaffian system",
      "offset": 6811
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-6952e95d0da3f2b339bc397a",
    "occ-3a67da8fa77d419382223afc"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "9a04243ebc69ab5f1f8ef0540a7d6837dbef7f12a5cf847c747617bf7b5ff377",
  "optional_enrichments": []
}