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        "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>",
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        "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",
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