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A differential form $ \omega$ is a section of the exterior algebra $\Lambda^* T^* X$ of a cotangent bundle,
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Differential ideals of Pfaffian forms on jet bundles (Integrability)
(I asked this question on math.stackexchange, but got no reaction in several weeks. So, my conclusion is, that it is harder to answer than I thought, and maybe admissible for the attribute 'research l …