Differential Equations, Spencer Cohomology, and Computing Resolutions

Co-author(s): Larry A. Lambe

Reference: Georgian Mathematical Journal, 9 (2002) 723-772

Description: The Spencer cohomology forms the basis for an intrinsic definition of involutive symbols and thus involutive differential equations. We give a new interpretation of it using the language of coalgebras and comodules, making it a very natural object (a CoTor) and no longer an ad hoc construction. We further discuss algorithms for the explicit determination of minimal resolutions via tools from homological perturbation theory which will in the future be used for algorithmically deciding involution.

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