Abstract
It is proved that for a system of linear partial differential equations with polynomial coefficients, the Gröbner basis in the Weyl algebra is sufficient for the computation of the characteristic variety. In particular, this yields a correct algorithm of computing the singular locus of a holonomic system with polynomial coefficients. The characteristic variety is defined analytically, i.e. by using the ring of power series, and it has not been obvious that it can be computed by purely algebraic procedure. Thus the algorithm of computing the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients can be readily implemented on a computer algebra system.
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Oaku, T. Computation of the characteristic variety and the singular locus of a system of differential equations with polynomial coefficients. Japan J. Indust. Appl. Math. 11, 485–497 (1994). https://doi.org/10.1007/BF03167233
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DOI: https://doi.org/10.1007/BF03167233