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arXiv · 0811.1367

Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring

D. Grigoriev
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Abstract

We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to $D$-modules having infinite-dimensional space of solutions (i. e. non-holonomic $D$-modules). As applications we design algorithms for treating first-order factors of a linear partial differential operator, in particular for finding all (right or left) first-order factors.

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D. Grigoriev. 2008-11-09. Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring. https://arxiv.org/abs/0811.1367

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