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arXiv · 1301.0917

Desingularization Explains Order-Degree Curves for Ore Operators

Shaoshi Chen·Maximilian Jaroschek·Manuel Kauers·Michael F. Singer
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Abstract

Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-degree curve for a given Ore operator is a curve in the $(r,d)$-plane such that for all points $(r,d)$ above this curve, there exists a left multiple of order $r$ and degree $d$ of the given operator. We give a new proof of a desingularization result by Abramov and van Hoeij for the shift case, and show how desingularization implies order-degree curves which are extremely accurate in examples.

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Shaoshi Chen, Maximilian Jaroschek, Manuel Kauers, Michael F. Singer. 2013-01-05. Desingularization Explains Order-Degree Curves for Ore Operators. https://arxiv.org/abs/1301.0917

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