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Desingularization explains order-degree curves for Ore operators

By Shaoshi Chen, Maximilian Jaroschek, Michael F. Singer and Manuel Kauers


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. Categories and Subject Descriptor

Topics: I.1.2 [Computing Methodologies, Symbolic and Algebraic Manipulation—Algorithms General Terms Algorithms Keywords Ore Operators, Singular Points
Year: 2013
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