English

Desingularization Explains Order-Degree Curves for Ore Operators

Symbolic Computation 2013-01-08 v1

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)(r,d)-plane such that for all points (r,d)(r,d) above this curve, there exists a left multiple of order rr and degree dd 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.

Cite

@article{arxiv.1301.0917,
  title  = {Desingularization Explains Order-Degree Curves for Ore Operators},
  author = {Shaoshi Chen and Maximilian Jaroschek and Manuel Kauers and Michael F. Singer},
  journal= {arXiv preprint arXiv:1301.0917},
  year   = {2013}
}
R2 v1 2026-06-21T23:04:23.877Z