Contraction of ore ideals with applications

Yi Zhang*

*Corresponding author for this work

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Abstract

Ore operators form a common algebraic abstraction of linear ordinary differential and recurrence equations. Given an Ore operator L with polynomial coefficients in x, it generates a left ideal I in the Ore algebra over the field k(x) of rational functions. We present an algorithm for computing a basis of the contraction ideal of I in the Ore algebra over the ring R[x] of polynomials, where R may be either k or a domain with k as its fraction field. This algorithm is based on recent work on desingularization for Ore operators by Chen, Jaroschek, Kauers and Singer. Using a basis of the contraction ideal, we compute a completely desingularized operator for L whose leading coefficient not only has minimal degree in x but also has minimal content. Completely desingularized operators have interesting applications such as certifying integer sequences and checking special cases of a conjecture of Krattenthaler.

Original languageEnglish
Title of host publicationISSAC 2016 - Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation
EditorsMarkus Rosenkranz
PublisherAssociation for Computing Machinery
Pages413-420
Number of pages8
ISBN (Electronic)9781450343800
DOIs
Publication statusPublished - 20 Jul 2016
Externally publishedYes
Event41st ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2016 - Waterloo, Canada
Duration: 20 Jul 201622 Jul 2016

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
Volume20-22-July-2016

Conference

Conference41st ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2016
Country/TerritoryCanada
CityWaterloo
Period20/07/1622/07/16

Keywords

  • Contraction
  • Desingularization
  • Ore Algebra
  • Syzygy

Cite this

Zhang, Y. (2016). Contraction of ore ideals with applications. In M. Rosenkranz (Ed.), ISSAC 2016 - Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation (pp. 413-420). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC; Vol. 20-22-July-2016). Association for Computing Machinery. https://doi.org/10.1145/2930889.2930890