TY - GEN

T1 - Contraction of ore ideals with applications

AU - Zhang, Yi

N1 - Publisher Copyright:
© 2016 Copyright held by the owner/author(s).

PY - 2016/7/20

Y1 - 2016/7/20

N2 - 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.

AB - 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.

KW - Contraction

KW - Desingularization

KW - Ore Algebra

KW - Syzygy

UR - http://www.scopus.com/inward/record.url?scp=84984633618&partnerID=8YFLogxK

U2 - 10.1145/2930889.2930890

DO - 10.1145/2930889.2930890

M3 - Conference Proceeding

AN - SCOPUS:84984633618

T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

SP - 413

EP - 420

BT - ISSAC 2016 - Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

A2 - Rosenkranz, Markus

PB - Association for Computing Machinery

T2 - 41st ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2016

Y2 - 20 July 2016 through 22 July 2016

ER -