Yi Zhang,
"Contraction of Ore Ideals with Applications"
: In Proceedings of the 2016 International Symposium on Symbolic and Algebraic Computation, pages 413-420, ACM Press, 2016., 5-2016
Original Titel:
Contraction of Ore Ideals with Applications
Sprache des Titels:
Englisch
Original Buchtitel:
In Proceedings of the 2016 International Symposium on Symbolic and Algebraic Computation, pages 413-420, ACM Press, 2016.
Original Kurzfassung:
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~$\mathbf{k}(x)$ 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~$\mathbf{k}$ or a domain with~$\mathbf{k}$ 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.