Contraction of Ore Ideals with Applications
Contraction of Ore Ideals with Applications
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矿石理想的收缩与应用
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Yi Zhang
中科院分区：
文献类型：
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作者：
Yi Zhang
矿石运营商形成一个共同的代数抽象的线性常微分方程和递归方程。给定一个在x中具有多项式系数的Ore算子L，它在有理函数域k（x）上的Ore代数中生成一个左理想I。给出了多项式环R[x]上Ore代数I的压缩理想的基的一个算法，其中R可以是k或以k为分式域的整环.该算法是基于陈，Jaroschek，Kauers和Singer最近的工作对Ore算子去奇异化。利用压缩理想的一个基，我们计算了L的一个完全去奇异化算子，它的导系数不仅在x中具有最小度，而且具有最小内容。完全去奇异化算子在证明整数序列和检验Krattenthaler猜想的特殊情况等方面有着有趣的应用。
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.