Integral P-Recursive Sequences

论某些 P-递归序列的整性

On the integrality of some P-recursive sequences

本文基于微分代数工具研究 P-recursive 序列的算术性质，提出一种统一方法分析 holonomic 序列的全局有界性与代数性，并开发算法判定二阶递归解的全局有界性，成功应用于 OEIS 中的知名序列。

基于积分基的P-递归序列归约型创造性望远镜法

Reduction-based Creative Telescoping for P-recursive Sequences via Integral Bases

本研究提出一种二元P-递归序列的分解方法，能得到某种意义下最小的不可求和部分，并基于此结合积分基概念构建了新的归约型创造性望远镜算法。

关于P-递归序列的望远镜算子的存在性

On the Existence of Telescopers for P-recursive Sequences

本文将超几何项望远镜算子存在性判据推广至P-递归序列，基于积分基与广义Abramov-Petkovsek约化，给出存在性条件。

Subresultants in Recursive Polynomial Remainder Sequence

We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we calculate "recursively" with new PRS for the GCD and its derivative, until a constant is derived. We call such a PRS a recursive PRS. We define recursive subresultants to be determinants representing the coefficients in recursive PRS by coefficients of initial polynomials. Finally, we discuss usage of recursive subresultants in approximate algebraic computation, w…

Effective Bounds for P-Recursive Sequences

We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq v_n$ for all $n$. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of $u_n$. We discuss applications to the evaluation of power series with guaranteed precision.

Recursive Polynomial Remainder Sequence and its Subresultants

We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," along with investigation of their properties. A recursive PRS is defined as, if there exists the GCD (greatest common divisor) of initial polynomials, a sequence of PRSs calculated "recursively" for the GCD and its derivative until a constant is derived, and recursive subresultants are defined by determinants representing the coefficients in recursive PRS as functions of coefficients of initial polynomials. We give three different constructions of subresultant matrices for recursive subresult…