Effective Bounds for P-Recursive Sequences

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。

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。

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…

Integral P-Recursive Sequences

In an earlier paper, the notion of integrality known from algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive sequences. In order to do so, we formulate a general algorithm for finding all integral elements for valued vector spaces and then show that this algorithm includes not only the algebraic and the D-finite cases but also covers the case of P-recursive sequences.

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…

Recursive Polynomial Remainder Sequence and the Nested Subresultants

We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the size of the subresultant matrix drastically compared with the recursive subresultant proposed by the authors before, hence it is much more useful for investigation of the recursive PRS. Finally, we discuss usage of the reduced nested subresultant in approximate algebraic computation, which motivates the present work.