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- Ziming Li
- ISSAC
- 1998

The subresultant theory for univariate commutative polynomials is generalized to Ore polynomials. The generalization includes: the subresultant theorem, gap structure, and subresultant algorithm. Using this generalization, we de ne Sylvester's resultant of two Ore polynomials, derive the respective determinantal formulas for the greatest common right… (More)

- Ziming Li, István Nemes
- ISSAC
- 1997

This paper presents a modular algorithm for computing the greatest common right divisor (gcrd) of two univariate Ore polynomials over Z[t]. The subresultants of Ore polynomials are used to compute the evaluation homomorphic images of the gcrd. Rational number and rational function reconstructions are used to recover coefficients. The experimental results… (More)

- Ziming Li, Fritz Schwarz, Serguei P. Tsarev
- J. Symb. Comput.
- 2003

A D-finite system is a finite set of linear homogeneous partial differential equations in several independent and dependent variables, whose solution space is of finite dimension. Let L be a D-finite system with rational function coefficients. We present an algorithm for computing all hyperexponential solutions of L , and an algorithm for computing all… (More)

- Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li
- ISSAC
- 2010

The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain tight degree bounds on the various expressions involved in the method. To make the problem more tractable, we restrict… (More)

- Manuel Bronstein, Ziming Li, Min Wu
- ISSAC
- 2005

Picard-Vessiot extensions for ordinary differential and difference equations are well known and are at the core of the associated Galois theories. In this paper, we construct fundamental matrices and Picard-Vessiot extensions for systems of linear partial functional equations having finite linear dimension. We then use those extensions to show that all the… (More)

- Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, Guoce Xin
- ISSAC
- 2013

We present a new reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition that allows to decide hyperexponential integrability. Based on this reduction algorithm, we design a new algorithm to compute minimal telescopers… (More)

- George Labahn, Ziming Li
- ISSAC
- 2004

An orthogonal Ore ring is an abstraction of common properties of linear partial differential, shift and q-shift operators. Using orthogonal Ore rings, we present an algorithm for finding hyperexponential solutions of a system of linear differential, shift and q-shift operators, or any mixture thereof, whose solution space is finite-dimensional. The… (More)

- Keith O. Geddes, Ha Q. Le, Ziming Li
- ISSAC
- 2004

We describe differential rational normal forms of a rational function and their properties. Based on these normal forms, we present an algorithm which, given a hyperexponential function T(x), constructs two hyperexponential functions T;<sub>1;</sub>(x) and T;<sub>2;</sub>(x) such that T(x) = T;<sub>1;</sub><sup>'</sup>(x) + T;<sub>2;</sub>(x) and… (More)

- Ziming Li, Michael F. Singer, Min Wu, Dabin Zheng
- ISSAC
- 2006

We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and one-dimensional submodules. The hyperexponential solutions are computed recursively by solving a sequence of first-order ordinary matrix equations. As the recursion… (More)

- Alin Bostan, Frédéric Chyzak, Bruno Salvy, Ziming Li
- ISSAC
- 2011

We study tight bounds and fast algorithms for LCLMs of <i>several</i> linear differential operators with polynomial coefficients. We analyse the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We propose a new algorithm that recasts the LCLM computation in a linear algebra problem on a polynomial matrix. This… (More)