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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)
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)
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)
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)
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)
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)
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)
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)