20 citations · 52 across the 16 of their papers we have counts for
16 papers
Complete Reduction for Derivatives in a Transcendental Liouvillian Extension
Shaoshi Chen, Hao Du, Yiman Gao +3
Transcendental Liouvillian extensions are differential fields, in which one can model poly-logarithmic, hyperexponential, and trigonometric functions, logarithmic integrals, and th…
Complete Reduction for Derivatives in a Primitive Tower
Hao Du, Yiman Gao, Wenqiao Li +1
A complete reduction for derivatives in a differential field is a linear operator on the field over its constant subfield. The reduction enables us to decompose an element …
A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping
Shaoshi Chen, Hao Du, Yiman Gao +2
We adapt the theory of normal and special polynomials from symbolic integration to the summation setting, and then built up a general framework embracing both the usual shift case…
Reducing Hyperexponential Functions over Monomial Extensions
Shaoshi Chen, Hao Du, Yiman Gao +1
We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into…
An Additive Decomposition in S-Primitive Towers
Hao Du, Jing Guo, Ziming Li +1
We consider the additive decomposition problem in primitive towers and present an algorithm to decompose a function in an S-primitive tower as a sum of a derivative in the tower an…
Additive Decompositions in Primitive Extensions
Shaoshi Chen, Hao Du, Ziming Li
This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element in suc…
Apparent Singularities of D-finite Systems
Shaoshi Chen, Manuel Kauers, Ziming Li +1
We generalize the notions of singularities and ordinary points from linear ordinary differential equations to D-finite systems. Ordinary points of a D-finite system are characteriz…
A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms
Shaoshi Chen, Hui Huang, Manuel Kauers +1
The Abramov-Petkovsek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric s…
Parallel Telescoping and Parameterized Picard--Vessiot Theory
Shaoshi Chen, Ruyong Feng, Ziming Li +1
Parallel telescoping is a natural generalization of differential creative-telescoping for single integrals to line integrals. It computes a linear ordinary differential operator $L…
On the Structure of Compatible Rational Functions
Shaoshi Chen, Ruyong Feng, Guofeng Fu +1
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shif…
Complexity of Creative Telescoping for Bivariate Rational Functions
Alin Bostan, Shaoshi Chen, Frédéric Chyzak +1
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) creativ…
Hermite Reduction and Creative Telescoping for Hyperexponential Functions
Alin Bostan, Shaoshi Chen, Frédéric Chyzak +2
We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a u…
On the Existence of Telescopers for Mixed Hypergeometric Terms
Shaoshi Chen, Frédéric Chyzak, Ruyong Feng +2
We present a criterion for the existence of telescopers for mixed hypergeometric terms, which is based on multiplicative and additive decompositions. The criterion enables us to de…
Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators
Alin Bostan, Frédéric Chyzak, Ziming Li +1
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorith…
A Note on Lipshitz's Lemma 3
Shaoshi Chen, Ziming Li
In this note, we give a remark on the proof of Lemma 3 in Lipshitz's paper "The diagonal of a D-Finite power series is D-Finite". This remark is motivated by the observation that t…
A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules
Ziming Li, Michael F. Singer, Min Wu +1
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…