Trading order for degree in creative telescoping

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• 作者：Shaoshi Chen^a ; ^{schen@amss.ac.cn} ; Manuel Kauers^b ; ¹ ; ^{mkauers@risc.jku.at}
• 关键词：Definite integration ; Hyperexponential terms ; Zeilberger&rsquo ; s algorithm
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 出版时间：August, 2012
• 年：2012
• 卷：47
• 期：8
• 页码：968-995
• 全文大小：448 K

文摘

We analyze the differential equations produced by the method of creative telescoping applied to a hyperexponential term in two variables. We show that equations of low order have high degree, and that higher order equations have lower degree. More precisely, we derive degree bounding formulas which allow to estimate the degree of the output equations from creative telescoping as a function of the order. As an application, we show how the knowledge of these formulas can be used to improve, at least in principle, the performance of creative telescoping implementations, and we deduce bounds on the asymptotic complexity of creative telescoping for hyperexponential terms.