Hermite reduction and creative telescoping for hyperexponential functions
Hermite reduction and creative telescoping for hyperexponential functions
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DOI：
10.1145/2465506.2465946
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发表时间：
2013-01
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影响因子：
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通讯作者：
A. Bostan;Shaoshi Chen;F. Chyzak;Ziming Li;G. Xin
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文献类型：
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作者：
A. Bostan;Shaoshi Chen;F. Chyzak;Ziming Li;G. Xin
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 for bivariate hyperexponential functions. One of its main features is that it can avoid the costly computation of certificates. Its implementation outperforms Maple's function DEtools[Zeilberger]. We also derive an order bound on minimal telescopers that is tighter than the known ones.
