Abstract
We present an additive decomposition algorithm for q-hypergeometric terms. It decomposes a given term T as the sum of two terms, in which the former is q-summable and the latter is minimal in some technical sense. Moreover, the latter is zero if and only if T is q-summable. Although our additive decomposition is a q-analogue of the modified Abramov-Petkovšek reduction for usual hypergeometric terms, they differ in some subtle details. For instance, we need to reduce Laurent polynomials instead of polynomials in the q-case. The experimental results illustrate that the additive decomposition is more efficient than q-Gosper’s algorithm for determining q-summability when some q-dispersion concerning the input term becomes large. Moreover, the additive decomposition may serve as a starting point to develop a reduction-based creative-telesco** method for q-hypergeometric terms.
Dedicated to Professor Sergei A. Abramov on the occasion of his 70th birthday
H. Du—Supported by the NSFC grants 11501552.
H. Huang—Funded by the Austrian Science Fund (FWF) under grants Y464-N18 and W1214-N15 (project part 13).
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Notes
- 1.
We thank Dr. Haitao ** for sending us his maple scripts on q-Gosper’s algorithm.
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We thank the anonymous referee for helpful comments and valuable references.
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Du, H., Huang, H., Li, Z. (2018). A q-Analogue of the Modified Abramov-Petkovšek Reduction. In: Schneider, C., Zima, E. (eds) Advances in Computer Algebra. WWCA 2016. Springer Proceedings in Mathematics & Statistics, vol 226. Springer, Cham. https://doi.org/10.1007/978-3-319-73232-9_5
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