A q-Analogue of the Modified Abramov-Petkovšek Reduction
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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-telescoping method for q-hypergeometric terms.
KeywordsAdditive decomposition q-hypergeometric term Reduction Symbolic summation
We thank the anonymous referee for helpful comments and valuable references.
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