The Abramov-Petkovysek reduction computes an additive decomposition of a hypergeometric term, which extends the functionality of the Gosper algorithm for indefinite hypergeometric summation. We improve the Abramov- Petkovysek reduction so as to decompose a hypergeometric term as the sum of a summable term and a non-summable one. The improved reduction does not solve any auxiliary linear difference equation explicitly. It is also more efficient than the original reduction according to computational experiments. Based on this reduction, we design a new algorithm to compute minimal telescopers for bivariate hypergeometric terms. The new algorithm can avoid the costly computation of certificates.
['Shaoshi Chen', 'Hui Huang', 'Ziming Li']
Improved Abramov-Petkovšek's Reduction and Creative Telescoping for Hypergeometric Terms