Speaker: 黄辉副教授, 大连理工大学

Time & Venue: 2023.06.30 10:00-11:00 思源楼525

Abstract:

We adapt the theory of normal and special polynomials from the symbolic integration to the summation setting, and then built up a general framework embracing both the usual shift case and the q-shift case. In the context of this general framework, we develop a reduction algorithm, and subsequently a creative telescoping algorithm, applicable to both hypergeometric terms and their q-analogues. Our algorithms generalize existing ones for the usual shift case presented at ISSAC 2015, and can also avoid the costly computation of certificates. Moreover, our algorithms allow to split up the usual shift case and the q-shift case only when it is really necessary, and thus instantly reveal the intrinsic differences between these two cases. Tight order bounds on the telescopers, as well as experimental results, are also provided.