On certain computations of Pisot numbers

Authors:
Qi Cheng;Jincheng Zhuang
Affiliations:
School of Computer Science, The University of Oklahoma, Norman, OK 73019, USA;School of Computer Science, The University of Oklahoma, Norman, OK 73019, USA
Venue:
Information Processing Letters
Year:
2013

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Abstract

This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number @a such that Q[@a]=F given a real Galois extension F of Q by its integral basis. This algorithm is based on the lattice reduction, and it runs in time polynomial in the size of the integral basis. Next, we show that for a fixed Pisot number @a, one can compute [@a^n](modm) in time polynomial in (log(mn))^O^(^1^), where m and n are positive integers.