Abstract
This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number α such that Q[α]=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 α, one can compute [αn](modm) in time polynomial in (log(mn))O(1), where m and n are positive integers.
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