Polynomial factorization: An exploration of Lenstra's algorithm

We describe various design decisions and problems encountered during the implementation of the Lenstra factoriser [Lenstra82] in REDUCE. A practical viewpoint is taken with descriptions of both successful and unsuccessful attempts at tackling some of the problems. Particular areas considered include bounding coefficients of factors, the Cantor-Zassenhaus factoriser [Cantor81], Hensel lifting, basis reduction, and trial division of polynomials. We give an empirical formula which estimates the running time of our basis reduction routine.

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