The PSLQ procedure can be regarded as a jazzed-up version of an integer-relation algorithm dating back more than 2,000 years to the Greek geometer Euclid of Alexandria (365–300 B.C.). The Euclidean ...

Mathematics of Computation, Vol. 77, No. 261 (Jan., 2008), pp. 589-607 (19 pages) We describe a new subquadratic left-to-right GCD algorithm, inspired by Schönhage's algorithm for reduction of binary ...

Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only ...