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ANTS
2004
Springer

Binary GCD Like Algorithms for Some Complex Quadratic Rings

9 years 7 months ago
Binary GCD Like Algorithms for Some Complex Quadratic Rings
On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in Q( √ d) where d ∈ {−2, −7, −11, −19}. Thus a binary gcd like algorithm is presented for a unique factorization domain which is not Euclidean (case d = −19). Together with the earlier known binary gcd like algorithms for the ring of integers in Q( √ −1) and Q( √ −3), one now has binary gcd like algorithms for all complex quadratic Euclidean domains. The running time of our algorithms is O(n2 ) in each ring. While there exists an O(n2 ) algorithm for computing the gcd in quadratic number rings by Erich Kaltofen and Heinrich Rolletschek, it has large constants hidden under the big-oh notation and it is not practical for medium sized inputs. On the other hand our algorithms are quite fast and very simple to implement.
Saurabh Agarwal, Gudmund Skovbjerg Frandsen
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where ANTS
Authors Saurabh Agarwal, Gudmund Skovbjerg Frandsen
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