Abstract
A theorem by Lamé (1845) answers the following questions: given N, what is the maximum number of divisions, if the Euclidean algorithm is applied to integers u, v with N≥u≥n≥0? In this paper we give an analogous result for the Euclidean algorithm applied to Gaussian integers, that is, complex numbers a+bi, where a and b are integers.
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References
B. F. Caviness, G. E. Collins: Algorithms for Gaussian Integer Arithmetic. In: Proceedings of the 1976 Symposium on Symbolic and Algebraic Computation.
H. Hasse: Vorlesunger ueber Zahlentheorie. Springer-Verlag, Berlin. 1964.
D. E. Knuth: The Act of Computer Programming. Vol. 2: Seminumerical Algorithms Addison-Wesley, Reading, Massachusetts 1981.
H. Rolletschek: The Euclidean Algorithm for Gaussian Integers. Technical report, University of Delaware, to appear.
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© 1983 Springer-Verlag
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Rolletschek, H. (1983). The Euclidean algorithm for Gaussian integers. In: van Hulzen, J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12868-9_87
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DOI: https://doi.org/10.1007/3-540-12868-9_87
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Print ISBN: 978-3-540-12868-7
Online ISBN: 978-3-540-38756-5
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