The number of steps in the Euclidean algorithm over complex quadratic fields

DOI10.1007/BF01931288zbMath0731.11057MaRDI QIDQ807674

John Knopfmacher, Arnold Knopfmacher

Publication date: 1991

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

Euclidean algorithmimaginary-quadratic number fields

Mathematics Subject Classification ID

Quadratic extensions (11R11) Algebraic numbers; rings of algebraic integers (11R04) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05) Euclidean rings and generalizations (13F07)

Related Items (1)

\((1+i)\)-ary GCD computation in \(\mathbb Z[i\) as an analogue to the binary GCD algorithm.]

Cites Work

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• On the number of divisions of the Euclidean algorithm applied to Gaussian integers
• Shortest division chains in imaginary quadratic number fields
• The exact length of the Euclidean algorithm in [ X ]
• A Simple Estimate for the Number of Steps in the Euclidean Algorithm
• The number of steps in the Euclidean algorithm

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