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On the l-ary GCD-algorithm in rings of integers
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0003-4157-1371
2005 (English)In: AUTOMATA, LANGUAGES AND PROGRAMMING, PROCEEDINGS / [ed] Caires, L; Italiano, GE; Monteiro, L; Palamidessi, C; Yung, M, 2005, Vol. 3580, 1189-1201 p.Conference paper (Refereed)
Abstract [en]

The greatest common divisor (GCD) of two integers a and b is the largest integer d such that d divides both a and b. The problem of finding the GCD of two integers efficiently is one of the oldest problems studied in number theory. The corresponding problem can be considered for two elements alpha and beta in any factorial ring R. Then lambda is an element of R is a GCD of alpha and beta if it divides both elements, and whenever lambda is an element of R divides both alpha and beta it also holds that lambda' divides lambda. A precise understanding of the complexity of different GCD algorithms gives a better understanding of the arithmetic in the domain under consideration.

Place, publisher, year, edition, pages
2005. Vol. 3580, 1189-1201 p.
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-42729DOI: 10.1007/11523468_96ISI: 000230880500096ScopusID: 2-s2.0-26444569340ISBN: 3-540-27580-0OAI: diva2:448079
32nd International Colloquium on Automata, Languages and Programming (ICALP 2005) Location: Lisbon, PORTUGAL Date: JUL 11-15, 2005
QC 20111014Available from: 2011-10-14 Created: 2011-10-12 Last updated: 2012-01-24Bibliographically approved

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