Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions

Revision as of 04:42, 29 April 2009

Revision as of 04:59, 29 April 2009

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uniquely with a (degree) condition on r (and some conditions on a and b). They are related, of course, but I was wondering if it might be worthwhile saying something to that effect off the bat. [[User:Fowler&amp;fowler|<font color="#B8860B">Fowler&amp;fowler</font>]][[User talk:Fowler&amp;fowler|<font color="#708090">«Talk»</font>]] 17:43, 28 April 2009 (UTC)

:Perhaps you're referring to the "division lemma" or [[division algorithm]]? If so, the article mentions it in the subsection "Calculating the quotients and remainders". But I haven't encountered a source that calls it the "Euclidean algorithm"; could you point me towards one? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 02:45, 29 April 2009 (UTC)

::I had a vague feeling Fowler had a point there, so I dug through some books I had handy. I found that (as expected) Hardy & Wright's number theory book states that "Euclid's algorithm" is defined by generating the sequence of remainders which terminates (it seems to give no name for the "division algorithm", merely calling it division with remainder at times), Dummit & Foote's abstract algebra book states that the "Euclidean algorithm" comes from the ''division algorithm'', but Herstein's ''Topics in Algebra'' does indeed call the above, ''the'' Euclidean algorithm. Herstein is a pretty well-known algebra book, so I dug a bit more and I found that a source on the [[Euclidean ___domain]] article, which was published in the Bulletin of the American Mathematical Society in 1949, also uses the term Euclidean algorithm for division algorithm (see [http://projecteuclid.org/euclid.bams/1183514381]). I think in number theory books there is a pretty well-established tradition of using "Euclidean algorithm" to mean generating the sequence of remainders from the two initial numbers. In algebra texts that discuss Euclidean domains, my suspicion is that books here and there may use Euclidean algorithm to mean division algorithm but I suspect that modern books generally don't; I find Dummit & Foote is pretty reliable regarding modern terminology, while Herstein is from 1961 and sometimes a bit outdates on terminology. In any case, I think a note or footnote is in order. --[[User:C S|C S]] ([[User talk:C S|talk]]) 04:59, 29 April 2009 (UTC)