Talk:Euclidean algorithm

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Featured articleEuclidean algorithm is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. Even so, if you can update or improve it, please do so.
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April 24, 2009Peer reviewReviewed
May 19, 2009Featured article candidatePromoted
February 7, 2015Featured article reviewKept
Current status: Featured article

Bibliography[edit]

Would there be any objections to moving the "Bibliography" section to a subsection of "References". This is not a major move but there is more than one reason why it would make sense.

  • On Wikipedia a bibliography section is normally the first section in the appendices, usually for biographies, or otherwise "Works" per Works or publications.
  • A bibliography of sources, along with a references or notes section providing text-source integrity, constitute the citations so are certainly related.
  • The number of GA and FA articles that use a separate sourcing "Bibliography" section is small so it becomes an "exception".

This has nothing to do with any article rating but as "approaching" (GA) and attaining the "best articles Wikipedia has to offer" (FA) other articles are often styled accordingly. The use of "Bibliography" sections in more than one place is confusing and this would remove that aspect and show the relationship as we normally would in subsections. Otr500 (talk) 18:53, 24 July 2018 (UTC)[reply]

I see no value in complicating a simple structure, comprising two distinct sections:
  1. (hundreds of) specific references, each supporting specific parts of the article, in one (References) section; and
  2. a list of (more than a dozen) relevant books for further reading in another (Bibliography) section.
Your proposed alternative puts the books of the bibliography under the heading "References", which implies that they each support some specific assertions made in the article. But that's not necessarily so; and it's not the purpose of a bibliography to do that. yoyo (talk) 12:14, 6 November 2018 (UTC)[reply]

Integers: ordinary, normal, usual, real, Gaussian[edit]

In the § Gaussian integers section, we find these expressions:

  • "ordinary integers"
  • "normal integers".

I found these terms confusing, since

  1. I don't recall seeing them used, in decades of reading maths, before this; and
  2. The phrase "normal integers" occurs in close proximity to a discussion of a norm.

Perhaps both of the above phrases were meant to specify the usual or everyday integers, namely those in (or isomorphic to those in) the real numbers? In any case, the sense of the section wouldn't suffer, and accuracy would improve, if we were to replace both "ordinary integers" and "normal integers" by "real integers".

Before I make such a change, I'd like to hear other opinions.

yoyo (talk) 11:55, 6 November 2018 (UTC)[reply]

The phrase "ordinary integer" is commonly used for distinguishing usual integers from Gaussian integers, and more generally from algebraic integers. The phrase "normal integer" is less common and must changed into "ordinary integer". "Real integer" is not a good idea, because it would be WP:OR, and also because (for example) is an algebraic integer and a real number. I'll change "normal" to "ordinary", and add an explanatory footnote after the first use of "ordinary". D.Lazard (talk) 12:35, 6 November 2018 (UTC)[reply]
I agree with D.Lazard. "Ordinary integers" is not at all confusing, "normal integers" may be slightly confusing, but "real integers" is definitely confusing. Maproom (talk) 14:28, 6 November 2018 (UTC)[reply]

Inconsistent history[edit]

The present text of the article says that the Euclidean algorithm was first described in Europe by Bachet in 1624. This can hardly be true if it was already described in Euclid's Elements, which was known in Europe in various editions and translations long before Bachet.109.149.2.98 (talk) 13:49, 7 April 2019 (UTC)[reply]

Point well taken. The source only says that Bachet gave the first numerical description of the algorithm in Europe. I'll edit this. --Bill Cherowitzo (talk) 19:02, 7 April 2019 (UTC)[reply]

Section "Non commutative rings"[edit]

It seems that the only known example is the ring of Hurwitz quaternions. This must be clarified. If is true, the section must be renamed "Hurwitz quaternions". Otherwise, it must be named "Non commutative Euclidean rings" and moved to Euclidean domain. D.Lazard (talk) 08:47, 18 June 2019 (UTC)[reply]

Inaccurate implementations[edit]

I feel the implementations given in the Implementations sections are all inaccurate. For example, gcd(-6, 0) is 6, but the implementations return -6. This is wrong because GCDs are always non-negative. Hexagonalpedia (talk) 12:18, 23 May 2021 (UTC)[reply]

 Fixed D.Lazard (talk) 16:39, 24 May 2021 (UTC)[reply]