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

Revision as of 01:40, 18 May 2009

Revision as of 02:01, 20 May 2009

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**<s>It seems odd that the ''Bezout's identity'' section is a subsection of ''Applications''. Applications sections, in my (probably biased) experience, generally deal with how the subject applies to real world problems, not theoretical mumbo jumbo. Some readers will probably jump down to ''Applications'' thinking that they are going to be reading about how the EA can be used in sailing or accounting or whatever. To avoid crushing their tiny little hearts, consider changing ''Applications'' to ''Mathematical applications'', though I may be alone in thinking that this is a good idea.</s>

**::That does seem like a good suggestion; more specific section headings are always better. Changed to "Mathematical applications". [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 14:11, 16 May 2009 (UTC)

**<s>"to the set of multiples of a single number, their GCD g" This would probably be slightly less confusing if "a single number, their GCD g" were replaced with "GCD(a, b)". Much simpler.</s>

**::Excellent idea; changed wording as you suggest. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 01:39, 18 May 2009 (UTC)

**<s>"For example, suppose that a cook has two measuring cups of volume a and b, respectively. By adding and subtracting multiples of these two volumes, the cook can measure out any volume ua + vb. These volumes are all multiples of g = GCD(a, b)." Although I appreciate the real world connection, the inclusion of the cook is somewhat unnecessary and unencyclopedic. This analogy should work with just the measuring cups.</s>

**::Good point; I hope you like the new wording. Thanks for your continued keen reviewing! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 01:39, 18 May 2009 (UTC)

**"For example, consider two measuring cups of volume a and b, respectively" Why "respectively"?

**"By assumption, this can be written as" I've never heard the term "by assumption" before. If it is indeed the correct term here, perhaps it should be wikilinked.

**The closing lines of ''Extended Euclidean algorithm'' (before ''Equivalent matrix method'') are, to borrow a term of yours, a "wall of math". I think an example with real numbers would be very helpful here, something I'm sure you can find in any math textbook.

**The term ''matrix'' should probably be wikilinked somewhere in the section ''Equivalent matrix method''.

**"The inverse is well-defined" I have the feeling "well-defined" is jargon that should either be wikilinked, explained, or reworded.

**"Bézout's identity is essential to many higher applications" I think "higher" was supposed to be "higher-level", though omitting it entirely would also work.

**"For if the greatest common divisor of u and w is 1, then integers s and t can be found such that" Extraneous "for" at the beginning of this sentence? Perhaps I'm misreading this section.

**"Specifically, if a prime number ''p'' divides ''L'', it must divide at least one factor of ''L''" If you want to introduce a new letter for this sentence, be sure to actually use it: "Specifically, if a prime number ''p'' divides ''L'', ''p'' must divide at least one factor of ''L''". One the other hand, if you want to be brief and reduce the number of letters being thrown at the reader, try this: "Specifically, if a prime number divides ''L'', it must divide at least one factor of ''L''" or "Specifically, if a prime number ''p'' divides ''L'', that prime number must also divide at least one factor of ''L''".

**"where ''a'', ''b'' and ''c'' are also integers" It may be helpful for the reader if "also" were swapped out for "given". This clarifies the distinction between the variables (x, y) and the constants (a, b, c).

**"where s and t can be found by the extended Euclidean algorithm" Throughout the article, you've mentioned several times how the EA is extremely helpful in solving Diophantine equations. However, this is the only line (along with the bit about Bezout's identity, although that is arguably a separate topic) of the section ''Linear Diophantine equations'' that mentions the EA. Perhaps I may be missing something here, but it seems to me that whatever connections exist between the EA and linear Diophantine equations need to be spelled out more explicitly in this section.

--'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)

:::Thank you very much for your careful reviewing! The article is definitely improving. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)