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

Revision as of 02:29, 6 May 2009

Revision as of 00:57, 8 May 2009

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**::Eh, better, but instead of "although the simpler notation is also used for unrelated mathematical objects, such as two-dimensional vectors." how about "although the latter notation is also used for various other mathematical concepts, such as two-dimensional [[vector]]s."

**:::That's a good suggestion! I followed your wording more-or-less exactly. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 02:29, 6 May 2009 (UTC)

**::::I was hesitant to use the word "unrelated", but I couldn't figure out exactly why. Here's why: "unrelated" may imply that the two components, ''a'' and ''b'', are unrelated, which is obviously never the case. "other" makes it clear that the concepts are unrelated to EA without introducing the ambiguity. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 00:57, 8 May 2009 (UTC)

**<s>"neither 6 = 2×3 nor 35 = 5×7 is a prime number, since they both have two prime factors" I think it may be a tad confusing to include the prime factorization at first; perhaps this should be added later: "neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2x3 and 35 = 5x7." or something like that.</s> Also, shouldn't it be "neither 6 nor 35 '''are''' prime number'''s'''" ?

**:Excellent suggestion for the rewording. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:59, 4 May 2009 (UTC)

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**<s>"the GCD(462, 1071) = 3×7" In all other instances thus far, you have chosen not to use an article before GCD. Did you mean to say "the'''n''' GCD(462, 1071) = 3×7"?</s>

**:Thank you for catching that inconsistency, which I've fixed. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**<s>"Integer factorization is thought to be a difficult problem for large numbers." A bit weaselly, and it's not particularly difficult if you have a calculator handy. Perhaps "can be" instead of "is thought to be" ?</s>

**:I clarified the sentence, although perhaps I should have been more clear about "large numbers". A pocket calculator might help in factoring numbers up to 20,000 (5 digits), but it won't be useful in factoring numbers with 500 digits, the rough size of number used in modern cryptography. Nevertheless, the Euclidean algorithm can quickly find the greatest common divisor of two 500-digit numbers. That was the point I was trying to convey. Should I spell that out in the article, do you think? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**::I corrected the statement the first time from asserting "is a difficult problem" to "is thought to be..." since it is "only" thought to be difficult, not proven. The new version which states "The computational difficulty of integer factorization grows exponentially with the size of the number being factored" is a step backwards in that regards. The computational difficulty of integer factorization is in fact unknown. --[[User:C S|C S]] ([[User talk:C S|talk]]) 11:36, 4 May 2009 (UTC)

**:::You are right that I was inferring too much about the specific scaling of factorization. I've re-worded this sentence to "Factorization of large integers is believed to be such a difficult problem that many modern cryptography systems are based upon it.", which is supported by the Schroeder reference. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 13:59, 4 May 2009 (UTC)

**::::Good enough for me. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 00:57, 8 May 2009 (UTC)

**<s>"A more subtle definition of the GCD is helpful in advanced mathematics, particularly ring theory." This statement should probably be accompanied by a ref.</s>

**:OK. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

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**<s>"The sequence ends when there is no residual rectangle, i.e., when the square tiles cover the previous residual rectangle exactly." This paragraph desperately needs to end with: "The length of the sides of the smallest square tile is the GCD of the dimensions of the original rectangle." or something like that.</s>

**:Excellent suggestion, thanks! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 17:04, 5 May 2009 (UTC)

**<s>"where the magnitude of rk is strictly less than that of rk−1" The use of 'magnitude' here strikes me as being a bit odd. Why not just write a simple inequality? r_k < r_k-1</s>

**:The "magnitude" wording also covers versions of the algorithm when the remainder can be negative. For example, -37628 < 4, but 4 has a smaller magnitude. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**::True. I wonder if using absolute value notation |r_k| would be better. Up to you. In any case, magnitude or absolute value should be linked to avoid confusion for math noobs. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:04, 5 May 2009 (UTC)

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**<s>"''r''_''k'' &equiv; ''r''_''k''−2 mod ''r''_''k''−1" Is there some article to which we can link '&equiv;'? I'm not sure I know what it means.</s>

**:It means "equivalent to" in [[modular arithmetic]]. I'll make a link. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**I don't think the ''implementations'' section belongs in this article. [[WP:NOT|Wikipedia is not]] a how-to guide, and this section does not contain any new relevant information.

**"if the resulting negative remainder is smaller in absolute value than the typical positive remainder" You used "magnitude" earlier. I recommend swapping out "absolute value" for "magnitude" for consistency.

**"to the greatest length g that measures a and b evenly" The word "measures" seems a bit off. Shouldn't it be "divides"?

**"in other words, the lengths a and b are both multiples of the length g" I suggest the injection of the word "integer" before "multiples", without it, the whole concept is meaningless.

**"The algorithm was likely known by Eudoxus of Cnidus (about 375 BC). The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that the algorithm predates Eudoxus." I see what you're getting at, but to some readers, these sentences may seem to contradict each other. Suggested rewrite: "The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that what we now know as the Euclidean Algorithm may have predated [[Eudoxus of Cnidus]], a Greek mathematician who died in approximately 350 BC." or some such. Meh. That's not exactly perfect either. Give it some thought.

**"Euclid's algorithm was re-invented both in India and in China" "re-invent" often implies that an existing concept was significantly improved. I think "independently developed" or "independently discovered" might serve better.

**"the Indian mathematician and astronomer Aryabhata described the algorithm as the "pulverizer"" Erm... why?

**"and applied it solving linear Diophantine equations" Consider changing "applied it solving" to "used it to solve".

**"Although a special case of the Chinese remainder theorem was described earlier by Chinese mathematician and astronomer Sun Tzu" The use of "earlier" implies a relation to the previous sentence rather than the following clause. Suggest "was described earlier" to "had already been described".

**"The algorithm was first described in Europe in the second edition of Bachet's ''Problèmes plaisants et délectables'' (1624)." Which algorithm? The EA? Or the Chinese Remainder Theorem? Also, do you have a translation for that French title?

* More to come. Good work thus far. --'''[[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)