Defactoring algorithms: Difference between revisions

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= Defactoring methods =

Even better than identifying enfactored mappings is actually full-on defactoring them. Here are ~~two~~ methods that do just that: Smith defactoring, developed by Gene Ward Smith<ref>but the name comes from a different Smith: [https://en.wikipedia.org/wiki/Henry_John_Stephen_Smith Henry John Stephen Smith], for whom the [[Smith normal form]] is named, which this method uses</ref>; Pernet-Stein defactoring, described by Clément Pernet and William Stein; and column Hermite defactoring, developed by Dave and Douglas (the name comes, of course, from Hermite normal form, which it uses<ref>named for Charles Hermite, who was French, by the way, and so his name is pronounced more like err-MEET, not like HER-might</ref>).

Even better than identifying enfactored mappings is actually full-on defactoring them. Here are three methods that do just that: Smith defactoring, developed by Gene Ward Smith<ref>but the name comes from a different Smith: [https://en.wikipedia.org/wiki/Henry_John_Stephen_Smith Henry John Stephen Smith], for whom the [[Smith normal form]] is named, which this method uses</ref>; Pernet-Stein defactoring, described by Clément Pernet and William Stein; and column Hermite defactoring, developed by Dave and Douglas (the name comes, of course, from Hermite normal form, which it uses<ref>named for Charles Hermite, who was French, by the way, and so his name is pronounced more like err-MEET, not like HER-might</ref>).

Smith defactoring has not yet been mathematically proven to always defactor mappings, while Pernet-Stein and column Hermite defactoring have been proven. Tests Douglas ran on thousands of random mappings, however, have empirically proven that all three methods work all of the time. Pernet-Stein and column Hermite are more closely related, and so they give the exact same results as each other every time, whereas Smith defactoring sometimes gives different results; however, after taking the HNF of the results, all three do become exactly the same.

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 = Defactoring methods =
-Even better than identifying enfactored mappings is actually full-on defactoring them. Here are two methods that do just that: Smith defactoring, developed by Gene Ward Smith<ref>but the name comes from a different Smith: [https://en.wikipedia.org/wiki/Henry_John_Stephen_Smith Henry John Stephen Smith], for whom the [[Smith normal form]] is named, which this method uses</ref>; Pernet-Stein defactoring, described by Clément Pernet and William Stein; and column Hermite defactoring, developed by Dave and Douglas (the name comes, of course, from Hermite normal form, which it uses<ref>named for Charles Hermite, who was French, by the way, and so his name is pronounced more like err-MEET, not like HER-might</ref>).
+Even better than identifying enfactored mappings is actually full-on defactoring them. Here are three methods that do just that: Smith defactoring, developed by Gene Ward Smith<ref>but the name comes from a different Smith: [https://en.wikipedia.org/wiki/Henry_John_Stephen_Smith Henry John Stephen Smith], for whom the [[Smith normal form]] is named, which this method uses</ref>; Pernet-Stein defactoring, described by Clément Pernet and William Stein; and column Hermite defactoring, developed by Dave and Douglas (the name comes, of course, from Hermite normal form, which it uses<ref>named for Charles Hermite, who was French, by the way, and so his name is pronounced more like err-MEET, not like HER-might</ref>).
 Smith defactoring has not yet been mathematically proven to always defactor mappings, while Pernet-Stein and column Hermite defactoring have been proven. Tests Douglas ran on thousands of random mappings, however, have empirically proven that all three methods work all of the time. Pernet-Stein and column Hermite are more closely related, and so they give the exact same results as each other every time, whereas Smith defactoring sometimes gives different results; however, after taking the HNF of the results, all three do become exactly the same.