Cmloegcmluin: extract into centralized defactoring algorithms article

2021-11-14T18:33:51Z

extract into centralized defactoring algorithms article

← Older revision		Revision as of 18:33, 14 November 2021
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	A failed defactoring technique which was experimented with during the development of [[column Hermite defactoring]] took advantage of the fact that the list of minor determinants (or simply "minors") of a mapping is guaranteed to include any common factor as its entries' GCD. So, if one simply converted a mapping to its list of minors, removed the GCD (at which point you would have what in RTT is called a [[User:Cmloegcmluin/RTT_How-To#~~multimaps\|canonical multimap]], or [~~[~~wedgie]]), and then performed an "anti-minors" operation to get back to a mapping form, any common factors should be removed.~~		#REDIRECT [[Defactoring_algorithms#MADAM_defactoring]]

	~~Inspired by Gene Ward Smith's method for computing anti-minors as described~~ [~~[Mathematical_theory_of_regular_temperaments~~#Wedgies\|here]] and [[Basic_abstract_temperament_translation_code\|here]], an anti-minors method was implemented in Wolfram Language. It was found that a defactoring algorithm based on '''M'''inors '''A'''nd '''D'''ivide-out-GCG, '''A'''nti-'''M'''inors, or '''MADAM defactoring''', does indeed work. However, it runs 10 to 20 times slower than Smith defactoring and column Hermite defactoring, and it is not compellingly easier to understand than either of them, so it is not considered to be of significant interest.

	[[Dave Keenan]] and [[Douglas Blumeyer]] record a summary of their work here in case it may be helpful to anyone else who might want to iterate on this later. The other major failed experimental defactoring technique was [[Sum-and-difference_defactoring\|SAD defactoring]].

Cmloegcmluin: extract development notes type stuff from main defactoring page

2021-10-08T02:07:19Z

extract development notes type stuff from main defactoring page

New page

A failed defactoring technique which was experimented with during the development of [[column Hermite defactoring]] took advantage of the fact that the list of minor determinants (or simply "minors") of a mapping is guaranteed to include any common factor as its entries' GCD. So, if one simply converted a mapping to its list of minors, removed the GCD (at which point you would have what in RTT is called a [[User:Cmloegcmluin/RTT_How-To#multimaps|canonical multimap]], or [[wedgie]]), and then performed an "anti-minors" operation to get back to a mapping form, any common factors should be removed.

Inspired by Gene Ward Smith's method for computing anti-minors as described [[Mathematical_theory_of_regular_temperaments#Wedgies|here]] and [[Basic_abstract_temperament_translation_code|here]], an anti-minors method was implemented in Wolfram Language. It was found that a defactoring algorithm based on '''M'''inors '''A'''nd '''D'''ivide-out-GCG, '''A'''nti-'''M'''inors, or '''MADAM defactoring''', does indeed work. However, it runs 10 to 20 times slower than Smith defactoring and column Hermite defactoring, and it is not compellingly easier to understand than either of them, so it is not considered to be of significant interest.

[[Dave Keenan]] and [[Douglas Blumeyer]] record a summary of their work here in case it may be helpful to anyone else who might want to iterate on this later. The other major failed experimental defactoring technique was [[Sum-and-difference_defactoring|SAD defactoring]].

MADAM defactoring - Revision history

Cmloegcmluin: extract into centralized defactoring algorithms article

Cmloegcmluin: extract development notes type stuff from main defactoring page