Defactoring algorithms: Difference between revisions

Line 890:

===MADAM defactoring ===

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.

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 a [[Douglas_Blumeyer_and_Dave_Keenan%27s_Intro_to_exterior_algebra_for_RTT#Canonical_form|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.

@@ Line 890: / Line 890: @@
 ===MADAM defactoring ===
-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.
+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 a [[Douglas_Blumeyer_and_Dave_Keenan%27s_Intro_to_exterior_algebra_for_RTT#Canonical_form|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.