Defactoring: Difference between revisions

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'''Defactoring''' is a operation on the mapping for a regular temperament which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for comma-bases, the duals of mappings, where it instead checks its columns for enfactoring.

'''Defactoring''' is a operation on the [[mapping]] for a [[regular temperament]] which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for [[comma-basis|comma-bases]], the duals of mappings, where it instead checks its columns for enfactoring.

Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[defactoring#the_pathology_of_enfactoredness|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.

Revision as of 22:46, 8 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits →enfactored, to replace contorted: hyphenate and link comma-basis ← Older edit		Revision as of 22:50, 8 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits add links Newer edit →
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	'''Defactoring''' is a operation on the mapping for a regular temperament which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for comma-bases, the duals of mappings, where it instead checks its columns for enfactoring.		'''Defactoring''' is a operation on the [[mapping]] for a [[regular temperament]] which ensures it represents the same information but without any enfactoring, or in other words, redundancies due to a common factor found in its rows. It is also defined for [[comma-basis\|comma-bases]], the duals of mappings, where it instead checks its columns for enfactoring.

	Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[defactoring#the_pathology_of_enfactoredness\|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.		Being enfactored is a bad thing. Enfactored matrices — those in the RTT domain, at least — are sick, in a way<ref>According to [[saturation]], "...if [an RTT matrix] isn't saturated the supposed temperament it defines may be regarded as pathological..." </ref>; it's no accident that "enfactored" sounds sort of like "infected". We'll discuss this pathology in detail in [[defactoring#the_pathology_of_enfactoredness\|a later section of this article]]. Fortunately, the remedy is simple: all one has to do is "defactor" it — identify and divide out the common factor — to produce a healthy mapping.