Defactoring algorithms: Difference between revisions

Line 1:

This article discusses how to identify enfactoring and then [[defactor]] it.

This article discusses how to identify enfactoring and then [[defactoring|defactor]] it.

A major use case for defactoring is to enable a [[canonical form]] for [[regular temperament]] [[mappings]], or in other words, to achieve a unique ID for temperaments in the form of a matrix. Previously this was only available by using lists of largest possible minor determinants AKA [[wedgie|wedge products of mapping rows]], which by virtue of reducing the information down to a single list of numbers, could be checked for enfactoring by simply checking the single row's GCD<ref>At the time [[Dave Keenan]] and [[Douglas Blumeyer]] began their investigation into Exterior Algebra (EA), most of the math involved in RTT could be handled using only Linear Algebra (LA), a relatively basic and commonplace subject that many people get a chance to learn in high school or university along with subjects like calculus or trigonometry. But there was one crucial task which LA hadn't proven able to handle yet: providing a "fingerprint" — a unique mathematical representation — for each distinct temperament, to allow it to be recognized as the same temperament even though it might be derived in different ways, or in other words, a canonical form for them. For many years, EA had provided this service for RTT, using a structure called a "[[wedgie]]".

Revision as of 20:52, 12 January 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits increase precision of language re: minor determinants, to be explicit about them being the largest possible minors ← Older edit		Revision as of 22:46, 13 January 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits I've asked for the clutter of pages of different forms for the words defactor and enfactor to be deleted, so now pages that linked to them need to be updated to use the remaining working link Newer edit →
Line 1:		Line 1:
	This article discusses how to identify enfactoring and then [[defactor]] it.		This article discusses how to identify enfactoring and then [[defactoring\|defactor]] it.

	A major use case for defactoring is to enable a [[canonical form]] for [[regular temperament]] [[mappings]], or in other words, to achieve a unique ID for temperaments in the form of a matrix. Previously this was only available by using lists of largest possible minor determinants AKA [[wedgie\|wedge products of mapping rows]], which by virtue of reducing the information down to a single list of numbers, could be checked for enfactoring by simply checking the single row's GCD<ref>At the time [[Dave Keenan]] and [[Douglas Blumeyer]] began their investigation into Exterior Algebra (EA), most of the math involved in RTT could be handled using only Linear Algebra (LA), a relatively basic and commonplace subject that many people get a chance to learn in high school or university along with subjects like calculus or trigonometry. But there was one crucial task which LA hadn't proven able to handle yet: providing a "fingerprint" — a unique mathematical representation — for each distinct temperament, to allow it to be recognized as the same temperament even though it might be derived in different ways, or in other words, a canonical form for them. For many years, EA had provided this service for RTT, using a structure called a "[[wedgie]]".		A major use case for defactoring is to enable a [[canonical form]] for [[regular temperament]] [[mappings]], or in other words, to achieve a unique ID for temperaments in the form of a matrix. Previously this was only available by using lists of largest possible minor determinants AKA [[wedgie\|wedge products of mapping rows]], which by virtue of reducing the information down to a single list of numbers, could be checked for enfactoring by simply checking the single row's GCD<ref>At the time [[Dave Keenan]] and [[Douglas Blumeyer]] began their investigation into Exterior Algebra (EA), most of the math involved in RTT could be handled using only Linear Algebra (LA), a relatively basic and commonplace subject that many people get a chance to learn in high school or university along with subjects like calculus or trigonometry. But there was one crucial task which LA hadn't proven able to handle yet: providing a "fingerprint" — a unique mathematical representation — for each distinct temperament, to allow it to be recognized as the same temperament even though it might be derived in different ways, or in other words, a canonical form for them. For many years, EA had provided this service for RTT, using a structure called a "[[wedgie]]".