Defactoring algorithms: Difference between revisions

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== Development ==

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 had not 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]]".

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 had not 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]]".

Dave and Douglas began their investigations with the hypothesis that canonicalization via wedgies was the primary reason it was important for RTT beginners to learn EA, and that if a canonical form could be developed using only LA, then EA could be reframed as an advanced topic. Gene himself, upon introducing the wedgie (which he initially called a "wedge invariant"), dismissed it as a bad idea to use for identifying temperaments:

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 == Development ==
-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 had not 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]]".
+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 had not proven able to handle yet: providing a "fingerprint"&mdash;a unique mathematical representation&mdash;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]]".
 Dave and Douglas began their investigations with the hypothesis that canonicalization via wedgies was the primary reason it was important for RTT beginners to learn EA, and that if a canonical form could be developed using only LA, then EA could be reframed as an advanced topic. Gene himself, upon introducing the wedgie (which he initially called a "wedge invariant"), dismissed it as a bad idea to use for identifying temperaments: