Defactoring algorithms: Difference between revisions
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Regarding the development of a canonical form for temperaments using only linear algebra, Dave and Douglas did manage to develop such a form, which is documented here: [[defactored Hermite form]]. It was Gene himself who first described this form (as the result of his "saturation" algorithm), so he either did not realize the full implications of his discovery, or it was simply not popularized and plugged in with the rest of the hive knowledge. | Regarding the development of a canonical form for temperaments using only linear algebra, Dave and Douglas did manage to develop such a form, which is documented here: [[defactored Hermite form]]. It was Gene himself who first described this form (as the result of his "saturation" algorithm), so he either did not realize the full implications of his discovery, or it was simply not popularized and plugged in with the rest of the hive knowledge. | ||
=== Failed defactoring methods === | |||
When in development on an ideal defactoring method—the effort which culminated in column Hermite defactoring—Dave and Douglas experimented on other methods, which are imperfect (don't work all the time, are very slow, or too complicated). | When in development on an ideal defactoring method—the effort which culminated in column Hermite defactoring—Dave and Douglas experimented on other methods, which are imperfect (don't work all the time, are very slow, or too complicated). | ||
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==== Addabilization defactoring ==== | ==== Addabilization defactoring ==== | ||
This defactoring technique is used specifically in the process of preparing matrices for [[temperament addition]]; it defactors while managing to change only a single row of the original matrix, a necessary constraint of that problem. But this method is not computationally efficient or easier to understand, so unless you have this specific need, it is not your best option. Details can be found in [[Temperament addition #3. Addabiliziation defactoring]]. | This defactoring technique is used specifically in the process of preparing matrices for [[temperament addition]]; it defactors while managing to change only a single row of the original matrix, a necessary constraint of that problem. But this method is not computationally efficient or easier to understand, so unless you have this specific need, it is not your best option. Details can be found in [[Temperament addition #3. Addabiliziation defactoring]]. | ||
== Finding the greatest factor == | == Finding the greatest factor == | ||