Generator form manipulation: Difference between revisions

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Using these two tricks, you do not have to worry about enfactoring the mapping, i.e. introducing a common factor in one of the maps. This is because neither of these tricks ever involve replacing a map with a multiple of that map; we always replace a map with a combination of at least one each of two different maps, as in trick 1, or with the map negated, as in trick 2.

== Tuning ~~strategy~~ ==

== Tuning ==

In order to ~~define~~ the size of the generators, you need to ~~specify~~ a tuning ~~strategy. Though if you have two generators that are close enough that their size ranking depends on the tuning, then you probably have other problems~~. ~~In any case, the~~ tuning ~~strategy that~~ we'~~ll be~~ using here is [[minimax-ES]], because ~~it's~~ decent enough and easy to compute.<ref>Note from Douglas Blumeyer: though if I had written this article today having done a lot of tuning theory and built a library for optimizing tunings, I would have gone with TILT minimax-U instead.</ref>

In order to determine the relative size of the generators, you need to have chosen a tuning for each them. The tuning we're using here comes from the [[minimax-ES]] tuning scheme, because this scheme is decent enough and easy to compute.<ref>Note from Douglas Blumeyer: though if I had written this article today having done a lot of tuning theory and built a library for optimizing tunings, I would have gone with TILT minimax-U instead.</ref>

== Easy instructions table to achieve mingen form for rank-2 mapping ==

@@ Line 105: / Line 105: @@
 Using these two tricks, you do not have to worry about enfactoring the mapping, i.e. introducing a common factor in one of the maps. This is because neither of these tricks ever involve replacing a map with a multiple of that map; we always replace a map with a combination of at least one each of two different maps, as in trick 1, or with the map negated, as in trick 2.
-== Tuning strategy ==
+== Tuning ==
-In order to define the size of the generators, you need to specify a tuning strategy. Though if you have two generators that are close enough that their size ranking depends on the tuning, then you probably have other problems. In any case, the tuning strategy that we'll be using here is [[minimax-ES]], because it's decent enough and easy to compute.<ref>Note from Douglas Blumeyer: though if I had written this article today having done a lot of tuning theory and built a library for optimizing tunings, I would have gone with TILT minimax-U instead.</ref>
+In order to determine the relative size of the generators, you need to have chosen a tuning for each them. The tuning we're using here comes from the [[minimax-ES]] tuning scheme, because this scheme is decent enough and easy to compute.<ref>Note from Douglas Blumeyer: though if I had written this article today having done a lot of tuning theory and built a library for optimizing tunings, I would have gone with TILT minimax-U instead.</ref>
 == Easy instructions table to achieve mingen form for rank-2 mapping ==