Kite's thoughts on pergens: Difference between revisions

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 Pergens were discovered by [[KiteGiedraitis|Kite Giedraitis]] in 2017, and developed with the help of [[PraveenVenkataramana|Praveen Venkataramana]].
-== Addendum (late 2023) ==
+== Addenda (late 2023) ==
 WORK IN PROGRESS
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 ===Simplifying "doubled" EI's===
-Consider an EI of v<sup>3</sup>AA1. AA1 is "doubled" in the sense that AA1 = A1 + A1. The EI's 2.3.^ monzo is [-22 14 -3]. The doubledness is apparent from the first two numbers both being even. The EI implies a mapping of [(1 2 2) (0 -3 -14)]. The pergen is (P8, P4/3).
+Consider an EI of v<sup>3</sup>AA1. AA1 is "doubled" in the sense that AA1 = A1 + A1. The EI's 2.3.^ monzo is [-22 14 -3]. The doubledness is apparent from the first two numbers both being even. The EI implies a mapping of [(1 2 2) (0 -3 -14)]. The pergen is (P8, P4/3). Here are the [[twin squares]].
-We can derive P and G from this matrix. P = P8 = [1 0 0] and G = ^m2 = [8 -5 1]. We can make a 3x3 gencom matrix from P, G and EI.
+<math>
+\begin{array} {rrr}
+P8 \\
+^m2 \\
+v<sup>3</sup>AA1 \\
+\end{array}
+\left[ \begin{array} {rrr}
+& 0 & 0 \\
+& -5 & 1 \\
+\hline
+\style{background-color:#C6DC67;padding:5px}{-22} & 14 & -3 \\
+\end{array} \right]
+\longleftrightarrow
+\left[ \begin{array} {rrr}
+& 2 & 2 \\
+& -3 & -14 \\
+\hline
+& -1 & -5 \\
+\end{array} \right]
+</math>
-Consider the twin squares
-<nowiki><tt></nowiki>
-P8       (1  0  0)
-vm3    (5 -3 -1)
-v<sup>3</sup>AA1  (-22 14 -3)
 Certain uninflected EI's naturally split into smaller pieces, because both numbers of the 2.3 monzo are even (or [[threeven]], fourven, etc.)