Interior product: Difference between revisions

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: <math>M_\text{Marvel} ∨ \frac{9801}{9800} = \bitval{-12 & 2 & -20 & 6 & 31 & 2 & 51 & -52 & 7 & 86}</math> gives wizard.

The interior product is also useful in finding the temperament mapping given the wedgie. Given a rank-''r'' ''p''-limit wedgie, we can find a collection of vals belonging to it by taking the interior product with every set of {{nowrap|''r'' − 1}} primes less than or equal to ''p'', and reducing this to the mapping. For instance, for ''M''Marvel we take [{{nowrap|''M''Marvel ∨ 2 ∨ 3}}, {{nowrap|''M''Marvel ∨ 2 ∨ 5}}, ..., {{nowrap|''M''Marvel ∨ 7 ∨ 11}}], which gives:

The interior product is also useful in finding the temperament mapping given the wedgie. Given a rank-''r'' ''p''-limit wedgie, we can find a collection of vals belonging to it by taking the interior product with every set of {{nowrap|''r'' − 1}} primes less than or equal to ''p'', and reducing this to the mapping. For instance, for ''M''Marvel we take {{nowrap|{{!(}}''M''Marvel ∨ 2 ∨ 3}}, {{nowrap|''M''Marvel ∨ 2 ∨ 5}}, ..., {{nowrap|''M''Marvel ∨ 7 ∨ 11{{)!}}}}, which gives:

<math>\left[\tmonzo{0 & 0 & -1 & -2 & 3},\right.</math> <math>\tmonzo{0 & 1 & 0 & 2 & -1},</math> <math>\tmonzo{0 & 2 & -2 & 0 & 4},</math> <math>\tmonzo{0 & -3 & 1 & -4 & 0},</math> <math>\tmonzo{-1 & 0 & 0 & 5 & -12},</math> <math>\tmonzo{-2 & 0 & -5 & 0 & -9},</math> <math>\tmonzo{3 & 0 & 12 & 9 & 0},</math> <math>\tmonzo{2 & 5 & 0 & 0 & 19},</math> <math>\tmonzo{-1 & -12 & 0 & -19 & 0},</math> <math>\left.\tmonzo{4 & -9 & 19 & 0 & 0}\right].</math>

@@ Line 35: / Line 35: @@
 : <math>M_\text{Marvel} ∨ \frac{9801}{9800} = \bitval{-12 & 2 & -20 & 6 & 31 & 2 & 51 & -52 & 7 & 86}</math> gives wizard.
-The interior product is also useful in finding the temperament mapping given the wedgie. Given a rank-''r'' ''p''-limit wedgie, we can find a collection of vals belonging to it by taking the interior product with every set of {{nowrap|''r'' &minus; 1}} primes less than or equal to ''p'', and reducing this to the mapping. For instance, for ''M''<sub>Marvel</sub> we take [{{nowrap|''M''<sub>Marvel</sub> ∨ 2 ∨ 3}}, {{nowrap|''M''<sub>Marvel</sub> ∨ 2 ∨ 5}}, ..., {{nowrap|''M''<sub>Marvel</sub> ∨ 7 ∨ 11}}], which gives:
+The interior product is also useful in finding the temperament mapping given the wedgie. Given a rank-''r'' ''p''-limit wedgie, we can find a collection of vals belonging to it by taking the interior product with every set of {{nowrap|''r'' &minus; 1}} primes less than or equal to ''p'', and reducing this to the mapping. For instance, for ''M''<sub>Marvel</sub> we take {{nowrap|{{!(}}''M''<sub>Marvel</sub> ∨ 2 ∨ 3}}, {{nowrap|''M''<sub>Marvel</sub> ∨ 2 ∨ 5}}, ..., {{nowrap|''M''<sub>Marvel</sub> ∨ 7 ∨ 11{{)!}}}}, which gives:
 <math>\left[\tmonzo{0 & 0 & -1 & -2 & 3},\right.</math> <math>\tmonzo{0 & 1 & 0 & 2 & -1},</math> <math>\tmonzo{0 & 2 & -2 & 0 & 4},</math> <math>\tmonzo{0 & -3 & 1 & -4 & 0},</math> <math>\tmonzo{-1 & 0 & 0 & 5 & -12},</math> <math>\tmonzo{-2 & 0 & -5 & 0 & -9},</math> <math>\tmonzo{3 & 0 & 12 & 9 & 0},</math> <math>\tmonzo{2 & 5 & 0 & 0 & 19},</math> <math>\tmonzo{-1 & -12 & 0 & -19 & 0},</math> <math>\left.\tmonzo{4 & -9 & 19 & 0 & 0}\right].</math>