Wedgie/Archived version: Difference between revisions

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The result is the wedgie of the rank-n temperament ''V''<sub>1</sub>&...&''V''<sub>r</sub>, whose entries are
The result is the wedgie of the rank-n temperament ''V''<sub>1</sub>&...&''V''<sub>r</sub>, whose entries are


<math>W(q_{k_1}, ..., q_{k_n}) = \det[V_i(q_{k_j})]_{i,j},</math>
<math>W(q_{k_1}, ..., q_{k_r}) = \det[V_i(q_{k_j})]_{i,j}, \ \text{for} \ 1 < k_j < n, </math>


where <math>[V_i(q_{k_j})]_{i,j}</math> denotes the ''n''×''n'' matrix whose (''i'', ''j'') entry is <math>V_i(q_{k_j})</math>. These are ''n''-dimensional quantities, the volumes of the ''n''-dimensional parallelograms spanned by ''q''<sub>''k''<sub>''j''</sub></sub> in the temperament's lattice.
where <math>[V_i(q_{k_j})]_{i,j}</math> denotes the ''r''×''r'' matrix whose (''i'', ''j'') entry is <math>V_i(q_{k_j})</math>. These are ''r''-dimensional quantities, the volumes of the ''r''-dimensional parallelograms spanned by ''q''<sub>''k''<sub>''j''</sub></sub> in the temperament's lattice.


==How the period and generator falls out of a rank-2 wedgie==
==How the period and generator falls out of a rank-2 wedgie==