Wedgie/Archived version: Difference between revisions
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The result is the wedgie of the rank-''r'' temperament ''V''<sub>1</sub>&…&''V''<sub>r</sub>, whose entries are (ignoring steps 2 and 3): | The result is the wedgie of the rank-''r'' temperament ''V''<sub>1</sub>&…&''V''<sub>r</sub>, whose entries are (ignoring steps 2 and 3): | ||
<math>W(q_{k_1}, ldots, q_{k_r}) = \det[V_i(q_{k_j})]_{i,j}, \ \text{for} \ 1 < k_j < n, </math> | <math>W(q_{k_1}, \ldots, 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 ''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. | 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. | ||