Wedgie/Archived version: Difference between revisions

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More generally, if one takes ''r'' independent [[vals]] ''V''1, ..., ''V''''r'' in a rank-''n'' [[JI subgroup]] ''q''1.[...].''q''''n'', then the wedgie for the rank-''r'' temperament ''V''1& ...&''V''''r'' is defined by:

# ~~taking~~ the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals ~~(called a~~ '''multival'''~~), and~~

# Take the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals, producing an ''r'-'''multival'''.

# ~~dividing~~ out the greatest common divisior of the coefficients~~, to produce an ''r''-multival~~.

# Divide out the greatest common divisior of the coefficients.

# If the first non-zero coefficient of ~~this multival~~ is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive.

# If the first non-zero coefficient of the result of step 2 is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive.

The result is the wedgie of the rank-''r'' temperament ''V''1&...&''V''r, whose entries are (ignoring steps 2 and 3):

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 More generally, if one takes ''r'' independent [[vals]] ''V''<sub>1</sub>, ..., ''V''<sub>''r''</sub> in a rank-''n'' [[JI subgroup]] ''q''<sub>1</sub>.[...].''q''<sub>''n''</sub>, then the wedgie for the rank-''r'' temperament ''V''<sub>1</sub>& ...&''V''<sub>''r''</sub> is defined by:
-# taking the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals (called a '''multival'''), and
+# Take the [https://en.wikipedia.org/wiki/Wedge_product wedge product] of the vals, producing an ''r'-'''multival'''.
-# dividing out the greatest common divisior of the coefficients, to produce an ''r''-multival.
+# Divide out the greatest common divisior of the coefficients.
-# If the first non-zero coefficient of this multival is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive.
+# If the first non-zero coefficient of the result of step 2 is negative, the multival is then scalar multiplied by -1, changing the sign of the first non-zero coefficient to be positive.
 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):