Recoverability: Difference between revisions

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=Complete searches for temperaments=

~~By a~~ complete search for regular temperaments is ~~meant~~ a search which is guaranteed to find all temperaments meeting certain specified conditions. Recoverability conditions provide one approach to these. The first segment of W∨2 consists of C(n-1, r-1) zeros, and the second segment of C(n-1, r) integers identical to the initial, 2 containing, segment of W. By beginning with such a multivector of integer coefficients, wedging with J, and rounding, we obtain a multivector which is a candidate for a p-limit rank r wedgie, defining a regular temperament. It will not in general be a wedgie, but all recoverable wedgies can be obtained in this way. Hence all that remains to do, as discussed in [[The_wedgie|The wedgie]], is to test if the multivector in question is actually a wedgie, and also if it passes any further conditions on complexity, error, or badness we wish to place on our list of wedgies.

A complete search for regular temperaments is a search which is guaranteed to find all temperaments meeting certain specified conditions. Recoverability conditions provide one approach to these. The first segment of W∨2 consists of C(n-1, r-1) zeros, and the second segment of C(n-1, r) integers identical to the initial, 2 containing, segment of W. By beginning with such a multivector of integer coefficients, wedging with J, and rounding, we obtain a multivector which is a candidate for a p-limit rank r wedgie, defining a regular temperament. It will not in general be a wedgie, but all recoverable wedgies can be obtained in this way. Hence all that remains to do, as discussed in [[The_wedgie|The wedgie]], is to test if the multivector in question is actually a wedgie, and also if it passes any further conditions on complexity, error, or badness we wish to place on our list of wedgies.

[[Category:math]]

[[Category:todo:add_examples]]

[[Category:todo:add_links]]

[[Category:Exterior algebra]]

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 =Complete searches for temperaments=
-By a complete search for regular temperaments is meant a search which is guaranteed to find all temperaments meeting certain specified conditions. Recoverability conditions provide one approach to these. The first segment of W∨2 consists of C(n-1, r-1) zeros, and the second segment of C(n-1, r) integers identical to the initial, 2 containing, segment of W. By beginning with such a multivector of integer coefficients, wedging with J, and rounding, we obtain a multivector which is a candidate for a p-limit rank r wedgie, defining a regular temperament. It will not in general be a wedgie, but all recoverable wedgies can be obtained in this way. Hence all that remains to do, as discussed in [[The_wedgie|The wedgie]], is to test if the multivector in question is actually a wedgie, and also if it passes any further conditions on complexity, error, or badness we wish to place on our list of wedgies.
+A complete search for regular temperaments is a search which is guaranteed to find all temperaments meeting certain specified conditions. Recoverability conditions provide one approach to these. The first segment of W∨2 consists of C(n-1, r-1) zeros, and the second segment of C(n-1, r) integers identical to the initial, 2 containing, segment of W. By beginning with such a multivector of integer coefficients, wedging with J, and rounding, we obtain a multivector which is a candidate for a p-limit rank r wedgie, defining a regular temperament. It will not in general be a wedgie, but all recoverable wedgies can be obtained in this way. Hence all that remains to do, as discussed in [[The_wedgie|The wedgie]], is to test if the multivector in question is actually a wedgie, and also if it passes any further conditions on complexity, error, or badness we wish to place on our list of wedgies.
 [[Category:math]]
 [[Category:todo:add_examples]]
 [[Category:todo:add_links]]
 [[Category:Exterior algebra]]