Recoverability: Difference between revisions
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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 {{nowrap| C(''n'' - 1, ''r'' - 1) }} zeros, and the second segment of {{nowrap| 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 [[Wedgies and multivals]], 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 {{nowrap| C(''n'' - 1, ''r'' - 1) }} zeros, and the second segment of {{nowrap| 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 [[Wedgies and multivals]], 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:Exterior algebra]] | [[Category:Exterior algebra]] | ||
{{Todo|add examples|add links}} | {{Todo|add examples|add links}} | ||