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| Maple code for the parts of these which do not call the Maple functions for Hermite normal form, Smith normal form or the pseudoinverse can be found in the article [[Basic abstract temperament translation code]]. | | Maple code for the parts of these which do not call the Maple functions for Hermite normal form, Smith normal form or the pseudoinverse can be found in the article [[Basic abstract temperament translation code]]. |
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| === Wedgies ===
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| To translate to wedgies from RREF simply take the wedge product of the rows of the RREF and then reduce the resulting multivector to a wedgie. To translate from wedgies to RREF, for a wedgie of rank ''r'' in ''n'' dimensions (where {{nowrap|''n'' {{=}} π(''p'')}} is the number of primes in the ''p''-limit) take a wedge product of basis vectors involving {{nowrap|''r'' − 1}} basis elements (i.e., the wedge product of {{nowrap|''r'' − 1}} elements representing primes) and wedge these with the basis element for each prime, obtaining either 0 or an ''r''-fold wedge product with sign ±1. Take the corresponding element of the wedgie times the ±1 sign (which is computed from the parity of the permutation of the ''r'' elements.) This gives a val; do this for every combination of {{nowrap|''r'' − 1}} basis elements to obtain ''n'' choose {{nowrap|''r'' − 1}} vals, and reduce the result to an RREF by the usual Gaussian reduction. If possible, this should be done using rational arithmetic, not floating point numbers.
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| An alternative explanation of this process is provided here: [[Intro to exterior algebra for RTT#Converting varianced multivectors to matrices]]
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| === Frobenius projection matrices === | | === Frobenius projection matrices === |