Tp tuning: Difference between revisions
→Definition: Perhaps better math notation |
→Definition: swap m and b in accordance with other articles |
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== Definition == | == Definition == | ||
If ''p'' ≥ 1, define the T''p'' norm, which we may also call the T''p'' complexity, of any monzo in weighted coordinates | If ''p'' ≥ 1, define the T''p'' norm, which we may also call the T''p'' complexity, of any monzo in weighted coordinates m as | ||
<math>||\ | | <math>||\ |m_2 \ m_3 \ \ldots \ m_k> ||_p = (|m_2|^p + |m_3|^p + \ldots + |m_k|^p)^{1/p}</math> | ||
where 2, 3, … , ''k'' are the primes up to ''k'' in order. In unweighted coordinates, this would be, for unweighted monzo | where 2, 3, … , ''k'' are the primes up to ''k'' in order. In unweighted coordinates, this would be, for unweighted monzo b, | ||
<math>||\ | | <math>||\ |b_2 \ b_3 \ \ldots \ b_k> ||_p = (|b_2 \log_2 2 |^p + |b_3 \log_2 3|^p + \ldots + |b_k \log_2 k |^p)^{1/p}</math> | ||
If ''q'' is any positive rational number, ||''q''||<sub>''p''</sub> is the T''p'' norm defined by its monzo. | If ''q'' is any positive rational number, ||''q''||<sub>''p''</sub> is the T''p'' norm defined by its monzo. | ||