Gradus suavitatis: Difference between revisions
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Created page with "Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. It is somewhat similar to the Wilson norm, in that it depends on the prime factorization. == Definition == Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. For example <mat..." |
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Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. | Euler's '''gradus suavitatis''',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. | ||
It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization. | It is somewhat similar to the [[Wilson norm]], in that it depends on the prime factorization. | ||
Revision as of 16:44, 19 June 2025
Euler's gradus suavitatis,[1] which is probably the first complexity measure historically. It is somewhat similar to the Wilson norm, in that it depends on the prime factorization.
Definition
Given s, the sum of prime factors, and n the number of prime factors, Euler's gradus function is s - n + 1. For example [math]\displaystyle{ \text{Gradus}\left(\tfrac{15}{8}\right) = 14 - 5 + 1 = 10 }[/math].
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- ↑ Leonhard Euler (1739) Tentamen novae theoriae musicae (Attempt at a New Theory of Music), St. Petersburg.