S-expression: Difference between revisions
Added summarized S-expression infographic for the mortals |
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== Equivalent S-expressions == | == Equivalent S-expressions == | ||
All S-expressions have other equivalent S-expressions; however, | All S-expressions have other equivalent S-expressions; however, a comma might appear in more than one family of S-commas or arise as a specific product of them. This often means nontrivial, deep tempering opportunities, usually leading to multiple of the most elegant and efficient temperaments that we know of depending on how the tempering is further realized. Generally we exclude 1/''n''-square-particulars, only noting up to 1/3-square-particulars, because equivalent 1/''n''-square-particular expressions become very common for higher ''n'', but are still quite rare for small ''n''. | ||
=== A useful general rule === | === A useful general rule === | ||
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$$ | $$ | ||
This is important to note because using this simple rule we can derive an infinite amount of | This is important to note because using this simple rule we can derive an infinite amount of trivial equivalent S-expressions. See [[S-expression/Advanced results]] for mathematical details. | ||
=== Examples === | === Examples === | ||
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| [[176/175]] | | [[176/175]] | ||
| S8/S10, S22⋅S23⋅S24 | | S8/S10, S22⋅S23⋅S24 | ||
|- | |||
|[[225/224]] | |||
|S15, S25*S26*S27 | |||
|- | |- | ||
| [[243/242]] | | [[243/242]] | ||
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| [[676/675]] | | [[676/675]] | ||
| S26, S13/S15 | | S26, S13/S15 | ||
|- | |||
|[[1216/1215]] | |||
|S16/S18, S64*S65*S76*S77 | |||
|- | |- | ||
| [[1225/1224]] | | [[1225/1224]] | ||
| S35, S49⋅S50 | | S35, S49⋅S50 | ||
|- | |||
|[[2080/2079]] | |||
|S64⋅S65, S78⋅S79⋅S80 | |||
|- | |- | ||
| [[2601/2600]] | | [[2601/2600]] | ||
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| [[3025/3024]] | | [[3025/3024]] | ||
| S55, S22/S24, (S25/S27)⋅S99 | | S55, S22/S24, (S25/S27)⋅S99 | ||
|- | |||
|[[3136/3135]] | |||
|S56, S96*S97*S98 | |||
|- | |||
|[[4000/3993]] | |||
|S10/S11, (S12/S14)/S99, S25*(S64*S65)/S55 | |||
|- | |||
|[[4375/4374]] | |||
|S25/S27, S55/S99 | |||
|- | |||
|[[6656/6655]] | |||
|(S64*S65)/S55, S64*S351/S99 | |||
|- | |- | ||
| [[9801/9800]] | | [[9801/9800]] | ||
| S99, S33/S35 | | S99, S33/S35 | ||
|- | |||
|[[10985/10976]] | |||
|S13/S14, (S64*S65^2)*S99 | |||
|- | |- | ||
| [[25921/25920]] | | [[25921/25920]] | ||
| S161, S46/S48 | | S161, S46/S48 | ||
|- | |||
|[[32805/32768]] | |||
|S15/(S8/S9), S19/(S16/S18)^2 | |||
|- | |||
|[[43904/43875]] | |||
|S14/S15, S49*S64, S56*S76*S77 | |||
|- | |- | ||
| <small>[[123201/123200]]</small> | | <small>[[123201/123200]]</small> | ||
| S351, S78/S80 | | S351, S78/S80, S25/S27/S65 | ||
|} | |} | ||