S-expression: Difference between revisions
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== Quick rules of S-expressions == | == Quick rules of S-expressions == | ||
[[File:S(expression).svg|thumb|Here is a summarized infographic of what many of these S-expression types do to a harmonic series segment when tempered out.]] | [[File:S(expression).svg|thumb|Here is a summarized infographic of what many of these S-expression types do to a harmonic series segment when tempered out.]] | ||
As S-expressions are deployed widely on the wiki and in the broader xen community, below is a list of what the most common S-expression categories imply when they are [[tempering out|tempered out]]. The linked sections provide deeper information into each comma family. | As S-expressions are deployed widely on the wiki and in the broader xen community, below is a list of what the most common S-expression categories imply is equated when they are [[tempering out|tempered out]]. The linked sections provide deeper information into each comma family. | ||
* [[#Sk (square-particulars)|Square-particulars]]: '''S''k''''', superparticular fractions of the form {{sfrac|''k''<sup>2</sup>|''k''<sup>2</sup> − 1}}. <br>Tempering out S''k'' equates {{sfrac|''k'' + 1|''k''}} with {{sfrac|''k''|''k'' − 1}} and splits {{sfrac|''k'' + 1|''k'' − 1}} in two. | * [[#Sk (square-particulars)|Square-particulars]]: '''S''k''''', superparticular fractions of the form {{sfrac|''k''<sup>2</sup>|''k''<sup>2</sup> − 1}}. <br>Tempering out S''k'' equates {{sfrac|''k'' + 1|''k''}} with {{sfrac|''k''|''k'' − 1}} and splits {{sfrac|''k'' + 1|''k'' − 1}} in two. | ||
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* [[#Sk/S(k + 1) (ultraparticulars)|Ultraparticulars]]: {{nowrap|'''S''k''/S(''k'' + 1)'''}}. Tempering this out splits {{sfrac|''k'' + 2|''k'' − 1}} into {{pars|{{sfrac|''k'' + 1|''k''}}}}<sup>3</sup>. | * [[#Sk/S(k + 1) (ultraparticulars)|Ultraparticulars]]: {{nowrap|'''S''k''/S(''k'' + 1)'''}}. Tempering this out splits {{sfrac|''k'' + 2|''k'' − 1}} into {{pars|{{sfrac|''k'' + 1|''k''}}}}<sup>3</sup>. | ||
* [[#Sk/S(k + 2) (semiparticulars)|Semiparticulars]]: {{nowrap|'''S''k''/S(''k'' + 2)'''}}. Tempering this out splits {{sfrac|''k'' + 3|''k'' − 1}} into {{pars|{{sfrac|''k'' + 2|''k''}}}}<sup>2</sup>. | * [[#Sk/S(k + 2) (semiparticulars)|Semiparticulars]]: {{nowrap|'''S''k''/S(''k'' + 2)'''}}. Tempering this out splits {{sfrac|''k'' + 3|''k'' − 1}} into {{pars|{{sfrac|''k'' + 2|''k''}}}}<sup>2</sup>. | ||
* [[#Ck and Cpk (cube-particulars)|Cube-particulars]]: '''C''k''''' and '''Cp''k''''', superparticular fractions of the form {{sfrac|''k''<sup>3</sup>|''k''<sup>3</sup> − 1}} and {{sfrac|''k''<sup>3</sup> + 1|''k''<sup>3</sup>}}, respectively. | * [[#Ck and Cpk (cube-particulars)|Cube-particulars]]: '''C''k''''' and '''Cp''k''''', superparticular fractions of the form {{sfrac|''k''<sup>3</sup>|''k''<sup>3</sup> − 1}} and {{sfrac|''k''<sup>3</sup> + 1|''k''<sup>3</sup>}}, respectively. | ||
== S''k'' (square-particulars) == | == S''k'' (square-particulars) == | ||