S-expression: Difference between revisions

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Godtone (talk | contribs)
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S(''k''-1) * S''k''<sup>2</sup> = [''k''-2, ''k''-1, ''k'', ''k''+1]^([-1, 2, -1, 0] + 2[0, -1, 2, -1] = [-1, 2, -1, 0] + [0, -2, 4, -2] = [-1, 0, 3, -2]) implies:
S(''k''-1) * S''k''<sup>2</sup> = [''k''-2, ''k''-1, ''k'', ''k''+1]^([-1, 2, -1, 0] + 2[0, -1, 2, -1] = [-1, 2, -1, 0] + [0, -2, 4, -2] = [-1, 0, 3, -2]) implies:


S(''k''-1) * S''k''<sup>2</sup> = (''k''/(''k''+1))<sup>2</sup> / ((''k''-2)/''k'') through [-1, 0, 3, -2] = [0, 0, 2, -2] - [1, 0, -1, 0].
S(''k''-1) * S''k''<sup>2</sup> = (''k''/(''k''-2)) / ((''k''+1)/''k'')<sup>2</sup>  through [-1, 0, 3, -2] = [-1, 0, 1, 0] - [0, 0, -2, 2].


A computer-generated table of both of these forms of commas is currently pending creation and will be added soon.
Below is a table of [[43-limit]] commas. This table is so big because it can be thought of as two tables interleaved (for the two types of commas) and because these commas are quite large so the more interesting commas appear later.
 
{| class="wikitable center-all
|-
! S-expression
! Square Relation
! Comma
|-
 
|}


== Equivalent S-expressions ==
== Equivalent S-expressions ==