S-expression: Difference between revisions

Second pass. Wrap proofs in boxes. Adopt templates to distinguish editorial stuff from article contents.
- alternative S-expressions in the tables as they are off topic for the sections, already covered in #Equivalent S-expressions, and break the flow. Sort the table of equivalent S-expressions from simple to complex. Collapse the tables for 1/4- and 1/5-square-particulars
Line 55: Line 55:
| 5
| 5
|-
|-
| S6 = S8⋅S9
| S6
| ([[6/5]])/([[7/6]])
| ([[6/5]])/([[7/6]])
| [[36/35]]
| [[36/35]]
Line 70: Line 70:
| 7
| 7
|-
|-
| S9 = S6/S8
| S9
| ([[9/8]])/([[10/9]])
| ([[9/8]])/([[10/9]])
| [[81/80]]
| [[81/80]]
Line 155: Line 155:
| 13
| 13
|-
|-
| S26 = S13/S15
| S26
| ([[26/25]])/([[27/26]])
| ([[26/25]])/([[27/26]])
| [[676/675]]
| [[676/675]]
Line 200: Line 200:
| 17
| 17
|-
|-
| S35 = S49⋅S50
| S35
| ([[35/34]])/([[36/35]])
| ([[35/34]])/([[36/35]])
| [[1225/1224]]
| [[1225/1224]]
Line 230: Line 230:
| 17
| 17
|-
|-
| S55 = S22/S24
| S55
| ([[55/54]])/([[56/55]])
| ([[55/54]])/([[56/55]])
| [[3025/3024]]
| [[3025/3024]]
Line 285: Line 285:
| 31
| 31
|-
|-
| S99 = S33/S35
| S99
| ([[99/98]])/([[100/99]])
| ([[99/98]])/([[100/99]])
| [[9801/9800]]
| [[9801/9800]]
Line 330: Line 330:
| 31
| 31
|-
|-
| S161 = S46/S48
| S161
| ([[161/160]])/([[162/161]])
| ([[161/160]])/([[162/161]])
| [[25921/25920]]
| [[25921/25920]]
Line 390: Line 390:
| 31
| 31
|-
|-
| S351 = S78/S80
| S351
| ([[351/350]])/([[352/351]])
| ([[351/350]])/([[352/351]])
| [[123201/123200]]
| [[123201/123200]]
Line 560: Line 560:
| 7
| 7
|-
|-
| S7⋅S8 = S4/S6
| S7⋅S8
| ([[7/6]])([[9/8]])
| ([[7/6]])([[9/8]])
| [[28/27]]
| [[28/27]]
| 7
| 7
|-
|-
| S8⋅S9 = S6
| S8⋅S9
| ([[8/7]])/([[10/9]])
| ([[8/7]])/([[10/9]])
| [[36/35]]
| [[36/35]]
Line 650: Line 650:
| 23
| 23
|-
|-
| S25⋅S26 = S10/S12
| S25⋅S26
| ([[25/24]])/([[27/26]])
| ([[25/24]])/([[27/26]])
| [[325/324]]
| [[325/324]]
Line 700: Line 700:
| 17
| 17
|-
|-
| S49⋅S50 = S35
| S49⋅S50
| ([[49/48]])/([[51/50]])
| ([[49/48]])/([[51/50]])
| [[1225/1224]]
| [[1225/1224]]
Line 1,218: Line 1,218:
|}
|}


{| class="wikitable center-all"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | 23-limit {{frac|1|4}}-square particulars
|+ style="font-size: 105%; white-space: nowrap;" | 23-limit {{frac|1|4}}-square particulars
|-
|-
! S-expression
! S-expression
Line 1,407: Line 1,407:
|}
|}


{| class="wikitable center-all"
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style="font-size: 105%;" | 23-limit {{frac|1|5}}-square particulars
|+ style="font-size: 105%; white-space: nowrap;" | 23-limit {{frac|1|5}}-square particulars
|-
|-
! S-expression
! S-expression
Line 2,576: Line 2,576:
! Comma
! Comma
! S-expressions
! S-expressions
|-
| [[28/27]]
| S7⋅S8, S4/S6
|-
| [[36/35]]
| S6, S8⋅S9
|-
|-
| [[64/63]]
| [[64/63]]
| (S4⋅S5⋅S6)/S3 = S4/(S6⋅S7) = S8
| S8, S4/(S6⋅S7), (S4⋅S5⋅S6)/S3
|-
|-
| [[81/80]]
| [[81/80]]
| S6/S8 = S9
| S9, S6/S8
|-
|-
| [[176/175]]
| [[176/175]]
| S8/S10 = S22⋅S23⋅S24
| S8/S10, S22⋅S23⋅S24
|-
|-
| [[243/242]]
| [[243/242]]
| S9/S11 = S15/([[3025/3024|S22/S24 = S55]])
| S9/S11, S15/([[3025/3024|S22/S24 = S55]])
|-
|-
| [[325/324]]
| [[325/324]]
| S10/S12 = S25⋅S26
| S25⋅S26, S10/S12
|-
|-
| [[540/539]]
| [[540/539]]
| S12/S14 = (S9⋅S10)/S7 = (S6/S7)/(S8/S10)
| S12/S14, (S9⋅S10)/S7, (S6/S7)/(S8/S10)
|-
|-
| [[676/675]]
| [[676/675]]
| S13/S15 = S26
| S26, S13/S15
|-
|-
| [[1225/1224]]
| [[1225/1224]]
| S35 = S49⋅S50
| S35, S49⋅S50
|-
|-
| [[3025/3024]]
| [[3025/3024]]
| S22/S24 = S55 = (S25/S27)⋅S99
| S55, S22/S24, (S25/S27)⋅S99
|-
|-
| [[2601/2600]]
| [[2601/2600]]
| S17/(S25⋅S26) = S51
| S51, S17/(S25⋅S26)
|-
|-
| [[9801/9800]]
| [[9801/9800]]
| S99 = S33/S35
| S99, S33/S35
|-
|-
| [[25921/25920]]
| [[25921/25920]]
| S161 = S46/S48
| S161, S46/S48
|-
|-
| [[123201/123200]]
| [[123201/123200]]
| S351 = S78/S80
| S351, S78/S80
|}
|}