File:Free modular lattice with 3 generators (x,y,z).gif
Size of this preview: 535 × 599 pixels. Other resolutions: 214 × 240 pixels | 428 × 480 pixels | 807 × 904 pixels.
Original file (807 × 904 pixels, file size: 23 KB, MIME type: image/gif)
Summary
| Description | English: 3-dimensional diagram of the free modular lattice generated by {x,y,z}. Constructed in 1900 by R. Dedekind.
O=x∧y∧z, I=x∨y∨z, p=x∧y, p'=x∨y, q=x∧z, q'=x∨z, r=y∧z, r'=y∨z, u=p∨q, u'=p∧q, v=p∨r, v'=p∧r, w=q∨r, w'=q∧r, a=x∧r', a'=x∨r, b=y∧q', b'=y∨q, c=z∧p', c'=z∨p, o=p∨q∨r, i=p'∧q'∧r', e=a∨o=a'∧i, f=b∨o=b'∧i, g=c∨o=c'∧i. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
Gnuplot source code |
|---|
set parametric set hidden3d unset key set xrange [-10:10] set yrange [-10:10] set zrange [-10:10] unset border unset xtics unset ytics unset ztics set style data line set view 30,330,1.0,1.0 set view 55,335,1.0,1.0 set view 25,340,1.0,1.0 set title "Free modular lattice with 3 generators (x,y,z)" font ",16" splot "m28c.gpdat" index 0:08 with lines 1, "m28c.gpdat" index 09:26 with lines 3, "m28c.gpdat" index 27:35 with lines 1, "m28c.gpdat" index 36:38 with lines 1, "m28c.gpdat" index 39:41 with lines 2, "m28c.gpdat" index 42:44 with lines 2, "m28c.gpdat" index 45:47 with lines 1 set label "O" at 0,0,3 front font ",18" tc rgb "#606060" set label "p" at 0,2,3 front font ",18" tc rgb "#606060" set label "q" at 0,0,5 front font ",18" tc rgb "#606060" set label "r" at 2,0,3 front font ",18" tc rgb "#606060" set label "u" at 0,2,5 front font ",18" tc rgb "#606060" set label "v" at 2,2,3 front font ",18" tc rgb "#606060" set label "w" at 2,0,5 front font ",18" tc rgb "#606060" set label "a" at 2,4,5 front font ",18" tc rgb "#606060" set label "b" at 3,3,4 front font ",18" tc rgb "#606060" set label "c" at 4,2,5 front font ",18" tc rgb "#606060" set label "e" at 2,4,7 front font ",18" tc rgb "#606060" set label "f" at 3,3,7 front font ",18" tc rgb "#606060" set label "g" at 4,2,7 front font ",18" tc rgb "#606060" set label "a'" at 4,6,7 front font ",18" tc rgb "#606060" set label "b'" at 4,4,8 front font ",18" tc rgb "#606060" set label "c'" at 6,4,7 front font ",18" tc rgb "#606060" set label "u'" at 5,7,7 front font ",18" tc rgb "#606060" set label "v'" at 5,5,9 front font ",18" tc rgb "#606060" set label "w'" at 7,5,7 front font ",18" tc rgb "#606060" set label "p'" at 5,7,9 front font ",18" tc rgb "#606060" set label "q'" at 7,7,7 front font ",18" tc rgb "#606060" set label "r'" at 7,5,9 front font ",18" tc rgb "#606060" set label "I" at 7,7,9 front font ",18" tc rgb "#606060" set label "o" at 2,2,5 front font ",18" tc rgb "#606060" set label "i" at 5,5,7 front font ",18" tc rgb "#606060" set label "x" at 4,6,5 front font ",18" tc rgb "#000000" set label "y" at 4,4,5 front font ",18" tc rgb "#000000" set label "z" at 6,4,5 front font ",18" tc rgb "#000000" pause -1 "Press Return" |
Data file "m28c.gpdat" used by gnuplot code |
|---|
0 0 3 0 2 3 0 0 3 0 0 5 0 0 3 2 0 3 0 2 3 0 2 5 0 2 3 2 2 3 0 0 5 0 2 5 0 0 5 2 0 5 2 0 3 2 2 3 2 0 3 2 0 5 0 2 5 2 4 5 2 2 3 3 3 4 2 0 5 4 2 5 2 4 5 4 6 5 2 4 5 2 4 7
3 3 4 4 4 5
3 3 4 3 3 7
4 2 5 6 4 5
4 2 5 4 2 7
2 4 7 4 6 7
4 6 5 4 6 7
3 3 7 4 4 8
4 4 5 4 4 8
4 2 7 6 4 7
6 4 5 6 4 7
4 6 7 5 7 7
4 4 8 5 5 9
6 4 7 7 5 7
5 7 7 5 7 9
5 7 7 7 7 7
5 5 9 5 7 9
5 5 9 7 5 9
7 5 7 7 7 7
7 5 7 7 5 9
5 7 9 7 7 9
7 7 7 7 7 9
7 5 9 7 7 9
0 2 5 2 2 5
2 2 3 2 2 5
2 0 5 2 2 5
2 2 5 2 4 7
2 2 5 3 3 7
2 2 5 4 2 7
2 4 7 5 5 7
3 3 7 5 5 7
4 2 7 5 5 7
5 5 7 5 7 7
5 5 7 5 5 9
5 5 7 7 5 7 |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:33, 31 August 2013 | | 807 × 904 (23 KB) | Jochen Burghardt | User created page with UploadWizard |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on fr.wikipedia.org
.gif){kind=link}