File:Integrality of root systems.svg
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Summary
| Description |
English: Conditions on the placement of roots in a root system.
Given a root in a root system, this image shows the possible positions for another root within the 2-dimensional subspace that they span. The blue lines show the possible half-integer values of and the red circles show the possible half-integer values of . The black line shows which are all (except 0) possible values for . The black points show possible values for and are labeled with the angle . |
| Source | Own work |
| Author | Smithers888 |
Licensing
|
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:32, 8 December 2009 | | 750 × 400 (10 KB) | JWB | More tweaking |
| 04:26, 4 December 2009 |  | 750 × 450 (9 KB) | JWB | Scrap purple lines in favor of (x,y) coordinate labels at points | |
| 23:31, 29 November 2009 |  | 750 × 450 (7 KB) | JWB | *Make Y axis both blue and red to indicate both products zero on that line *Label pi/2 angle | |
| 22:54, 29 November 2009 |  | 750 × 450 (7 KB) | JWB | Indicate angles with labeled green rays instead of labels on points Indicate Y coordinates of points Add red circles for >2 to illustrate increase towards origin Indicate end root used in series A-G with same color as alpha, similar arrowhead, and length | |
| 07:47, 29 November 2009 |  | 800 × 550 (15 KB) | Sam Derbyshire | Corrected height of vertical lines and changed the colour of the vertical line through 0 to reflect that any point on it is a valid choice of β. | |
| 21:40, 27 November 2009 |  | 800 × 550 (7 KB) | JWB | Correct labeling of red circles. Add couple of additional labels. Trim uninteresting outer portions. | |
| 12:15, 27 November 2009 |  | 900 × 800 (7 KB) | Smithers888 | ((Information |Description=((en|1=Conditions on the placement of roots in a root system. Given a root <math>\alpha</math> in a root system, this image shows the possible positions for another root <math>\beta \neq \pm \alpha</math> within the 2-dimensiona |
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Credit:
(see original file).
