Difference between revisions of "Template:Dynkin/testcases"
imported>John of Reading m (Typo fixing, replaced: correponds → corresponds (2) using AWB) |
imported>Jonesey95 (Fix Linter errors) |
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!Valued<BR>graph<sup>2</sup> | !Valued<BR>graph<sup>2</sup> | ||
!<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | !<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | ||
| − | ![[Determinant]]<P>(4-a<sub>21</sub>*a<sub>12</sub>) | + | ![[Determinant]]<P>(4-a<sub>21</sub>*a<sub>12</sub>)</p> |
|- align=center | |- align=center | ||
!colspan=7|[[Dynkin_diagram#Finite_Dynkin_diagrams|Finite]] (Determinant>0) | !colspan=7|[[Dynkin_diagram#Finite_Dynkin_diagrams|Finite]] (Determinant>0) | ||
| Line 125: | Line 125: | ||
!Valued<BR>graph<sup>2</sup> | !Valued<BR>graph<sup>2</sup> | ||
!<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | !<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | ||
| − | ![[Determinant]]<P>(4-a<sub>21</sub>*a<sub>12</sub>) | + | ![[Determinant]]<P>(4-a<sub>21</sub>*a<sub>12</sub>)</p> |
|- align=center | |- align=center | ||
!colspan=7|[[Dynkin_diagram#Finite_Dynkin_diagrams|Finite]] (Determinant>0) | !colspan=7|[[Dynkin_diagram#Finite_Dynkin_diagrams|Finite]] (Determinant>0) | ||
Latest revision as of 00:19, 3 April 2020
| 42px | This is the template test cases page for the sandbox of Template:Dynkin. Script error: No such module "Purge". to update the examples. If there are many examples of a complicated template, later ones may break due to limits in MediaWiki, see the HTML comment "NewPP limit report" in the rendered page. You can also use Special:ExpandTemplates to examine the results of template uses. You can test how this page looks in the different skins with these links: |
Testing sandbox version
{{Dynkin/sandbox}}
| Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
|---|---|---|---|---|---|---|
| (Standard) multi-edged graph1 |
Valued graph2 |
<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | Determinant (4-a21*a12) | |||
| Finite (Determinant>0) | ||||||
| A1xA1 | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&0\\0&2\end{smallmatrix}\right ]</math> | 4 | 2 | |
| A2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}\right ]</math> | 3 | 3 | |
| B2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
| C2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
| G2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}\right ]</math> | 1 | 6 | <math>{D}_4</math> File:Dynkin affine D3 folding.png |
| Affine (Determinant=0) | ||||||
| A1(1) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{A}}_3</math> File:Dynkin affine A3 folding.png |
| A2(2) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{D}}_4</math> File:Dynkin affine D4 folding.png |
| Hyperbolic (Determinant<0) | ||||||
| Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}\right ]</math> | -1 | ∞ | H5(6) File:Dynkin hyperbolic pentstar folding.png | ||
| Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}\right ]</math> | 4-ab | ∞ | |||
|
Note1: The multi-edged diagram corresponds to the nondiagonal Cartan matrix elements a21, a12, with the number of edges drawn equal to max(a21, a12), and an arrow pointing towards nonunity element(s). Note2: For hyperbolic groups, (a12*a21>4), the multiedge style is abandoned in favor of an explicit labeling (a21, a12) on the edge. These are usually not applied to finite and affine graphs. Note3: Many multi-edged groups are automorphic via a folding operation with a higher ranked simply-laced group. | ||||||
Testing main template
{{Dynkin}}
| Group name |
Dynkin diagram | Cartan matrix | Symmetry order |
Related simply-laced automorphic group3 | ||
|---|---|---|---|---|---|---|
| (Standard) multi-edged graph1 |
Valued graph2 |
<math>\left [\begin{matrix}2&a_{12}\\a_{21}&2\end{matrix}\right ]</math> | Determinant (4-a21*a12) | |||
| Finite (Determinant>0) | ||||||
| A1xA1 | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | Script error: No such module "Dynkin". Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&0\\0&2\end{smallmatrix}\right ]</math> | 4 | 2 | |
| A2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-1&2\end{smallmatrix}\right ]</math> | 3 | 3 | |
| B2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-1&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
| C2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-2&2\end{smallmatrix}\right ]</math> | 2 | 4 | <math>{A}_3</math> Script error: No such module "Dynkin". |
| G2 | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-3&2\end{smallmatrix}\right ]</math> | 1 | 6 | <math>{D}_4</math> File:Dynkin affine D3 folding.png |
| Affine (Determinant=0) | ||||||
| A1(1) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-2\\-2&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{A}}_3</math> File:Dynkin affine A3 folding.png |
| A2(2) | Script error: No such module "Dynkin". | Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-4&2\end{smallmatrix}\right ]</math> | 0 | ∞ | <math>{\tilde{D}}_4</math> File:Dynkin affine D4 folding.png |
| Hyperbolic (Determinant<0) | ||||||
| Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-1\\-5&2\end{smallmatrix}\right ]</math> | -1 | ∞ | H5(6) File:Dynkin hyperbolic pentstar folding.png | ||
| Script error: No such module "Dynkin". | <math>\left [\begin{smallmatrix}2&-b\\-a&2\end{smallmatrix}\right ]</math> | 4-ab | ∞ | |||
|
Note1: The multi-edged diagram corresponds to the nondiagonal Cartan matrix elements a21, a12, with the number of edges drawn equal to max(a21, a12), and an arrow pointing towards nonunity element(s). Note2: For hyperbolic groups, (a12*a21>4), the multiedge style is abandoned in favor of an explicit labeling (a21, a12) on the edge. These are usually not applied to finite and affine graphs. Note3: Many multi-edged groups are automorphic via a folding operation with a higher ranked simply-laced group. | ||||||