"Root systems and Dynkin diagrams(mathematica)"의 두 판 사이의 차이
| 17번째 줄: | 17번째 줄: | ||
<h5>B_n root systems</h5> | <h5>B_n root systems</h5> | ||
| − | (*B_r type Cartan matrix*)<br> r := | + | Clear[rt]<br> (*B_r type Cartan matrix*)<br> r := 4<br> rt[i_] :=<br> If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i], UnitVector[r, r]]<br> a[i_, j_] := (2 Dot[rt[i], rt[j]])/Dot[rt[j], rt[j]]<br> A := Table[a[i, j], {i, 1, r}, {j, 1, r}]<br> Print["root vectors"]<br> Table[rt[i], {i, 1, r}] // TableForm<br> Print["Cartan matrix"]<br> A // MatrixForm |
| 25번째 줄: | 25번째 줄: | ||
<h5>C_n root systems</h5> | <h5>C_n root systems</h5> | ||
| − | + | ||
2010년 3월 14일 (일) 11:30 판
- Root Systems and Dynkin diagrams
- http://en.wikipedia.org/wiki/root_systems
- [1][2][3][4]http://en.wikipedia.org/wiki/Dynkin_diagram
A_n root systems
(* A_n type Cartan matrix *)
r := 2
rt[i_] := UnitVector[r + 1, i] - UnitVector[r + 1, i + 1]
a[i_, j_] := (2 Dot[rt[i], rt[j]])/Dot[rt[j], rt[j]]
A := Table[a[i, j], {i, 1, r}, {j, 1, r}]
A // MatrixForm
B_n root systems
Clear[rt]
(*B_r type Cartan matrix*)
r := 4
rt[i_] :=
If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i], UnitVector[r, r]]
a[i_, j_] := (2 Dot[rt[i], rt[j]])/Dot[rt[j], rt[j]]
A := Table[a[i, j], {i, 1, r}, {j, 1, r}]
Print["root vectors"]
Table[rt[i], {i, 1, r}] // TableForm
Print["Cartan matrix"]
A // MatrixForm
C_n root systems
D_n root systems
(* A_n type Cartan matrix *)
r := 2
rt[i_] := UnitVector[r + 1, i] - UnitVector[r + 1, i + 1]
a[i_, j_] := (2 Dot[rt[i], rt[j]])/Dot[rt[j], rt[j]]
A := Table[a[i, j], {i, 1, r}, {j, 1, r}]
A // MatrixForm