"Root systems and Dynkin diagrams(mathematica)"의 두 판 사이의 차이

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<h5>root systems and Dynkin diagrams</h5>
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Clear[Unirt, rt, r, alp]<br> Clear[A, B, CC, DD, E6, E7, E8, F, G]<br> (* choose the one of types *)<br> ty := B<br> (* define the rank *)<br> r := 4<br> Unirt[A, i_] := UnitVector[r + 1, i] - UnitVector[r + 1, i + 1]<br> Unirt[B, i_] :=<br>  If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i], UnitVector[r, r]]<br> Unirt[CC, i_] :=<br>  If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i], 2*UnitVector[r, r]]<br> Unirt[DD, i_] :=<br>  If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i],<br>   UnitVector[r, r - 1] + UnitVector[r, r]]<br> Unirt[G, 1] := {1, -1, 0}<br> Unirt[G, 2] := {-1, 2, -1}<br> Unirt[F, 1] := {1, -1, 0, 0}<br> Unirt[F, 2] := {0, 1, -1, 0}<br> Unirt[F, 3] := {0, 0, 1, 0}<br> Unirt[F, 4] := {-1, -1, -1, -1}/2<br> Unirt[E6, 1] := {0, 0, 0, 0, 0, 0, 0, 1, \[Minus]1}<br> Unirt[E6, 2] := {0, 0, 0, 0, 0, 0, 1, -1, 0}<br> Unirt[E6, 3] := {1, -2, 1, -2, 1, 1, -2, 1, 1}/3<br> Unirt[E6, 4] := {0, 0, 0, 1, -1, 0, 0, 0, 0}<br> Unirt[E6, 5] := {0, 0, 0, 0, 1, -1, 0, 0, 0}<br> Unirt[E6, 6] := {0, 1, -1, 0, 0, 0, 0, 0, 0}<br> Unirt[E7, i_] :=<br>  Piecewise[{{UnitVector[r + 1, i + 2] - UnitVector[r + 1, 1 + i],<br>     i < 7}, {{1/2, 1/2, 1/2, 1/2, -(1/2), -(1/2), -(1/2), -(1/2)},<br>     i == 7}}, {i, 1, r}]<br> Unirt[E8, i_] :=<br>  Piecewise[{{UnitVector[r, i] - UnitVector[r, 1 + i],<br>     i < 7}, {UnitVector[r, i] + UnitVector[r, i - 1],<br>     i == 7}, {{-(1/2), -(1/2), -(1/2), -(1/2), -(1/2), -(1/2), -(1/<br>       2), -(1/2)}, i == 8}}, {i, Range[r]}]<br> rt[i_] := Unirt[ty, i]<br> b[i_, j_] := (2 Dot[rt[i], rt[j]])/Dot[rt[j], rt[j]]<br> CA := Table[b[i, j], {i, 1, r}, {j, 1, r}]<br> Print["root vectors of ", ty, r]<br> Table[rt[i], {i, 1, r}] // TableForm<br> Print["Cartan matrix of ", ty, r]<br> CA // MatrixForm<br> Print["Dynkin diagram of ", ty, r]<br> GraphPlot[CA, VertexLabeling -> True]
 

2010년 3월 14일 (일) 14:24 판

 

root systems and Dynkin diagrams
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