"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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==encyclopedia==
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# Clear[Unirt, rt, r, alp]<br> Clear[a, b, c, d, e6, e7, e8, f, g]<br> (* choose the one of types above *)<br> ty := b<br> (* define the rank *)<br> r := 5<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[c, i_] :=<br>  If[i < r, UnitVector[r, i] - UnitVector[r, 1 + i], 2*UnitVector[r, r]]<br> Unirt[d, 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> ed[i_, j_] := If[i < j, b[i, j] b[j, i], 0]<br> Ed := Table[ed[i, j], {i, 1, r}, {j, 1, r}]<br> Ed // MatrixForm<br> GraphPlot[Ed, VertexLabeling -> True, MultiedgeStyle -> True]<br> ls[i_] := Sqrt[Dot[rt[i], rt[i]]]<br> Print["length of each root"]<br> Table[{\[Alpha][i], ls[i]}, {i, 1, r}] // TableForm
 
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<h5>related items</h5>
 
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* [[Root Systems and Dynkin diagrams]]
 
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<h5>encyclopedia</h5>
 
  
 
* http://en.wikipedia.org/wiki/root_systems
 
* http://en.wikipedia.org/wiki/root_systems
 
* http://en.wikipedia.org/wiki/Dynkin_diagram
 
* http://en.wikipedia.org/wiki/Dynkin_diagram
 
* http://mathworld.wolfram.com/DynkinDiagram.html
 
* http://mathworld.wolfram.com/DynkinDiagram.html
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[[분류:개인노트]]
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[[분류:math and physics]]
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[[분류:Lie theory]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q534131 Q534131]
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===Spacy 패턴 목록===
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* [{'LOWER': 'root'}, {'LEMMA': 'system'}]

2021년 2월 17일 (수) 02:17 기준 최신판

encyclopedia

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'root'}, {'LEMMA': 'system'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Root_systems_and_Dynkin_diagrams(mathematica)&oldid=51954"