https://github.com/HEPTHools/Adinkra
Tip revision: 2bef4cc5565bdf33bdd2d6a305fd487ae2e74b87 authored by Kory Stiffler on 06 March 2022, 05:40:09 UTC
Depreciated NColors[DColor,Phi,Psi]
Depreciated NColors[DColor,Phi,Psi]
Tip revision: 2bef4cc
Adinkra.m
AdinkraFullReport[Rep_] := AdinkraReport[Rep, 8]
AdinkraReport[Rep_, 0] := Column[If[CorrectDimensions[Rep],
{StringJoin["N = ", ToString[NColors[Rep]]],
StringJoin["dbosons x dfermions = ", ToString[dbosons[Rep]],
" \[Times] ", ToString[dfermions[Rep]]], StringJoin["GATest = ",
ToString[GATest[Rep]]], StringJoin["InverseTest = ",
ToString[InverseTest[Rep]]], StringJoin["TransposeTest = ",
ToString[TransposeTest[Rep]]], Chi0Report[Rep]},
{Print[StringJoin["N = ", ToString[NColors[Rep]]]],
Print[StringJoin["dbosons x dfermions = ", ToString[dbosons[Rep]],
" \[Times] ", ToString[dfermions[Rep]]]],
Print["Incorrect Dimensions"], Abort[]}], Spacings -> DefaultSpacing]
AdinkraReport[Rep_] := AdinkraReport[Rep, 0]
AdinkraReport[Rep_, 1] := Column[Join[{AdinkraReport[Rep, 0]},
NewAdinkraReportMaterial[Rep, 1]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 2] := Column[Join[{AdinkraReport[Rep, 0]},
NewAdinkraReportMaterial[Rep, 2]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 3] := Column[Join[{AdinkraReport[Rep, 1]},
NewAdinkraReportMaterial[Rep, 2]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 4] := Column[Join[{AdinkraReport[Rep, 0]},
NewAdinkraReportMaterial[Rep, 4]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 5] := Column[Join[{AdinkraReport[Rep, 1]},
NewAdinkraReportMaterial[Rep, 4]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 6] := Column[Join[{AdinkraReport[Rep, 2]},
NewAdinkraReportMaterial[Rep, 4]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 7] := Column[Join[{AdinkraReport[Rep, 3]},
NewAdinkraReportMaterial[Rep, 4]], Spacings -> DefaultSpacing]
AdinkraReport[Rep_, 8] := Column[Join[{AdinkraReport[Rep, 7]},
NewAdinkraReportMaterial[Rep, 8]], Spacings -> DefaultSpacing]
CorrectDimensions[L_, R_] := dbosons[L, R] == nColumns[R] &&
dfermions[L, R] == nColumns[L] && NColors[L, R] == nMatrices[R]
CorrectDimensions[Rep_] := CorrectDimensions[L[Rep], R[Rep]]
L[Q] = {{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0, -1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, -1, 0}, {0, 0,
0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 0, -1, 0}, {0,
1, 0, 0}, {1, 0, 0, 0}}}
L[Qtilde] = {{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0,
1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, 0, 1,
0}, {0, -1, 0, 0}, {1, 0, 0, 0}}}
L[RepNumber_] := BC4Boson[NegToOnePosToTwo[RepNumber],
Digit[Abs[RepNumber], 5], Digit[Abs[RepNumber], 4],
Digit[Abs[RepNumber], 3]][BC4Color[2, Digit[Abs[RepNumber], 2],
Digit[Abs[RepNumber], 1], 1][L[TildeIndex[[Digit[Abs[RepNumber],
0]]]]]]
BC4Boson[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4[[If[EvenQ[ni], 2, 1],ai,mu,Ai]][[ii,ji]]*L[[Ii,ji,jhat]],
{ji, 1, 4}], {Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
BC4 = {{{{{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{0,
-1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, -1,
0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0,
0, -1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {-1, 0,
0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, 0, -1}, {0, 0, -1, 0}, {-1, 0,
0, 0}, {0, -1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0},
{-1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 0, -1}}, {{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1,
0}}, {{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0, 0}},
{{0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}},
{{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}}, {{0,
-1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, -1,
0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0,
-1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {-1, 0,
0, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0, -1}, {0, -1, 0, 0},
{-1, 0, 0, 0}, {0, 0, -1, 0}}, {{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, -1}, {0, -1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0},
{-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0,
0, 0, -1}}, {{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {0, 0, -1,
0}}, {{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}},
{{0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}}},
{{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{0, 1,
0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, 1, 0},
{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, 0, 1,
0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {1, 0, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, -1}}, {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0,
-1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0, 0,
0}}}, {{{0, 0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}},
{{0, 0, 0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}}, {{1, 0,
0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, 1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}}, {{{1, 0, 0, 0}, {0, 0,
1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, 1, 0, 0}, {0, 0, 0, 1},
{-1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, -1, 0}, {-1,
0, 0, 0}}}, {{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}}, {{0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, -1, 0}},
{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}}, {{0, 1,
0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {-1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}}, {{1, 0,
0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, -1, 0}}, {{0, 0, 0, 1},
{1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, 0, 1, 0}, {0, 1, 0,
0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}}},
{{{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}, {{0, 1,
0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, 1, 0},
{0, 0, 0, -1}, {1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, 0,
-1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {-1, 0, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, -1}}, {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}, {0, 0, -1, 0}}, {{0, 0, 0, 1}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0,
-1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {-1, 0, 0,
0}}}, {{{0, 0, 1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}},
{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}}, {{1, 0,
0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, 1, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}, {{{1, 0, 0, 0}, {0, 0,
-1, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}, {{0, 1, 0, 0}, {0, 0, 0, -1},
{1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, 1, 0}, {-1,
0, 0, 0}}}, {{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0,
-1}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1, 0}},
{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}, {{0, 1,
0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {-1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}}, {{1, 0,
0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, -1, 0}}, {{0, 0, 0, 1},
{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, 0, 1, 0}, {0, -1,
0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}},
{{{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}, {{0, -1,
0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 0, 1,
0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {1, 0, 0, 0}, {0,
0, 1, 0}, {0, 0, 0, -1}}, {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1},
{0, 0, -1, 0}}, {{0, 0, 0, -1}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1,
0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0, 0, 0}}},
{{{0, 0, -1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}}, {{0, 0,
0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}}, {{-1, 0, 0, 0},
{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}, {{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0,
1, 0, 0}, {0, 0, 0, -1}}, {{0, -1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0},
{0, 0, -1, 0}}, {{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1,
0, 0}}, {{0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}}},
{{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}, {{0, 0,
0, -1}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1, 0}}, {{-1, 0, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}, {-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {0, 0, 1, 0}, {1,
0, 0, 0}, {0, 0, 0, -1}}, {{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0},
{0, 0, -1, 0}}, {{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1,
0, 0}}, {{0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}},
{{{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{0, 1,
0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, 1, 0},
{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, 0,
-1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {-1, 0, 0,
0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, 0, 1}, {0, 0, -1, 0}, {-1, 0, 0,
0}, {0, -1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {-1,
0, 0, 0}}}, {{{0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}, {{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}},
{{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, 1,
0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}},
{{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, 1,
0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, 1, 0},
{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, -1,
0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}}, {{{0, 0, 1, 0}, {-1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0,
0, 0}, {0, 0, -1, 0}}, {{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}, {-1, 0,
0, 0}}}, {{{0, 1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}, {{1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {0, 0, -1, 0}},
{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, 0,
1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}}},
{{{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}, {{0, -1,
0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 0,
1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {1, 0, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, -1}}, {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
0, -1}, {0, 0, -1, 0}}, {{0, 0, 0, -1}, {0, 0, 1, 0}, {-1, 0, 0, 0},
{0, -1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0,
0, 0}}}, {{{0, 0, -1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}, {{0, 0, 0, -1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}},
{{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, -1,
0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}},
{{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, -1,
0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, -1, 0},
{1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 1,
0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0, -1}, {0, 1, 0, 0}, {-1, 0,
0, 0}, {0, 0, -1, 0}}, {{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {-1, 0,
0, 0}}}, {{{0, -1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}, {{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, -1, 0}},
{{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}}, {{0, 0,
-1, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}}},
{{{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}, {{0, -1,
0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, -1}, {1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 0,
-1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {-1, 0, 0,
0}, {0, 0, 1, 0}, {0, 0, 0, -1}}, {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, 0, -1}, {0, 0, -1, 0}, {1, 0, 0,
0}, {0, -1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {-1,
0, 0, 0}}}, {{{0, 0, -1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}}, {{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}},
{{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, -1,
0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}},
{{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}, {{0, -1,
0, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, -1, 0}}, {{0, 0, -1, 0},
{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, -1,
0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {-1, 0, 0, 0},
{0, 1, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0,
0, 0}, {0, 0, -1, 0}}, {{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1},
{0, -1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {-1, 0,
0, 0}}}, {{{0, -1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}}, {{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, -1, 0}},
{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, 0,
-1, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}},
{{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}, {{0, 1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, 1, 0}, {0, 0,
0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {0,
1, 0, 0}, {-1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, -1}}, {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1, 0, 0}},
{{0, 0, 1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0, 0, 0}}},
{{{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0,
1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}}, {{1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}, {-1, 0, 0, 0}}}, {{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0,
0}, {0, 0, 0, -1}}, {{0, 1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0,
-1, 0}}, {{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}},
{{0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}}},
{{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}, {{0, 0, 0,
1}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1, 0}}, {{1, 0, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 0, 1}, {0,
0, 1, 0}, {-1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0,
0}, {0, 0, 0, -1}}, {{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0,
-1, 0}}, {{0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}},
{{0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}}}},
{{{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0, 1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}, {{0, 0, 1, 0}, {0, 0,
0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {0,
1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0, 1,
0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0,
0, 1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {1, 0, 0, 0}}},
{{{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}, {{0, 0, 0,
1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}, {1, 0, 0, 0}}}, {{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0},
{0, 0, 0, 1}}, {{0, 1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1,
0}}, {{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}, {{0,
0, 0, 1}, {0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}}},
{{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}, {{0, 0, 0,
1}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}, {{0, 1, 0, 0}, {0, 0, 0, 1}, {0,
0, 1, 0}, {1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0},
{0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, 1,
0}}, {{0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0,
0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}}},
{{{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{0, -1,
0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, 0,
-1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {-1, 0, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}}, {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}, {{0, 0, 0, -1}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0,
1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {1, 0, 0,
0}}}, {{{0, 0, -1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}},
{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}, {{-1, 0,
0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0, -1, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}}, {{{-1, 0, 0, 0}, {0, 0,
-1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}, {{0, -1, 0, 0}, {0, 0, 0, -1},
{1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, -1, 0, 0}, {0, 0, 1, 0}, {1,
0, 0, 0}}}, {{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0,
1}}, {{0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}},
{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}, {{0, -1,
0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {1, 0, 0, 0}}},
{{{0, -1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}, {{-1, 0,
0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, -1},
{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, -1,
0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}}},
{{{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}, {{0, -1,
0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, -1, 0},
{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, 0, 1,
0}, {0, -1, 0, 0}, {1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {1, 0, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, 1}}, {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0,
-1}, {0, 0, 1, 0}}, {{0, 0, 0, -1}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0,
1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {1, 0, 0,
0}}}, {{{0, 0, -1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}},
{{0, 0, 0, -1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}}, {{-1, 0,
0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0}}, {{0, -1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}}, {{{-1, 0, 0, 0}, {0, 0,
1, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}}, {{0, -1, 0, 0}, {0, 0, 0, 1},
{-1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, -1, 0}, {1,
0, 0, 0}}}, {{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}, {{0, 0, 0, -1}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1, 0}},
{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}, {{0, -1,
0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {1, 0, 0, 0}}},
{{{0, -1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}, {{-1, 0,
0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, -1},
{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, 1, 0,
0}, {0, 0, 0, -1}, {1, 0, 0, 0}}}},
{{{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}, {{0, 1,
0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, 1, 0},
{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, 1}, {0, 0,
-1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {-1, 0, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0,
1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0, 0,
0}}}, {{{0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}},
{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}}, {{1, 0,
0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0, 0}}, {{0, 1, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}}, {{{1, 0, 0, 0}, {0, 0,
-1, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}}, {{0, 1, 0, 0}, {0, 0, 0, -1},
{-1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 1, 0, 0}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, -1, 0}, {1,
0, 0, 0}}}, {{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1, 0}}, {{1,
0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}, {{0, 1, 0, 0},
{0, 0, 0, -1}, {0, 0, -1, 0}, {1, 0, 0, 0}}}, {{{0, 1, 0, 0}, {0, 0,
-1, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}, {{1, 0, 0, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0,
-1, 0}, {0, 1, 0, 0}}, {{0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1},
{1, 0, 0, 0}}}}, {{{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0,
0, 1}}, {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}},
{{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0,
-1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}},
{{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{-1, 0,
0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}, {{0, 0, 0, -1}, {0,
0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, 1},
{0, 1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {0, 1, 0, 0}, {1, 0,
0, 0}, {0, 0, 0, 1}}, {{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 1, 0}}, {{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}},
{{0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}},
{{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}, {{0, -1,
0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, -1, 0}, {1,
0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}, {{0, 0, 0, -1}, {0, 1, 0, 0},
{0, 0, 1, 0}, {1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 1,
0, 0}, {0, 0, 0, 1}}, {{0, 0, 0, -1}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0,
0, 1, 0}}, {{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}},
{{0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}, {1, 0, 0, 0}}},
{{{0, -1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}, {{-1, 0,
0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, -1}, {1,
0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, 1, 0, 0},
{0, 0, 0, 1}, {1, 0, 0, 0}}}}, {{{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, 1}}, {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, 1, 0}}, {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}},
{{0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}, {{1, 0, 0,
0}, {0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {0, 0,
-1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, -1},
{0, 1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 0, 1, 0}, {0, -1, 0, 0}, {1, 0,
0, 0}, {0, 0, 0, 1}}, {{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}},
{{0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}},
{{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}, {{0, 1, 0,
0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 1, 0}, {-1,
0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}, {{0, 0, 0, 1}, {0, -1, 0, 0},
{0, 0, 1, 0}, {1, 0, 0, 0}}}, {{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 1,
0, 0}, {0, 0, 0, 1}}, {{0, 0, 0, 1}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0,
0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}},
{{0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}, {{1, 0, 0,
0}, {0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {-1,
0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}, {{0, 0, 1, 0}, {0, -1, 0, 0},
{0, 0, 0, 1}, {1, 0, 0, 0}}}}, {{{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}, {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1},
{0, 0, 1, 0}}, {{0, 0, 1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 1, 0,
0}}, {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}, {{1, 0, 0,
0}, {0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {0, 0,
1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, 1}, {0,
-1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0,
0}, {0, 0, 0, 1}}, {{0, 0, 0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}}, {{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0}},
{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}},
{{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}}, {{0, 1, 0,
0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 1, 0}, {1, 0,
0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}, {{0, 0, 0, 1}, {0, 1, 0, 0}, {0,
0, -1, 0}, {1, 0, 0, 0}}}, {{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1, 0,
0}, {0, 0, 0, 1}}, {{0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
1, 0}}, {{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}},
{{0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {1, 0, 0, 0}}},
{{{0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}, {{1, 0, 0,
0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, 1}, {1, 0,
0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}}, {{0, 0, 1, 0}, {0, 1, 0, 0}, {0,
0, 0, -1}, {1, 0, 0, 0}}}}, {{{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}, {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1},
{0, 0, 1, 0}}, {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1,
0, 0}}, {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}}},
{{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}, {{-1, 0,
0, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, 0, -1},
{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, 0,
0, -1}, {0, -1, 0, 0}, {1, 0, 0, 0}}}, {{{0, 0, -1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}, {{0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
-1, 0, 0}, {0, 0, 1, 0}}, {{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1,
0}, {0, 1, 0, 0}}, {{0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {1,
0, 0, 0}}}, {{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}, {{0, -1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, 1, 0}},
{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}, {{0, 0,
0, -1}, {0, -1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}}},
{{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}}, {{0, 0,
0, -1}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1, 0}}, {{-1, 0, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}, {{0, -1, 0, 0}, {0, 0,
0, -1}, {0, 0, -1, 0}, {1, 0, 0, 0}}}, {{{0, -1, 0, 0}, {0, 0, -1,
0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}, {{-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
-1, 0, 0}, {0, 0, 1, 0}}, {{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 0, -1,
0}, {0, 1, 0, 0}}, {{0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0, -1}, {1,
0, 0, 0}}}}}}
NegToOnePosToTwo[number_] := (Abs[number]/number + 1)*(1/2) + 1
Digit[Num_, Pow_] := Floor[Mod[Num, 10^(Pow + 1)]/10^Pow]
Pow[0][NCol_] := NCol/2
Pow[1][NCol_] := (NCol + 1)/2
Pow[2][NCol_] := NCol/2
Pow[3][NCol_] := (NCol - 1)/2
Pow[4][NCol_] := (NCol - 2)/2
BC4Color[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4[[If[EvenQ[ni], 2, 1],ai,mu,Ai]][[Ii,Ji]]*L[[Ji,ii,jhat]],
{Ji, 1, 4}], {Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
TildeIndex = {Q, Qtilde}
dbosons[L_, R_] := Length[L[[1]]]
dbosons[Rep_] := dbosons[L[Rep], R[Rep]]
nColumns[Matrices_] := Length[Matrices[[1,1]]]
dfermions[L_, R_] := Length[L[[1,1]]]
dfermions[Rep_] := dfermions[L[Rep], R[Rep]]
NColors[L_, R_] := Length[L]
NColors[Rep_] := NColors[L[Rep], R[Rep]]
nMatrices[Matrices_] := Length[Matrices]
GATest[L_, R_] := Table[Simplify[L[[Ii]] . R[[Ji]] + L[[Ji]] . R[[Ii]]],
{Ii, 1, NColors[L, R]}, {Ji, 1, NColors[L, R]}] ==
Table[2*KroneckerDelta[Ii, Ji]*IdentityMatrix[dbosons[L, R]],
{Ii, 1, NColors[L, R]}, {Ji, 1, NColors[L, R]}] &&
Table[Simplify[R[[Ii]] . L[[Ji]] + R[[Ji]] . L[[Ii]]],
{Ii, 1, NColors[L, R]}, {Ji, 1, NColors[L, R]}] ==
Table[2*KroneckerDelta[Ii, Ji]*IdentityMatrix[dfermions[L, R]],
{Ii, 1, NColors[L, R]}, {Ji, 1, NColors[L, R]}]
GATest[Rep_] := GATest[L[Rep], R[Rep]]
InverseTest[L_, R_] := If[SquareMatrixQ[R[[1]]],
Simplify[Table[L[[Ii]], {Ii, 1, NColors[L, R]}] ==
Table[Simplify[Inverse[R[[Ii]]]], {Ii, 1, NColors[L, R]}]],
"R is not a square matrix"]
InverseTest[Rep_] := InverseTest[L[Rep], R[Rep]]
TransposeTest[L_, R_] := Simplify[Table[L[[Ii]], {Ii, 1, NColors[L, R]}] ==
Table[Simplify[Transpose[R[[Ii]]]], {Ii, 1, NColors[L, R]}]]
TransposeTest[Rep_] := TransposeTest[L[Rep], R[Rep]]
Chi0Report[L_, R_] := If[NColors[L, R] == 4, StringJoin["chi0 = ",
ToString[CalculateChi0[L, R], FormatType -> StandardForm],
", (ncis = ", ToString[CalculateNcis[L, R], FormatType ->
StandardForm], ", ntrans = ", ToString[CalculateNtrans[L, R],
FormatType -> StandardForm], ")"], Nothing]
Chi0Report[Rep_] := Chi0Report[L[Rep], R[Rep]]
CalculateChi0[L_, R_] := Simplify[(1/dmin[NColors[L, R]])*
Tr[L[[1]] . R[[2]] . L[[3]] . R[[4]]]]
CalculateChi0[Rep_] := CalculateChi0[L[Rep], R[Rep]]
dmin[NCol_] := 2^Pow[ModSet[NCol]][NCol]
ModSet[NCol_] := Abs[4 - Mod[NCol, 8]]
CalculateNcis[L_, R_] := Simplify[(dbosons[L, R]/dmin[NColors[L, R]] +
CalculateChi0[L, R])/2]
CalculateNcis[Rep_] := CalculateNcis[L[Rep], R[Rep]]
CalculateNtrans[L_, R_] := Simplify[(dbosons[L, R]/dmin[NColors[L, R]] -
CalculateChi0[L, R])/2]
CalculateNtrans[Rep_] := CalculateNtrans[L[Rep], R[Rep]]
DefaultSpacing = 1.5
NewAdinkraReportMaterial[Rep_, 1] := {StringJoin["LinearlyIndependent[V] = ",
ToString[LinearlyIndependent[V[Rep]]]],
StringJoin["LinearlyIndependent[Vtilde] = ",
ToString[LinearlyIndependent[Vtilde[Rep]]]]}
NewAdinkraReportMaterial[Rep_, 2] :=
Flatten[{If[AllZetaGenNonSingular[Rep],
{StringJoin[ToString[NumDistinctHoloOrMono[Holoraumy, Rep],
FormatType -> StandardForm],
" distinct \!\(\*SubscriptBox[\(\[Zeta]\), \(I\)]\); ",
ToString[NumDistinctHoloOrMono[Monodromy, Rep],
FormatType -> StandardForm], " distinct \
|\!\(\*SubscriptBox[OverscriptBox[\(\[Zeta]\), \(~\)], \(I\)]\)|"]},
{"ZetaGen has singular elements"}], If[AllZetatildeGenNonSingular[
Rep], {StringJoin[ToString[NumDistinctHoloOrMono[Holoraumytilde,
Rep], FormatType -> StandardForm], " distinct \
\!\(\*SubscriptBox[OverscriptBox[\(\[Zeta]\), \(~\)], \(I\)]\); ",
ToString[NumDistinctHoloOrMono[Monodromytilde, Rep],
FormatType -> StandardForm], " distinct \
|\!\(\*SubscriptBox[OverscriptBox[\(\[Zeta]\), \(~\)], \(I\)]\)|"]},
{"ZetatildeGen has singular elements"}],
{StringJoin["\!\(\*SubscriptBox[\(\[Zeta]\), \(I\)]\) \[Alpha] \
\!\(\*SubscriptBox[\(V\), \(1 I\)]\) = ", ToString[ZetaPropV[Rep]], "; \
\!\(\*SubscriptBox[OverscriptBox[\(\[Zeta]\), \(~\)], \(I\)]\) \[Alpha] \
\!\(\*SubscriptBox[OverscriptBox[\(V\), \(~\)], \(1 I\)]\) = ",
ToString[ZetatildePropVtilde[Rep]]]}}]
NewAdinkraReportMaterial[Rep_, 4] :=
Flatten[{If[NColors[Rep] == 4, {StringJoin["AllsoNTest = ",
ToString[soNTest[VsoN[Rep]] && soNTest[VtildesoN[Rep]] &&
soNTest[VsoNPM[-1][Rep]] && soNTest[VtildesoNPM[1][Rep]] &&
soNTest[VtildesoNPM[-1][Rep]] && soNTest[VsoNPM[1][Rep]]]],
StringJoin["Allsu2MutuallyCommute = ", ToString[
su2Test[VsoNPM[-1]][Rep] && su2Test[VsoNPM[1]][Rep] &&
MutuallyCommuteTest[VPM[1][Rep], VPM[-1][Rep]] &&
su2Test[VtildesoNPM[-1]][Rep] && su2Test[VtildesoNPM[1]][Rep] &&
MutuallyCommuteTest[VtildePM[1][Rep], VtildePM[-1][Rep]]]]},
{StringJoin["AllsoNTest = ", ToString[soNTest[VsoN[Rep]] &&
soNTest[VtildesoN[Rep]]]]}]}]
NewAdinkraReportMaterial[Rep_, 8] :=
Flatten[{{StringJoin["soNTest[VsoN] = ", ToString[soNTest[VsoN[Rep]]]],
StringJoin["soNTest[VtildesoN] = ", ToString[
soNTest[VtildesoN[Rep]]]]}, If[NColors[Rep] == 4,
{StringJoin["soNTest[VsoNPM[-1]] = ", ToString[
soNTest[VsoNPM[-1][Rep]]]], StringJoin["soNTest[VsoNPM[1]] = ",
ToString[soNTest[VsoNPM[1][Rep]]]], StringJoin[
"soNTest[VtildesoNPM[-1]] = ", ToString[soNTest[VtildesoNPM[-1][
Rep]]]], StringJoin["soNTest[VtildesoNPM[1]] = ",
ToString[soNTest[VtildesoNPM[1][Rep]]]],
StringJoin["su2Test[VsoNPM[-1]] = ", ToString[su2Test[VsoNPM[-1]][
Rep]]], StringJoin["su2Test[VsoNPM[1]] = ",
ToString[su2Test[VsoNPM[1]][Rep]]], StringJoin[
"VPM[1] and VPM[-1] mutually commute = ",
ToString[MutuallyCommuteTest[VPM[1][Rep], VPM[-1][Rep]]]],
StringJoin["su2Test[VtildesoNPM[-1]] = ",
ToString[su2Test[VtildesoNPM[-1]][Rep]]],
StringJoin["su2Test[VtildesoNPM[1]] = ",
ToString[su2Test[VtildesoNPM[1]][Rep]]],
StringJoin["VtildePM[1] and VtildePM[-1] mutually commute = ",
ToString[MutuallyCommuteTest[VtildePM[1][Rep], VtildePM[-1][
Rep]]]]}, {Nothing}]}]
LinearlyIndependent[Vmat_] :=
{cLinearlyIndependent = Table[0, {Ii, 1, NColors[Vmat, Vmat] - 1},
{Ji, Ii + 1, NColors[Vmat, Vmat]}];
cTable = Table[c[Ii, Ji], {Ii, 1, NColors[Vmat, Vmat] - 1},
{Ji, Ii + 1, NColors[Vmat, Vmat]}]; cList = cTable[[1]];
Do[cList = Join[cList, cTable[[Ii]]], {Ii, 2, NColors[Vmat, Vmat] -
1}]; cSoln[Vmat] = Solve[Sum[c[Ii, Ji]*Vmat[[Ii,Ji]],
{Ii, 1, NColors[Vmat, Vmat] - 1}, {Ji, Ii + 1, NColors[Vmat,
Vmat]}] == 0, cList]; (cTable /. cSoln[Vmat][[1]]) ==
cLinearlyIndependent}[[1]]
AllZetaGenNonSingular[Rep_] := Simplify[Table[Det[ZetaGen[Rep][[Ii]]] == 0,
{Ii, 1, NColors[Rep]}] == Table[False, {Ii, 1, NColors[Rep]}]]
NumDistinctHoloOrMono[HoloOrMono_, Rep_] :=
If[AllZetatildeGenNonSingular[Rep], HoldForm[2]^
(N - (Log[2, Length[ListOfIdenticalMonoOrHolo[HoloOrMono, Rep]]] -
NColors[Rep])), Print["Zeta or Zetatilde has singular elements"]]
AllZetatildeGenNonSingular[Rep_] :=
Simplify[Table[Det[ZetatildeGen[Rep][[Ii]]] == 0,
{Ii, 1, NColors[Rep]}] == Table[False, {Ii, 1, NColors[Rep]}]]
ListOfIdenticalMonoOrHolo[MonoOrHolo_, Rep_] :=
If[AllZetatildeGenNonSingular[Rep],
Position[Table[MonoOrHolo[Rep][[Ii]] == MonoOrHolo[Rep][[Ji]],
{Ii, 1, 2^NColors[Rep]}, {Ji, 1, 2^NColors[Rep]}], True],
Print["Zeta or Zetatilde has singular elements"]]
ZetaPropV[Rep_] := Simplify[Table[VScaleFactor*ZetaGen[Rep][[Ii]],
{Ii, 2, NColors[Rep]}] == Table[V[Rep][[Ii,1]], {Ii, 2, NColors[Rep]}]]
VScaleFactor = -I
ZetatildePropVtilde[Rep_] := Simplify[
Table[VtildeScaleFactor*ZetatildeGen[Rep][[Ii]],
{Ii, 2, NColors[Rep]}] == Table[Vtilde[Rep][[Ii,1]],
{Ii, 2, NColors[Rep]}]]
VtildeScaleFactor = -I
soNTest[Mgen_] := Simplify[Table[Commute[Mgen[[Ii,Ji]], Mgen[[Ki,Li]]],
{Ii, 1, NColors[Mgen, Mgen]}, {Ji, 1, NColors[Mgen, Mgen]},
{Ki, 1, NColors[Mgen, Mgen]}, {Li, 1, NColors[Mgen, Mgen]}] ==
Table[soNTestterms[Mgen][Ii, Ji, Ki, Li], {Ii, 1, NColors[Mgen, Mgen]},
{Ji, 1, NColors[Mgen, Mgen]}, {Ki, 1, NColors[Mgen, Mgen]},
{Li, 1, NColors[Mgen, Mgen]}]]
Commute[M1_, M2_] := M1 . M2 - M2 . M1
soNTestterms[Mgen_][Ii_, Ji_, Ki_, Li_] :=
I*(KroneckerDelta[Ii, Li]*Mgen[[Ki,Ji]] - KroneckerDelta[Ii, Ki]*
Mgen[[Li,Ji]] - KroneckerDelta[Ji, Li]*Mgen[[Ki,Ii]] +
KroneckerDelta[Ji, Ki]*Mgen[[Li,Ii]])
VsoN[Rep_] := VsoNScaleFactor*V[Rep]
VsoNScaleFactor = 1/2
VtildesoN[Rep_] := VtildesoNScaleFactor*Vtilde[Rep]
VtildesoNScaleFactor = 1/2
VsoNPM[1][Rep_] := VsoNScaleFactor*VPM[1][Rep]
VsoNPM[-1][Rep_] := VsoNScaleFactor*VPM[-1][Rep]
VtildesoNPM[1][Rep_] := VtildesoNScaleFactor*VtildePM[1][Rep]
VtildesoNPM[-1][Rep_] := VtildesoNScaleFactor*VtildePM[-1][Rep]
su2Test[(MPM_)[pm_]][Rep_] := Simplify[
(MPM[pm][Rep][[1,2]] == pm*MPM[pm][Rep][[3,4]] &&
MPM[pm][Rep][[1,3]] == pm*MPM[pm][Rep][[4,2]] &&
MPM[pm][Rep][[1,4]] == pm*MPM[pm][Rep][[2,3]]) ==
soNTest[MPM[pm][Rep]] == True]
MutuallyCommuteTest[M1_, M2_] :=
Simplify[Table[Commute[M1[[Ii,Ji]], M2[[Ki,Li]]],
{Ii, 1, NColors[M1, M1] - 1}, {Ji, Ii, NColors[M1, M1]},
{Ki, 1, NColors[M2, M2] - 1}, {Li, Ki, NColors[M2, M2]}] ==
Table[0*M1[[1,2]], {Ii, 1, NColors[M1, M1] - 1},
{Ji, Ii, NColors[M1, M1]}, {Ki, 1, NColors[M1, M1] - 1},
{Li, Ki, NColors[M1, M1]}]]
AdinkraGreen = RGBColor[0.10196079, 0.61176473, 0.21960784]
AdinkraHoloMonoReport[Rep_] := AdinkraReport[Rep, 2]
AdinkraOrange = RGBColor[0.89803922, 0.57647061, 0.27450982]
AdinkraPreliminaryReport[L_, R_] := Column[If[CorrectDimensions[L, R],
{StringJoin["N = ", ToString[NColors[L, R]]],
StringJoin["dbosons x dfermions = ", ToString[dbosons[L, R]],
" \[Times] ", ToString[dfermions[L, R]]], StringJoin["GATest = ",
ToString[GATest[L, R]]], StringJoin["InverseTest = ",
ToString[InverseTest[L, R]]], StringJoin["TransposeTest = ",
ToString[TransposeTest[L, R]]], Chi0Report[L, R]},
{Print[StringJoin["N = ", ToString[NColors[L, R]]]],
Print[StringJoin["dbosons x dfermions = ", ToString[dbosons[L, R]],
" \[Times] ", ToString[dfermions[L, R]]]],
Print["Incorrect Dimensions"], Abort[]}], Spacings -> DefaultSpacing]
AdinkraPreliminaryReport[Rep_] :=
Column[{StringJoin["Rep = ", ToString[Rep]], AdinkraPreliminaryReport[
L[Rep], R[Rep]]}, Spacings -> DefaultSpacing]
AdinkraPreliminaryReportO[Rep_] :=
Column[{StringJoin["Rep = ", ToString[Rep]], AdinkraPreliminaryReport[
L[Rep], RO[Rep]]}, Spacings -> DefaultSpacing]
RO[Rep_] := Table[Transpose[L[Rep][[Ii]]], {Ii, 1, NColors[Rep]}]
AdinkraRed = RGBColor[0.78431374, 0, 0.12156863]
AdinkraSummaryReport[Rep_] := AdinkraReport[Rep, 6]
AdinkraViolet = RGBColor[0.42352942, 0.15294118, 0.4509804]
adjacencyToEdge[Pre12, mat_, col_] :=
Select[Flatten[Table[If[mat[[ii,jj]] =!= 0, {ii -> jj, mat[[ii,jj]]*col},
{}], {ii, 1, Length[mat]}, {jj, 1, Length[mat]}], 1], #1 =!= {} & ]
adjacencyToEdge[TwelvePlus, mat_, col_] :=
Select[Flatten[Table[If[mat[[ii,jj]] =!= 0, {UndirectedEdge[ii, jj],
mat[[ii,jj]]*col}, {}], {ii, 1, Length[mat]}, {jj, 1, Length[mat]}],
1], #1 =!= {} & ]
adjacencyToEdge[mat_, col_] := adjacencyToEdge[VerSwitch, mat, col]
VerSwitch = TwelvePlus
AdjacencyToEdgeList[Rep_] := Table[AdjacencyToEdgeListColored[Rep][[EIndex,
1]], {EIndex, 1, Length[AdjacencyToEdgeListColored[Rep]]}]
AdjacencyToEdgeListColored[Rep_] :=
Sort[Join[adjacencyToEdge[padLmatrix[L[Rep][[1]]], 1],
adjacencyToEdge[padLmatrix[L[Rep][[2]]], 2],
adjacencyToEdge[padLmatrix[L[Rep][[3]]], 3],
adjacencyToEdge[padLmatrix[L[Rep][[4]]], 4]]]
padLmatrix[L_] := Transpose[ArrayPad[L, {{4, 0}, {0, 4}}]]
AlphaBetaToLogicCode = {\[Alpha][1] -> 1, \[Alpha][2] -> 2, \[Alpha][3] -> 3,
\[Beta][1] -> 4, \[Beta][2] -> 5, \[Beta][3] -> 6}
AlphaBetaToSuperscripts =
{\[Alpha][1] -> "\!\(\*SuperscriptBox[\(\[Alpha]\), \(1\)]\)",
\[Alpha][2] -> "\!\(\*SuperscriptBox[\(\[Alpha]\), \(2\)]\)",
\[Alpha][3] -> "\!\(\*SuperscriptBox[\(\[Alpha]\), \(3\)]\)",
\[Beta][1] -> "\!\(\*SuperscriptBox[\(\[Beta]\), \(1\)]\)",
\[Beta][2] -> "\!\(\*SuperscriptBox[\(\[Beta]\), \(2\)]\)",
\[Beta][3] -> "\!\(\*SuperscriptBox[\(\[Beta]\), \(3\)]\)"}
AntiCommute[a_, b_] := a . b + b . a
AntiCommuteGamma[0, 0] = {{-2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, -2, 0}, {0, 0,
0, -2}}
AntiCommuteGamma[0, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[0, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[0, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[1, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[1, 1] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
2}}
AntiCommuteGamma[1, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[1, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[2, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[2, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[2, 2] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
2}}
AntiCommuteGamma[2, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[3, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[3, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[3, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
AntiCommuteGamma[3, 3] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
2}}
AntisymmetryCheck[Object1_] := Table[Object1[Ii, Ji], {Ii, 1, 4},
{Ji, 1, 4}] == -Table[Object1[Ji, Ii], {Ii, 1, 4}, {Ji, 1, 4}]
Basis[di_][ai_, mu_, nu_] := ArrayFlatten[Outer[Times,
\[Omega]matrix[di/4][ai], \[Rho]matrix[mu, nu]]]
\[Omega]matrix[1][0] = {{1}}
\[Omega]matrix[1][1] = {{1}}
\[Omega]matrix[3][0] = {{1/(3*nz[3]), 0, 0}, {0, 1/(3*nz[3]), 0},
{0, 0, 1/(3*nz[3])}}
\[Omega]matrix[3][1] = {{0, 1/(2*nz[3]), 0}, {1/(2*nz[3]), 0, 0}, {0, 0, 0}}
\[Omega]matrix[3][2] = {{0, -1/2*1/nz[3], 0}, {1/(2*nz[3]), 0, 0}, {0, 0, 0}}
\[Omega]matrix[3][3] = {{1/(2*nz[3]), 0, 0}, {0, -1/2*1/nz[3], 0}, {0, 0, 0}}
\[Omega]matrix[3][4] = {{0, 0, 1/(2*nz[3])}, {0, 0, 0}, {1/(2*nz[3]), 0, 0}}
\[Omega]matrix[3][5] = {{0, 0, -1/2*1/nz[3]}, {0, 0, 0}, {1/(2*nz[3]), 0, 0}}
\[Omega]matrix[3][6] = {{0, 0, 0}, {0, 0, 1/(2*nz[3])}, {0, 1/(2*nz[3]), 0}}
\[Omega]matrix[3][7] = {{0, 0, 0}, {0, 0, -1/2*1/nz[3]}, {0, 1/(2*nz[3]), 0}}
\[Omega]matrix[3][8] = {{1/(6*nz[3]), 0, 0}, {0, 1/(6*nz[3]), 0},
{0, 0, -1/3*1/nz[3]}}
\[Omega]matrix[3][9] = {{1/(3*nz[3]), 0, 0}, {0, 1/(3*nz[3]), 0},
{0, 0, 1/(3*nz[3])}}
\[Omega]matrix[5][0] = {{1/(5*nz[5]), 0, 0, 0, 0}, {0, 1/(5*nz[5]), 0, 0, 0},
{0, 0, 1/(5*nz[5]), 0, 0}, {0, 0, 0, 1/(5*nz[5]), 0},
{0, 0, 0, 0, 1/(5*nz[5])}}
\[Omega]matrix[5][1] = {{0, 1/(2*nz[5]), 0, 0, 0}, {1/(2*nz[5]), 0, 0, 0, 0},
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][2] = {{0, -1/2*1/nz[5], 0, 0, 0},
{1/(2*nz[5]), 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}}
\[Omega]matrix[5][3] = {{1/(2*nz[5]), 0, 0, 0, 0}, {0, -1/2*1/nz[5], 0, 0,
0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][4] = {{0, 0, 1/(2*nz[5]), 0, 0}, {0, 0, 0, 0, 0},
{1/(2*nz[5]), 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][5] = {{0, 0, -1/2*1/nz[5], 0, 0}, {0, 0, 0, 0, 0},
{1/(2*nz[5]), 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][6] = {{0, 0, 0, 0, 0}, {0, 0, 1/(2*nz[5]), 0, 0},
{0, 1/(2*nz[5]), 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][7] = {{0, 0, 0, 0, 0}, {0, 0, -1/2*1/nz[5], 0, 0},
{0, 1/(2*nz[5]), 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][8] = {{1/(6*nz[5]), 0, 0, 0, 0}, {0, 1/(6*nz[5]), 0, 0, 0},
{0, 0, -1/3*1/nz[5], 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][9] = {{0, 0, 0, 1/(2*nz[5]), 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}, {1/(2*nz[5]), 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][10] = {{0, 0, 0, -1/2*1/nz[5], 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}, {1/(2*nz[5]), 0, 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][11] = {{0, 0, 0, 0, 0}, {0, 0, 0, 1/(2*nz[5]), 0},
{0, 0, 0, 0, 0}, {0, 1/(2*nz[5]), 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][12] = {{0, 0, 0, 0, 0}, {0, 0, 0, -1/2*1/nz[5], 0},
{0, 0, 0, 0, 0}, {0, 1/(2*nz[5]), 0, 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][13] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 1/(2*nz[5]), 0}, {0, 0, 1/(2*nz[5]), 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][14] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, -1/2*1/nz[5], 0}, {0, 0, 1/(2*nz[5]), 0, 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][15] = {{1/(12*nz[5]), 0, 0, 0, 0},
{0, 1/(12*nz[5]), 0, 0, 0}, {0, 0, 1/(12*nz[5]), 0, 0},
{0, 0, 0, -1/4*1/nz[5], 0}, {0, 0, 0, 0, 0}}
\[Omega]matrix[5][16] = {{0, 0, 0, 0, 1/(2*nz[5])}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {1/(2*nz[5]), 0, 0, 0, 0}}
\[Omega]matrix[5][17] = {{0, 0, 0, 0, -1/2*1/nz[5]}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {1/(2*nz[5]), 0, 0, 0, 0}}
\[Omega]matrix[5][18] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 1/(2*nz[5])},
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1/(2*nz[5]), 0, 0, 0}}
\[Omega]matrix[5][19] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, -1/2*1/nz[5]},
{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 1/(2*nz[5]), 0, 0, 0}}
\[Omega]matrix[5][20] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 1/(2*nz[5])}, {0, 0, 0, 0, 0}, {0, 0, 1/(2*nz[5]), 0, 0}}
\[Omega]matrix[5][21] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, -1/2*1/nz[5]}, {0, 0, 0, 0, 0}, {0, 0, 1/(2*nz[5]), 0, 0}}
\[Omega]matrix[5][22] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, 1/(2*nz[5])}, {0, 0, 0, 1/(2*nz[5]), 0}}
\[Omega]matrix[5][23] = {{0, 0, 0, 0, 0}, {0, 0, 0, 0, 0}, {0, 0, 0, 0, 0},
{0, 0, 0, 0, -1/2*1/nz[5]}, {0, 0, 0, 1/(2*nz[5]), 0}}
\[Omega]matrix[5][24] = {{1/(20*nz[5]), 0, 0, 0, 0},
{0, 1/(20*nz[5]), 0, 0, 0}, {0, 0, 1/(20*nz[5]), 0, 0},
{0, 0, 0, 1/(20*nz[5]), 0}, {0, 0, 0, 0, -1/5*1/nz[5]}}
\[Omega]matrix[5][25] = {{1/(5*nz[5]), 0, 0, 0, 0},
{0, 1/(5*nz[5]), 0, 0, 0}, {0, 0, 1/(5*nz[5]), 0, 0},
{0, 0, 0, 1/(5*nz[5]), 0}, {0, 0, 0, 0, 1/(5*nz[5])}}
\[Rho]matrix[0, 0] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Rho]matrix[0, 1] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Rho]matrix[0, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Rho]matrix[0, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Rho]matrix[0, 4] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Rho]matrix[1, 0] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Rho]matrix[1, 1] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Rho]matrix[1, 2] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, I, 0}}
\[Rho]matrix[1, 3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Rho]matrix[1, 4] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Rho]matrix[2, 0] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, I, 0}}
\[Rho]matrix[2, 1] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Rho]matrix[2, 2] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Rho]matrix[2, 3] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, -I}}
\[Rho]matrix[2, 4] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, I, 0}}
\[Rho]matrix[3, 0] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Rho]matrix[3, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Rho]matrix[3, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Rho]matrix[3, 3] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, I, 0, 0}, {I, 0, 0, 0}}
\[Rho]matrix[3, 4] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Rho]matrix[4, 0] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Rho]matrix[4, 1] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Rho]matrix[4, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Rho]matrix[4, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Rho]matrix[4, 4] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
BasisMF[di_][ai_, mu_, nu_] := MatrixForm[Basis[di/4][ai, mu, nu]]
BasisReport[di_] := TableForm[{StringJoin["TestOrthogonal\[Sigma] = ",
ToString[TestOrthogonal\[Sigma]]], "",
StringJoin["Test\[Rho]Orthogonal = ", ToString[Test\[Rho]Orthogonal]],
"", StringJoin["Test\[Omega]Orthogonal[", ToString[di/4], "] = ",
ToString[Test\[Omega]Orthogonal[di/4]]], "",
StringJoin["TestBasisOrthogonal[", ToString[di], "] = ",
ToString[TestBasisOrthogonal[di]]]}]
TestOrthogonal\[Sigma] :=
Table[Tr[SigmaProduct[mu, nu] . SigmaProduct[ap, bt]], {mu, 0, 3},
{nu, 0, 3}, {ap, 0, 3}, {bt, 0, 3}] ==
4*Table[KroneckerDelta[mu, ap]*KroneckerDelta[nu, bt], {mu, 0, 3},
{nu, 0, 3}, {ap, 0, 3}, {bt, 0, 3}]
SigmaProduct[ii_, ji_] := ArrayFlatten[Outer[Times, sigma[ii], sigma[ji]]]
SigmaProduct[ii_, ji_, ki_] := ArrayFlatten[Outer[Times, sigma[ii],
SigmaProduct[ji, ki]]]
SigmaProduct[ii_, ji_, ki_, li_] := ArrayFlatten[Outer[Times, sigma[ii],
SigmaProduct[ji, ki, li]]]
SigmaProduct[ii_, ji_, ki_, li_, mi_] := ArrayFlatten[
Outer[Times, sigma[ii], SigmaProduct[ji, ki, li, mi]]]
SigmaProduct[ii_, ji_, ki_, li_, mi_, ni_] :=
ArrayFlatten[Outer[Times, sigma[ii], SigmaProduct[ji, ki, li, mi, ni]]]
SigmaProduct[ii_, ji_, ki_, li_, mi_, ni_, pi_] :=
ArrayFlatten[Outer[Times, sigma[ii], SigmaProduct[ji, ki, li, mi, ni,
pi]]]
SigmaProduct[ii_, ji_, ki_, li_, mi_, ni_, pi_, qi_] :=
ArrayFlatten[Outer[Times, sigma[ii], SigmaProduct[ji, ki, li, mi, ni, pi,
qi]]]
sigma[0] = {{1, 0}, {0, 1}}
sigma[1] = {{0, 1}, {1, 0}}
sigma[2] = {{0, -I}, {I, 0}}
sigma[3] = {{1, 0}, {0, -1}}
Test\[Rho]Orthogonal :=
Table[Tr[\[Rho]matrix[mu, nu] . ConjugateTranspose[\[Rho]matrix[ap,
bt]]], {mu, 0, 3}, {nu, 0, 3}, {ap, 0, 3}, {bt, 0, 3}] ==
Table[4*KroneckerDelta[mu, ap]*KroneckerDelta[nu, bt], {mu, 0, 3},
{nu, 0, 3}, {ap, 0, 3}, {bt, 0, 3}]
Test\[Omega]Orthogonal[sl_] :=
Table[4*Wfcn[sl][[ai]]*Tr[\[Omega]matrix[sl][ai] .
Transpose[\[Omega]matrix[sl][bi]]], {ai, 1, sl^2}, {bi, 1, sl^2}] ==
IdentityMatrix[sl^2]
Wfcn[1] = {1/4}
Wfcn[3] = {nz[3]^2/2, nz[3]^2/2, nz[3]^2/2, nz[3]^2/2, nz[3]^2/2, nz[3]^2/2,
nz[3]^2/2, (3*nz[3]^2)/2, (3*nz[3]^2)/4}
Wfcn[5] = {nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2,
nz[5]^2/2, (3*nz[5]^2)/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2,
nz[5]^2/2, nz[5]^2/2, 3*nz[5]^2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2,
nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, nz[5]^2/2, 5*nz[5]^2,
(5*nz[5]^2)/4}
TestBasisOrthogonal[di_] := Table[TestBasisOrthogonalTerms[di][mu, nu, ap,
bt], {mu, 1, 4}, {nu, 1, 4}, {ap, 1, 4}, {bt, 1, 4}] ==
Table[True, {mu, 1, 4}, {nu, 1, 4}, {ap, 1, 4}, {bt, 1, 4}]
TestBasisOrthogonalTerms[di_][mu_, nu_, ap_, bt_] :=
-Table[Tr[Basis[di][ai, mu, nu] . Transpose[Basis[di][bi, ap, bt]]],
{ai, 1, (di/4)^2}, {bi, 1, (di/4)^2}] ==
Table[(KroneckerDelta[ai, bi]*KroneckerDelta[mu, ap]*
KroneckerDelta[nu, bt])/Wfcn[di/4][[ai]], {ai, 1, (di/4)^2},
{bi, 1, (di/4)^2}]
BasisReportTerms[di_][mu_, nu_, ap_, bt_] :=
TableForm[{StringJoin["TestOrthogonal\[Sigma] = ",
ToString[TestOrthogonal\[Sigma]]], "",
StringJoin["Test\[Rho]Orthogonal = ", ToString[Test\[Rho]Orthogonal]],
"", StringJoin["Test\[Omega]Orthogonal[", ToString[di/4], "] = ",
ToString[Test\[Omega]Orthogonal[di/4]]], "",
StringJoin["TestBasisOrthogonalTerms[", ToString[di], "][",
ToString[mu], ",", ToString[nu], ",", ToString[ap], ",", ToString[bt],
"] = ", ToString[TestBasisOrthogonalTerms[di][mu, nu, ap, bt]]]}]
BC4BosonPerm[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4Perm[ni, ai, mu, Ai][[ii,ji]]*L[[Ii,ji,jhat]], {ji, 1, 4}],
{Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
BC4Perm[ni_, ai_, mu_, Ai_] := (-1)^ni*HPerm[ai] . S3Perm[mu] . VierPerm[Ai]
HPerm[0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
HPerm[1] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
HPerm[2] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
HPerm[3] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}
HPerm[12] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
HPerm[13] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}
HPerm[23] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}
HPerm[123] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}
S3Perm[0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
S3Perm[12] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
S3Perm[13] = {{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}
S3Perm[23] = {{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}
S3Perm[123] = {{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}
S3Perm[132] = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}
VierPerm[0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
VierPerm[1234] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}
VierPerm[1324] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}}
VierPerm[1423] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}
BC4ColorPerm[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4Perm[ni, ai, mu, Ai][[Ii,Ji]]*L[[Ji,ii,jhat]], {Ji, 1, 4}],
{Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
BC4Fermion[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4[[If[EvenQ[ni], 2, 1],ai,mu,Ai]][[jhat,khat]]*
L[[Ii,ii,khat]], {khat, 1, 4}], {Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
BC4FermionPerm[ni_, ai_, mu_, Ai_][L_] :=
Table[Sum[BC4Perm[ni, ai, mu, Ai][[jhat,khat]]*L[[Ii,ii,khat]],
{khat, 1, 4}], {Ii, 1, 4}, {ii, 1, 4}, {jhat, 1, 4}]
BC4MatrixForm = {{{{MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0},
{0, 0, 0, -1}}], MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, -1}, {-1,
0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1, 0},
{0, -1, 0, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {-1, 0,
0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}],
MatrixForm[{{0, 0, 0, -1}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0, -1, 0,
0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {-1,
0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {0, -1, 0, 0}, {-1, 0, 0,
0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
-1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}]},
{MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, -1, 0, 0}, {0,
0, -1, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0,
0}, {0, -1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, -1}, {0,
-1, 0, 0}, {-1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{-1, 0, 0,
0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}}],
MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}, {-1, 0, 0,
0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0,
0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, -1, 0,
0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
0, -1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, -1, 0,
0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0,
-1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 0, -1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0},
{-1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0,
1}, {0, -1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
-1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1},
{-1, 0, 0, 0}}]}, {MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1,
0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1}, {-1,
0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0},
{0, 0, 0, -1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0,
0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
-1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {0,
-1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0,
0, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, 1}, {0,
-1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {1, 0, 0, 0},
{0, 0, -1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 1, 0,
0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, 0, 1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1, 0},
{1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0,
-1}, {0, 1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1},
{-1, 0, 0, 0}}]}, {MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1,
0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1}, {1,
0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0, 0},
{0, 0, 0, 1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, -1, 0,
0}, {0, 0, 1, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {-1,
0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, 1},
{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{1, 0, 0,
0}, {0, 0, -1, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}],
MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}, {-1, 0, 0,
0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0,
0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0},
{0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0, 1,
0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0,
0, 1}, {-1, 0, 0, 0}}]}}, {{MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, -1, 0, 0}, {1, 0, 0,
0}, {0, 0, 0, 1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0,
0, 1}, {1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0,
0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {0, 1, 0, 0}, {1, 0,
0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, -1}, {1, 0, 0, 0}, {0,
1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, 1},
{0, 0, 1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0,
0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, -1, 0, 0},
{0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, -1,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}}],
MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0,
0}}]}, {MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 0, -1}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {1, 0, 0, 0},
{0, 0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}, {0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, 1, 0},
{1, 0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {1, 0,
0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0,
1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, -1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 0, -1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1,
0}, {-1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0,
0, -1}, {0, -1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
-1}, {-1, 0, 0, 0}}]}, {MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0,
-1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1},
{-1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0,
0}, {0, 0, 0, -1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0,
-1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {-1,
0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0,
0}, {0, 0, -1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0,
-1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0},
{0, 0, 0, -1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1,
0}, {-1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0,
0, 0, 1}, {0, -1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, -1}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
-1}, {-1, 0, 0, 0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0,
-1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1},
{-1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {1, 0, 0,
0}, {0, 0, 0, -1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0,
1, 0, 0}, {0, 0, -1, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {-1, 0, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0, -1,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, 1, 0}, {-1,
0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, 1},
{0, -1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {1, 0, 0,
0}, {0, 0, -1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0,
1, 0, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 1, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 0, 1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1,
0}, {1, 0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0,
0, -1}, {0, 1, 0, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0},
{0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
1}, {-1, 0, 0, 0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0,
1, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1},
{1, 0, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0,
0}, {0, 0, 0, 1}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0,
-1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0, 0, 0}, {0,
0, -1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1},
{0, -1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1,
0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0}, {1,
0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1},
{0, 1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0,
0}, {0, 0, 1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0,
-1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0,
-1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {1,
0, 0, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1},
{0, 1, 0, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, 1}, {1, 0,
0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0,
0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}]},
{MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0,
-1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0,
-1, 0}}], MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
-1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, 1, 0},
{-1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0,
0}, {0, 0, 0, -1}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {1, 0,
0, 0}, {0, 0, -1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}, {0, -1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1},
{0, 0, 1, 0}, {-1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, 1,
0}, {1, 0, 0, 0}, {0, 0, 0, -1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0,
0, 1}, {0, 1, 0, 0}, {0, 0, -1, 0}}], MatrixForm[{{0, 0, 0, 1}, {1,
0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}}], MatrixForm[{{0, 0, 1, 0},
{0, 1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}}]}}},
{{{MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}],
MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}],
MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}}],
MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0,
0}}]}, {MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0,
0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}, {0,
0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {1, 0, 0, 0},
{0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {0, 1, 0,
0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0,
0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {1, 0, 0, 0}, {0,
1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, 1},
{0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]}, {MatrixForm[{{1, 0, 0, 0}, {0, 0,
1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {0,
0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 1, 0},
{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0,
1}, {0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}],
MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}}],
MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}],
MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}, {1, 0, 0,
0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}, {0,
0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0, 1, 0},
{0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0,
1}, {1, 0, 0, 0}}]}}, {{MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0,
0}, {0, 0, 0, 1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0,
0, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0,
0, -1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}], MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1, 0}, {1, 0, 0, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {0, -1, 0, 0}, {1, 0,
0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1},
{0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, -1,
0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0,
0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, -1, 0, 0},
{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, -1,
0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 1, 0, 0}}],
MatrixForm[{{0, 0, 0, -1}, {0, -1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0,
0}}]}, {MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 0, 1}}], MatrixForm[{{0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0, 0, 0},
{0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
1}, {0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0,
1, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0},
{1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {-1,
0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0},
{0, -1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]}},
{{MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0}, {0, -1, 0, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0,
0, 0, -1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0},
{-1, 0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0,
1}, {0, -1, 0, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {0,
1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, -1},
{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0,
0}, {0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0}}],
MatrixForm[{{0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0,
0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}, {0,
0, 0, 1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0},
{0, 0, 1, 0}}], MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0,
0}, {-1, 0, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0,
0, 0, 1}, {0, 0, -1, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, -1, 0, 0}, {0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0, -1, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, -1},
{1, 0, 0, 0}}]}}, {{MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 0, -1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1},
{-1, 0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1,
0}, {0, -1, 0, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {-1,
0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0,
1}, {0, 0, -1, 0}, {-1, 0, 0, 0}, {0, 1, 0, 0}}],
MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1}, {0, -1, 0, 0}, {1, 0, 0,
0}}]}, {MatrixForm[{{0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1,
0}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, -1}, {1, 0, 0, 0}}]}, {MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0},
{0, -1, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0,
-1}, {-1, 0, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 1, 0}, {-1,
0, 0, 0}, {0, 0, 0, -1}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, 1},
{0, -1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 0, 0, 1}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}, {0,
1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, -1, 0}, {-1, 0,
0, 0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 0, -1}, {0,
-1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0, 0, 0},
{0, 0, -1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, -1, 0,
0}, {0, 0, 0, -1}, {1, 0, 0, 0}}]}},
{{MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
0, 1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, 1, 0}, {1,
0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, 1},
{0, 1, 0, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, -1}, {1, 0,
0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0,
0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]},
{MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, -1, 0}, {1, 0, 0, 0}, {0, 1, 0,
0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, -1}, {0, 1, 0, 0}, {1, 0,
0, 0}, {0, 0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}, {0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, 1},
{0, 0, 1, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, 1,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0,
0, 1}, {0, 1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {1,
0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0},
{0, 1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
0, 1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, -1, 0}, {1,
0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, -1},
{0, 1, 0, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {0, -1, 0,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {-1, 0,
0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0,
0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]},
{MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, -1, 0, 0}, {0, 0, 1, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {-1, 0, 0, 0}, {0, 1, 0,
0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {0, -1, 0, 0}, {1, 0,
0, 0}, {0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, -1, 0}, {0,
0, 0, 1}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, -1},
{0, 0, 1, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, -1,
0}, {1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0,
0, -1}, {0, 1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {-1,
0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0},
{0, -1, 0, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}}]}},
{{MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, -1,
0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
0, -1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {-1,
0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1},
{0, -1, 0, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {0, 1, 0,
0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {1, 0,
0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0,
0, 0, 1}, {0, 0, -1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}]},
{MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0, 0,
1, 0}}], MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0,
1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {0, 0, -1, 0},
{1, 0, 0, 0}}]}, {MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, -1, 0,
0}, {0, 0, 0, 1}}], MatrixForm[{{0, 0, 0, 1}, {0, 1, 0, 0}, {-1, 0,
0, 0}, {0, 0, 1, 0}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, -1}, {0, 1, 0, 0}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 0, 1},
{0, 0, -1, 0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, 1, 0, 0}, {0, 0, 1,
0}, {-1, 0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0,
0, 1}, {0, -1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, 1}, {1,
0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 1, 0},
{0, 1, 0, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}]}},
{{MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, 1, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0},
{0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0,
0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, -1, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 0, -1}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {0, 0, -1,
0}, {-1, 0, 0, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0, 0,
0, -1}, {0, -1, 0, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0},
{0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0,
-1}, {1, 0, 0, 0}}]}, {MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0,
-1, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1},
{-1, 0, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0,
0}, {0, 0, 0, -1}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, -1}, {0,
-1, 0, 0}, {0, 0, -1, 0}, {1, 0, 0, 0}}]},
{MatrixForm[{{0, 0, -1, 0}, {-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 0,
1}}], MatrixForm[{{0, 0, 0, -1}, {0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 1, 0}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1},
{0, 1, 0, 0}}], MatrixForm[{{0, -1, 0, 0}, {0, 0, 0, -1}, {0, 0, -1,
0}, {1, 0, 0, 0}}]}, {MatrixForm[{{0, -1, 0, 0}, {0, 0, -1, 0}, {-1,
0, 0, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 0, 0, -1},
{0, -1, 0, 0}, {0, 0, 1, 0}}], MatrixForm[{{0, 0, 0, -1}, {-1, 0, 0,
0}, {0, 0, -1, 0}, {0, 1, 0, 0}}], MatrixForm[{{0, 0, -1, 0}, {0,
-1, 0, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}}]}}}}
BC4PermMatrixForm[ni_, ai_, mu_, Ai_] := MatrixForm[BC4Perm[ni, ai, mu, Ai]]
BosonGadget[Rep1_, Rep2_] := Simplify[
(1/(dmin[NColors[Rep1]]*NColors[Rep1]*(NColors[Rep1] - 1)))*
(-(1/VScaleFactor^2))*Sum[Tr[V[Rep1][[Ii,Ji]] . V[Rep2][[Ii,Ji]]],
{Ii, 1, NColors[Rep1]}, {Ji, 1, NColors[Rep1]}]]
BuildDate[Adinkra] = 220305
buildrules[list_] := Module[{rules = {}, layerlengths :=
Map[Length, list, {1}]}, For[ii = 1, ii <= Length[list], ii++,
For[jj = 1, jj <= layerlengths[[ii]], jj++, AppendTo[rules,
list[[ii]][[jj]] -> {Range[1 - Mean[Range[layerlengths[[ii]]]],
layerlengths[[ii]] + 1 - layerlengths[[ii]]/2][[jj]], -ii}]]];
Clear[ii, jj]; Return[rules]]
CheckGALRCoeffs[Rep_] := If[CMessage[Rep][3, 1] != "",
Simplify[Table[GALR[Rep][[Ii,Ji]], {Ii, 1, NColors[Rep]},
{Ji, Ii, NColors[Rep]}] == Table[Sum[Wfcn[slndimb[Rep]][[ai]]*
GALRCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*Basis[dbosons[Rep]][ai, mu,
nu], {ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}, {Ji, Ii, NColors[Rep]}]], CMessage[Rep][3, 2]]
slndimb[Rep_] := dbosons[Rep]/4
Num\[Omega]b[Rep_] := slndimb[Rep]^2
CheckGARLCoeffs[Rep_] := If[CMessage[Rep][4, 1] != "",
Simplify[Table[GARL[Rep][[Ii,Ji]], {Ii, 1, NColors[Rep]},
{Ji, Ii, NColors[Rep]}] == Table[Sum[Wfcn[slndimf[Rep]][[ai]]*
GARLCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*Basis[dfermions[Rep]][ai, mu,
nu], {ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}, {Ji, Ii, NColors[Rep]}]], CMessage[Rep][4, 2]]
slndimf[Rep_] := dfermions[Rep]/4
Num\[Omega]f[Rep_] := slndimf[Rep]^2
CheckID1 = {{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}}}
CheckID2 = {{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}},
{{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0,
0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}}}
CheckID3 = {{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}},
{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}}
CheckLCoeffs[Rep_] := If[CMessage[Rep][1, 1] != "",
Simplify[L[Rep] == Table[Sum[Wfcn[slndimb[Rep]][[ai]]*
LCoeffs[Rep][Ii][[ai,mu,nu]]*Basis[dbosons[Rep]][ai, mu, nu],
{ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}]], CMessage[Rep][1, 2]]
CheckRCoeffs[Rep_] := If[CMessage[Rep][2, 1] != "",
Simplify[R[Rep] == Table[Sum[Wfcn[slndimf[Rep]][[ai]]*
RCoeffs[Rep][Ii][[ai,mu,nu]]*Basis[dbosons[Rep]][ai, mu, nu],
{ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}]], CMessage[Rep][2, 2]]
CheckVCoeffs[Rep_] := If[CMessage[Rep][5, 1] != "",
Simplify[Table[V[Rep][[Ii,Ji]], {Ii, 1, NColors[Rep] - 1},
{Ji, Ii + 1, NColors[Rep]}] ==
Table[Sum[Wfcn[slndimb[Rep]][[ai]]*VCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
Basis[dbosons[Rep]][ai, mu, nu], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], {Ii, 1, NColors[Rep] - 1},
{Ji, Ii + 1, NColors[Rep]}]], CMessage[Rep][5, 2]]
CheckVPMCoeffs[pm_][Rep_] := If[CMessage[Rep][7, 1] != "",
Simplify[Table[VPM[pm][Rep][[Ii,Ji]], {Ii, 1, 2}, {Ji, Ii + 1, 3}] ==
Table[Sum[Wfcn[slndimb[Rep]][[ai]]*VPMCoeffs[pm][Rep][Ii, Ji][[ai,mu,
nu]]*Basis[dbosons[Rep]][ai, mu, nu], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], {Ii, 1, 2}, {Ji, Ii + 1, 3}]],
CMessage[Rep][7, 2]]
CheckVtildeCoeffs[Rep_] := If[CMessage[Rep][6, 1] != "",
Simplify[Table[Vtilde[Rep][[Ii,Ji]], {Ii, 1, NColors[Rep] - 1},
{Ji, Ii + 1, NColors[Rep]}] ==
Table[Sum[Wfcn[slndimf[Rep]][[ai]]*VtildeCoeffs[Rep][Ii, Ji][[ai,mu,
nu]]*Basis[dbosons[Rep]][ai, mu, nu], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], {Ii, 1, NColors[Rep] - 1},
{Ji, Ii + 1, NColors[Rep]}]], CMessage[Rep][6, 2]]
CheckVtildePMCoeffs[pm_][Rep_] := If[CMessage[Rep][8, 1] != "",
Simplify[Table[VtildePM[pm][Rep][[Ii,Ji]], {Ii, 1, 2},
{Ji, Ii + 1, 3}] == Table[Sum[Wfcn[slndimf[Rep]][[ai]]*
VtildePMCoeffs[pm][Rep][Ii, Ji][[ai,mu,nu]]*Basis[dbosons[Rep]][ai,
mu, nu], {ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, 2}, {Ji, Ii + 1, 3}]], VtildePMCMessage]
Cmetric = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}
Coeffs[di_][Matrix_][0, mu_, nu_] :=
Simplify[-Tr[Transpose[Basis[di][0, mu, nu]] . Matrix]]
Coeffs[di_][Matrix_][ai_, mu_, nu_] :=
Simplify[-Tr[Transpose[Basis[di][ai, mu, nu]] . Matrix]]
CoeffsFullReport[Rep_] := TableForm[{StringJoin["Rep = ", ToString[Rep]], "",
StringJoin["CheckLCoeffs = ", ToString[CheckLCoeffs[Rep]]], "",
StringJoin["CheckRCoeffs = ", ToString[CheckRCoeffs[Rep]]], "",
StringJoin["CheckGALRCoeffs = ", ToString[CheckGALRCoeffs[Rep]]], "",
StringJoin["CheckGARLCoeffs = ", ToString[CheckGARLCoeffs[Rep]]], "",
StringJoin["CheckVCoeffs = ", ToString[CheckVCoeffs[Rep]]], "",
StringJoin["CheckVtildeCoeffs = ", ToString[CheckVtildeCoeffs[Rep]]],
"", StringJoin["CheckVPMCoeffs[-1] = ",
ToString[CheckVPMCoeffs[-1][Rep]]], "",
StringJoin["CheckVPMCoeffs[1] = ", ToString[CheckVPMCoeffs[1][Rep]]],
"", StringJoin["CheckVtildePMCoeffs[-1] = ",
ToString[CheckVtildePMCoeffs[-1][Rep]]], "",
StringJoin["CheckVtildePMCoeffs[1] = ",
ToString[CheckVtildePMCoeffs[1][Rep]]]}]
CoeffsSummaryReport[Rep_] := StringJoin["All Coeffs For Rep = ",
ToString[Rep], " Check Out = "]*(CheckLCoeffs[Rep] &&
CheckRCoeffs[Rep] && CheckGALRCoeffs[Rep] && CheckGARLCoeffs[Rep] &&
CheckVCoeffs[Rep] && CheckVtildeCoeffs[Rep] &&
CheckVPMCoeffs[-1][Rep] && CheckVPMCoeffs[1][Rep] &&
CheckVtildePMCoeffs[-1][Rep] && CheckVtildePMCoeffs[1][Rep])
Color1 = RGBColor[0.10196079, 0.61176473, 0.21960784]
Color2 = RGBColor[0.42352942, 0.15294118, 0.4509804]
Color3 = RGBColor[0.89803922, 0.57647061, 0.27450982]
Color4 = RGBColor[0.78431374, 0, 0.12156863]
CommuteGamma[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
CommuteGamma[0, 1] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, -2, 0}, {0, 0, 0,
2}}
CommuteGamma[0, 2] = {{0, 0, 2, 0}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0, 2, 0, 0}}
CommuteGamma[0, 3] = {{0, -2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, 2}, {0, 0, 2,
0}}
CommuteGamma[1, 0] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
-2}}
CommuteGamma[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
CommuteGamma[1, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0}, {0, 2, 0,
0}}
CommuteGamma[1, 3] = {{0, -2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2}, {0, 0, 2,
0}}
CommuteGamma[2, 0] = {{0, 0, -2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0}, {0, -2, 0,
0}}
CommuteGamma[2, 1] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0, -2, 0,
0}}
CommuteGamma[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
CommuteGamma[2, 3] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, -2, 0, 0}, {-2, 0, 0,
0}}
CommuteGamma[3, 0] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2}, {0, 0, -2,
0}}
CommuteGamma[3, 1] = {{0, 2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, 2}, {0, 0, -2,
0}}
CommuteGamma[3, 2] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, 2, 0, 0}, {2, 0, 0,
0}}
CommuteGamma[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
CommuteGammadown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammadown[0, 1] = {{0, -2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, -2}, {0, 0,
-2, 0}}
CommuteGammadown[0, 2] = {{0, 0, 0, 2}, {0, 0, -2, 0}, {0, -2, 0, 0}, {2, 0,
0, 0}}
CommuteGammadown[0, 3] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0}, {0, 0,
0, 2}}
CommuteGammadown[1, 0] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, 2}, {0, 0, 2,
0}}
CommuteGammadown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammadown[1, 2] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, 2, 0, 0}, {2, 0, 0,
0}}
CommuteGammadown[1, 3] = {{-2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0}, {0, 0,
0, 2}}
CommuteGammadown[2, 0] = {{0, 0, 0, -2}, {0, 0, 2, 0}, {0, 2, 0, 0}, {-2, 0,
0, 0}}
CommuteGammadown[2, 1] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, -2, 0, 0}, {-2,
0, 0, 0}}
CommuteGammadown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammadown[2, 3] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {-2, 0, 0, 0}, {0, 2,
0, 0}}
CommuteGammadown[3, 0] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0}, {0, 0,
0, -2}}
CommuteGammadown[3, 1] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0}, {0, 0,
0, -2}}
CommuteGammadown[3, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {2, 0, 0, 0}, {0, -2,
0, 0}}
CommuteGammadown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammastdown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
CommuteGammastdown[0, 1] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0,
0, -2}}
CommuteGammastdown[0, 2] = {{0, 0, -2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0}, {0,
-2, 0, 0}}
CommuteGammastdown[0, 3] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2}, {0, 0,
-2, 0}}
CommuteGammastdown[1, 0] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, -2, 0}, {0,
0, 0, 2}}
CommuteGammastdown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
CommuteGammastdown[1, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0}, {0,
2, 0, 0}}
CommuteGammastdown[1, 3] = {{0, -2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2}, {0,
0, 2, 0}}
CommuteGammastdown[2, 0] = {{0, 0, 2, 0}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0, 2,
0, 0}}
CommuteGammastdown[2, 1] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {2, 0, 0, 0}, {0,
-2, 0, 0}}
CommuteGammastdown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
CommuteGammastdown[2, 3] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, -2, 0, 0}, {-2,
0, 0, 0}}
CommuteGammastdown[3, 0] = {{0, -2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, 2}, {0,
0, 2, 0}}
CommuteGammastdown[3, 1] = {{0, 2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, 2}, {0, 0,
-2, 0}}
CommuteGammastdown[3, 2] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, 2, 0, 0}, {2,
0, 0, 0}}
CommuteGammastdown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
CommuteGammastdowndown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdowndown[0, 1] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, 2}, {0,
0, 2, 0}}
CommuteGammastdowndown[0, 2] = {{0, 0, 0, -2}, {0, 0, 2, 0}, {0, 2, 0, 0},
{-2, 0, 0, 0}}
CommuteGammastdowndown[0, 3] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0},
{0, 0, 0, -2}}
CommuteGammastdowndown[1, 0] = {{0, -2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, -2},
{0, 0, -2, 0}}
CommuteGammastdowndown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdowndown[1, 2] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, 2, 0, 0}, {2,
0, 0, 0}}
CommuteGammastdowndown[1, 3] = {{-2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0},
{0, 0, 0, 2}}
CommuteGammastdowndown[2, 0] = {{0, 0, 0, 2}, {0, 0, -2, 0}, {0, -2, 0, 0},
{2, 0, 0, 0}}
CommuteGammastdowndown[2, 1] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, -2, 0, 0},
{-2, 0, 0, 0}}
CommuteGammastdowndown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdowndown[2, 3] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {-2, 0, 0, 0},
{0, 2, 0, 0}}
CommuteGammastdowndown[3, 0] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0},
{0, 0, 0, 2}}
CommuteGammastdowndown[3, 1] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0},
{0, 0, 0, -2}}
CommuteGammastdowndown[3, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {2, 0, 0, 0},
{0, -2, 0, 0}}
CommuteGammastdowndown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdownstup[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdownstup[0, 1] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0},
{0, 0, 0, -2}}
CommuteGammastdownstup[0, 2] = {{0, 0, -2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0},
{0, -2, 0, 0}}
CommuteGammastdownstup[0, 3] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2},
{0, 0, -2, 0}}
CommuteGammastdownstup[1, 0] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0},
{0, 0, 0, -2}}
CommuteGammastdownstup[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdownstup[1, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0},
{0, 2, 0, 0}}
CommuteGammastdownstup[1, 3] = {{0, -2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2},
{0, 0, 2, 0}}
CommuteGammastdownstup[2, 0] = {{0, 0, -2, 0}, {0, 0, 0, -2}, {-2, 0, 0, 0},
{0, -2, 0, 0}}
CommuteGammastdownstup[2, 1] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {2, 0, 0, 0},
{0, -2, 0, 0}}
CommuteGammastdownstup[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdownstup[2, 3] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, -2, 0, 0},
{-2, 0, 0, 0}}
CommuteGammastdownstup[3, 0] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, -2},
{0, 0, -2, 0}}
CommuteGammastdownstup[3, 1] = {{0, 2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, 2},
{0, 0, -2, 0}}
CommuteGammastdownstup[3, 2] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, 2, 0, 0},
{2, 0, 0, 0}}
CommuteGammastdownstup[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
CommuteGammastdownstupdown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
CommuteGammastdownstupdown[0, 1] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, 2},
{0, 0, 2, 0}}
CommuteGammastdownstupdown[0, 2] = {{0, 0, 0, -2}, {0, 0, 2, 0}, {0, 2, 0,
0}, {-2, 0, 0, 0}}
CommuteGammastdownstupdown[0, 3] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2,
0}, {0, 0, 0, -2}}
CommuteGammastdownstupdown[1, 0] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, 2},
{0, 0, 2, 0}}
CommuteGammastdownstupdown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
CommuteGammastdownstupdown[1, 2] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, 2, 0, 0},
{2, 0, 0, 0}}
CommuteGammastdownstupdown[1, 3] = {{-2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2,
0}, {0, 0, 0, 2}}
CommuteGammastdownstupdown[2, 0] = {{0, 0, 0, -2}, {0, 0, 2, 0}, {0, 2, 0,
0}, {-2, 0, 0, 0}}
CommuteGammastdownstupdown[2, 1] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, -2, 0,
0}, {-2, 0, 0, 0}}
CommuteGammastdownstupdown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
CommuteGammastdownstupdown[2, 3] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {-2, 0, 0,
0}, {0, 2, 0, 0}}
CommuteGammastdownstupdown[3, 0] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2,
0}, {0, 0, 0, -2}}
CommuteGammastdownstupdown[3, 1] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2,
0}, {0, 0, 0, -2}}
CommuteGammastdownstupdown[3, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {2, 0, 0,
0}, {0, -2, 0, 0}}
CommuteGammastdownstupdown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
CommuteGammaup[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammaup[0, 1] = {{0, 2, 0, 0}, {2, 0, 0, 0}, {0, 0, 0, 2}, {0, 0, 2,
0}}
CommuteGammaup[0, 2] = {{0, 0, 0, -2}, {0, 0, 2, 0}, {0, 2, 0, 0}, {-2, 0, 0,
0}}
CommuteGammaup[0, 3] = {{2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
-2}}
CommuteGammaup[1, 0] = {{0, -2, 0, 0}, {-2, 0, 0, 0}, {0, 0, 0, -2}, {0, 0,
-2, 0}}
CommuteGammaup[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammaup[1, 2] = {{0, 0, 0, 2}, {0, 0, 2, 0}, {0, 2, 0, 0}, {2, 0, 0,
0}}
CommuteGammaup[1, 3] = {{-2, 0, 0, 0}, {0, -2, 0, 0}, {0, 0, 2, 0}, {0, 0, 0,
2}}
CommuteGammaup[2, 0] = {{0, 0, 0, 2}, {0, 0, -2, 0}, {0, -2, 0, 0}, {2, 0, 0,
0}}
CommuteGammaup[2, 1] = {{0, 0, 0, -2}, {0, 0, -2, 0}, {0, -2, 0, 0}, {-2, 0,
0, 0}}
CommuteGammaup[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
CommuteGammaup[2, 3] = {{0, 0, -2, 0}, {0, 0, 0, 2}, {-2, 0, 0, 0}, {0, 2, 0,
0}}
CommuteGammaup[3, 0] = {{-2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0}, {0, 0, 0,
2}}
CommuteGammaup[3, 1] = {{2, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, -2, 0}, {0, 0, 0,
-2}}
CommuteGammaup[3, 2] = {{0, 0, 2, 0}, {0, 0, 0, -2}, {2, 0, 0, 0}, {0, -2, 0,
0}}
CommuteGammaup[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0,
0}}
ConstructBasis[4, Matrix_] := Sum[Wfcn[1][[1]]*Coeffs[4][Matrix][1, mu, nu]*
\[Omega]matrix[1][1][[1,1]]*\[Rho][Mod[mu, 4], Mod[nu, 4]], {mu, 1, 4},
{nu, 1, 4}]
ConstructBasis[Matrix_] := Sum[Wfcn[Length[Matrix]/4][[ai]]*
Coeffs[Length[Matrix]][Matrix][ai, mu, nu]*
\[Omega][Length[Matrix]/4][Mod[ai, (Length[Matrix]/4)^
2]] \[CircleTimes] \[Rho][Mod[mu, 4], Mod[nu, 4]],
{ai, 1, (Length[Matrix]/4)^2}, {mu, 1, 4}, {nu, 1, 4}]
ConstructGALRBasis[4, Rep_][Ii_, Ji_] := If[CMessage[Rep][3, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*GALRCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][3, 2]]
ConstructGALRBasis[Rep_][Ii_, Ji_] := If[CMessage[Rep][3, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*GALRCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimb[Rep]][Mod[ai, Num\[Omega]b[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][3, 2]]
ConstructGARLBasis[4, Rep_][Ii_, Ji_] := If[CMessage[Rep][4, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*GARLCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][4, 2]]
ConstructGARLBasis[Rep_][Ii_, Ji_] := If[CMessage[Rep][4, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*GARLCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimf[Rep]][Mod[ai, Num\[Omega]f[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][4, 2]]
ConstructLBasis[4, Rep_][Ii_] := If[CMessage[Rep][1, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*LCoeffs[Rep][Ii][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][1, 2]]
ConstructLBasis[Rep_][Ii_] := If[CMessage[Rep][1, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*LCoeffs[Rep][Ii][[ai,mu,nu]]*
\[Omega][slndimb[Rep]][Mod[ai, Num\[Omega]b[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][1, 2]]
ConstructRBasis[4, Rep_][Ii_] := If[CMessage[Rep][2, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*RCoeffs[Rep][Ii][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][2, 2]]
ConstructRBasis[Rep_][Ii_] := If[CMessage[Rep][2, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*RCoeffs[Rep][Ii][[ai,mu,nu]]*
\[Omega][slndimf[Rep]][Mod[ai, Num\[Omega]f[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][2, 2]]
ConstructSigmaProduct[Matrix_] :=
{Hold[Sum[SigmaProductCoeffs[Matrix][mu]*Subscript[\[Sigma], mu],
{mu, 0, 3}]], Hold[Sum[SigmaProductCoeffs[Matrix][mu, nu]*
Subscript[\[Sigma], mu] \[CircleTimes] Subscript[\[Sigma], nu],
{mu, 0, 3}, {nu, 0, 3}]],
Hold[Sum[SigmaProductCoeffs[Matrix][mu1, mu2, mu3]*
Subscript[\[Sigma], mu1] \[CircleTimes] Subscript[\[Sigma],
mu2] \[CircleTimes] Subscript[\[Sigma], mu3], {mu1, 0, 3},
{mu2, 0, 3}, {mu3, 0, 3}]],
Hold[Sum[SigmaProductCoeffs[Matrix][mu1, mu2, mu3, mu4]*
Subscript[\[Sigma], mu1] \[CircleTimes] Subscript[\[Sigma],
mu2] \[CircleTimes] Subscript[\[Sigma], mu3] \[CircleTimes]
Subscript[\[Sigma], mu4], {mu1, 0, 3}, {mu2, 0, 3}, {mu3, 0, 3},
{mu4, 0, 3}]], Hold[Sum[SigmaProductCoeffs[Matrix][mu1, mu2, mu3, mu4,
mu5]*Subscript[\[Sigma], mu1] \[CircleTimes] Subscript[\[Sigma],
mu2] \[CircleTimes] Subscript[\[Sigma], mu3] \[CircleTimes]
Subscript[\[Sigma], mu4] \[CircleTimes] Subscript[\[Sigma], mu5],
{mu1, 0, 3}, {mu2, 0, 3}, {mu3, 0, 3}, {mu4, 0, 3}, {mu5, 0, 3}]],
Hold[Sum[SigmaProductCoeffs[Matrix][mu1, mu2, mu3, mu4, mu5, mu6]*
Subscript[\[Sigma], mu1] \[CircleTimes] Subscript[\[Sigma],
mu2] \[CircleTimes] Subscript[\[Sigma], mu3] \[CircleTimes]
Subscript[\[Sigma], mu4] \[CircleTimes] Subscript[\[Sigma],
mu5] \[CircleTimes] Subscript[\[Sigma], mu6], {mu1, 0, 3},
{mu2, 0, 3}, {mu3, 0, 3}, {mu4, 0, 3}, {mu5, 0, 3}, {mu6, 0, 3}]],
Hold[Sum[SigmaProductCoeffs[Matrix][mu1, mu2, mu3, mu4, mu5, mu6, mu7]*
Subscript[\[Sigma], mu1] \[CircleTimes] Subscript[\[Sigma],
mu2] \[CircleTimes] Subscript[\[Sigma], mu3] \[CircleTimes]
Subscript[\[Sigma], mu4] \[CircleTimes] Subscript[\[Sigma],
mu5] \[CircleTimes] Subscript[\[Sigma], mu6] \[CircleTimes]
Subscript[\[Sigma], mu7], {mu1, 0, 3}, {mu2, 0, 3}, {mu3, 0, 3},
{mu4, 0, 3}, {mu5, 0, 3}, {mu6, 0, 3}, {mu7, 0, 3}]]}
SigmaProductCoeffs[Matrix_][mu_] := Simplify[(1/2)*Tr[sigma[mu] . Matrix]]
SigmaProductCoeffs[Matrix_][mu_, nu_] :=
Simplify[(1/2^2)*Tr[SigmaProduct[mu, nu] . Matrix]]
SigmaProductCoeffs[Matrix_][mu1_, mu2_, mu3_] :=
Simplify[(1/2^3)*Tr[SigmaProduct[mu1, mu2, mu3] . Matrix]]
SigmaProductCoeffs[Matrix_][mu1_, mu2_, mu3_, mu4_] :=
Simplify[(1/2^4)*Tr[SigmaProduct[mu1, mu2, mu3, mu4] . Matrix]]
SigmaProductCoeffs[Matrix_][mu1_, mu2_, mu3_, mu4_, mu5_] :=
Simplify[(1/2^5)*Tr[SigmaProduct[mu1, mu2, mu3, mu4, mu5] . Matrix]]
SigmaProductCoeffs[Matrix_][mu1_, mu2_, mu3_, mu4_, mu5_, mu6_] :=
Simplify[(1/2^6)*Tr[SigmaProduct[mu1, mu2, mu3, mu4, mu5, mu6] . Matrix]]
SigmaProductCoeffs[Matrix_][mu1_, mu2_, mu3_, mu4_, mu5_, mu6_, mu7_] :=
Simplify[(1/2^7)*Tr[SigmaProduct[mu1, mu2, mu3, mu4, mu5, mu6, mu7] .
Matrix]]
\[Sigma][0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
\[Sigma][0, 1] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, -I, 0}, {0, 0, 0, I}}
\[Sigma][0, 2] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Sigma][0, 3] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, I, 0}}
\[Sigma][1, 0] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, -I}}
\[Sigma][1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
\[Sigma][1, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0}, {0, I, 0, 0}}
\[Sigma][1, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, I, 0}}
\[Sigma][2, 0] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Sigma][2, 1] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0}, {0, -I, 0, 0}}
\[Sigma][2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
\[Sigma][2, 3] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Sigma][3, 0] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, -I, 0}}
\[Sigma][3, 1] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, -I, 0}}
\[Sigma][3, 2] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0}, {I, 0, 0, 0}}
\[Sigma][3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
ConstructVBasis[4, Rep_][Ii_, Ji_] := If[CMessage[Rep][5, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*VCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][5, 2]]
ConstructVBasis[Rep_][Ii_, Ji_] := If[CMessage[Rep][5, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*VCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimb[Rep]][Mod[ai, Num\[Omega]b[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][5, 2]]
ConstructVPMBasis[pm_][4, Rep_][Ii_, Ji_] := If[CMessage[Rep][7, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*VPMCoeffs[pm][Rep][Ii, Ji][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][7, 2]]
ConstructVPMBasis[pm_][Rep_][Ii_, Ji_] := If[CMessage[Rep][7, 1] != "",
Sum[Wfcn[slndimb[Rep]][[ai]]*VPMCoeffs[pm][Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimb[Rep]][Mod[ai, Num\[Omega]b[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]b[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][7, 2]]
ConstructVtildeBasis[4, Rep_][Ii_, Ji_] := If[CMessage[Rep][6, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*VtildeCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][6, 2]]
ConstructVtildeBasis[Rep_][Ii_, Ji_] := If[CMessage[Rep][6, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*VtildeCoeffs[Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimf[Rep]][Mod[ai, Num\[Omega]f[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][6, 2]]
ConstructVtildePMBasis[pm_][4, Rep_][Ii_, Ji_] :=
If[CMessage[Rep][8, 1] != "", Sum[Wfcn[slndimf[Rep]][[ai]]*
VtildePMCoeffs[pm][Rep][Ii, Ji][[ai,mu,nu]]*\[Rho][Mod[mu, 4],
Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
CMessage[Rep][8, 2]]
ConstructVtildePMBasis[pm_][Rep_][Ii_, Ji_] := If[CMessage[Rep][8, 1] != "",
Sum[Wfcn[slndimf[Rep]][[ai]]*VtildePMCoeffs[pm][Rep][Ii, Ji][[ai,mu,nu]]*
\[Omega][slndimf[Rep]][Mod[ai, Num\[Omega]f[Rep]]] \[CircleTimes]
\[Rho][Mod[mu, 4], Mod[nu, 4]], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], CMessage[Rep][8, 2]]
coordinates = {t, x, y, z}
DeletewlString[MAC] =
"/Users/kstiffle/Library/Mathematica/Applications/Adinkra.wl"
DeletewlString[PC] =
"/Users/kstiffle/Library/Mathematica\\Applications\\Adinkra.wl"
DOWN = 2
EdgeShapeFunctionList[Rep_] := Table[AdjacencyToEdgeListColored[Rep][[DIndex,
1]] -> Switch[Sign[AdjacencyToEdgeListColored[Rep][[DIndex,2]]], -1,
"DashedLine", 1, "Line"], {DIndex, 1,
Length[AdjacencyToEdgeListColored[Rep]]}]
EdgeStyleList[Rep_] := Table[AdjacencyToEdgeListColored[Rep][[EIndex,1]] ->
{Switch[AdjacencyToEdgeListColored[Rep][[EIndex,2]], 1, Color1, 2,
Color2, 3, Color3, 4, Color4, -1, Color1, -2, Color2, -3, Color3, -4,
Color4], Thick}, {EIndex, 1, Length[AdjacencyToEdgeListColored[Rep]]}]
ell[Rep_][TildeIndex_, ahat_][Ii_, Ji_] :=
(-I)*(Tr[su2matrix[TildeIndex, ahat] . Vtilde[Rep][[Ii,Ji]]]/
(4*VtildeScaleFactor))
su2matrix[1, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0}, {I, 0, 0, 0}}
su2matrix[1, 2] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, I, 0}}
su2matrix[1, 3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0}, {0, -I, 0, 0}}
su2matrix[2, 1] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0}, {I, 0, 0, 0}}
su2matrix[2, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
su2matrix[2, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, -I, 0}}
ExportAdinkra[Rep_, raise_, filename_] := Export[filename,
GraphAdinkra[Rep, raise]]
GraphAdinkra[Pre12, Rep_, raise_] :=
GraphPlot[Sort[Join[adjacencyToEdge[padLmatrix[L[Rep][[1]]], 1],
adjacencyToEdge[padLmatrix[L[Rep][[2]]], 2], adjacencyToEdge[
padLmatrix[L[Rep][[3]]], 3], adjacencyToEdge[padLmatrix[L[Rep][[4]]],
4]]], EdgeRenderingFunction ->
(Switch[#3, 1, {Color1, Thickness[0.007], Line[#1]}, -1,
{Color1, Dashing[0.03], Thickness[0.007], Line[#1]}, 2,
{Color2, Thickness[0.007], Line[#1]}, -2, {Color2, Dashing[0.03],
Thickness[0.007], Line[#1]}, 3, {Color3, Thickness[0.007],
Line[#1]}, -3, {Color3, Dashing[0.03], Thickness[0.007], Line[#1]},
4, {Color4, Thickness[0.007], Line[#1]}, -4, {Color4, Dashing[0.03],
Thickness[0.007], Line[#1]}] & ), VertexRenderingFunction ->
(If[#2 <= 4, Inset[Graphics[{Black, EdgeForm[Black],
Disk[{0, 0}, 0.05], White, Text[Style[#2, Bold, Larger], {0, 0}]},
ImageSize -> 30], #1], Inset[Graphics[{White, EdgeForm[Black],
Disk[{0, 0}, 0.05], Black, Text[Style[#2 - 4, Bold, Larger],
{0, 0}]}, ImageSize -> 30], #1]] & ), VertexCoordinateRules ->
raise]
GraphAdinkra[TwelvePlus, Rep_, raise_] := GraphPlot[AdjacencyToEdgeList[Rep],
EdgeStyle -> EdgeStyleList[Rep], VertexShapeFunction ->
(If[#2 <= 4, Inset[Graphics[{Black, EdgeForm[Black],
Disk[{0, 0}, 0.05], White, Text[Style[#2, Bold, Larger], {0, 0}]},
ImageSize -> 30], #1], Inset[Graphics[{White, EdgeForm[Black],
Disk[{0, 0}, 0.05], Black, Text[Style[#2 - 4, Bold, Larger],
{0, 0}]}, ImageSize -> 30], #1]] & ), EdgeShapeFunction ->
EdgeShapeFunctionList[Rep], VertexCoordinates -> raise]
GraphAdinkra[Rep_, Raise_] := GraphAdinkra[VerSwitch, Rep, Raise]
GraphAdinkra[Rep_] := GraphAdinkra[Rep, Valise]
Valise = {1 -> {-3/2, -1}, 2 -> {-1/2, -1}, 3 -> {1/2, -1}, 4 -> {3/2, -1},
5 -> {-3/2, -2}, 6 -> {-1/2, -2}, 7 -> {1/2, -2}, 8 -> {3/2, -2}}
FermionIdentity = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
FlipCode[ni_, ai_] := If[EvenQ[ni], If[ai == 0, "", ai], FlipComplement[ai]]
FlipComplement[0] := 1234
FlipComplement[1] = 123
FlipComplement[2] = 134
FlipComplement[3] = 124
FlipComplement[12] = 34
FlipComplement[13] = 24
FlipComplement[23] = 14
FlipComplement[123] = 4
FlopString[mu_] := If[mu == 0, "", StringJoin["(", ToString[mu], ")"]]
FunctionList[Adinkra] = "SpaceTime:\nIndexRange[SpaceTime][Index], Index = \
mu, a, or RaiseCode\n\ncoordinates, \[CapitalStigma][mu], \[Eta][mu,nu], \
Cmetric[[a,b]], InverseCmetric[[a,b]], UD[Field,\[CapitalStigma][mu]] , \
Lap[Field], UP, DOWN, \
RaiseSTIndex[Field,RaiseCode1,RaiseCode2,...,RaiseCoden], \
RaiseFermionIndex[Field]\n\n*************************************************\
***************************************\n************************************\
****************************************************\n\nGenerateLandR:\nNColo\
rs[DColor,PhiOrPsi], LTable[DColor,Phi,Psi], \
RTable[DColor,Phi,Psi],GenerateLandR[DColor,Phi,Psi,Rep]\n\n*****************\
***********************************************************************\n****\
*****************************************************************************\
*******\n\nAdinkraEssentials:\nIndexRange[AdinkraEssentials][Index], Index = \
p1, II, ReportLevel, or pm\n\n***IMPORTANT****: Default Settings are \
VScaleFactor = VtildeScaleFactor = -I, VsoNScaleFactor = -I/(2 \
VsoNScaleFactor), VtildesoNScaleFactor = -I/(2 \
VtildesoNScaleFactor)\n\nReports: AdinkraReport[Rep,ReportLevel], \
AdinkraPreliminaryReport[L,R], AdinkraPreliminaryReport[Rep], \
AdinkraPreliminaryReportO[Rep], AdinkraHoloMonoReport[Rep], \
AdinkraSummaryReport[Rep], AdinkraFullReport[Rep]\n\nBasic Functions: \
nMatrices[Matrices], nRows[Matrices], nColumns[Matrices], \
Commute[Matrix1,Matrix2], NColors[Rep], NColors[L,R], dmin[N], dbosons[Rep], \
dbosons[L,R], dfermions[Rep], dfermions[L,R], \
WordW[{p1,p2,...,pN}]\n\nIntense Calculations: Gadget[Rep1,Rep2], \
BosonGadget[Rep1,Rep2], ListOfIdenticalMonoOrHolo[MonoOrHolo,Rep], \
NumDistinctHoloOrMono[HoloOrMono,Rep]\n\nPrint Functions: PrintL[Rep][II], \
PrintR[Rep][II], PrintGALR[Rep][II,JJ], PrintGARL[Rep][II,JJ], \
PrintV[Rep][II,JJ], PrintVtilde[Rep][II,JJ], PrintZetaGen[Rep][II], \
PrintHoloraumy[Rep][{p1,p2,...,pN}], \
PrintMonodromy[Rep][{p1,p2,...,pN}],PrintZetatildeGen[Rep][II], \
PrintHoloraumytilde[Rep][{p1,p2,...,pN}], \
PrintMonodromytilde[Rep][{p1,p2,...,pN}], PrintVtildePM[pm][Rep][II,JJ], \
PrintVtildePM[pm][Rep][II,JJ], PrintAllL[Rep], PrintAllR[Rep], \
PrintAllGALR[Rep], PrintAllGARL[Rep], PrintAllV[Rep], PrintAllVtilde[Rep], \
PrintAllZetaGen[Rep], PrintAllHoloraumy[Rep], \
PrintAllMonodromy[Rep],PrintAllZetatildeGen[Rep], \
PrintAllHoloraumytilde[Rep], PrintAllMonodromytilde[Rep], \
PrintAllVtildePM[pm][Rep], PrintAllVtildePM[pm][Rep], \
,PrintSigmaProduct[Matrix], PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\n\nTest Functions: CorrectDimensions[Rep], \
CorrectDimensions[L,R], TransposeTest[Rep], TransposeTest[L,R], \
InverseTest[Rep], InverseTest[L,R], RO[Rep], Chi0Report[L,R], GATest[Rep], \
GATest[L,R], soNTest[Matrices], su2Test[MgenPM[pm]][Rep], \
MutuallyCommuteTest[M1,M2], LinearlyIndependent[Mgen]\n\nData generated by \
GenerateAdinkraData[Rep], GenerateAdinkraData[Rep,Orthogonal], \
GenerateAdinkraDataO[Rep], GenerateAdinkraData[Rep,L], or \
GenerateAdinkraData[Rep,L,R]:\nL[Rep], R[Rep], GALR[Rep], GARL[Rep], \
chi0[Rep], ncis[Rep], ntrans[Rep], V[Rep], Vtilde[Rep], VsoN[Rep], \
VtildesoN[Rep], ZetaGen[Rep], Holoraumy[Rep], Monodromy[Rep], \
ZetatildeGen[Rep], Holoraumytilde[Rep], Monodromytilde[Rep], VPM[pm][Rep], \
VtildePM[pm][Rep], VsoNPM[pm][Rep], VtildesoNPM[pm][Rep] cSoln[V[Rep]], \
cSoln[Vtilde[Rep]]\n\n*******************************************************\
*********************************\n******************************************\
**********************************************\n\nBasisDecomposition:\nIndexR\
ange[BasisDecomposition][Index], Index = mu, ahat, a, d, or n\n\nGeneral \
Matrix Tools:\nsigma[mu], \[Alpha]matrix[ahat], \[Beta]matrix[ahat], \
SigmaProduct[mu1,mu2,...,mun], SigmaProductMF[mu1,mu2,...,mun], \
SigmaMatrixProduct[mu,AnyMatrix], \[Rho]matrix[mu,nu], \[Omega]matrix[n][a], \
Basis[d][a,mu,nu], TestOrthogonal\[Sigma], Test\[Rho]Orthogonal, \
Test\[Omega]Orthogonal[n], TestBasisOrthogonal[d], \
Coeffs[d][Matrix][a,mu,nu]\n\nGenerateCoeffs[Rep] generates adinkra \
representation specific functions:\nLCoeffs[Rep][II], CheckLCoeffs[Rep], \
RCoeffs[Rep][II], CheckRCoeffs[Rep], VCoeffs[Rep][II,JJ], CheckVCoeffs[Rep], \
VtildeCoeffs[Rep][II,JJ], CheckVtildeCoeffs[Rep], VPMCoeffs[pm][Rep][II,JJ], \
CheckVPMCoeffs[pm][Rep], VtildePMCoeffs[pm][Rep][II,JJ], \
CheckVtildePMCoeffs[pm][Rep], NumberNonZero[LCoeffsMat], \
CoeffsSummaryReport[Rep], CoeffsFullReport[Rep], \
CMessage[Rep][mi,si]\n\nPrint Functions:\n PrintSigmaProduct[Matrix], \
PrintBasis[Matrix], PrintLBasis[Rep][II], PrintRBasis[Rep][II], \
PrintGALRBasis[Rep][II,JJ], PrintGARLBasis[Rep][II,JJ], \
PrintVBasis[Rep][II,JJ], PrintVtildeBasis[Rep][II,JJ], \
PrintVPMBasis[pm][Rep][II,JJ], PrintVtildePMBasis[pm][Rep][II,JJ], \
PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\n\n**************************************************\
**************************************\n*************************************\
***************************************************\n\nBC4Tools:\n\nIndexRang\
e[BC4Tools][Index], Index = n, a, \[Mu], A, II, or tt\n\nFunctions: \
\nHPerm[a], H[[a]], S3Perm[\[Mu]], S3[[\[Mu]]], VierPerm[A], Vier[[A]], \
BC4[[n,a,\[Mu],A,II,JJ]] , BC4Perm[n,a,\[Mu],A][[II,JJ]], \
QuaternionTestIJK[Quat], QuaternionTestKJI[Quat], Digit[Num,Pow], \
ell[Rep][tt,a][II,JJ], kappa[Rep][ti,a][II,JJ], IellABColor[Rep][[a]], \
PrintIell[Rep][[a]], IellABCode[Rep][[a]], AntisymmetryCheck[Object1], \
BC4Color[n,a,\[Mu],A][L], \
BC4ColorPerm[n,a,\[Mu],A][L],BC4Boson[n,a,\[Mu],A][L],BC4BosonPerm[n,a,\[Mu],\
A][L], \
HList,S3List,VierList,PrintBC4Perm[n,a,\[Mu],A],PrintBC4BosonPerm[n,a,\[Mu],A\
],PrintBC4FermionPerm[n,a,\[Mu],A],PrintBC4ColorPerm[n,a,\[Mu],A],L[Q],L[Qtil\
de],L[RepCode]\n\n***********************************************************\
*****************************\n**********************************************\
******************************************\n\nGraphingTools:\nIndexRange[Grap\
hingTools][list]\n\n AdinkraGreen, AdinkraViolet, AdinkraOrange, AdinkraRed, \
padLmatrix[L], adjacencyToEdge[mat,col], buildrules[list], Valise, \
GraphAdinkra[Rep], GraphAdinkra[Rep,BuildRules[list], \
ExportAdinkra[Rep,BuildRules[list],filename]\n\n*****************************\
***********************************************************\n****************\
************************************************************************"
FunctionList[AdinkraEssentials] = "IndexRange[AdinkraEssentials][Index], \
Index = p1, II, ReportLevel, or pm\n\n***IMPORTANT****: Default Settings are \
VScaleFactor = VtildeScaleFactor = -I, VsoNScaleFactor = -I/(2 \
VsoNScaleFactor), VtildesoNScaleFactor = -I/(2 \
VtildesoNScaleFactor)\n\nReports: AdinkraReport[Rep,ReportLevel], \
AdinkraPreliminaryReport[L,R], AdinkraPreliminaryReport[Rep], \
AdinkraPreliminaryReportO[Rep], AdinkraHoloMonoReport[Rep], \
AdinkraSummaryReport[Rep], AdinkraFullReport[Rep]\n\nBasic Functions: \
nMatrices[Matrices], nRows[Matrices], nColumns[Matrices], \
Commute[Matrix1,Matrix2], NColors[Rep], NColors[L,R], dmin[N], dbosons[Rep], \
dbosons[L,R], dfermions[Rep], dfermions[L,R], \
WordW[{p1,p2,...,pN}]\n\nIntense Calculations: Gadget[Rep1,Rep2], \
BosonGadget[Rep1,Rep2], ListOfIdenticalMonoOrHolo[MonoOrHolo,Rep], \
NumDistinctHoloOrMono[HoloOrMono,Rep]\n\nPrint Functions: PrintL[Rep][II], \
PrintR[Rep][II], PrintGALR[Rep][II,JJ], PrintGARL[Rep][II,JJ], \
PrintV[Rep][II,JJ], PrintVtilde[Rep][II,JJ], PrintZetaGen[Rep][II], \
PrintHoloraumy[Rep][{p1,p2,...,pN}], \
PrintMonodromy[Rep][{p1,p2,...,pN}],PrintZetatildeGen[Rep][II], \
PrintHoloraumytilde[Rep][{p1,p2,...,pN}], \
PrintMonodromytilde[Rep][{p1,p2,...,pN}], PrintVtildePM[pm][Rep][II,JJ], \
PrintVtildePM[pm][Rep][II,JJ], PrintAllL[Rep], PrintAllR[Rep], \
PrintAllGALR[Rep], PrintAllGARL[Rep], PrintAllV[Rep], PrintAllVtilde[Rep], \
PrintAllZetaGen[Rep], PrintAllHoloraumy[Rep], \
PrintAllMonodromy[Rep],PrintAllZetatildeGen[Rep], \
PrintAllHoloraumytilde[Rep], PrintAllMonodromytilde[Rep], \
PrintAllVtildePM[pm][Rep], PrintAllVtildePM[pm][Rep], \
,PrintSigmaProduct[Matrix], PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\n\nTest Functions: CorrectDimensions[Rep], \
CorrectDimensions[L,R], TransposeTest[Rep], TransposeTest[L,R], \
InverseTest[Rep], InverseTest[L,R], RO[Rep], Chi0Report[L,R], GATest[Rep], \
GATest[L,R], soNTest[Matrices], su2Test[MgenPM[pm]][Rep], \
MutuallyCommuteTest[M1,M2], LinearlyIndependent[Mgen]\n\nData generated by \
GenerateAdinkraData[Rep], GenerateAdinkraData[Rep,Orthogonal], \
GenerateAdinkraDataO[Rep], GenerateAdinkraData[Rep,L], or \
GenerateAdinkraData[Rep,L,R]:\nL[Rep], R[Rep], GALR[Rep], GARL[Rep], \
chi0[Rep], ncis[Rep], ntrans[Rep], V[Rep], Vtilde[Rep], VsoN[Rep], \
VtildesoN[Rep], ZetaGen[Rep], Holoraumy[Rep], Monodromy[Rep], \
ZetatildeGen[Rep], Holoraumytilde[Rep], Monodromytilde[Rep], VPM[pm][Rep], \
VtildePM[pm][Rep], VsoNPM[pm][Rep], VtildesoNPM[pm][Rep] cSoln[V[Rep]], \
cSoln[Vtilde[Rep]]\n\n*******************************************************\
*********************************\n******************************************\
**********************************************"
FunctionList[BasisDecomposition] = "IndexRange[BasisDecomposition][Index], \
Index = mu, ahat, a, d, or n\n\nGeneral Matrix Tools:\nsigma[mu], \
\[Alpha]matrix[ahat], \[Beta]matrix[ahat], SigmaProduct[mu1,mu2,...,mun], \
SigmaProductMF[mu1,mu2,...,mun], SigmaMatrixProduct[mu,AnyMatrix], \
\[Rho]matrix[mu,nu], \[Omega]matrix[n][a], Basis[d][a,mu,nu], \
TestOrthogonal\[Sigma], Test\[Rho]Orthogonal, Test\[Omega]Orthogonal[n], \
TestBasisOrthogonal[d], Coeffs[d][Matrix][a,mu,nu]\n\nGenerateCoeffs[Rep] \
generates adinkra representation specific functions:\nLCoeffs[Rep][II], \
CheckLCoeffs[Rep], RCoeffs[Rep][II], CheckRCoeffs[Rep], VCoeffs[Rep][II,JJ], \
CheckVCoeffs[Rep], VtildeCoeffs[Rep][II,JJ], CheckVtildeCoeffs[Rep], \
VPMCoeffs[pm][Rep][II,JJ], CheckVPMCoeffs[pm][Rep], \
VtildePMCoeffs[pm][Rep][II,JJ], CheckVtildePMCoeffs[pm][Rep], \
NumberNonZero[LCoeffsMat], CoeffsSummaryReport[Rep], CoeffsFullReport[Rep], \
CMessage[Rep][mi,si]\n\nPrint Functions:\n PrintSigmaProduct[Matrix], \
PrintBasis[Matrix], PrintLBasis[Rep][II], PrintRBasis[Rep][II], \
PrintGALRBasis[Rep][II,JJ], PrintGARLBasis[Rep][II,JJ], \
PrintVBasis[Rep][II,JJ], PrintVtildeBasis[Rep][II,JJ], \
PrintVPMBasis[pm][Rep][II,JJ], PrintVtildePMBasis[pm][Rep][II,JJ], \
PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\n\n**************************************************\
**************************************\n*************************************\
***************************************************"
FunctionList[BC4Tools] = "\nIndexRange[BC4Tools][Index], Index = n, a, \[Mu], \
A, II, or tt\n\nFunctions: \nHPerm[a], H[[a]], S3Perm[\[Mu]], S3[[\[Mu]]], \
VierPerm[A], Vier[[A]], BC4[[n,a,\[Mu],A,II,JJ]] , \
BC4Perm[n,a,\[Mu],A][[II,JJ]], QuaternionTestIJK[Quat], \
QuaternionTestKJI[Quat], Digit[Num,Pow], ell[Rep][tt,a][II,JJ], \
kappa[Rep][ti,a][II,JJ], IellABColor[Rep][[a]], PrintIell[Rep][[a]], \
IellABCode[Rep][[a]], AntisymmetryCheck[Object1], BC4Color[n,a,\[Mu],A][L], \
BC4ColorPerm[n,a,\[Mu],A][L],BC4Boson[n,a,\[Mu],A][L],BC4BosonPerm[n,a,\[Mu],\
A][L], \
HList,S3List,VierList,PrintBC4Perm[n,a,\[Mu],A],PrintBC4BosonPerm[n,a,\[Mu],A\
],PrintBC4FermionPerm[n,a,\[Mu],A],PrintBC4ColorPerm[n,a,\[Mu],A],L[Q],L[Qtil\
de],L[RepCode]\n\n***********************************************************\
*****************************\n**********************************************\
******************************************"
FunctionList[GenerateLandR] = "NColors[DColor,PhiOrPsi], \
LTable[DColor,Phi,Psi], \
RTable[DColor,Phi,Psi],GenerateLandR[DColor,Phi,Psi,Rep]\n\n*****************\
***********************************************************************\n****\
*****************************************************************************\
*******"
FunctionList[GraphingTools] = "IndexRange[GraphingTools][list]\n\n \
AdinkraGreen, AdinkraViolet, AdinkraOrange, AdinkraRed, padLmatrix[L], \
adjacencyToEdge[mat,col], buildrules[list], Valise, GraphAdinkra[Rep], \
GraphAdinkra[Rep,BuildRules[list], \
ExportAdinkra[Rep,BuildRules[list],filename]\n\n*****************************\
***********************************************************\n****************\
************************************************************************"
FunctionList[SpaceTime] = "IndexRange[SpaceTime][Index], Index = mu, a, or \
RaiseCode\n\ncoordinates, \[CapitalStigma][mu], \[Eta][mu,nu], \
Cmetric[[a,b]], InverseCmetric[[a,b]], UD[Field,\[CapitalStigma][mu]] , \
Lap[Field], UP, DOWN, \
RaiseSTIndex[Field,RaiseCode1,RaiseCode2,...,RaiseCoden], \
RaiseFermionIndex[Field]\n\n*************************************************\
***************************************\n************************************\
****************************************************"
GenerateLandR[DColor_, Phi_, Psi_, Rep_] :=
{L[Rep] = LTable[DColor, Phi, Psi]; R[Rep] = RTable[DColor, Phi, Psi];
StringJoin["L and R are loaded for Rep = ", ToString[Rep]]}
LTable[DColor_, Phi_, Psi_] := Simplify[
Table[Coefficient[DColor[Phi[[iRow]]][[Color]], I*Psi[[jhatColumn]]],
{Color, 1, Length[DColor[Phi[[1]]]]}, {iRow, 1, Length[Phi]},
{jhatColumn, 1, Length[Psi]}]]
RTable[DColor_, Phi_, Psi_] := Simplify[
Table[Coefficient[DColor[Psi[[jhatRow]]][[Color]],
D[Phi[[iColumn]], t]], {Color, 1, Length[DColor[Psi[[1]]]]},
{jhatRow, 1, Length[Psi]}, {iColumn, 1, Length[Phi]}]]
Gadget[Rep1_, Rep2_] := Simplify[(1/(dmin[NColors[Rep1]]*NColors[Rep1]*
(NColors[Rep1] - 1)))*(-(1/VtildeScaleFactor^2))*
Sum[Tr[Vtilde[Rep1][[Ii,Ji]] . Vtilde[Rep2][[Ii,Ji]]],
{Ii, 1, NColors[Rep1]}, {Ji, 1, NColors[Rep1]}]]
GATerms[L_, R_][II_, JJ_] := L[[II]] . R[[JJ]] + L[[JJ]] . R[[II]]
GeneralNPrintString[Rep_, MonodromyIsToBeGenerated_] :=
If[MonodromyIsToBeGenerated, StringJoin["L, R, GALR, GARL, V, Vtilde, \
ZetaGen, Holoraumy, Monodromy, ZetatildeGen, Holoraumytilde, Monodromytilde, \
cSoln[V[Rep]], cSoln[Vtilde[Rep]] are loaded for Rep = ", ToString[Rep]],
StringJoin["L, R, GALR, GARL, V, Vtilde, cSoln[V[Rep]], \
cSoln[Vtilde[Rep]] are loaded for Rep = ", ToString[Rep]]]
MonodromyIsToBeGenerated = False
GenerateAdinkraData[Rep_] := If[CorrectDimensions[Rep],
{GALR[Rep] = Table[GATerms[L[Rep], R[Rep]][II, JJ],
{II, 1, NColors[Rep]}, {JJ, 1, NColors[Rep]}];
GARL[Rep] = Table[GATerms[R[Rep], L[Rep]][II, JJ],
{II, 1, NColors[Rep]}, {JJ, 1, NColors[Rep]}];
V[Rep] = Table[Vterms[Rep][Ii, Ji], {Ii, 1, NColors[Rep]},
{Ji, 1, NColors[Rep]}]; Vtilde[Rep] =
Table[Vtildeterms[Rep][Ii, Ji], {Ii, 1, NColors[Rep]},
{Ji, 1, NColors[Rep]}]; If[MonodromyIsToBeGenerated,
{ZetaGen[Rep] = Table[Zetaterms[Rep][Ii], {Ii, 1, NColors[Rep]}];
ZetatildeGen[Rep] = Table[Zetatildeterms[Rep][Ii],
{Ii, 1, NColors[Rep]}]; GenerateHoloraumyMonodromy[Rep];
GenerateHoloraumyMonodromytilde[Rep]; }; ];
LinearlyIndependent[V[Rep]]; LinearlyIndependent[Vtilde[Rep]];
If[NColors[Rep] == 4, {chi0[Rep] = CalculateChi0[Rep];
ncis[Rep] = CalculateNcis[Rep]; ntrans[Rep] = CalculateNtrans[
Rep]; Do[VPM[pmList[[ai]]][Rep] = Table[VPMterms[pmList[[ai]]][
Rep][Ii, Ji], {Ii, 1, NColors[Rep]}, {Ji, 1, NColors[Rep]}],
{ai, 1, 2}]; Do[VtildePM[pmList[[ai]]][Rep] =
Table[VtildePMterms[pmList[[ai]]][Rep][Ii, Ji], {Ii, 1,
NColors[Rep]}, {Ji, 1, NColors[Rep]}], {ai, 1, 2}];
Print[StringJoin["chi0, ncis, ntrans, VPM[pm], VtildePM[pm], ",
GeneralNPrintString[Rep, MonodromyIsToBeGenerated]]]; }; ,
Print[GeneralNPrintString[Rep, MonodromyIsToBeGenerated]]; ]}; ,
"IncorrectDimensions, No Data Generated"]
GenerateAdinkraData[Rep_, Orthogonal] :=
{R[Rep] = RO[Rep]; GenerateAdinkraData[Rep]}
GenerateAdinkraData[Rep_, Lmatrices_] :=
{L[Rep] = Lmatrices; R[Rep] = RO[Rep]; GenerateAdinkraData[Rep]}
GenerateAdinkraData[Rep_, Lmatrices_, Rmatrices_] :=
{L[Rep] = Lmatrices; R[Rep] = Rmatrices; GenerateAdinkraData[Rep]}
Vterms[Rep_][Ii_, Ji_] := Simplify[(1/2)*VScaleFactor*
(L[Rep][[Ii]] . R[Rep][[Ji]] - L[Rep][[Ji]] . R[Rep][[Ii]])]
Vtildeterms[Rep_][Ii_, Ji_] := Simplify[(1/2)*VtildeScaleFactor*
(R[Rep][[Ii]] . L[Rep][[Ji]] - R[Rep][[Ji]] . L[Rep][[Ii]])]
Zetaterms[Rep_][Ii_] := L[Rep][[Ii]] . R[Rep][[1]]
Zetatildeterms[Rep_][Ii_] := R[Rep][[Ii]] . L[Rep][[1]]
GenerateHoloraumyMonodromy[Rep_] := If[AllZetaGenNonSingular[Rep],
{Do[HoloraumyTerms[Rep][WordNumber] =
(-1)^IntegerDigits[WordNumber, 2, NColors[Rep]][[1]]*
IdentityMatrix[Length[ZetaGen[Rep][[1]]]];
For[Ii = 2, Ii <= NColors[Rep], Ii++, HoloraumyTerms[Rep][
WordNumber] = HoloraumyTerms[Rep][WordNumber] .
MatrixPower[ZetaGen[Rep][[Ii]], IntegerDigits[WordNumber, 2,
NColors[Rep]][[Ii]]]], {WordNumber, 1, 2^NColors[Rep]}];
Holoraumy[Rep] = Table[HoloraumyTerms[Rep][WordNumber],
{WordNumber, 1, 2^NColors[Rep]}]; Monodromy[Rep] =
Abs[Holoraumy[Rep]]; Clear[HoloraumyTerms, Ii]; },
{Holoraumy[Rep] = Table["ZetaGen has singular elements",
{WordNumber, 1, 2^NColors[Rep]}]; Monodromy[Rep] =
Table["ZetaGen has singular elements", {WordNumber, 1,
2^NColors[Rep]}]}]
GenerateHoloraumyMonodromytilde[Rep_] := If[AllZetatildeGenNonSingular[Rep],
{Do[HoloraumytildeTerms[Rep][WordNumber] =
(-1)^IntegerDigits[WordNumber, 2, NColors[Rep]][[1]]*
IdentityMatrix[Length[ZetatildeGen[Rep][[1]]]];
For[Ii = 2, Ii <= NColors[Rep], Ii++, HoloraumytildeTerms[Rep][
WordNumber] = HoloraumytildeTerms[Rep][WordNumber] .
MatrixPower[ZetatildeGen[Rep][[Ii]], IntegerDigits[WordNumber, 2,
NColors[Rep]][[Ii]]]], {WordNumber, 1, 2^NColors[Rep]}];
Holoraumytilde[Rep] = Table[HoloraumytildeTerms[Rep][WordNumber],
{WordNumber, 1, 2^NColors[Rep]}]; Monodromytilde[Rep] =
Abs[Holoraumytilde[Rep]]; Clear[HoloraumytildeTerms, Ii]; },
{Holoraumytilde[Rep] = Table["ZetatildeGen has singular elements",
{WordNumber, 1, 2^NColors[Rep]}]; Monodromytilde[Rep] =
Holoraumytilde[Rep]}]
pmList = {-1, 1}
VPMterms[pm_][Rep_][Ii_, Ji_] :=
Simplify[(1/2)*(V[Rep][[Ii,Ji]] + pm*(1/2)*
Sum[Signature[{Ii, Ji, Ki, Li}]*V[Rep][[Ki,Li]], {Ki, 1, 4},
{Li, 1, 4}])]
VtildePMterms[pm_][Rep_][Ii_, Ji_] :=
Simplify[(1/2)*(Vtilde[Rep][[Ii,Ji]] +
pm*(1/2)*Sum[Signature[{Ii, Ji, Ki, Li}]*Vtilde[Rep][[Ki,Li]],
{Ki, 1, 4}, {Li, 1, 4}])]
GenerateAdinkraDataO[Rep_] := GenerateAdinkraData[Rep, Orthogonal]
GenerateCoeffs[Rep_] :=
{If[SquareMatrixQ[L[Rep][[1]]] && Mod[dbosons[Rep], 4] == 0,
{Do[LCoeffs[Rep][Ii] = Table[Coeffs[dbosons[Rep]][L[Rep][[Ii]]][ai,
mu, nu], {ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}], CMessage[Rep][1, 1] = "LCoeffs, "},
{CMessage[Rep][1, 1] = "", CMessage[Rep][1, 2] =
"\!\(\*SubscriptBox[\(L\), \(I\)]\) are not 4n x 4n square matrices"}\
]; If[SquareMatrixQ[R[Rep][[1]]] && Mod[dfermions[Rep], 4] == 0,
{Do[RCoeffs[Rep][Ii] = Table[Coeffs[dbosons[Rep]][R[Rep][[Ii]]][ai,
mu, nu], {ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}], CMessage[Rep][2, 1] = "RCoeffs, "},
{CMessage[Rep][2, 1] = "", CMessage[Rep][2, 2] =
"\!\(\*SubscriptBox[\(R\), \(I\)]\) are not 4n x 4n square matrices"}\
]; If[Mod[dbosons[Rep], 4] == 0, {Do[GALRCoeffs[Rep][Ii, Ji] =
Table[Coeffs[dbosons[Rep]][GALR[Rep][[Ii,Ji]]][ai, mu, nu],
{ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}, {Ji, Ii, NColors[Rep]}],
CMessage[Rep][3, 1] = "GALRCoeffs, "}, {CMessage[Rep][3, 1] = "",
CMessage[Rep][3, 2] = "\!\(\*SubscriptBox[\(L\), \
\(I\)]\)\!\(\*SubscriptBox[\(R\), \(J\)]\) are not 4n x 4n square matrices"}]\
; If[Mod[dfermions[Rep], 4] == 0, {Do[GARLCoeffs[Rep][Ii, Ji] =
Table[Coeffs[dfermions[Rep]][GARL[Rep][[Ii,Ji]]][ai, mu, nu],
{ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep]}, {Ji, Ii, NColors[Rep]}],
CMessage[Rep][4, 1] = "GARLCoeffs, "}, {CMessage[Rep][4, 1] = "",
CMessage[Rep][4, 2] = "\!\(\*SubscriptBox[\(R\), \
\(I\)]\)\!\(\*SubscriptBox[\(L\), \(J\)]\) are not 4n x 4n square matrices"}]\
; If[Mod[dbosons[Rep], 4] == 0, {Do[VCoeffs[Rep][Ii, Ji] =
Table[Coeffs[dbosons[Rep]][V[Rep][[Ii,Ji]]][ai, mu, nu],
{ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{Ii, 1, NColors[Rep] - 1}, {Ji, Ii + 1, NColors[Rep]}],
CMessage[Rep][5, 1] = "VCoeffs, "}, {CMessage[Rep][5, 1] = "",
CMessage[Rep][5, 2] =
"\!\(\*SubscriptBox[\(V\), \(IJ\)]\) are not 4n x 4n square \
matrices"}]; If[Mod[dfermions[Rep], 4] == 0,
{Do[VtildeCoeffs[Rep][Ii, Ji] = Table[Coeffs[dfermions[Rep]][
Vtilde[Rep][[Ii,Ji]]][ai, mu, nu], {ai, 1, Num\[Omega]f[Rep]},
{mu, 1, 4}, {nu, 1, 4}], {Ii, 1, NColors[Rep] - 1},
{Ji, Ii + 1, NColors[Rep]}], CMessage[Rep][6, 1] =
"VtildeCoeffs, "}, {CMessage[Rep][6, 1] = "", CMessage[Rep][6, 2] =
"\!\(\*SubscriptBox[OverscriptBox[\(V\), \(~\)], \(IJ\)]\) are not \
4n x 4n square matrices"}]; If[Mod[dbosons[Rep], 4] == 0 &&
NColors[Rep] == 4, {Do[VPMCoeffs[pm][Rep][Ii, Ji] =
Table[Coeffs[dbosons[Rep]][VPM[pm][Rep][[Ii,Ji]]][ai, mu, nu],
{ai, 1, Num\[Omega]b[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{pm, {-1, 1}}, {Ii, 1, 2}, {Ji, Ii + 1, 3}], CMessage[Rep][7, 1] =
"VPMCoeffs, "}, {CMessage[Rep][7, 1] = "", CMessage[Rep][7, 2] = "\!\
\(\*SubsuperscriptBox[\(V\), \(IJ\), \(+-\)]\) are not 4n x 4n square \
matrices and/or N \[NotEqual] 4"}]; If[Mod[dfermions[Rep], 4] == 0 &&
NColors[Rep] == 4, {Do[VtildePMCoeffs[pm][Rep][Ii, Ji] =
Table[Coeffs[dfermions[Rep]][VtildePM[pm][Rep][[Ii,Ji]]][ai, mu,
nu], {ai, 1, Num\[Omega]f[Rep]}, {mu, 1, 4}, {nu, 1, 4}],
{pm, {-1, 1}}, {Ii, 1, 2}, {Ji, Ii + 1, 3}], CMessage[Rep][8, 1] =
"VtildePMCoeffs"}, {CMessage[Rep][8, 1] = "", CMessage[Rep][8, 2] =
"\!\(\*SubsuperscriptBox[OverscriptBox[\(V\), \(~\)], \(IJ\), \
\(+-\)]\) are not 4n x 4n square matrices and/or N \[NotEqual] 4"}];
StringJoin[CMessage[Rep][1, 1], CMessage[Rep][2, 1],
CMessage[Rep][3, 1], CMessage[Rep][4, 1], CMessage[Rep][5, 1],
CMessage[Rep][6, 1], CMessage[Rep][7, 1], CMessage[Rep][8, 1],
" and CMessage[Rep][mi,si] are loaded for Rep = ", ToString[Rep]]}
H = {{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}},
{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}},
{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}},
{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}}
HList = {0, 12, 13, 23, 1, 2, 3, 123}
HMatrixForm = {MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0},
{0, 0, 1, 0}, {0, 0, 0, 1}}], MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0},
{0, 0, -1, 0}, {0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0},
{0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}],
MatrixForm[{{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}],
MatrixForm[{{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}],
MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}],
MatrixForm[{{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}]}
HPermMatrixForm[ai_] := MatrixForm[HPerm[ai]]
IellABCode[Rep_] := IellABColor[Rep] /. AlphaBetaToLogicCode
IellABColor[Rep_] := {IellABColorCoefficients[Rep][1][1] .
{\[Alpha][1], \[Alpha][2], \[Alpha][3]} +
IellABColorCoefficients[Rep][1][2] . {\[Beta][1], \[Beta][2],
\[Beta][3]}, IellABColorCoefficients[Rep][2][1] .
{\[Alpha][1], \[Alpha][2], \[Alpha][3]} +
IellABColorCoefficients[Rep][2][2] . {\[Beta][1], \[Beta][2],
\[Beta][3]}}
IellABColorCoefficients[Rep_][TildeIndex_][su2color_] :=
Table[Tr[Table[I*ell[Rep][TildeIndex, ahat][Ii, Ji], {Ii, 1, 4},
{Ji, 1, 4}] . su2matrix[su2color, bhat]]/4, {ahat, 1, 3},
{bhat, 1, 3}]
IkappaABColorCoefficients[Rep_][TildeIndex_][su2color_] :=
Table[Tr[Table[I*kappa[Rep][TildeIndex, ahat][Ii, Ji], {Ii, 1, 4},
{Ji, 1, 4}] . su2matrix[su2color, bhat]]/4, {ahat, 1, 3},
{bhat, 1, 3}]
kappa[Rep_][TildeIndex_, ahat_][Ii_, Ji_] :=
(-I)*(Tr[su2matrix[TildeIndex, ahat] . V[Rep][[Ii,Ji]]]/(4*VScaleFactor))
IndexRange[AdinkraEssentials][II] = "1, 2,..., NColors"
IndexRange[AdinkraEssentials][p1] = "0, 1"
IndexRange[AdinkraEssentials][pm] = "-1, 1"
IndexRange[AdinkraEssentials][ReportLevel] = "1, 2, 3, 4, 5, 6, 7, 8"
IndexRange[BasisDecomposition][a] = "0(Num\[Omega]b[Rep]),1,2,...,Num\[Omega]\
b[Rep]-1 or 0(Num\[Omega]f[Rep]),1,2,...,Num\[Omega]f[Rep]-1"
IndexRange[BasisDecomposition][ahat] = "1,2,3"
IndexRange[BasisDecomposition][d] = "dbosons[Rep] or dfermions[Rep]"
IndexRange[BasisDecomposition][mi] =
"mi = 1(L), 2(R), 3(GALR), 4(GARL), 5(V), 6(Vtilde), 7(VPM), 8(VtildePM)"
IndexRange[BasisDecomposition][mu] = "0(4),1,2,3"
IndexRange[BasisDecomposition][n] = "n = d/4, the n in sl(n)"
IndexRange[BasisDecomposition][si] =
"si := 1(check string), 2(message string)"
IndexRange[BC4Tools][a] =
"1,2,3,4,5,6,7,8 for Table, 0,12,13,23,1,2,3,123 for Perm"
IndexRange[BC4Tools][A] = "1,2,3,4 for Table, 0,1234,1324,1423 for Perm"
IndexRange[BC4Tools][II] = "1,2,3,...,NColors"
IndexRange[BC4Tools][n] = "1,2 for Table, Integers for Perm"
IndexRange[BC4Tools][tt] = "1,2"
IndexRange[BC4Tools][\[Mu]] =
"1,2,3,4,5,6 for Table, 0,12,13,23,123,132 for Perm"
IndexRange[GraphingTools][list] = "{{7,8},{1,2,3,4},{5,6}} for a 242 adinkra, \
{{8},{1,2,3,4},{5,6,7}} for a 341 adinkra, etc."
IndexRange[SpaceTime][a] = "1,2,3,4"
IndexRange[SpaceTime][mu] = "0,1,2,3"
IndexRange[SpaceTime][RaiseCode] = "UP=1, DOWN=2"
InverseCmetric = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}
Lap[Field_] := -D[Field, t, t] + D[Field, x, x] + D[Field, y, y] +
D[Field, z, z]
Attributes[layerlengths$] = {Temporary}
MachineType = MAC
MetersToFeet[Meters_] := Meters*(39.4/12)
nRows[Matrices_] := Length[Matrices[[1]]]
NumberNonZero[Matrix_] := {CountNonZero = 16*Length[Matrix];
Do[If[Matrix[[ai,mu,nu]] == 0, CountNonZero--],
{ai, 1, Length[Matrix]}, {mu, 1, 4}, {nu, 1, 4}], CountNonZero,
Clear[CountNonZero]; }[[2]]
PrintAllGALR[Rep_] := Flatten[Table[PrintGALR[Rep][II, JJ],
{II, 1, NColors[Rep]}, {JJ, II, NColors[Rep]}]]
PrintGALR[Rep_][II_, JJ_] := MatrixForm[GALR[Rep][[II,JJ]]]
PrintAllGARL[Rep_] := Flatten[Table[PrintGARL[Rep][II, JJ],
{II, 1, NColors[Rep]}, {JJ, II, NColors[Rep]}]]
PrintGARL[Rep_][II_, JJ_] := MatrixForm[GARL[Rep][[II,JJ]]]
PrintAllHoloraumy[Rep_] := Table[MatrixForm[Holoraumy[Rep][[Ii]]],
{Ii, 1, 2^NColors[Rep]}]
PrintAllHoloraumytilde[Rep_] := Table[MatrixForm[Holoraumytilde[Rep][[Ii]]],
{Ii, 1, 2^NColors[Rep]}]
PrintAllL[Rep_] := Table[PrintL[Rep][Ii], {Ii, 1, NColors[Rep]}]
PrintL[Rep_][Ii_] := MatrixForm[L[Rep][[Ii]]]
PrintAllMonodromy[Rep_] := Table[MatrixForm[Monodromy[Rep][[Ii]]],
{Ii, 1, 2^NColors[Rep]}]
PrintAllMonodromytilde[Rep_] := Table[MatrixForm[Monodromytilde[Rep][[Ii]]],
{Ii, 1, 2^NColors[Rep]}]
PrintAllR[Rep_] := Table[PrintR[Rep][Ii], {Ii, 1, NColors[Rep]}]
PrintR[Rep_][Ii_] := MatrixForm[R[Rep][[Ii]]]
PrintAllV[Rep_] := Flatten[Table[PrintV[Rep][Ii, Ji],
{Ii, 1, NColors[Rep] - 1}, {Ji, Ii + 1, NColors[Rep]}]]
PrintV[Rep_][Ii_, Ji_] := MatrixForm[V[Rep][[Ii,Ji]]]
PrintAllVPM[pm_][Rep_] := Flatten[Table[PrintVPM[pm][Rep][Ii, Ji],
{Ii, 1, 2}, {Ji, Ii + 1, 3}]]
PrintVPM[pm_][Rep_][Ii_, Ji_] := MatrixForm[VPM[pm][Rep][[Ii,Ji]]]
PrintAllVtilde[Rep_] := Flatten[Table[PrintVtilde[Rep][Ii, Ji],
{Ii, 1, NColors[Rep] - 1}, {Ji, Ii + 1, NColors[Rep]}]]
PrintVtilde[Rep_][Ii_, Ji_] := MatrixForm[Vtilde[Rep][[Ii,Ji]]]
PrintAllVtildePM[pm_][Rep_] := Flatten[Table[PrintVtildePM[pm][Rep][Ii, Ji],
{Ii, 1, 2}, {Ji, Ii + 1, 3}]]
PrintVtildePM[pm_][Rep_][Ii_, Ji_] := MatrixForm[VtildePM[pm][Rep][[Ii,Ji]]]
PrintAllZetaGen[Rep_] := Table[PrintZetaGen[Rep][Ii], {Ii, 2, NColors[Rep]}]
PrintZetaGen[Rep_][Ii_] := MatrixForm[ZetaGen[Rep][[Ii]]]
PrintAllZetatildeGen[Rep_] := Table[PrintZetatildeGen[Rep][Ii],
{Ii, 2, NColors[Rep]}]
PrintZetatildeGen[Rep_][Ii_] := MatrixForm[ZetatildeGen[Rep][[Ii]]]
PrintBasis[Matrix_] := If[SquareMatrixQ[Matrix] && Mod[Length[Matrix], 4] ==
0, If[Length[Matrix] == 4, ConstructBasis[4, Matrix] /.
ToSubscriptsAlphaBeta, ConstructBasis[Matrix] /. ToSubscripts],
Print["Error: Not a 4n x 4n square matrix"]]
ToSubscriptsAlphaBeta = {\[Rho][0, 0] -> I*Subscript["I", 4],
\[Rho][0, bhat_] -> Subscript[\[Beta], bhat],
\[Rho][ahat_, 0] -> Subscript[\[Alpha], ahat],
\[Rho][ahat_, bhat_] -> I*Subscript[\[Alpha], ahat]*
Subscript[\[Beta], bhat]}
ToSubscripts = {\[Omega][sl_][ai_] \[CircleTimes] \[Rho][0, 0] ->
I*Subscript[\[Omega], ai]^sl \[CircleTimes] Subscript["I", 4],
\[Omega][sl_][ai_] \[CircleTimes] \[Rho][0, bhat_] ->
Subscript[\[Omega], ai]^sl \[CircleTimes] Subscript[\[Beta], bhat],
\[Omega][sl_][ai_] \[CircleTimes] \[Rho][ahat_, 0] ->
Subscript[\[Omega], ai]^sl \[CircleTimes] Subscript[\[Alpha], ahat],
\[Omega][sl_][ai_] \[CircleTimes] \[Rho][ahat_, bhat_] ->
I*Subscript[\[Omega], ai]^sl \[CircleTimes] (Subscript[\[Alpha], ahat]*
Subscript[\[Beta], bhat])}
PrintBC4BosonPerm[ni_, ai_, mu_, Ai_] := If[EvenQ[ni] && ai == 0,
If[mu == Ai == 0,
"(\!\(\*SuperscriptBox[SubscriptBox[\()\), \(i\)], \(j\)]\)",
StringJoin["(", FlopString[mu], VierString[Ai],
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(i\)], \(j\)]\)"]],
If[mu == Ai == 0, "("**OverBar[FlipCode[ni, ai]]**
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(i\)], \(j\)]\)",
"(("**OverBar[FlipCode[ni, ai]]**")"**StringJoin[FlopString[mu],
VierString[Ai],
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(i\)], \(j\)]\)"]]]
VierString[Ai_] := If[Ai == 0, "", StringJoin[
FlopString[Digit[Ai, 3]*10 + Digit[Ai, 2]],
FlopString[Digit[Ai, 1]*10 + Digit[Ai, 0]]]]
PrintBC4ColorPerm[ni_, ai_, mu_, Ai_] := If[EvenQ[ni] && ai == 0,
If[mu == Ai == 0,
"(\!\(\*SuperscriptBox[SubscriptBox[\()\), \(I\)], \(J\)]\)",
StringJoin["(", FlopString[mu], VierString[Ai],
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(I\)], \(J\)]\)"]],
If[mu == Ai == 0, "("**OverBar[FlipCode[ni, ai]]**
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(I\)], \(J\)]\)",
"(("**OverBar[FlipCode[ni, ai]]**")"**StringJoin[FlopString[mu],
VierString[Ai],
"\!\(\*SuperscriptBox[SubscriptBox[\()\), \(I\)], \(J\)]\)"]]]
PrintBC4FermionPerm[ni_, ai_, mu_, Ai_] := If[EvenQ[ni] && ai == 0,
If[mu == Ai == 0, "(\!\(\*SuperscriptBox[SubscriptBox[\()\), \
OverscriptBox[\(i\), \(^\)]], OverscriptBox[\(j\), \(^\)]]\)",
StringJoin["(", FlopString[mu], VierString[Ai], "\!\(\*SuperscriptBox[S\
ubscriptBox[\()\), OverscriptBox[\(i\), \(^\)]], OverscriptBox[\(j\), \
\(^\)]]\)"]], If[mu == Ai == 0, "("**OverBar[FlipCode[ni, ai]]**"\!\(\*Supers\
criptBox[SubscriptBox[\()\), OverscriptBox[\(i\), \(^\)]], \
OverscriptBox[\(j\), \(^\)]]\)", "(("**OverBar[FlipCode[ni, ai]]**")"**
StringJoin[FlopString[mu], VierString[Ai], "\!\(\*SuperscriptBox[Subsc\
riptBox[\()\), OverscriptBox[\(i\), \(^\)]], OverscriptBox[\(j\), \(^\)]]\)"]]\
]
PrintBC4Perm[ni_, ai_, mu_, Ai_] := If[EvenQ[ni] && ai == 0,
If[mu == Ai == 0, "()", StringJoin[FlopString[mu], VierString[Ai]]],
"("**OverBar[FlipCode[ni, ai]]**")"**StringJoin[FlopString[mu],
VierString[Ai]]]
PrintGALRBasis[Rep_][Ii_, Ji_] := If[Num\[Omega]b[Rep] == 1,
ConstructGALRBasis[4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructGALRBasis[Rep][Ii, Ji] /. ToSubscripts]
PrintGARLBasis[Rep_][Ii_, Ji_] := If[Num\[Omega]f[Rep] == 1,
ConstructGARLBasis[4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructGARLBasis[Rep][Ii, Ji] /. ToSubscripts]
PrintHoloraumy[Rep_][WordVector_] := MatrixForm[Holoraumy[Rep][[
WordW[WordVector]]]]
WordW[PowerList_] := Sum[PowerList[[ii]]*2^(Length[PowerList] - ii),
{ii, 1, Length[PowerList]}]
PrintHoloraumytilde[Rep_][WordVector_] :=
MatrixForm[Holoraumytilde[Rep][[WordW[WordVector]]]]
PrintIell[Rep_] := IellABColor[Rep] /. AlphaBetaToSuperscripts
PrintLBasis[Rep_][Ii_] := If[Num\[Omega]b[Rep] == 1,
ConstructLBasis[4, Rep][Ii] /. ToSubscriptsAlphaBeta,
ConstructLBasis[Rep][Ii] /. ToSubscripts]
PrintLSigmaProduct[Rep_] := If[SquareMatrixQ[L[Rep][[1]]] &&
IntegerQ[Log[2, Length[L[Rep][[1]]]]],
Table[PrintSigmaProduct[L[Rep][[Ii]]], {Ii, 1, NColors[Rep]}],
Print["Error: Not \!\(\*SuperscriptBox[\(2\), \(n\)]\) x \
\!\(\*SuperscriptBox[\(2\), \(n\)]\) square matrices"]]
PrintSigmaProduct[Matrix_] := If[SquareMatrixQ[Matrix] &&
IntegerQ[Log[2, Length[Matrix]]],
Release[ConstructSigmaProduct[Matrix][[
Log[2, Length[Matrix[[1]]]]]]] //. Subscript[\[Sigma], 0] ->
ToString[I], Print["Error: Not a \!\(\*SuperscriptBox[\(2\), \(n\)]\) \
x \!\(\*SuperscriptBox[\(2\), \(n\)]\) square matrix"]]
PrintMonodromy[Rep_][WordVector_] := MatrixForm[Monodromy[Rep][[
WordW[WordVector]]]]
PrintMonodromytilde[Rep_][WordVector_] :=
MatrixForm[Monodromytilde[Rep][[WordW[WordVector]]]]
PrintRBasis[Rep_][Ii_] := If[Num\[Omega]f[Rep] == 1,
ConstructRBasis[4, Rep][Ii] /. ToSubscriptsAlphaBeta,
ConstructRBasis[Rep][Ii] /. ToSubscripts]
PrintRSigmaProduct[Rep_] := If[SquareMatrixQ[R[Rep][[1]]] &&
IntegerQ[Log[2, Length[R[Rep][[1]]]]],
Table[PrintSigmaProduct[R[Rep][[Ii]]], {Ii, 1, NColors[Rep]}],
Print["Error: Not \!\(\*SuperscriptBox[\(2\), \(n\)]\) x \
\!\(\*SuperscriptBox[\(2\), \(n\)]\) square matrices"]]
PrintVBasis[Rep_][Ii_, Ji_] := If[Num\[Omega]b[Rep] == 1,
ConstructVBasis[4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructVBasis[Rep][Ii, Ji] /. ToSubscripts]
PrintVPMBasis[pm_][Rep_][Ii_, Ji_] := If[Num\[Omega]b[Rep] == 1,
ConstructVPMBasis[pm][4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructVPMBasis[pm][Rep][Ii, Ji] /. ToSubscripts]
PrintVtildeBasis[Rep_][Ii_, Ji_] := If[Num\[Omega]f[Rep] == 1,
ConstructVtildeBasis[4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructVtildeBasis[Rep][Ii, Ji] /. ToSubscripts]
PrintVtildePMBasis[pm_][Rep_][Ii_, Ji_] := If[Num\[Omega]f[Rep] == 1,
ConstructVtildePMBasis[pm][4, Rep][Ii, Ji] /. ToSubscriptsAlphaBeta,
ConstructVtildePMBasis[pm][Rep][Ii, Ji] /. ToSubscripts]
QuaternionTestIJK[Quat_] := Quat[[1]] . Quat[[1]] ==
-Quat[[2]] . Quat[[2]] == -Quat[[3]] . Quat[[3]] ==
-Quat[[4]] . Quat[[4]] == IdentityMatrix[Length[Quat[[1]]]] &&
Quat[[2]] . Quat[[3]] == Quat[[4]]
QuaternionTestKJI[Quat_] := Quat[[1]] . Quat[[1]] ==
-Quat[[2]] . Quat[[2]] == -Quat[[3]] . Quat[[3]] ==
-Quat[[4]] . Quat[[4]] == IdentityMatrix[Length[Quat[[1]]]] &&
Quat[[4]] . Quat[[3]] == Quat[[2]]
RaiseFermionIndex[Field_] := If[Depth[Field[[0,0]]] == 1,
Sum[InverseCmetric[[Field[[0,1]],bi]]*Field[[0,0]][bi][t, x, y, z],
{bi, 1, 4}], Sum[InverseCmetric[[Field[[0,1]],bi]]*
Field[[0,0]][bi][t, x, y, z], {bi, 1, 4}]]
RaiseSTIndex[Field_] := If[Depth[Field[[0,0]]] == 1,
SignCoordinate[Field[[0,1]]]*Field, SignCoordinate[Field[[0,0,1]]]*Field]
RaiseSTIndex[Field_, RaiseCode1_, RaiseCode2_] :=
If[Depth[Field[[0,0]]] == 1, SignCoordinate[Field[[0,1]]]^RaiseCode1*
SignCoordinate[Field[[0,2]]]^RaiseCode2*Field,
SignCoordinate[Field[[0,0,1]]]^RaiseCode1*SignCoordinate[Field[[0,0,2]]]^
RaiseCode2*Field]
RaiseSTIndex[Field_, RaiseCode1_, RaiseCode2_, RaiseCode3_] :=
If[Depth[Field[[0,0]]] == 1, SignCoordinate[Field[[0,1]]]^RaiseCode1*
SignCoordinate[Field[[0,2]]]^RaiseCode2*SignCoordinate[Field[[0,3]]]^
RaiseCode3*Field, SignCoordinate[Field[[0,0,1]]]^RaiseCode1*
SignCoordinate[Field[[0,0,2]]]^RaiseCode2*
SignCoordinate[Field[[0,0,3]]]^RaiseCode3*Field]
RaiseSTIndex[Field_, RaiseCode1_, RaiseCode2_, RaiseCode3_, RaiseCode4_] :=
If[Depth[Field[[0,0]]] == 1, SignCoordinate[Field[[0,1]]]^RaiseCode1*
SignCoordinate[Field[[0,2]]]^RaiseCode2*SignCoordinate[Field[[0,3]]]^
RaiseCode3*SignCoordinate[Field[[0,4]]]^RaiseCode4*Field,
SignCoordinate[Field[[0,0,1]]]^RaiseCode1*SignCoordinate[Field[[0,0,2]]]^
RaiseCode2*SignCoordinate[Field[[0,0,3]]]^RaiseCode3*
SignCoordinate[Field[[0,0,4]]]^RaiseCode4*Field]
SignCoordinate[0] := -1
SignCoordinate[1] := 1
SignCoordinate[2] := 1
SignCoordinate[3] := 1
SignCoordinate[t] := -1
SignCoordinate[x] := 1
SignCoordinate[y] := 1
SignCoordinate[z] := 1
Attributes[rules$] = {Temporary}
S3 = {{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}},
{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}},
{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 0, 1}},
{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}}}
S3List = {0, 12, 13, 23, 123, 132}
S3MatrixForm = {MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}], MatrixForm[{{0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0},
{0, 0, 0, 1}}], MatrixForm[{{1, 0, 0, 0}, {0, 0, 1, 0}, {0, 1, 0, 0},
{0, 0, 0, 1}}], MatrixForm[{{0, 0, 1, 0}, {1, 0, 0, 0}, {0, 1, 0, 0},
{0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 0},
{0, 0, 0, 1}}]}
S3PermMatrixForm[mu_] := MatrixForm[S3Perm[mu]]
SaveString[MAC] = "../Adinkra.m"
SaveString[PC] = "..\\Adinkra.m"
SigmaMatrixProduct[ii_, Matrix_] := ArrayFlatten[Outer[Times, sigma[ii],
Matrix]]
SigmaProductMF[mu_, nu_] := MatrixForm[SigmaProduct[mu, nu]]
SigmaProductMF[mu_, nu_, ap_] := MatrixForm[SigmaProduct[mu, nu, ap]]
SigmaProductMF[mu_, nu_, ap_, bt_] := MatrixForm[SigmaProduct[mu, nu, ap, bt]]
SigmaProductMF[mu_, nu_, ap_, bt_, ro_] :=
MatrixForm[SigmaProduct[mu, nu, ap, bt, ro]]
SigmaProductMF[mu_, nu_, ap_, bt_, ro_, sg_] :=
MatrixForm[SigmaProduct[mu, nu, ap, bt, ro, sg]]
SigmaProductMF[mu_, nu_, ap_, bt_, ro_, sg_, dl_] :=
MatrixForm[SigmaProduct[mu, nu, ap, bt, ro, sg, dl]]
SigmaProductMF[mu_, nu_, ap_, bt_, ro_, sg_, dl_, gm_] :=
MatrixForm[SigmaProduct[mu, nu, ap, bt, ro, sg, dl, gm]]
ToSubscriptsRho = {\[Omega][sl_][ai_] -> Subscript[\[Omega], ai]^sl,
\[Rho][mu_, nu_] -> Subscript[\[Rho], mu, nu]}
UD[Field_, var_] := SignCoordinate[var]*D[Field, var]
UP = 1
Vanishes[Object_] := If[Object == 0*Object, True, False]
Vanishing[Rep_] := Flatten[Table[If[Vanishes[VPM[1][Rep][[II,JJ]]],
SuperMinus[Subscript[V, II*10 + JJ]]], {II, 1, NColors[Rep] - 1},
{JJ, II + 1, NColors[Rep]}]]
Vier = {{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}},
{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}},
{{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}},
{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0, 0, 0}}}
VierList = {0, 1234, 1324, 1423}
VierMatrixForm = {MatrixForm[{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}], MatrixForm[{{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1},
{0, 0, 1, 0}}], MatrixForm[{{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0},
{0, 1, 0, 0}}], MatrixForm[{{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0},
{1, 0, 0, 0}}]}
VierPermMatrixForm[Ai_] := MatrixForm[VierPerm[Ai]]
VList = {V, Vtilde}
\[Alpha]matrix[1] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0}, {I, 0, 0, 0}}
\[Alpha]matrix[2] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, I, 0}}
\[Alpha]matrix[3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0}, {0, -I, 0, 0}}
\[Beta]matrix[1] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0}, {I, 0, 0, 0}}
\[Beta]matrix[2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Beta]matrix[3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, -I, 0}}
\[Gamma][0] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}
\[Gamma][1] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}
\[Gamma][2] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}
\[Gamma][3] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}
\[Gamma]5 = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5down = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5test = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}
\[Gamma]5testdownupupup = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Gamma]5\[Gamma][0] = {{0, 0, I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0},
{0, -I, 0, 0}}
\[Gamma]5\[Gamma][1] = {{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Gamma]5\[Gamma][2] = {{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, I}}
\[Gamma]5\[Gamma][3] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]down[0] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]down[1] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]down[2] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]down[3] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]stdown[0] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]stdown[1] = {{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Gamma]5\[Gamma]stdown[2] = {{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, I}}
\[Gamma]5\[Gamma]stdown[3] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]stdowndown[0] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Gamma]5\[Gamma]stdowndown[1] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]stdowndown[2] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]stdowndown[3] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]stdownup[0] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]stdownup[1] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]stdownup[2] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]stdownup[3] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]up[0] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Gamma]5\[Gamma]up[1] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]up[2] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]up[3] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][0, 0] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][0, 1] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][0, 2] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma][0, 3] = {{0, 0, I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][1, 0] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][1, 1] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][1, 2] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma][1, 3] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][2, 0] = {{0, -I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma][2, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma][2, 2] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][2, 3] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma][3, 0] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][3, 1] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma][3, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma][3, 3] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[0, 0] = {{0, 0, I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[0, 1] = {{0, 0, -I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[0, 2] = {{I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]down[0, 3] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[1, 0] = {{0, 0, I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[1, 1] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[1, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]down[1, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[2, 0] = {{-I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]down[2, 1] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]down[2, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[2, 3] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[3, 0] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[3, 1] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[3, 2] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]down[3, 3] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[0, 0] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[0, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[0, 2] = {{0, -I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[0, 3] = {{0, 0, -I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[1, 0] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[1, 1] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[1, 2] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[1, 3] = {{0, 0, I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[2, 0] = {{0, I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[2, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[2, 2] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[2, 3] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[3, 0] = {{0, 0, I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[3, 1] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[3, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdown[3, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[0, 0] =
{{0, 0, I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[0, 1] =
{{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[0, 2] =
{{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[0, 3] =
{{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[1, 0] =
{{0, 0, -I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[1, 1] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[1, 2] =
{{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[1, 3] =
{{0, 0, 0, I}, {0, 0, -I, 0}, {0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[2, 0] =
{{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[2, 1] =
{{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[2, 2] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[2, 3] =
{{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[3, 0] =
{{0, 0, 0, I}, {0, 0, I, 0}, {0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[3, 1] =
{{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[3, 2] =
{{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstdowndown[3, 3] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[0, 0] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[0, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[0, 2] = {{0, -I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[0, 3] = {{0, 0, -I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[1, 0] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[1, 1] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[1, 2] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[1, 3] = {{0, 0, I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[2, 0] = {{0, -I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[2, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[2, 2] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[2, 3] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[3, 0] = {{0, 0, -I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[3, 1] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[3, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstup[3, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[0, 0] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[0, 1] = {{0, 0, I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[0, 2] =
{{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[0, 3] =
{{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[1, 0] = {{0, 0, I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[1, 1] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[1, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[1, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[2, 0] =
{{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[2, 1] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[2, 2] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[2, 3] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[3, 0] =
{{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[3, 1] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[3, 2] =
{{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stdownstupdown[3, 3] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[0, 0] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[0, 1] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[0, 2] = {{0, I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[0, 3] = {{0, 0, I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[1, 0] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[1, 1] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[1, 2] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[1, 3] = {{0, 0, I, 0}, {0, 0, 0, I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[2, 0] = {{0, I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[2, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[2, 2] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[2, 3] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[3, 0] = {{0, 0, I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[3, 1] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[3, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdown[3, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[0, 0] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[0, 1] = {{0, 0, -I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[0, 2] = {{I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[0, 3] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[1, 0] = {{0, 0, -I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[1, 1] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[1, 2] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[1, 3] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[2, 0] = {{I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[2, 1] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[2, 2] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[2, 3] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[3, 0] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[3, 1] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[3, 2] =
{{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]stupstdowndown[3, 3] =
{{0, 0, -I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[0, 0] = {{0, 0, -I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[0, 1] = {{0, 0, -I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[0, 2] = {{I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]up[0, 3] = {{0, 0, 0, I}, {0, 0, I, 0},
{0, I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[1, 0] = {{0, 0, I, 0}, {0, 0, 0, -I},
{I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[1, 1] = {{0, 0, I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[1, 2] = {{-I, 0, 0, 0}, {0, I, 0, 0},
{0, 0, -I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]up[1, 3] = {{0, 0, 0, -I}, {0, 0, I, 0},
{0, I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[2, 0] = {{-I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, I}}
\[Gamma]5\[Gamma]\[Gamma]up[2, 1] = {{I, 0, 0, 0}, {0, -I, 0, 0},
{0, 0, I, 0}, {0, 0, 0, -I}}
\[Gamma]5\[Gamma]\[Gamma]up[2, 2] = {{0, 0, I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[2, 3] = {{0, -I, 0, 0}, {-I, 0, 0, 0},
{0, 0, 0, -I}, {0, 0, -I, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[3, 0] = {{0, 0, 0, -I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {-I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[3, 1] = {{0, 0, 0, I}, {0, 0, -I, 0},
{0, -I, 0, 0}, {I, 0, 0, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[3, 2] = {{0, I, 0, 0}, {I, 0, 0, 0},
{0, 0, 0, I}, {0, 0, I, 0}}
\[Gamma]5\[Gamma]\[Gamma]up[3, 3] = {{0, 0, I, 0}, {0, 0, 0, I},
{-I, 0, 0, 0}, {0, -I, 0, 0}}
\[Gamma]down[0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
\[Gamma]down[1] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, 1}}
\[Gamma]down[2] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}}
\[Gamma]down[3] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}
\[Gamma]stdown[0] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}
\[Gamma]stdown[1] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 0}}
\[Gamma]stdown[2] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {-1, 0, 0, 0}}
\[Gamma]stdown[3] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}
\[Gamma]stdowndown[0] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, -1}}
\[Gamma]stdowndown[1] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, 1}}
\[Gamma]stdowndown[2] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0,
0}}
\[Gamma]stdowndown[3] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}
\[Gamma]up[0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}
\[Gamma]up[1] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, -1}}
\[Gamma]up[2] = {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, -1, 0, 0}}
\[Gamma]up[3] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma][0, 0] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, -1}}
\[Gamma]\[Gamma][0, 1] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, 1}}
\[Gamma]\[Gamma][0, 2] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0,
0}}
\[Gamma]\[Gamma][0, 3] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}
\[Gamma]\[Gamma][1, 0] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0,
0, -1}}
\[Gamma]\[Gamma][1, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}
\[Gamma]\[Gamma][1, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0, 1,
0, 0}}
\[Gamma]\[Gamma][1, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0,
1, 0}}
\[Gamma]\[Gamma][2, 0] = {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0, 0}, {0,
-1, 0, 0}}
\[Gamma]\[Gamma][2, 1] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0}, {0, -1,
0, 0}}
\[Gamma]\[Gamma][2, 2] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}
\[Gamma]\[Gamma][2, 3] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0, 0}, {-1, 0,
0, 0}}
\[Gamma]\[Gamma][3, 0] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, -1}, {0, 0,
-1, 0}}
\[Gamma]\[Gamma][3, 1] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}
\[Gamma]\[Gamma][3, 2] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0, 0}, {1, 0,
0, 0}}
\[Gamma]\[Gamma][3, 3] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0,
1}}
\[Gamma]\[Gamma]down[0, 0] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, 1, 0}}
\[Gamma]\[Gamma]down[0, 1] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1},
{0, 0, -1, 0}}
\[Gamma]\[Gamma]down[0, 2] = {{0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1, 0, 0}, {1,
0, 0, 0}}
\[Gamma]\[Gamma]down[0, 3] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0,
0, 0, 1}}
\[Gamma]\[Gamma]down[1, 0] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, 1, 0}}
\[Gamma]\[Gamma]down[1, 1] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, -1, 0}}
\[Gamma]\[Gamma]down[1, 2] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1,
0, 0, 0}}
\[Gamma]\[Gamma]down[1, 3] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}}
\[Gamma]\[Gamma]down[2, 0] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {-1,
0, 0, 0}}
\[Gamma]\[Gamma]down[2, 1] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0, 0},
{-1, 0, 0, 0}}
\[Gamma]\[Gamma]down[2, 2] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, -1, 0}}
\[Gamma]\[Gamma]down[2, 3] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0,
1, 0, 0}}
\[Gamma]\[Gamma]down[3, 0] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, -1}}
\[Gamma]\[Gamma]down[3, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0,
0, 0, -1}}
\[Gamma]\[Gamma]down[3, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0,
-1, 0, 0}}
\[Gamma]\[Gamma]down[3, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0,
0, -1, 0}}
\[Gamma]\[Gamma]stdownstdown[0, 0] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstdown[0, 1] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstdown[0, 2] = {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0,
0, 0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[0, 3] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstdown[1, 0] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdown[1, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdown[1, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0,
0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[1, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstdown[2, 0] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0,
0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[2, 1] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0,
0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[2, 2] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdown[2, 3] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[3, 0] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstdown[3, 1] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstdown[3, 2] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdown[3, 3] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdowndown[0, 0] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
0, -1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstdowndown[0, 1] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstdowndown[0, 2] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1,
0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[0, 3] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstdowndown[1, 0] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0,
0, 0, -1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstdowndown[1, 1] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstdowndown[1, 2] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1,
0, 0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[1, 3] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0,
0, 1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdowndown[2, 0] = {{0, 0, 0, 1}, {0, 0, -1, 0}, {0,
-1, 0, 0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[2, 1] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0,
-1, 0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[2, 2] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstdowndown[2, 3] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {-1,
0, 0, 0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[3, 0] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstdowndown[3, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstdowndown[3, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0,
0, 0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstdowndown[3, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstup[0, 0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstup[0, 1] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstup[0, 2] = {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0,
0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstup[0, 3] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstup[1, 0] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1,
0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstup[1, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstup[1, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0,
0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stdownstup[1, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstup[2, 0] = {{0, 0, -1, 0}, {0, 0, 0, -1}, {-1, 0, 0,
0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstup[2, 1] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0,
0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstup[2, 2] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstup[2, 3] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstup[3, 0] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstup[3, 1] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstup[3, 2] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstup[3, 3] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstupdown[0, 0] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstupdown[0, 1] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstupdown[0, 2] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1,
0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[0, 3] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstupdown[1, 0] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stdownstupdown[1, 1] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstupdown[1, 2] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[1, 3] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stdownstupdown[2, 0] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1,
0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[2, 1] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1,
0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[2, 2] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stdownstupdown[2, 3] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0,
0, 0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[3, 0] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstupdown[3, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stdownstupdown[3, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0,
0, 0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stdownstupdown[3, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdown[0, 0] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdown[0, 1] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdown[0, 2] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0},
{0, 1, 0, 0}}
\[Gamma]\[Gamma]stupstdown[0, 3] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stupstdown[1, 0] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, -1,
0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdown[1, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdown[1, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {-1, 0, 0,
0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stupstdown[1, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0,
-1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stupstdown[2, 0] = {{0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 0},
{0, 1, 0, 0}}
\[Gamma]\[Gamma]stupstdown[2, 1] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {1, 0, 0,
0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stupstdown[2, 2] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdown[2, 3] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, -1, 0,
0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdown[3, 0] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, 1, 0}}
\[Gamma]\[Gamma]stupstdown[3, 1] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0,
1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdown[3, 2] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdown[3, 3] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0},
{0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdowndown[0, 0] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdowndown[0, 1] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
0, -1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdowndown[0, 2] = {{0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1,
0, 0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[0, 3] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdowndown[1, 0] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0,
0, -1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdowndown[1, 1] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdowndown[1, 2] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0,
0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[1, 3] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0,
1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdowndown[2, 0] = {{0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1,
0, 0}, {1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[2, 1] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1,
0, 0}, {-1, 0, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[2, 2] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]stupstdowndown[2, 3] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0,
0, 0}, {0, 1, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[3, 0] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, 1}}
\[Gamma]\[Gamma]stupstdowndown[3, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0,
-1, 0}, {0, 0, 0, -1}}
\[Gamma]\[Gamma]stupstdowndown[3, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0,
0, 0}, {0, -1, 0, 0}}
\[Gamma]\[Gamma]stupstdowndown[3, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0,
0, 1}, {0, 0, -1, 0}}
\[Gamma]\[Gamma]up[0, 0] = {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, 1, 0}}
\[Gamma]\[Gamma]up[0, 1] = {{0, 1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
1, 0}}
\[Gamma]\[Gamma]up[0, 2] = {{0, 0, 0, -1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {-1,
0, 0, 0}}
\[Gamma]\[Gamma]up[0, 3] = {{1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0, 0,
0, -1}}
\[Gamma]\[Gamma]up[1, 0] = {{0, -1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, -1}, {0,
0, -1, 0}}
\[Gamma]\[Gamma]up[1, 1] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}
\[Gamma]\[Gamma]up[1, 2] = {{0, 0, 0, 1}, {0, 0, 1, 0}, {0, 1, 0, 0}, {1, 0,
0, 0}}
\[Gamma]\[Gamma]up[1, 3] = {{-1, 0, 0, 0}, {0, -1, 0, 0}, {0, 0, 1, 0}, {0,
0, 0, 1}}
\[Gamma]\[Gamma]up[2, 0] = {{0, 0, 0, 1}, {0, 0, -1, 0}, {0, -1, 0, 0}, {1,
0, 0, 0}}
\[Gamma]\[Gamma]up[2, 1] = {{0, 0, 0, -1}, {0, 0, -1, 0}, {0, -1, 0, 0}, {-1,
0, 0, 0}}
\[Gamma]\[Gamma]up[2, 2] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}
\[Gamma]\[Gamma]up[2, 3] = {{0, 0, -1, 0}, {0, 0, 0, 1}, {-1, 0, 0, 0}, {0,
1, 0, 0}}
\[Gamma]\[Gamma]up[3, 0] = {{-1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0,
0, 0, 1}}
\[Gamma]\[Gamma]up[3, 1] = {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, -1, 0}, {0, 0,
0, -1}}
\[Gamma]\[Gamma]up[3, 2] = {{0, 0, 1, 0}, {0, 0, 0, -1}, {1, 0, 0, 0}, {0,
-1, 0, 0}}
\[Gamma]\[Gamma]up[3, 3] = {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 1}, {0, 0,
-1, 0}}
\[Epsilon][0, 0, 0, 0] = 0
\[Epsilon][0, 0, 0, 1] = 0
\[Epsilon][0, 0, 0, 2] = 0
\[Epsilon][0, 0, 0, 3] = 0
\[Epsilon][0, 0, 1, 0] = 0
\[Epsilon][0, 0, 1, 1] = 0
\[Epsilon][0, 0, 1, 2] = 0
\[Epsilon][0, 0, 1, 3] = 0
\[Epsilon][0, 0, 2, 0] = 0
\[Epsilon][0, 0, 2, 1] = 0
\[Epsilon][0, 0, 2, 2] = 0
\[Epsilon][0, 0, 2, 3] = 0
\[Epsilon][0, 0, 3, 0] = 0
\[Epsilon][0, 0, 3, 1] = 0
\[Epsilon][0, 0, 3, 2] = 0
\[Epsilon][0, 0, 3, 3] = 0
\[Epsilon][0, 1, 0, 0] = 0
\[Epsilon][0, 1, 0, 1] = 0
\[Epsilon][0, 1, 0, 2] = 0
\[Epsilon][0, 1, 0, 3] = 0
\[Epsilon][0, 1, 1, 0] = 0
\[Epsilon][0, 1, 1, 1] = 0
\[Epsilon][0, 1, 1, 2] = 0
\[Epsilon][0, 1, 1, 3] = 0
\[Epsilon][0, 1, 2, 0] = 0
\[Epsilon][0, 1, 2, 1] = 0
\[Epsilon][0, 1, 2, 2] = 0
\[Epsilon][0, 1, 2, 3] = 1
\[Epsilon][0, 1, 3, 0] = 0
\[Epsilon][0, 1, 3, 1] = 0
\[Epsilon][0, 1, 3, 2] = -1
\[Epsilon][0, 1, 3, 3] = 0
\[Epsilon][0, 2, 0, 0] = 0
\[Epsilon][0, 2, 0, 1] = 0
\[Epsilon][0, 2, 0, 2] = 0
\[Epsilon][0, 2, 0, 3] = 0
\[Epsilon][0, 2, 1, 0] = 0
\[Epsilon][0, 2, 1, 1] = 0
\[Epsilon][0, 2, 1, 2] = 0
\[Epsilon][0, 2, 1, 3] = -1
\[Epsilon][0, 2, 2, 0] = 0
\[Epsilon][0, 2, 2, 1] = 0
\[Epsilon][0, 2, 2, 2] = 0
\[Epsilon][0, 2, 2, 3] = 0
\[Epsilon][0, 2, 3, 0] = 0
\[Epsilon][0, 2, 3, 1] = 1
\[Epsilon][0, 2, 3, 2] = 0
\[Epsilon][0, 2, 3, 3] = 0
\[Epsilon][0, 3, 0, 0] = 0
\[Epsilon][0, 3, 0, 1] = 0
\[Epsilon][0, 3, 0, 2] = 0
\[Epsilon][0, 3, 0, 3] = 0
\[Epsilon][0, 3, 1, 0] = 0
\[Epsilon][0, 3, 1, 1] = 0
\[Epsilon][0, 3, 1, 2] = 1
\[Epsilon][0, 3, 1, 3] = 0
\[Epsilon][0, 3, 2, 0] = 0
\[Epsilon][0, 3, 2, 1] = -1
\[Epsilon][0, 3, 2, 2] = 0
\[Epsilon][0, 3, 2, 3] = 0
\[Epsilon][0, 3, 3, 0] = 0
\[Epsilon][0, 3, 3, 1] = 0
\[Epsilon][0, 3, 3, 2] = 0
\[Epsilon][0, 3, 3, 3] = 0
\[Epsilon][1, 0, 0, 0] = 0
\[Epsilon][1, 0, 0, 1] = 0
\[Epsilon][1, 0, 0, 2] = 0
\[Epsilon][1, 0, 0, 3] = 0
\[Epsilon][1, 0, 1, 0] = 0
\[Epsilon][1, 0, 1, 1] = 0
\[Epsilon][1, 0, 1, 2] = 0
\[Epsilon][1, 0, 1, 3] = 0
\[Epsilon][1, 0, 2, 0] = 0
\[Epsilon][1, 0, 2, 1] = 0
\[Epsilon][1, 0, 2, 2] = 0
\[Epsilon][1, 0, 2, 3] = -1
\[Epsilon][1, 0, 3, 0] = 0
\[Epsilon][1, 0, 3, 1] = 0
\[Epsilon][1, 0, 3, 2] = 1
\[Epsilon][1, 0, 3, 3] = 0
\[Epsilon][1, 1, 0, 0] = 0
\[Epsilon][1, 1, 0, 1] = 0
\[Epsilon][1, 1, 0, 2] = 0
\[Epsilon][1, 1, 0, 3] = 0
\[Epsilon][1, 1, 1, 0] = 0
\[Epsilon][1, 1, 1, 1] = 0
\[Epsilon][1, 1, 1, 2] = 0
\[Epsilon][1, 1, 1, 3] = 0
\[Epsilon][1, 1, 2, 0] = 0
\[Epsilon][1, 1, 2, 1] = 0
\[Epsilon][1, 1, 2, 2] = 0
\[Epsilon][1, 1, 2, 3] = 0
\[Epsilon][1, 1, 3, 0] = 0
\[Epsilon][1, 1, 3, 1] = 0
\[Epsilon][1, 1, 3, 2] = 0
\[Epsilon][1, 1, 3, 3] = 0
\[Epsilon][1, 2, 0, 0] = 0
\[Epsilon][1, 2, 0, 1] = 0
\[Epsilon][1, 2, 0, 2] = 0
\[Epsilon][1, 2, 0, 3] = 1
\[Epsilon][1, 2, 1, 0] = 0
\[Epsilon][1, 2, 1, 1] = 0
\[Epsilon][1, 2, 1, 2] = 0
\[Epsilon][1, 2, 1, 3] = 0
\[Epsilon][1, 2, 2, 0] = 0
\[Epsilon][1, 2, 2, 1] = 0
\[Epsilon][1, 2, 2, 2] = 0
\[Epsilon][1, 2, 2, 3] = 0
\[Epsilon][1, 2, 3, 0] = -1
\[Epsilon][1, 2, 3, 1] = 0
\[Epsilon][1, 2, 3, 2] = 0
\[Epsilon][1, 2, 3, 3] = 0
\[Epsilon][1, 3, 0, 0] = 0
\[Epsilon][1, 3, 0, 1] = 0
\[Epsilon][1, 3, 0, 2] = -1
\[Epsilon][1, 3, 0, 3] = 0
\[Epsilon][1, 3, 1, 0] = 0
\[Epsilon][1, 3, 1, 1] = 0
\[Epsilon][1, 3, 1, 2] = 0
\[Epsilon][1, 3, 1, 3] = 0
\[Epsilon][1, 3, 2, 0] = 1
\[Epsilon][1, 3, 2, 1] = 0
\[Epsilon][1, 3, 2, 2] = 0
\[Epsilon][1, 3, 2, 3] = 0
\[Epsilon][1, 3, 3, 0] = 0
\[Epsilon][1, 3, 3, 1] = 0
\[Epsilon][1, 3, 3, 2] = 0
\[Epsilon][1, 3, 3, 3] = 0
\[Epsilon][2, 0, 0, 0] = 0
\[Epsilon][2, 0, 0, 1] = 0
\[Epsilon][2, 0, 0, 2] = 0
\[Epsilon][2, 0, 0, 3] = 0
\[Epsilon][2, 0, 1, 0] = 0
\[Epsilon][2, 0, 1, 1] = 0
\[Epsilon][2, 0, 1, 2] = 0
\[Epsilon][2, 0, 1, 3] = 1
\[Epsilon][2, 0, 2, 0] = 0
\[Epsilon][2, 0, 2, 1] = 0
\[Epsilon][2, 0, 2, 2] = 0
\[Epsilon][2, 0, 2, 3] = 0
\[Epsilon][2, 0, 3, 0] = 0
\[Epsilon][2, 0, 3, 1] = -1
\[Epsilon][2, 0, 3, 2] = 0
\[Epsilon][2, 0, 3, 3] = 0
\[Epsilon][2, 1, 0, 0] = 0
\[Epsilon][2, 1, 0, 1] = 0
\[Epsilon][2, 1, 0, 2] = 0
\[Epsilon][2, 1, 0, 3] = -1
\[Epsilon][2, 1, 1, 0] = 0
\[Epsilon][2, 1, 1, 1] = 0
\[Epsilon][2, 1, 1, 2] = 0
\[Epsilon][2, 1, 1, 3] = 0
\[Epsilon][2, 1, 2, 0] = 0
\[Epsilon][2, 1, 2, 1] = 0
\[Epsilon][2, 1, 2, 2] = 0
\[Epsilon][2, 1, 2, 3] = 0
\[Epsilon][2, 1, 3, 0] = 1
\[Epsilon][2, 1, 3, 1] = 0
\[Epsilon][2, 1, 3, 2] = 0
\[Epsilon][2, 1, 3, 3] = 0
\[Epsilon][2, 2, 0, 0] = 0
\[Epsilon][2, 2, 0, 1] = 0
\[Epsilon][2, 2, 0, 2] = 0
\[Epsilon][2, 2, 0, 3] = 0
\[Epsilon][2, 2, 1, 0] = 0
\[Epsilon][2, 2, 1, 1] = 0
\[Epsilon][2, 2, 1, 2] = 0
\[Epsilon][2, 2, 1, 3] = 0
\[Epsilon][2, 2, 2, 0] = 0
\[Epsilon][2, 2, 2, 1] = 0
\[Epsilon][2, 2, 2, 2] = 0
\[Epsilon][2, 2, 2, 3] = 0
\[Epsilon][2, 2, 3, 0] = 0
\[Epsilon][2, 2, 3, 1] = 0
\[Epsilon][2, 2, 3, 2] = 0
\[Epsilon][2, 2, 3, 3] = 0
\[Epsilon][2, 3, 0, 0] = 0
\[Epsilon][2, 3, 0, 1] = 1
\[Epsilon][2, 3, 0, 2] = 0
\[Epsilon][2, 3, 0, 3] = 0
\[Epsilon][2, 3, 1, 0] = -1
\[Epsilon][2, 3, 1, 1] = 0
\[Epsilon][2, 3, 1, 2] = 0
\[Epsilon][2, 3, 1, 3] = 0
\[Epsilon][2, 3, 2, 0] = 0
\[Epsilon][2, 3, 2, 1] = 0
\[Epsilon][2, 3, 2, 2] = 0
\[Epsilon][2, 3, 2, 3] = 0
\[Epsilon][2, 3, 3, 0] = 0
\[Epsilon][2, 3, 3, 1] = 0
\[Epsilon][2, 3, 3, 2] = 0
\[Epsilon][2, 3, 3, 3] = 0
\[Epsilon][3, 0, 0, 0] = 0
\[Epsilon][3, 0, 0, 1] = 0
\[Epsilon][3, 0, 0, 2] = 0
\[Epsilon][3, 0, 0, 3] = 0
\[Epsilon][3, 0, 1, 0] = 0
\[Epsilon][3, 0, 1, 1] = 0
\[Epsilon][3, 0, 1, 2] = -1
\[Epsilon][3, 0, 1, 3] = 0
\[Epsilon][3, 0, 2, 0] = 0
\[Epsilon][3, 0, 2, 1] = 1
\[Epsilon][3, 0, 2, 2] = 0
\[Epsilon][3, 0, 2, 3] = 0
\[Epsilon][3, 0, 3, 0] = 0
\[Epsilon][3, 0, 3, 1] = 0
\[Epsilon][3, 0, 3, 2] = 0
\[Epsilon][3, 0, 3, 3] = 0
\[Epsilon][3, 1, 0, 0] = 0
\[Epsilon][3, 1, 0, 1] = 0
\[Epsilon][3, 1, 0, 2] = 1
\[Epsilon][3, 1, 0, 3] = 0
\[Epsilon][3, 1, 1, 0] = 0
\[Epsilon][3, 1, 1, 1] = 0
\[Epsilon][3, 1, 1, 2] = 0
\[Epsilon][3, 1, 1, 3] = 0
\[Epsilon][3, 1, 2, 0] = -1
\[Epsilon][3, 1, 2, 1] = 0
\[Epsilon][3, 1, 2, 2] = 0
\[Epsilon][3, 1, 2, 3] = 0
\[Epsilon][3, 1, 3, 0] = 0
\[Epsilon][3, 1, 3, 1] = 0
\[Epsilon][3, 1, 3, 2] = 0
\[Epsilon][3, 1, 3, 3] = 0
\[Epsilon][3, 2, 0, 0] = 0
\[Epsilon][3, 2, 0, 1] = -1
\[Epsilon][3, 2, 0, 2] = 0
\[Epsilon][3, 2, 0, 3] = 0
\[Epsilon][3, 2, 1, 0] = 1
\[Epsilon][3, 2, 1, 1] = 0
\[Epsilon][3, 2, 1, 2] = 0
\[Epsilon][3, 2, 1, 3] = 0
\[Epsilon][3, 2, 2, 0] = 0
\[Epsilon][3, 2, 2, 1] = 0
\[Epsilon][3, 2, 2, 2] = 0
\[Epsilon][3, 2, 2, 3] = 0
\[Epsilon][3, 2, 3, 0] = 0
\[Epsilon][3, 2, 3, 1] = 0
\[Epsilon][3, 2, 3, 2] = 0
\[Epsilon][3, 2, 3, 3] = 0
\[Epsilon][3, 3, 0, 0] = 0
\[Epsilon][3, 3, 0, 1] = 0
\[Epsilon][3, 3, 0, 2] = 0
\[Epsilon][3, 3, 0, 3] = 0
\[Epsilon][3, 3, 1, 0] = 0
\[Epsilon][3, 3, 1, 1] = 0
\[Epsilon][3, 3, 1, 2] = 0
\[Epsilon][3, 3, 1, 3] = 0
\[Epsilon][3, 3, 2, 0] = 0
\[Epsilon][3, 3, 2, 1] = 0
\[Epsilon][3, 3, 2, 2] = 0
\[Epsilon][3, 3, 2, 3] = 0
\[Epsilon][3, 3, 3, 0] = 0
\[Epsilon][3, 3, 3, 1] = 0
\[Epsilon][3, 3, 3, 2] = 0
\[Epsilon][3, 3, 3, 3] = 0
\[Epsilon]downdowndownup[0, 0, 0, 0] = 0
\[Epsilon]downdowndownup[0, 0, 0, 1] = 0
\[Epsilon]downdowndownup[0, 0, 0, 2] = 0
\[Epsilon]downdowndownup[0, 0, 0, 3] = 0
\[Epsilon]downdowndownup[0, 0, 1, 0] = 0
\[Epsilon]downdowndownup[0, 0, 1, 1] = 0
\[Epsilon]downdowndownup[0, 0, 1, 2] = 0
\[Epsilon]downdowndownup[0, 0, 1, 3] = 0
\[Epsilon]downdowndownup[0, 0, 2, 0] = 0
\[Epsilon]downdowndownup[0, 0, 2, 1] = 0
\[Epsilon]downdowndownup[0, 0, 2, 2] = 0
\[Epsilon]downdowndownup[0, 0, 2, 3] = 0
\[Epsilon]downdowndownup[0, 0, 3, 0] = 0
\[Epsilon]downdowndownup[0, 0, 3, 1] = 0
\[Epsilon]downdowndownup[0, 0, 3, 2] = 0
\[Epsilon]downdowndownup[0, 0, 3, 3] = 0
\[Epsilon]downdowndownup[0, 1, 0, 0] = 0
\[Epsilon]downdowndownup[0, 1, 0, 1] = 0
\[Epsilon]downdowndownup[0, 1, 0, 2] = 0
\[Epsilon]downdowndownup[0, 1, 0, 3] = 0
\[Epsilon]downdowndownup[0, 1, 1, 0] = 0
\[Epsilon]downdowndownup[0, 1, 1, 1] = 0
\[Epsilon]downdowndownup[0, 1, 1, 2] = 0
\[Epsilon]downdowndownup[0, 1, 1, 3] = 0
\[Epsilon]downdowndownup[0, 1, 2, 0] = 0
\[Epsilon]downdowndownup[0, 1, 2, 1] = 0
\[Epsilon]downdowndownup[0, 1, 2, 2] = 0
\[Epsilon]downdowndownup[0, 1, 2, 3] = 1
\[Epsilon]downdowndownup[0, 1, 3, 0] = 0
\[Epsilon]downdowndownup[0, 1, 3, 1] = 0
\[Epsilon]downdowndownup[0, 1, 3, 2] = -1
\[Epsilon]downdowndownup[0, 1, 3, 3] = 0
\[Epsilon]downdowndownup[0, 2, 0, 0] = 0
\[Epsilon]downdowndownup[0, 2, 0, 1] = 0
\[Epsilon]downdowndownup[0, 2, 0, 2] = 0
\[Epsilon]downdowndownup[0, 2, 0, 3] = 0
\[Epsilon]downdowndownup[0, 2, 1, 0] = 0
\[Epsilon]downdowndownup[0, 2, 1, 1] = 0
\[Epsilon]downdowndownup[0, 2, 1, 2] = 0
\[Epsilon]downdowndownup[0, 2, 1, 3] = -1
\[Epsilon]downdowndownup[0, 2, 2, 0] = 0
\[Epsilon]downdowndownup[0, 2, 2, 1] = 0
\[Epsilon]downdowndownup[0, 2, 2, 2] = 0
\[Epsilon]downdowndownup[0, 2, 2, 3] = 0
\[Epsilon]downdowndownup[0, 2, 3, 0] = 0
\[Epsilon]downdowndownup[0, 2, 3, 1] = 1
\[Epsilon]downdowndownup[0, 2, 3, 2] = 0
\[Epsilon]downdowndownup[0, 2, 3, 3] = 0
\[Epsilon]downdowndownup[0, 3, 0, 0] = 0
\[Epsilon]downdowndownup[0, 3, 0, 1] = 0
\[Epsilon]downdowndownup[0, 3, 0, 2] = 0
\[Epsilon]downdowndownup[0, 3, 0, 3] = 0
\[Epsilon]downdowndownup[0, 3, 1, 0] = 0
\[Epsilon]downdowndownup[0, 3, 1, 1] = 0
\[Epsilon]downdowndownup[0, 3, 1, 2] = 1
\[Epsilon]downdowndownup[0, 3, 1, 3] = 0
\[Epsilon]downdowndownup[0, 3, 2, 0] = 0
\[Epsilon]downdowndownup[0, 3, 2, 1] = -1
\[Epsilon]downdowndownup[0, 3, 2, 2] = 0
\[Epsilon]downdowndownup[0, 3, 2, 3] = 0
\[Epsilon]downdowndownup[0, 3, 3, 0] = 0
\[Epsilon]downdowndownup[0, 3, 3, 1] = 0
\[Epsilon]downdowndownup[0, 3, 3, 2] = 0
\[Epsilon]downdowndownup[0, 3, 3, 3] = 0
\[Epsilon]downdowndownup[1, 0, 0, 0] = 0
\[Epsilon]downdowndownup[1, 0, 0, 1] = 0
\[Epsilon]downdowndownup[1, 0, 0, 2] = 0
\[Epsilon]downdowndownup[1, 0, 0, 3] = 0
\[Epsilon]downdowndownup[1, 0, 1, 0] = 0
\[Epsilon]downdowndownup[1, 0, 1, 1] = 0
\[Epsilon]downdowndownup[1, 0, 1, 2] = 0
\[Epsilon]downdowndownup[1, 0, 1, 3] = 0
\[Epsilon]downdowndownup[1, 0, 2, 0] = 0
\[Epsilon]downdowndownup[1, 0, 2, 1] = 0
\[Epsilon]downdowndownup[1, 0, 2, 2] = 0
\[Epsilon]downdowndownup[1, 0, 2, 3] = -1
\[Epsilon]downdowndownup[1, 0, 3, 0] = 0
\[Epsilon]downdowndownup[1, 0, 3, 1] = 0
\[Epsilon]downdowndownup[1, 0, 3, 2] = 1
\[Epsilon]downdowndownup[1, 0, 3, 3] = 0
\[Epsilon]downdowndownup[1, 1, 0, 0] = 0
\[Epsilon]downdowndownup[1, 1, 0, 1] = 0
\[Epsilon]downdowndownup[1, 1, 0, 2] = 0
\[Epsilon]downdowndownup[1, 1, 0, 3] = 0
\[Epsilon]downdowndownup[1, 1, 1, 0] = 0
\[Epsilon]downdowndownup[1, 1, 1, 1] = 0
\[Epsilon]downdowndownup[1, 1, 1, 2] = 0
\[Epsilon]downdowndownup[1, 1, 1, 3] = 0
\[Epsilon]downdowndownup[1, 1, 2, 0] = 0
\[Epsilon]downdowndownup[1, 1, 2, 1] = 0
\[Epsilon]downdowndownup[1, 1, 2, 2] = 0
\[Epsilon]downdowndownup[1, 1, 2, 3] = 0
\[Epsilon]downdowndownup[1, 1, 3, 0] = 0
\[Epsilon]downdowndownup[1, 1, 3, 1] = 0
\[Epsilon]downdowndownup[1, 1, 3, 2] = 0
\[Epsilon]downdowndownup[1, 1, 3, 3] = 0
\[Epsilon]downdowndownup[1, 2, 0, 0] = 0
\[Epsilon]downdowndownup[1, 2, 0, 1] = 0
\[Epsilon]downdowndownup[1, 2, 0, 2] = 0
\[Epsilon]downdowndownup[1, 2, 0, 3] = 1
\[Epsilon]downdowndownup[1, 2, 1, 0] = 0
\[Epsilon]downdowndownup[1, 2, 1, 1] = 0
\[Epsilon]downdowndownup[1, 2, 1, 2] = 0
\[Epsilon]downdowndownup[1, 2, 1, 3] = 0
\[Epsilon]downdowndownup[1, 2, 2, 0] = 0
\[Epsilon]downdowndownup[1, 2, 2, 1] = 0
\[Epsilon]downdowndownup[1, 2, 2, 2] = 0
\[Epsilon]downdowndownup[1, 2, 2, 3] = 0
\[Epsilon]downdowndownup[1, 2, 3, 0] = 1
\[Epsilon]downdowndownup[1, 2, 3, 1] = 0
\[Epsilon]downdowndownup[1, 2, 3, 2] = 0
\[Epsilon]downdowndownup[1, 2, 3, 3] = 0
\[Epsilon]downdowndownup[1, 3, 0, 0] = 0
\[Epsilon]downdowndownup[1, 3, 0, 1] = 0
\[Epsilon]downdowndownup[1, 3, 0, 2] = -1
\[Epsilon]downdowndownup[1, 3, 0, 3] = 0
\[Epsilon]downdowndownup[1, 3, 1, 0] = 0
\[Epsilon]downdowndownup[1, 3, 1, 1] = 0
\[Epsilon]downdowndownup[1, 3, 1, 2] = 0
\[Epsilon]downdowndownup[1, 3, 1, 3] = 0
\[Epsilon]downdowndownup[1, 3, 2, 0] = -1
\[Epsilon]downdowndownup[1, 3, 2, 1] = 0
\[Epsilon]downdowndownup[1, 3, 2, 2] = 0
\[Epsilon]downdowndownup[1, 3, 2, 3] = 0
\[Epsilon]downdowndownup[1, 3, 3, 0] = 0
\[Epsilon]downdowndownup[1, 3, 3, 1] = 0
\[Epsilon]downdowndownup[1, 3, 3, 2] = 0
\[Epsilon]downdowndownup[1, 3, 3, 3] = 0
\[Epsilon]downdowndownup[2, 0, 0, 0] = 0
\[Epsilon]downdowndownup[2, 0, 0, 1] = 0
\[Epsilon]downdowndownup[2, 0, 0, 2] = 0
\[Epsilon]downdowndownup[2, 0, 0, 3] = 0
\[Epsilon]downdowndownup[2, 0, 1, 0] = 0
\[Epsilon]downdowndownup[2, 0, 1, 1] = 0
\[Epsilon]downdowndownup[2, 0, 1, 2] = 0
\[Epsilon]downdowndownup[2, 0, 1, 3] = 1
\[Epsilon]downdowndownup[2, 0, 2, 0] = 0
\[Epsilon]downdowndownup[2, 0, 2, 1] = 0
\[Epsilon]downdowndownup[2, 0, 2, 2] = 0
\[Epsilon]downdowndownup[2, 0, 2, 3] = 0
\[Epsilon]downdowndownup[2, 0, 3, 0] = 0
\[Epsilon]downdowndownup[2, 0, 3, 1] = -1
\[Epsilon]downdowndownup[2, 0, 3, 2] = 0
\[Epsilon]downdowndownup[2, 0, 3, 3] = 0
\[Epsilon]downdowndownup[2, 1, 0, 0] = 0
\[Epsilon]downdowndownup[2, 1, 0, 1] = 0
\[Epsilon]downdowndownup[2, 1, 0, 2] = 0
\[Epsilon]downdowndownup[2, 1, 0, 3] = -1
\[Epsilon]downdowndownup[2, 1, 1, 0] = 0
\[Epsilon]downdowndownup[2, 1, 1, 1] = 0
\[Epsilon]downdowndownup[2, 1, 1, 2] = 0
\[Epsilon]downdowndownup[2, 1, 1, 3] = 0
\[Epsilon]downdowndownup[2, 1, 2, 0] = 0
\[Epsilon]downdowndownup[2, 1, 2, 1] = 0
\[Epsilon]downdowndownup[2, 1, 2, 2] = 0
\[Epsilon]downdowndownup[2, 1, 2, 3] = 0
\[Epsilon]downdowndownup[2, 1, 3, 0] = -1
\[Epsilon]downdowndownup[2, 1, 3, 1] = 0
\[Epsilon]downdowndownup[2, 1, 3, 2] = 0
\[Epsilon]downdowndownup[2, 1, 3, 3] = 0
\[Epsilon]downdowndownup[2, 2, 0, 0] = 0
\[Epsilon]downdowndownup[2, 2, 0, 1] = 0
\[Epsilon]downdowndownup[2, 2, 0, 2] = 0
\[Epsilon]downdowndownup[2, 2, 0, 3] = 0
\[Epsilon]downdowndownup[2, 2, 1, 0] = 0
\[Epsilon]downdowndownup[2, 2, 1, 1] = 0
\[Epsilon]downdowndownup[2, 2, 1, 2] = 0
\[Epsilon]downdowndownup[2, 2, 1, 3] = 0
\[Epsilon]downdowndownup[2, 2, 2, 0] = 0
\[Epsilon]downdowndownup[2, 2, 2, 1] = 0
\[Epsilon]downdowndownup[2, 2, 2, 2] = 0
\[Epsilon]downdowndownup[2, 2, 2, 3] = 0
\[Epsilon]downdowndownup[2, 2, 3, 0] = 0
\[Epsilon]downdowndownup[2, 2, 3, 1] = 0
\[Epsilon]downdowndownup[2, 2, 3, 2] = 0
\[Epsilon]downdowndownup[2, 2, 3, 3] = 0
\[Epsilon]downdowndownup[2, 3, 0, 0] = 0
\[Epsilon]downdowndownup[2, 3, 0, 1] = 1
\[Epsilon]downdowndownup[2, 3, 0, 2] = 0
\[Epsilon]downdowndownup[2, 3, 0, 3] = 0
\[Epsilon]downdowndownup[2, 3, 1, 0] = 1
\[Epsilon]downdowndownup[2, 3, 1, 1] = 0
\[Epsilon]downdowndownup[2, 3, 1, 2] = 0
\[Epsilon]downdowndownup[2, 3, 1, 3] = 0
\[Epsilon]downdowndownup[2, 3, 2, 0] = 0
\[Epsilon]downdowndownup[2, 3, 2, 1] = 0
\[Epsilon]downdowndownup[2, 3, 2, 2] = 0
\[Epsilon]downdowndownup[2, 3, 2, 3] = 0
\[Epsilon]downdowndownup[2, 3, 3, 0] = 0
\[Epsilon]downdowndownup[2, 3, 3, 1] = 0
\[Epsilon]downdowndownup[2, 3, 3, 2] = 0
\[Epsilon]downdowndownup[2, 3, 3, 3] = 0
\[Epsilon]downdowndownup[3, 0, 0, 0] = 0
\[Epsilon]downdowndownup[3, 0, 0, 1] = 0
\[Epsilon]downdowndownup[3, 0, 0, 2] = 0
\[Epsilon]downdowndownup[3, 0, 0, 3] = 0
\[Epsilon]downdowndownup[3, 0, 1, 0] = 0
\[Epsilon]downdowndownup[3, 0, 1, 1] = 0
\[Epsilon]downdowndownup[3, 0, 1, 2] = -1
\[Epsilon]downdowndownup[3, 0, 1, 3] = 0
\[Epsilon]downdowndownup[3, 0, 2, 0] = 0
\[Epsilon]downdowndownup[3, 0, 2, 1] = 1
\[Epsilon]downdowndownup[3, 0, 2, 2] = 0
\[Epsilon]downdowndownup[3, 0, 2, 3] = 0
\[Epsilon]downdowndownup[3, 0, 3, 0] = 0
\[Epsilon]downdowndownup[3, 0, 3, 1] = 0
\[Epsilon]downdowndownup[3, 0, 3, 2] = 0
\[Epsilon]downdowndownup[3, 0, 3, 3] = 0
\[Epsilon]downdowndownup[3, 1, 0, 0] = 0
\[Epsilon]downdowndownup[3, 1, 0, 1] = 0
\[Epsilon]downdowndownup[3, 1, 0, 2] = 1
\[Epsilon]downdowndownup[3, 1, 0, 3] = 0
\[Epsilon]downdowndownup[3, 1, 1, 0] = 0
\[Epsilon]downdowndownup[3, 1, 1, 1] = 0
\[Epsilon]downdowndownup[3, 1, 1, 2] = 0
\[Epsilon]downdowndownup[3, 1, 1, 3] = 0
\[Epsilon]downdowndownup[3, 1, 2, 0] = 1
\[Epsilon]downdowndownup[3, 1, 2, 1] = 0
\[Epsilon]downdowndownup[3, 1, 2, 2] = 0
\[Epsilon]downdowndownup[3, 1, 2, 3] = 0
\[Epsilon]downdowndownup[3, 1, 3, 0] = 0
\[Epsilon]downdowndownup[3, 1, 3, 1] = 0
\[Epsilon]downdowndownup[3, 1, 3, 2] = 0
\[Epsilon]downdowndownup[3, 1, 3, 3] = 0
\[Epsilon]downdowndownup[3, 2, 0, 0] = 0
\[Epsilon]downdowndownup[3, 2, 0, 1] = -1
\[Epsilon]downdowndownup[3, 2, 0, 2] = 0
\[Epsilon]downdowndownup[3, 2, 0, 3] = 0
\[Epsilon]downdowndownup[3, 2, 1, 0] = -1
\[Epsilon]downdowndownup[3, 2, 1, 1] = 0
\[Epsilon]downdowndownup[3, 2, 1, 2] = 0
\[Epsilon]downdowndownup[3, 2, 1, 3] = 0
\[Epsilon]downdowndownup[3, 2, 2, 0] = 0
\[Epsilon]downdowndownup[3, 2, 2, 1] = 0
\[Epsilon]downdowndownup[3, 2, 2, 2] = 0
\[Epsilon]downdowndownup[3, 2, 2, 3] = 0
\[Epsilon]downdowndownup[3, 2, 3, 0] = 0
\[Epsilon]downdowndownup[3, 2, 3, 1] = 0
\[Epsilon]downdowndownup[3, 2, 3, 2] = 0
\[Epsilon]downdowndownup[3, 2, 3, 3] = 0
\[Epsilon]downdowndownup[3, 3, 0, 0] = 0
\[Epsilon]downdowndownup[3, 3, 0, 1] = 0
\[Epsilon]downdowndownup[3, 3, 0, 2] = 0
\[Epsilon]downdowndownup[3, 3, 0, 3] = 0
\[Epsilon]downdowndownup[3, 3, 1, 0] = 0
\[Epsilon]downdowndownup[3, 3, 1, 1] = 0
\[Epsilon]downdowndownup[3, 3, 1, 2] = 0
\[Epsilon]downdowndownup[3, 3, 1, 3] = 0
\[Epsilon]downdowndownup[3, 3, 2, 0] = 0
\[Epsilon]downdowndownup[3, 3, 2, 1] = 0
\[Epsilon]downdowndownup[3, 3, 2, 2] = 0
\[Epsilon]downdowndownup[3, 3, 2, 3] = 0
\[Epsilon]downdowndownup[3, 3, 3, 0] = 0
\[Epsilon]downdowndownup[3, 3, 3, 1] = 0
\[Epsilon]downdowndownup[3, 3, 3, 2] = 0
\[Epsilon]downdowndownup[3, 3, 3, 3] = 0
\[Epsilon]downdownupup[0, 0, 0, 0] = 0
\[Epsilon]downdownupup[0, 0, 0, 1] = 0
\[Epsilon]downdownupup[0, 0, 0, 2] = 0
\[Epsilon]downdownupup[0, 0, 0, 3] = 0
\[Epsilon]downdownupup[0, 0, 1, 0] = 0
\[Epsilon]downdownupup[0, 0, 1, 1] = 0
\[Epsilon]downdownupup[0, 0, 1, 2] = 0
\[Epsilon]downdownupup[0, 0, 1, 3] = 0
\[Epsilon]downdownupup[0, 0, 2, 0] = 0
\[Epsilon]downdownupup[0, 0, 2, 1] = 0
\[Epsilon]downdownupup[0, 0, 2, 2] = 0
\[Epsilon]downdownupup[0, 0, 2, 3] = 0
\[Epsilon]downdownupup[0, 0, 3, 0] = 0
\[Epsilon]downdownupup[0, 0, 3, 1] = 0
\[Epsilon]downdownupup[0, 0, 3, 2] = 0
\[Epsilon]downdownupup[0, 0, 3, 3] = 0
\[Epsilon]downdownupup[0, 1, 0, 0] = 0
\[Epsilon]downdownupup[0, 1, 0, 1] = 0
\[Epsilon]downdownupup[0, 1, 0, 2] = 0
\[Epsilon]downdownupup[0, 1, 0, 3] = 0
\[Epsilon]downdownupup[0, 1, 1, 0] = 0
\[Epsilon]downdownupup[0, 1, 1, 1] = 0
\[Epsilon]downdownupup[0, 1, 1, 2] = 0
\[Epsilon]downdownupup[0, 1, 1, 3] = 0
\[Epsilon]downdownupup[0, 1, 2, 0] = 0
\[Epsilon]downdownupup[0, 1, 2, 1] = 0
\[Epsilon]downdownupup[0, 1, 2, 2] = 0
\[Epsilon]downdownupup[0, 1, 2, 3] = 1
\[Epsilon]downdownupup[0, 1, 3, 0] = 0
\[Epsilon]downdownupup[0, 1, 3, 1] = 0
\[Epsilon]downdownupup[0, 1, 3, 2] = -1
\[Epsilon]downdownupup[0, 1, 3, 3] = 0
\[Epsilon]downdownupup[0, 2, 0, 0] = 0
\[Epsilon]downdownupup[0, 2, 0, 1] = 0
\[Epsilon]downdownupup[0, 2, 0, 2] = 0
\[Epsilon]downdownupup[0, 2, 0, 3] = 0
\[Epsilon]downdownupup[0, 2, 1, 0] = 0
\[Epsilon]downdownupup[0, 2, 1, 1] = 0
\[Epsilon]downdownupup[0, 2, 1, 2] = 0
\[Epsilon]downdownupup[0, 2, 1, 3] = -1
\[Epsilon]downdownupup[0, 2, 2, 0] = 0
\[Epsilon]downdownupup[0, 2, 2, 1] = 0
\[Epsilon]downdownupup[0, 2, 2, 2] = 0
\[Epsilon]downdownupup[0, 2, 2, 3] = 0
\[Epsilon]downdownupup[0, 2, 3, 0] = 0
\[Epsilon]downdownupup[0, 2, 3, 1] = 1
\[Epsilon]downdownupup[0, 2, 3, 2] = 0
\[Epsilon]downdownupup[0, 2, 3, 3] = 0
\[Epsilon]downdownupup[0, 3, 0, 0] = 0
\[Epsilon]downdownupup[0, 3, 0, 1] = 0
\[Epsilon]downdownupup[0, 3, 0, 2] = 0
\[Epsilon]downdownupup[0, 3, 0, 3] = 0
\[Epsilon]downdownupup[0, 3, 1, 0] = 0
\[Epsilon]downdownupup[0, 3, 1, 1] = 0
\[Epsilon]downdownupup[0, 3, 1, 2] = 1
\[Epsilon]downdownupup[0, 3, 1, 3] = 0
\[Epsilon]downdownupup[0, 3, 2, 0] = 0
\[Epsilon]downdownupup[0, 3, 2, 1] = -1
\[Epsilon]downdownupup[0, 3, 2, 2] = 0
\[Epsilon]downdownupup[0, 3, 2, 3] = 0
\[Epsilon]downdownupup[0, 3, 3, 0] = 0
\[Epsilon]downdownupup[0, 3, 3, 1] = 0
\[Epsilon]downdownupup[0, 3, 3, 2] = 0
\[Epsilon]downdownupup[0, 3, 3, 3] = 0
\[Epsilon]downdownupup[1, 0, 0, 0] = 0
\[Epsilon]downdownupup[1, 0, 0, 1] = 0
\[Epsilon]downdownupup[1, 0, 0, 2] = 0
\[Epsilon]downdownupup[1, 0, 0, 3] = 0
\[Epsilon]downdownupup[1, 0, 1, 0] = 0
\[Epsilon]downdownupup[1, 0, 1, 1] = 0
\[Epsilon]downdownupup[1, 0, 1, 2] = 0
\[Epsilon]downdownupup[1, 0, 1, 3] = 0
\[Epsilon]downdownupup[1, 0, 2, 0] = 0
\[Epsilon]downdownupup[1, 0, 2, 1] = 0
\[Epsilon]downdownupup[1, 0, 2, 2] = 0
\[Epsilon]downdownupup[1, 0, 2, 3] = -1
\[Epsilon]downdownupup[1, 0, 3, 0] = 0
\[Epsilon]downdownupup[1, 0, 3, 1] = 0
\[Epsilon]downdownupup[1, 0, 3, 2] = 1
\[Epsilon]downdownupup[1, 0, 3, 3] = 0
\[Epsilon]downdownupup[1, 1, 0, 0] = 0
\[Epsilon]downdownupup[1, 1, 0, 1] = 0
\[Epsilon]downdownupup[1, 1, 0, 2] = 0
\[Epsilon]downdownupup[1, 1, 0, 3] = 0
\[Epsilon]downdownupup[1, 1, 1, 0] = 0
\[Epsilon]downdownupup[1, 1, 1, 1] = 0
\[Epsilon]downdownupup[1, 1, 1, 2] = 0
\[Epsilon]downdownupup[1, 1, 1, 3] = 0
\[Epsilon]downdownupup[1, 1, 2, 0] = 0
\[Epsilon]downdownupup[1, 1, 2, 1] = 0
\[Epsilon]downdownupup[1, 1, 2, 2] = 0
\[Epsilon]downdownupup[1, 1, 2, 3] = 0
\[Epsilon]downdownupup[1, 1, 3, 0] = 0
\[Epsilon]downdownupup[1, 1, 3, 1] = 0
\[Epsilon]downdownupup[1, 1, 3, 2] = 0
\[Epsilon]downdownupup[1, 1, 3, 3] = 0
\[Epsilon]downdownupup[1, 2, 0, 0] = 0
\[Epsilon]downdownupup[1, 2, 0, 1] = 0
\[Epsilon]downdownupup[1, 2, 0, 2] = 0
\[Epsilon]downdownupup[1, 2, 0, 3] = -1
\[Epsilon]downdownupup[1, 2, 1, 0] = 0
\[Epsilon]downdownupup[1, 2, 1, 1] = 0
\[Epsilon]downdownupup[1, 2, 1, 2] = 0
\[Epsilon]downdownupup[1, 2, 1, 3] = 0
\[Epsilon]downdownupup[1, 2, 2, 0] = 0
\[Epsilon]downdownupup[1, 2, 2, 1] = 0
\[Epsilon]downdownupup[1, 2, 2, 2] = 0
\[Epsilon]downdownupup[1, 2, 2, 3] = 0
\[Epsilon]downdownupup[1, 2, 3, 0] = 1
\[Epsilon]downdownupup[1, 2, 3, 1] = 0
\[Epsilon]downdownupup[1, 2, 3, 2] = 0
\[Epsilon]downdownupup[1, 2, 3, 3] = 0
\[Epsilon]downdownupup[1, 3, 0, 0] = 0
\[Epsilon]downdownupup[1, 3, 0, 1] = 0
\[Epsilon]downdownupup[1, 3, 0, 2] = 1
\[Epsilon]downdownupup[1, 3, 0, 3] = 0
\[Epsilon]downdownupup[1, 3, 1, 0] = 0
\[Epsilon]downdownupup[1, 3, 1, 1] = 0
\[Epsilon]downdownupup[1, 3, 1, 2] = 0
\[Epsilon]downdownupup[1, 3, 1, 3] = 0
\[Epsilon]downdownupup[1, 3, 2, 0] = -1
\[Epsilon]downdownupup[1, 3, 2, 1] = 0
\[Epsilon]downdownupup[1, 3, 2, 2] = 0
\[Epsilon]downdownupup[1, 3, 2, 3] = 0
\[Epsilon]downdownupup[1, 3, 3, 0] = 0
\[Epsilon]downdownupup[1, 3, 3, 1] = 0
\[Epsilon]downdownupup[1, 3, 3, 2] = 0
\[Epsilon]downdownupup[1, 3, 3, 3] = 0
\[Epsilon]downdownupup[2, 0, 0, 0] = 0
\[Epsilon]downdownupup[2, 0, 0, 1] = 0
\[Epsilon]downdownupup[2, 0, 0, 2] = 0
\[Epsilon]downdownupup[2, 0, 0, 3] = 0
\[Epsilon]downdownupup[2, 0, 1, 0] = 0
\[Epsilon]downdownupup[2, 0, 1, 1] = 0
\[Epsilon]downdownupup[2, 0, 1, 2] = 0
\[Epsilon]downdownupup[2, 0, 1, 3] = 1
\[Epsilon]downdownupup[2, 0, 2, 0] = 0
\[Epsilon]downdownupup[2, 0, 2, 1] = 0
\[Epsilon]downdownupup[2, 0, 2, 2] = 0
\[Epsilon]downdownupup[2, 0, 2, 3] = 0
\[Epsilon]downdownupup[2, 0, 3, 0] = 0
\[Epsilon]downdownupup[2, 0, 3, 1] = -1
\[Epsilon]downdownupup[2, 0, 3, 2] = 0
\[Epsilon]downdownupup[2, 0, 3, 3] = 0
\[Epsilon]downdownupup[2, 1, 0, 0] = 0
\[Epsilon]downdownupup[2, 1, 0, 1] = 0
\[Epsilon]downdownupup[2, 1, 0, 2] = 0
\[Epsilon]downdownupup[2, 1, 0, 3] = 1
\[Epsilon]downdownupup[2, 1, 1, 0] = 0
\[Epsilon]downdownupup[2, 1, 1, 1] = 0
\[Epsilon]downdownupup[2, 1, 1, 2] = 0
\[Epsilon]downdownupup[2, 1, 1, 3] = 0
\[Epsilon]downdownupup[2, 1, 2, 0] = 0
\[Epsilon]downdownupup[2, 1, 2, 1] = 0
\[Epsilon]downdownupup[2, 1, 2, 2] = 0
\[Epsilon]downdownupup[2, 1, 2, 3] = 0
\[Epsilon]downdownupup[2, 1, 3, 0] = -1
\[Epsilon]downdownupup[2, 1, 3, 1] = 0
\[Epsilon]downdownupup[2, 1, 3, 2] = 0
\[Epsilon]downdownupup[2, 1, 3, 3] = 0
\[Epsilon]downdownupup[2, 2, 0, 0] = 0
\[Epsilon]downdownupup[2, 2, 0, 1] = 0
\[Epsilon]downdownupup[2, 2, 0, 2] = 0
\[Epsilon]downdownupup[2, 2, 0, 3] = 0
\[Epsilon]downdownupup[2, 2, 1, 0] = 0
\[Epsilon]downdownupup[2, 2, 1, 1] = 0
\[Epsilon]downdownupup[2, 2, 1, 2] = 0
\[Epsilon]downdownupup[2, 2, 1, 3] = 0
\[Epsilon]downdownupup[2, 2, 2, 0] = 0
\[Epsilon]downdownupup[2, 2, 2, 1] = 0
\[Epsilon]downdownupup[2, 2, 2, 2] = 0
\[Epsilon]downdownupup[2, 2, 2, 3] = 0
\[Epsilon]downdownupup[2, 2, 3, 0] = 0
\[Epsilon]downdownupup[2, 2, 3, 1] = 0
\[Epsilon]downdownupup[2, 2, 3, 2] = 0
\[Epsilon]downdownupup[2, 2, 3, 3] = 0
\[Epsilon]downdownupup[2, 3, 0, 0] = 0
\[Epsilon]downdownupup[2, 3, 0, 1] = -1
\[Epsilon]downdownupup[2, 3, 0, 2] = 0
\[Epsilon]downdownupup[2, 3, 0, 3] = 0
\[Epsilon]downdownupup[2, 3, 1, 0] = 1
\[Epsilon]downdownupup[2, 3, 1, 1] = 0
\[Epsilon]downdownupup[2, 3, 1, 2] = 0
\[Epsilon]downdownupup[2, 3, 1, 3] = 0
\[Epsilon]downdownupup[2, 3, 2, 0] = 0
\[Epsilon]downdownupup[2, 3, 2, 1] = 0
\[Epsilon]downdownupup[2, 3, 2, 2] = 0
\[Epsilon]downdownupup[2, 3, 2, 3] = 0
\[Epsilon]downdownupup[2, 3, 3, 0] = 0
\[Epsilon]downdownupup[2, 3, 3, 1] = 0
\[Epsilon]downdownupup[2, 3, 3, 2] = 0
\[Epsilon]downdownupup[2, 3, 3, 3] = 0
\[Epsilon]downdownupup[3, 0, 0, 0] = 0
\[Epsilon]downdownupup[3, 0, 0, 1] = 0
\[Epsilon]downdownupup[3, 0, 0, 2] = 0
\[Epsilon]downdownupup[3, 0, 0, 3] = 0
\[Epsilon]downdownupup[3, 0, 1, 0] = 0
\[Epsilon]downdownupup[3, 0, 1, 1] = 0
\[Epsilon]downdownupup[3, 0, 1, 2] = -1
\[Epsilon]downdownupup[3, 0, 1, 3] = 0
\[Epsilon]downdownupup[3, 0, 2, 0] = 0
\[Epsilon]downdownupup[3, 0, 2, 1] = 1
\[Epsilon]downdownupup[3, 0, 2, 2] = 0
\[Epsilon]downdownupup[3, 0, 2, 3] = 0
\[Epsilon]downdownupup[3, 0, 3, 0] = 0
\[Epsilon]downdownupup[3, 0, 3, 1] = 0
\[Epsilon]downdownupup[3, 0, 3, 2] = 0
\[Epsilon]downdownupup[3, 0, 3, 3] = 0
\[Epsilon]downdownupup[3, 1, 0, 0] = 0
\[Epsilon]downdownupup[3, 1, 0, 1] = 0
\[Epsilon]downdownupup[3, 1, 0, 2] = -1
\[Epsilon]downdownupup[3, 1, 0, 3] = 0
\[Epsilon]downdownupup[3, 1, 1, 0] = 0
\[Epsilon]downdownupup[3, 1, 1, 1] = 0
\[Epsilon]downdownupup[3, 1, 1, 2] = 0
\[Epsilon]downdownupup[3, 1, 1, 3] = 0
\[Epsilon]downdownupup[3, 1, 2, 0] = 1
\[Epsilon]downdownupup[3, 1, 2, 1] = 0
\[Epsilon]downdownupup[3, 1, 2, 2] = 0
\[Epsilon]downdownupup[3, 1, 2, 3] = 0
\[Epsilon]downdownupup[3, 1, 3, 0] = 0
\[Epsilon]downdownupup[3, 1, 3, 1] = 0
\[Epsilon]downdownupup[3, 1, 3, 2] = 0
\[Epsilon]downdownupup[3, 1, 3, 3] = 0
\[Epsilon]downdownupup[3, 2, 0, 0] = 0
\[Epsilon]downdownupup[3, 2, 0, 1] = 1
\[Epsilon]downdownupup[3, 2, 0, 2] = 0
\[Epsilon]downdownupup[3, 2, 0, 3] = 0
\[Epsilon]downdownupup[3, 2, 1, 0] = -1
\[Epsilon]downdownupup[3, 2, 1, 1] = 0
\[Epsilon]downdownupup[3, 2, 1, 2] = 0
\[Epsilon]downdownupup[3, 2, 1, 3] = 0
\[Epsilon]downdownupup[3, 2, 2, 0] = 0
\[Epsilon]downdownupup[3, 2, 2, 1] = 0
\[Epsilon]downdownupup[3, 2, 2, 2] = 0
\[Epsilon]downdownupup[3, 2, 2, 3] = 0
\[Epsilon]downdownupup[3, 2, 3, 0] = 0
\[Epsilon]downdownupup[3, 2, 3, 1] = 0
\[Epsilon]downdownupup[3, 2, 3, 2] = 0
\[Epsilon]downdownupup[3, 2, 3, 3] = 0
\[Epsilon]downdownupup[3, 3, 0, 0] = 0
\[Epsilon]downdownupup[3, 3, 0, 1] = 0
\[Epsilon]downdownupup[3, 3, 0, 2] = 0
\[Epsilon]downdownupup[3, 3, 0, 3] = 0
\[Epsilon]downdownupup[3, 3, 1, 0] = 0
\[Epsilon]downdownupup[3, 3, 1, 1] = 0
\[Epsilon]downdownupup[3, 3, 1, 2] = 0
\[Epsilon]downdownupup[3, 3, 1, 3] = 0
\[Epsilon]downdownupup[3, 3, 2, 0] = 0
\[Epsilon]downdownupup[3, 3, 2, 1] = 0
\[Epsilon]downdownupup[3, 3, 2, 2] = 0
\[Epsilon]downdownupup[3, 3, 2, 3] = 0
\[Epsilon]downdownupup[3, 3, 3, 0] = 0
\[Epsilon]downdownupup[3, 3, 3, 1] = 0
\[Epsilon]downdownupup[3, 3, 3, 2] = 0
\[Epsilon]downdownupup[3, 3, 3, 3] = 0
\[Epsilon]downupupup[0, 0, 0, 0] = 0
\[Epsilon]downupupup[0, 0, 0, 1] = 0
\[Epsilon]downupupup[0, 0, 0, 2] = 0
\[Epsilon]downupupup[0, 0, 0, 3] = 0
\[Epsilon]downupupup[0, 0, 1, 0] = 0
\[Epsilon]downupupup[0, 0, 1, 1] = 0
\[Epsilon]downupupup[0, 0, 1, 2] = 0
\[Epsilon]downupupup[0, 0, 1, 3] = 0
\[Epsilon]downupupup[0, 0, 2, 0] = 0
\[Epsilon]downupupup[0, 0, 2, 1] = 0
\[Epsilon]downupupup[0, 0, 2, 2] = 0
\[Epsilon]downupupup[0, 0, 2, 3] = 0
\[Epsilon]downupupup[0, 0, 3, 0] = 0
\[Epsilon]downupupup[0, 0, 3, 1] = 0
\[Epsilon]downupupup[0, 0, 3, 2] = 0
\[Epsilon]downupupup[0, 0, 3, 3] = 0
\[Epsilon]downupupup[0, 1, 0, 0] = 0
\[Epsilon]downupupup[0, 1, 0, 1] = 0
\[Epsilon]downupupup[0, 1, 0, 2] = 0
\[Epsilon]downupupup[0, 1, 0, 3] = 0
\[Epsilon]downupupup[0, 1, 1, 0] = 0
\[Epsilon]downupupup[0, 1, 1, 1] = 0
\[Epsilon]downupupup[0, 1, 1, 2] = 0
\[Epsilon]downupupup[0, 1, 1, 3] = 0
\[Epsilon]downupupup[0, 1, 2, 0] = 0
\[Epsilon]downupupup[0, 1, 2, 1] = 0
\[Epsilon]downupupup[0, 1, 2, 2] = 0
\[Epsilon]downupupup[0, 1, 2, 3] = 1
\[Epsilon]downupupup[0, 1, 3, 0] = 0
\[Epsilon]downupupup[0, 1, 3, 1] = 0
\[Epsilon]downupupup[0, 1, 3, 2] = -1
\[Epsilon]downupupup[0, 1, 3, 3] = 0
\[Epsilon]downupupup[0, 2, 0, 0] = 0
\[Epsilon]downupupup[0, 2, 0, 1] = 0
\[Epsilon]downupupup[0, 2, 0, 2] = 0
\[Epsilon]downupupup[0, 2, 0, 3] = 0
\[Epsilon]downupupup[0, 2, 1, 0] = 0
\[Epsilon]downupupup[0, 2, 1, 1] = 0
\[Epsilon]downupupup[0, 2, 1, 2] = 0
\[Epsilon]downupupup[0, 2, 1, 3] = -1
\[Epsilon]downupupup[0, 2, 2, 0] = 0
\[Epsilon]downupupup[0, 2, 2, 1] = 0
\[Epsilon]downupupup[0, 2, 2, 2] = 0
\[Epsilon]downupupup[0, 2, 2, 3] = 0
\[Epsilon]downupupup[0, 2, 3, 0] = 0
\[Epsilon]downupupup[0, 2, 3, 1] = 1
\[Epsilon]downupupup[0, 2, 3, 2] = 0
\[Epsilon]downupupup[0, 2, 3, 3] = 0
\[Epsilon]downupupup[0, 3, 0, 0] = 0
\[Epsilon]downupupup[0, 3, 0, 1] = 0
\[Epsilon]downupupup[0, 3, 0, 2] = 0
\[Epsilon]downupupup[0, 3, 0, 3] = 0
\[Epsilon]downupupup[0, 3, 1, 0] = 0
\[Epsilon]downupupup[0, 3, 1, 1] = 0
\[Epsilon]downupupup[0, 3, 1, 2] = 1
\[Epsilon]downupupup[0, 3, 1, 3] = 0
\[Epsilon]downupupup[0, 3, 2, 0] = 0
\[Epsilon]downupupup[0, 3, 2, 1] = -1
\[Epsilon]downupupup[0, 3, 2, 2] = 0
\[Epsilon]downupupup[0, 3, 2, 3] = 0
\[Epsilon]downupupup[0, 3, 3, 0] = 0
\[Epsilon]downupupup[0, 3, 3, 1] = 0
\[Epsilon]downupupup[0, 3, 3, 2] = 0
\[Epsilon]downupupup[0, 3, 3, 3] = 0
\[Epsilon]downupupup[1, 0, 0, 0] = 0
\[Epsilon]downupupup[1, 0, 0, 1] = 0
\[Epsilon]downupupup[1, 0, 0, 2] = 0
\[Epsilon]downupupup[1, 0, 0, 3] = 0
\[Epsilon]downupupup[1, 0, 1, 0] = 0
\[Epsilon]downupupup[1, 0, 1, 1] = 0
\[Epsilon]downupupup[1, 0, 1, 2] = 0
\[Epsilon]downupupup[1, 0, 1, 3] = 0
\[Epsilon]downupupup[1, 0, 2, 0] = 0
\[Epsilon]downupupup[1, 0, 2, 1] = 0
\[Epsilon]downupupup[1, 0, 2, 2] = 0
\[Epsilon]downupupup[1, 0, 2, 3] = 1
\[Epsilon]downupupup[1, 0, 3, 0] = 0
\[Epsilon]downupupup[1, 0, 3, 1] = 0
\[Epsilon]downupupup[1, 0, 3, 2] = -1
\[Epsilon]downupupup[1, 0, 3, 3] = 0
\[Epsilon]downupupup[1, 1, 0, 0] = 0
\[Epsilon]downupupup[1, 1, 0, 1] = 0
\[Epsilon]downupupup[1, 1, 0, 2] = 0
\[Epsilon]downupupup[1, 1, 0, 3] = 0
\[Epsilon]downupupup[1, 1, 1, 0] = 0
\[Epsilon]downupupup[1, 1, 1, 1] = 0
\[Epsilon]downupupup[1, 1, 1, 2] = 0
\[Epsilon]downupupup[1, 1, 1, 3] = 0
\[Epsilon]downupupup[1, 1, 2, 0] = 0
\[Epsilon]downupupup[1, 1, 2, 1] = 0
\[Epsilon]downupupup[1, 1, 2, 2] = 0
\[Epsilon]downupupup[1, 1, 2, 3] = 0
\[Epsilon]downupupup[1, 1, 3, 0] = 0
\[Epsilon]downupupup[1, 1, 3, 1] = 0
\[Epsilon]downupupup[1, 1, 3, 2] = 0
\[Epsilon]downupupup[1, 1, 3, 3] = 0
\[Epsilon]downupupup[1, 2, 0, 0] = 0
\[Epsilon]downupupup[1, 2, 0, 1] = 0
\[Epsilon]downupupup[1, 2, 0, 2] = 0
\[Epsilon]downupupup[1, 2, 0, 3] = -1
\[Epsilon]downupupup[1, 2, 1, 0] = 0
\[Epsilon]downupupup[1, 2, 1, 1] = 0
\[Epsilon]downupupup[1, 2, 1, 2] = 0
\[Epsilon]downupupup[1, 2, 1, 3] = 0
\[Epsilon]downupupup[1, 2, 2, 0] = 0
\[Epsilon]downupupup[1, 2, 2, 1] = 0
\[Epsilon]downupupup[1, 2, 2, 2] = 0
\[Epsilon]downupupup[1, 2, 2, 3] = 0
\[Epsilon]downupupup[1, 2, 3, 0] = 1
\[Epsilon]downupupup[1, 2, 3, 1] = 0
\[Epsilon]downupupup[1, 2, 3, 2] = 0
\[Epsilon]downupupup[1, 2, 3, 3] = 0
\[Epsilon]downupupup[1, 3, 0, 0] = 0
\[Epsilon]downupupup[1, 3, 0, 1] = 0
\[Epsilon]downupupup[1, 3, 0, 2] = 1
\[Epsilon]downupupup[1, 3, 0, 3] = 0
\[Epsilon]downupupup[1, 3, 1, 0] = 0
\[Epsilon]downupupup[1, 3, 1, 1] = 0
\[Epsilon]downupupup[1, 3, 1, 2] = 0
\[Epsilon]downupupup[1, 3, 1, 3] = 0
\[Epsilon]downupupup[1, 3, 2, 0] = -1
\[Epsilon]downupupup[1, 3, 2, 1] = 0
\[Epsilon]downupupup[1, 3, 2, 2] = 0
\[Epsilon]downupupup[1, 3, 2, 3] = 0
\[Epsilon]downupupup[1, 3, 3, 0] = 0
\[Epsilon]downupupup[1, 3, 3, 1] = 0
\[Epsilon]downupupup[1, 3, 3, 2] = 0
\[Epsilon]downupupup[1, 3, 3, 3] = 0
\[Epsilon]downupupup[2, 0, 0, 0] = 0
\[Epsilon]downupupup[2, 0, 0, 1] = 0
\[Epsilon]downupupup[2, 0, 0, 2] = 0
\[Epsilon]downupupup[2, 0, 0, 3] = 0
\[Epsilon]downupupup[2, 0, 1, 0] = 0
\[Epsilon]downupupup[2, 0, 1, 1] = 0
\[Epsilon]downupupup[2, 0, 1, 2] = 0
\[Epsilon]downupupup[2, 0, 1, 3] = -1
\[Epsilon]downupupup[2, 0, 2, 0] = 0
\[Epsilon]downupupup[2, 0, 2, 1] = 0
\[Epsilon]downupupup[2, 0, 2, 2] = 0
\[Epsilon]downupupup[2, 0, 2, 3] = 0
\[Epsilon]downupupup[2, 0, 3, 0] = 0
\[Epsilon]downupupup[2, 0, 3, 1] = 1
\[Epsilon]downupupup[2, 0, 3, 2] = 0
\[Epsilon]downupupup[2, 0, 3, 3] = 0
\[Epsilon]downupupup[2, 1, 0, 0] = 0
\[Epsilon]downupupup[2, 1, 0, 1] = 0
\[Epsilon]downupupup[2, 1, 0, 2] = 0
\[Epsilon]downupupup[2, 1, 0, 3] = 1
\[Epsilon]downupupup[2, 1, 1, 0] = 0
\[Epsilon]downupupup[2, 1, 1, 1] = 0
\[Epsilon]downupupup[2, 1, 1, 2] = 0
\[Epsilon]downupupup[2, 1, 1, 3] = 0
\[Epsilon]downupupup[2, 1, 2, 0] = 0
\[Epsilon]downupupup[2, 1, 2, 1] = 0
\[Epsilon]downupupup[2, 1, 2, 2] = 0
\[Epsilon]downupupup[2, 1, 2, 3] = 0
\[Epsilon]downupupup[2, 1, 3, 0] = -1
\[Epsilon]downupupup[2, 1, 3, 1] = 0
\[Epsilon]downupupup[2, 1, 3, 2] = 0
\[Epsilon]downupupup[2, 1, 3, 3] = 0
\[Epsilon]downupupup[2, 2, 0, 0] = 0
\[Epsilon]downupupup[2, 2, 0, 1] = 0
\[Epsilon]downupupup[2, 2, 0, 2] = 0
\[Epsilon]downupupup[2, 2, 0, 3] = 0
\[Epsilon]downupupup[2, 2, 1, 0] = 0
\[Epsilon]downupupup[2, 2, 1, 1] = 0
\[Epsilon]downupupup[2, 2, 1, 2] = 0
\[Epsilon]downupupup[2, 2, 1, 3] = 0
\[Epsilon]downupupup[2, 2, 2, 0] = 0
\[Epsilon]downupupup[2, 2, 2, 1] = 0
\[Epsilon]downupupup[2, 2, 2, 2] = 0
\[Epsilon]downupupup[2, 2, 2, 3] = 0
\[Epsilon]downupupup[2, 2, 3, 0] = 0
\[Epsilon]downupupup[2, 2, 3, 1] = 0
\[Epsilon]downupupup[2, 2, 3, 2] = 0
\[Epsilon]downupupup[2, 2, 3, 3] = 0
\[Epsilon]downupupup[2, 3, 0, 0] = 0
\[Epsilon]downupupup[2, 3, 0, 1] = -1
\[Epsilon]downupupup[2, 3, 0, 2] = 0
\[Epsilon]downupupup[2, 3, 0, 3] = 0
\[Epsilon]downupupup[2, 3, 1, 0] = 1
\[Epsilon]downupupup[2, 3, 1, 1] = 0
\[Epsilon]downupupup[2, 3, 1, 2] = 0
\[Epsilon]downupupup[2, 3, 1, 3] = 0
\[Epsilon]downupupup[2, 3, 2, 0] = 0
\[Epsilon]downupupup[2, 3, 2, 1] = 0
\[Epsilon]downupupup[2, 3, 2, 2] = 0
\[Epsilon]downupupup[2, 3, 2, 3] = 0
\[Epsilon]downupupup[2, 3, 3, 0] = 0
\[Epsilon]downupupup[2, 3, 3, 1] = 0
\[Epsilon]downupupup[2, 3, 3, 2] = 0
\[Epsilon]downupupup[2, 3, 3, 3] = 0
\[Epsilon]downupupup[3, 0, 0, 0] = 0
\[Epsilon]downupupup[3, 0, 0, 1] = 0
\[Epsilon]downupupup[3, 0, 0, 2] = 0
\[Epsilon]downupupup[3, 0, 0, 3] = 0
\[Epsilon]downupupup[3, 0, 1, 0] = 0
\[Epsilon]downupupup[3, 0, 1, 1] = 0
\[Epsilon]downupupup[3, 0, 1, 2] = 1
\[Epsilon]downupupup[3, 0, 1, 3] = 0
\[Epsilon]downupupup[3, 0, 2, 0] = 0
\[Epsilon]downupupup[3, 0, 2, 1] = -1
\[Epsilon]downupupup[3, 0, 2, 2] = 0
\[Epsilon]downupupup[3, 0, 2, 3] = 0
\[Epsilon]downupupup[3, 0, 3, 0] = 0
\[Epsilon]downupupup[3, 0, 3, 1] = 0
\[Epsilon]downupupup[3, 0, 3, 2] = 0
\[Epsilon]downupupup[3, 0, 3, 3] = 0
\[Epsilon]downupupup[3, 1, 0, 0] = 0
\[Epsilon]downupupup[3, 1, 0, 1] = 0
\[Epsilon]downupupup[3, 1, 0, 2] = -1
\[Epsilon]downupupup[3, 1, 0, 3] = 0
\[Epsilon]downupupup[3, 1, 1, 0] = 0
\[Epsilon]downupupup[3, 1, 1, 1] = 0
\[Epsilon]downupupup[3, 1, 1, 2] = 0
\[Epsilon]downupupup[3, 1, 1, 3] = 0
\[Epsilon]downupupup[3, 1, 2, 0] = 1
\[Epsilon]downupupup[3, 1, 2, 1] = 0
\[Epsilon]downupupup[3, 1, 2, 2] = 0
\[Epsilon]downupupup[3, 1, 2, 3] = 0
\[Epsilon]downupupup[3, 1, 3, 0] = 0
\[Epsilon]downupupup[3, 1, 3, 1] = 0
\[Epsilon]downupupup[3, 1, 3, 2] = 0
\[Epsilon]downupupup[3, 1, 3, 3] = 0
\[Epsilon]downupupup[3, 2, 0, 0] = 0
\[Epsilon]downupupup[3, 2, 0, 1] = 1
\[Epsilon]downupupup[3, 2, 0, 2] = 0
\[Epsilon]downupupup[3, 2, 0, 3] = 0
\[Epsilon]downupupup[3, 2, 1, 0] = -1
\[Epsilon]downupupup[3, 2, 1, 1] = 0
\[Epsilon]downupupup[3, 2, 1, 2] = 0
\[Epsilon]downupupup[3, 2, 1, 3] = 0
\[Epsilon]downupupup[3, 2, 2, 0] = 0
\[Epsilon]downupupup[3, 2, 2, 1] = 0
\[Epsilon]downupupup[3, 2, 2, 2] = 0
\[Epsilon]downupupup[3, 2, 2, 3] = 0
\[Epsilon]downupupup[3, 2, 3, 0] = 0
\[Epsilon]downupupup[3, 2, 3, 1] = 0
\[Epsilon]downupupup[3, 2, 3, 2] = 0
\[Epsilon]downupupup[3, 2, 3, 3] = 0
\[Epsilon]downupupup[3, 3, 0, 0] = 0
\[Epsilon]downupupup[3, 3, 0, 1] = 0
\[Epsilon]downupupup[3, 3, 0, 2] = 0
\[Epsilon]downupupup[3, 3, 0, 3] = 0
\[Epsilon]downupupup[3, 3, 1, 0] = 0
\[Epsilon]downupupup[3, 3, 1, 1] = 0
\[Epsilon]downupupup[3, 3, 1, 2] = 0
\[Epsilon]downupupup[3, 3, 1, 3] = 0
\[Epsilon]downupupup[3, 3, 2, 0] = 0
\[Epsilon]downupupup[3, 3, 2, 1] = 0
\[Epsilon]downupupup[3, 3, 2, 2] = 0
\[Epsilon]downupupup[3, 3, 2, 3] = 0
\[Epsilon]downupupup[3, 3, 3, 0] = 0
\[Epsilon]downupupup[3, 3, 3, 1] = 0
\[Epsilon]downupupup[3, 3, 3, 2] = 0
\[Epsilon]downupupup[3, 3, 3, 3] = 0
\[Epsilon]up[0, 0, 0, 0] = 0
\[Epsilon]up[0, 0, 0, 1] = 0
\[Epsilon]up[0, 0, 0, 2] = 0
\[Epsilon]up[0, 0, 0, 3] = 0
\[Epsilon]up[0, 0, 1, 0] = 0
\[Epsilon]up[0, 0, 1, 1] = 0
\[Epsilon]up[0, 0, 1, 2] = 0
\[Epsilon]up[0, 0, 1, 3] = 0
\[Epsilon]up[0, 0, 2, 0] = 0
\[Epsilon]up[0, 0, 2, 1] = 0
\[Epsilon]up[0, 0, 2, 2] = 0
\[Epsilon]up[0, 0, 2, 3] = 0
\[Epsilon]up[0, 0, 3, 0] = 0
\[Epsilon]up[0, 0, 3, 1] = 0
\[Epsilon]up[0, 0, 3, 2] = 0
\[Epsilon]up[0, 0, 3, 3] = 0
\[Epsilon]up[0, 1, 0, 0] = 0
\[Epsilon]up[0, 1, 0, 1] = 0
\[Epsilon]up[0, 1, 0, 2] = 0
\[Epsilon]up[0, 1, 0, 3] = 0
\[Epsilon]up[0, 1, 1, 0] = 0
\[Epsilon]up[0, 1, 1, 1] = 0
\[Epsilon]up[0, 1, 1, 2] = 0
\[Epsilon]up[0, 1, 1, 3] = 0
\[Epsilon]up[0, 1, 2, 0] = 0
\[Epsilon]up[0, 1, 2, 1] = 0
\[Epsilon]up[0, 1, 2, 2] = 0
\[Epsilon]up[0, 1, 2, 3] = -1
\[Epsilon]up[0, 1, 3, 0] = 0
\[Epsilon]up[0, 1, 3, 1] = 0
\[Epsilon]up[0, 1, 3, 2] = 1
\[Epsilon]up[0, 1, 3, 3] = 0
\[Epsilon]up[0, 2, 0, 0] = 0
\[Epsilon]up[0, 2, 0, 1] = 0
\[Epsilon]up[0, 2, 0, 2] = 0
\[Epsilon]up[0, 2, 0, 3] = 0
\[Epsilon]up[0, 2, 1, 0] = 0
\[Epsilon]up[0, 2, 1, 1] = 0
\[Epsilon]up[0, 2, 1, 2] = 0
\[Epsilon]up[0, 2, 1, 3] = 1
\[Epsilon]up[0, 2, 2, 0] = 0
\[Epsilon]up[0, 2, 2, 1] = 0
\[Epsilon]up[0, 2, 2, 2] = 0
\[Epsilon]up[0, 2, 2, 3] = 0
\[Epsilon]up[0, 2, 3, 0] = 0
\[Epsilon]up[0, 2, 3, 1] = -1
\[Epsilon]up[0, 2, 3, 2] = 0
\[Epsilon]up[0, 2, 3, 3] = 0
\[Epsilon]up[0, 3, 0, 0] = 0
\[Epsilon]up[0, 3, 0, 1] = 0
\[Epsilon]up[0, 3, 0, 2] = 0
\[Epsilon]up[0, 3, 0, 3] = 0
\[Epsilon]up[0, 3, 1, 0] = 0
\[Epsilon]up[0, 3, 1, 1] = 0
\[Epsilon]up[0, 3, 1, 2] = -1
\[Epsilon]up[0, 3, 1, 3] = 0
\[Epsilon]up[0, 3, 2, 0] = 0
\[Epsilon]up[0, 3, 2, 1] = 1
\[Epsilon]up[0, 3, 2, 2] = 0
\[Epsilon]up[0, 3, 2, 3] = 0
\[Epsilon]up[0, 3, 3, 0] = 0
\[Epsilon]up[0, 3, 3, 1] = 0
\[Epsilon]up[0, 3, 3, 2] = 0
\[Epsilon]up[0, 3, 3, 3] = 0
\[Epsilon]up[1, 0, 0, 0] = 0
\[Epsilon]up[1, 0, 0, 1] = 0
\[Epsilon]up[1, 0, 0, 2] = 0
\[Epsilon]up[1, 0, 0, 3] = 0
\[Epsilon]up[1, 0, 1, 0] = 0
\[Epsilon]up[1, 0, 1, 1] = 0
\[Epsilon]up[1, 0, 1, 2] = 0
\[Epsilon]up[1, 0, 1, 3] = 0
\[Epsilon]up[1, 0, 2, 0] = 0
\[Epsilon]up[1, 0, 2, 1] = 0
\[Epsilon]up[1, 0, 2, 2] = 0
\[Epsilon]up[1, 0, 2, 3] = 1
\[Epsilon]up[1, 0, 3, 0] = 0
\[Epsilon]up[1, 0, 3, 1] = 0
\[Epsilon]up[1, 0, 3, 2] = -1
\[Epsilon]up[1, 0, 3, 3] = 0
\[Epsilon]up[1, 1, 0, 0] = 0
\[Epsilon]up[1, 1, 0, 1] = 0
\[Epsilon]up[1, 1, 0, 2] = 0
\[Epsilon]up[1, 1, 0, 3] = 0
\[Epsilon]up[1, 1, 1, 0] = 0
\[Epsilon]up[1, 1, 1, 1] = 0
\[Epsilon]up[1, 1, 1, 2] = 0
\[Epsilon]up[1, 1, 1, 3] = 0
\[Epsilon]up[1, 1, 2, 0] = 0
\[Epsilon]up[1, 1, 2, 1] = 0
\[Epsilon]up[1, 1, 2, 2] = 0
\[Epsilon]up[1, 1, 2, 3] = 0
\[Epsilon]up[1, 1, 3, 0] = 0
\[Epsilon]up[1, 1, 3, 1] = 0
\[Epsilon]up[1, 1, 3, 2] = 0
\[Epsilon]up[1, 1, 3, 3] = 0
\[Epsilon]up[1, 2, 0, 0] = 0
\[Epsilon]up[1, 2, 0, 1] = 0
\[Epsilon]up[1, 2, 0, 2] = 0
\[Epsilon]up[1, 2, 0, 3] = -1
\[Epsilon]up[1, 2, 1, 0] = 0
\[Epsilon]up[1, 2, 1, 1] = 0
\[Epsilon]up[1, 2, 1, 2] = 0
\[Epsilon]up[1, 2, 1, 3] = 0
\[Epsilon]up[1, 2, 2, 0] = 0
\[Epsilon]up[1, 2, 2, 1] = 0
\[Epsilon]up[1, 2, 2, 2] = 0
\[Epsilon]up[1, 2, 2, 3] = 0
\[Epsilon]up[1, 2, 3, 0] = 1
\[Epsilon]up[1, 2, 3, 1] = 0
\[Epsilon]up[1, 2, 3, 2] = 0
\[Epsilon]up[1, 2, 3, 3] = 0
\[Epsilon]up[1, 3, 0, 0] = 0
\[Epsilon]up[1, 3, 0, 1] = 0
\[Epsilon]up[1, 3, 0, 2] = 1
\[Epsilon]up[1, 3, 0, 3] = 0
\[Epsilon]up[1, 3, 1, 0] = 0
\[Epsilon]up[1, 3, 1, 1] = 0
\[Epsilon]up[1, 3, 1, 2] = 0
\[Epsilon]up[1, 3, 1, 3] = 0
\[Epsilon]up[1, 3, 2, 0] = -1
\[Epsilon]up[1, 3, 2, 1] = 0
\[Epsilon]up[1, 3, 2, 2] = 0
\[Epsilon]up[1, 3, 2, 3] = 0
\[Epsilon]up[1, 3, 3, 0] = 0
\[Epsilon]up[1, 3, 3, 1] = 0
\[Epsilon]up[1, 3, 3, 2] = 0
\[Epsilon]up[1, 3, 3, 3] = 0
\[Epsilon]up[2, 0, 0, 0] = 0
\[Epsilon]up[2, 0, 0, 1] = 0
\[Epsilon]up[2, 0, 0, 2] = 0
\[Epsilon]up[2, 0, 0, 3] = 0
\[Epsilon]up[2, 0, 1, 0] = 0
\[Epsilon]up[2, 0, 1, 1] = 0
\[Epsilon]up[2, 0, 1, 2] = 0
\[Epsilon]up[2, 0, 1, 3] = -1
\[Epsilon]up[2, 0, 2, 0] = 0
\[Epsilon]up[2, 0, 2, 1] = 0
\[Epsilon]up[2, 0, 2, 2] = 0
\[Epsilon]up[2, 0, 2, 3] = 0
\[Epsilon]up[2, 0, 3, 0] = 0
\[Epsilon]up[2, 0, 3, 1] = 1
\[Epsilon]up[2, 0, 3, 2] = 0
\[Epsilon]up[2, 0, 3, 3] = 0
\[Epsilon]up[2, 1, 0, 0] = 0
\[Epsilon]up[2, 1, 0, 1] = 0
\[Epsilon]up[2, 1, 0, 2] = 0
\[Epsilon]up[2, 1, 0, 3] = 1
\[Epsilon]up[2, 1, 1, 0] = 0
\[Epsilon]up[2, 1, 1, 1] = 0
\[Epsilon]up[2, 1, 1, 2] = 0
\[Epsilon]up[2, 1, 1, 3] = 0
\[Epsilon]up[2, 1, 2, 0] = 0
\[Epsilon]up[2, 1, 2, 1] = 0
\[Epsilon]up[2, 1, 2, 2] = 0
\[Epsilon]up[2, 1, 2, 3] = 0
\[Epsilon]up[2, 1, 3, 0] = -1
\[Epsilon]up[2, 1, 3, 1] = 0
\[Epsilon]up[2, 1, 3, 2] = 0
\[Epsilon]up[2, 1, 3, 3] = 0
\[Epsilon]up[2, 2, 0, 0] = 0
\[Epsilon]up[2, 2, 0, 1] = 0
\[Epsilon]up[2, 2, 0, 2] = 0
\[Epsilon]up[2, 2, 0, 3] = 0
\[Epsilon]up[2, 2, 1, 0] = 0
\[Epsilon]up[2, 2, 1, 1] = 0
\[Epsilon]up[2, 2, 1, 2] = 0
\[Epsilon]up[2, 2, 1, 3] = 0
\[Epsilon]up[2, 2, 2, 0] = 0
\[Epsilon]up[2, 2, 2, 1] = 0
\[Epsilon]up[2, 2, 2, 2] = 0
\[Epsilon]up[2, 2, 2, 3] = 0
\[Epsilon]up[2, 2, 3, 0] = 0
\[Epsilon]up[2, 2, 3, 1] = 0
\[Epsilon]up[2, 2, 3, 2] = 0
\[Epsilon]up[2, 2, 3, 3] = 0
\[Epsilon]up[2, 3, 0, 0] = 0
\[Epsilon]up[2, 3, 0, 1] = -1
\[Epsilon]up[2, 3, 0, 2] = 0
\[Epsilon]up[2, 3, 0, 3] = 0
\[Epsilon]up[2, 3, 1, 0] = 1
\[Epsilon]up[2, 3, 1, 1] = 0
\[Epsilon]up[2, 3, 1, 2] = 0
\[Epsilon]up[2, 3, 1, 3] = 0
\[Epsilon]up[2, 3, 2, 0] = 0
\[Epsilon]up[2, 3, 2, 1] = 0
\[Epsilon]up[2, 3, 2, 2] = 0
\[Epsilon]up[2, 3, 2, 3] = 0
\[Epsilon]up[2, 3, 3, 0] = 0
\[Epsilon]up[2, 3, 3, 1] = 0
\[Epsilon]up[2, 3, 3, 2] = 0
\[Epsilon]up[2, 3, 3, 3] = 0
\[Epsilon]up[3, 0, 0, 0] = 0
\[Epsilon]up[3, 0, 0, 1] = 0
\[Epsilon]up[3, 0, 0, 2] = 0
\[Epsilon]up[3, 0, 0, 3] = 0
\[Epsilon]up[3, 0, 1, 0] = 0
\[Epsilon]up[3, 0, 1, 1] = 0
\[Epsilon]up[3, 0, 1, 2] = 1
\[Epsilon]up[3, 0, 1, 3] = 0
\[Epsilon]up[3, 0, 2, 0] = 0
\[Epsilon]up[3, 0, 2, 1] = -1
\[Epsilon]up[3, 0, 2, 2] = 0
\[Epsilon]up[3, 0, 2, 3] = 0
\[Epsilon]up[3, 0, 3, 0] = 0
\[Epsilon]up[3, 0, 3, 1] = 0
\[Epsilon]up[3, 0, 3, 2] = 0
\[Epsilon]up[3, 0, 3, 3] = 0
\[Epsilon]up[3, 1, 0, 0] = 0
\[Epsilon]up[3, 1, 0, 1] = 0
\[Epsilon]up[3, 1, 0, 2] = -1
\[Epsilon]up[3, 1, 0, 3] = 0
\[Epsilon]up[3, 1, 1, 0] = 0
\[Epsilon]up[3, 1, 1, 1] = 0
\[Epsilon]up[3, 1, 1, 2] = 0
\[Epsilon]up[3, 1, 1, 3] = 0
\[Epsilon]up[3, 1, 2, 0] = 1
\[Epsilon]up[3, 1, 2, 1] = 0
\[Epsilon]up[3, 1, 2, 2] = 0
\[Epsilon]up[3, 1, 2, 3] = 0
\[Epsilon]up[3, 1, 3, 0] = 0
\[Epsilon]up[3, 1, 3, 1] = 0
\[Epsilon]up[3, 1, 3, 2] = 0
\[Epsilon]up[3, 1, 3, 3] = 0
\[Epsilon]up[3, 2, 0, 0] = 0
\[Epsilon]up[3, 2, 0, 1] = 1
\[Epsilon]up[3, 2, 0, 2] = 0
\[Epsilon]up[3, 2, 0, 3] = 0
\[Epsilon]up[3, 2, 1, 0] = -1
\[Epsilon]up[3, 2, 1, 1] = 0
\[Epsilon]up[3, 2, 1, 2] = 0
\[Epsilon]up[3, 2, 1, 3] = 0
\[Epsilon]up[3, 2, 2, 0] = 0
\[Epsilon]up[3, 2, 2, 1] = 0
\[Epsilon]up[3, 2, 2, 2] = 0
\[Epsilon]up[3, 2, 2, 3] = 0
\[Epsilon]up[3, 2, 3, 0] = 0
\[Epsilon]up[3, 2, 3, 1] = 0
\[Epsilon]up[3, 2, 3, 2] = 0
\[Epsilon]up[3, 2, 3, 3] = 0
\[Epsilon]up[3, 3, 0, 0] = 0
\[Epsilon]up[3, 3, 0, 1] = 0
\[Epsilon]up[3, 3, 0, 2] = 0
\[Epsilon]up[3, 3, 0, 3] = 0
\[Epsilon]up[3, 3, 1, 0] = 0
\[Epsilon]up[3, 3, 1, 1] = 0
\[Epsilon]up[3, 3, 1, 2] = 0
\[Epsilon]up[3, 3, 1, 3] = 0
\[Epsilon]up[3, 3, 2, 0] = 0
\[Epsilon]up[3, 3, 2, 1] = 0
\[Epsilon]up[3, 3, 2, 2] = 0
\[Epsilon]up[3, 3, 2, 3] = 0
\[Epsilon]up[3, 3, 3, 0] = 0
\[Epsilon]up[3, 3, 3, 1] = 0
\[Epsilon]up[3, 3, 3, 2] = 0
\[Epsilon]up[3, 3, 3, 3] = 0
\[Eta][0, 0] = -1
\[Eta][0, 1] = 0
\[Eta][0, 2] = 0
\[Eta][0, 3] = 0
\[Eta][1, 0] = 0
\[Eta][1, 1] = 1
\[Eta][1, 2] = 0
\[Eta][1, 3] = 0
\[Eta][2, 0] = 0
\[Eta][2, 1] = 0
\[Eta][2, 2] = 1
\[Eta][2, 3] = 0
\[Eta][3, 0] = 0
\[Eta][3, 1] = 0
\[Eta][3, 2] = 0
\[Eta][3, 3] = 1
\[Sigma]down[m_, n_] := \[Sigma][m, n] . Cmetric
\[Sigma]stdown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdown[0, 1] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdown[0, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdown[0, 3] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stdown[1, 0] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stdown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdown[1, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stdown[1, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, I, 0}}
\[Sigma]stdown[2, 0] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stdown[2, 1] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdown[2, 3] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdown[3, 0] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stdown[3, 1] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Sigma]stdown[3, 2] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stdown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdowndown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
\[Sigma]stdowndown[0, 1] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stdowndown[0, 2] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdowndown[0, 3] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdowndown[1, 0] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stdowndown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
\[Sigma]stdowndown[1, 2] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stdowndown[1, 3] = {{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, I}}
\[Sigma]stdowndown[2, 0] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stdowndown[2, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdowndown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
\[Sigma]stdowndown[2, 3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stdowndown[3, 0] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stdowndown[3, 1] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, -I}}
\[Sigma]stdowndown[3, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdowndown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0,
0, 0}}
\[Sigma]stdownstup[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdownstup[0, 1] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdownstup[0, 2] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdownstup[0, 3] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stdownstup[1, 0] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdownstup[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdownstup[1, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stdownstup[1, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, I, 0}}
\[Sigma]stdownstup[2, 0] = {{0, 0, -I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdownstup[2, 1] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdownstup[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdownstup[2, 3] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdownstup[3, 0] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stdownstup[3, 1] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Sigma]stdownstup[3, 2] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stdownstup[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stdownstupdown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stdownstupdown[0, 1] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stdownstupdown[0, 2] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdownstupdown[0, 3] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdownstupdown[1, 0] = {{0, I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stdownstupdown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stdownstupdown[1, 2] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stdownstupdown[1, 3] = {{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, I}}
\[Sigma]stdownstupdown[2, 0] = {{0, 0, 0, -I}, {0, 0, I, 0}, {0, I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdownstupdown[2, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stdownstupdown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stdownstupdown[2, 3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stdownstupdown[3, 0] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, -I}}
\[Sigma]stdownstupdown[3, 1] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, -I}}
\[Sigma]stdownstupdown[3, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stdownstupdown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stupstdown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stupstdown[0, 1] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stupstdown[0, 2] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stupstdown[0, 3] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stupstdown[1, 0] = {{I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stupstdown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stupstdown[1, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stupstdown[1, 3] = {{0, -I, 0, 0}, {I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, I, 0}}
\[Sigma]stupstdown[2, 0] = {{0, 0, I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stupstdown[2, 1] = {{0, 0, -I, 0}, {0, 0, 0, I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stupstdown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stupstdown[2, 3] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stupstdown[3, 0] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, I, 0}}
\[Sigma]stupstdown[3, 1] = {{0, I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, I},
{0, 0, -I, 0}}
\[Sigma]stupstdown[3, 2] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stupstdown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
{0, 0, 0, 0}}
\[Sigma]stupstdowndown[0, 0] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stupstdowndown[0, 1] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stupstdowndown[0, 2] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stupstdowndown[0, 3] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stupstdowndown[1, 0] = {{0, -I, 0, 0}, {-I, 0, 0, 0}, {0, 0, 0, -I},
{0, 0, -I, 0}}
\[Sigma]stupstdowndown[1, 1] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stupstdowndown[1, 2] = {{0, 0, 0, I}, {0, 0, I, 0}, {0, I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stupstdowndown[1, 3] = {{-I, 0, 0, 0}, {0, -I, 0, 0}, {0, 0, I, 0},
{0, 0, 0, I}}
\[Sigma]stupstdowndown[2, 0] = {{0, 0, 0, I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{I, 0, 0, 0}}
\[Sigma]stupstdowndown[2, 1] = {{0, 0, 0, -I}, {0, 0, -I, 0}, {0, -I, 0, 0},
{-I, 0, 0, 0}}
\[Sigma]stupstdowndown[2, 2] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[Sigma]stupstdowndown[2, 3] = {{0, 0, -I, 0}, {0, 0, 0, I}, {-I, 0, 0, 0},
{0, I, 0, 0}}
\[Sigma]stupstdowndown[3, 0] = {{-I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, I}}
\[Sigma]stupstdowndown[3, 1] = {{I, 0, 0, 0}, {0, I, 0, 0}, {0, 0, -I, 0},
{0, 0, 0, -I}}
\[Sigma]stupstdowndown[3, 2] = {{0, 0, I, 0}, {0, 0, 0, -I}, {I, 0, 0, 0},
{0, -I, 0, 0}}
\[Sigma]stupstdowndown[3, 3] = {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0,
0, 0, 0}}
\[CapitalStigma][0] := t
\[CapitalStigma][1] := x
\[CapitalStigma][2] := y
\[CapitalStigma][3] := z
