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}}, 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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, 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0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}}, {{{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}, {{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}, {{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}}, {{{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}, {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {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