diff --git a/FeynCalc/Dirac/DiracTrace.m b/FeynCalc/Dirac/DiracTrace.m index e2878250..12392e15 100755 --- a/FeynCalc/Dirac/DiracTrace.m +++ b/FeynCalc/Dirac/DiracTrace.m @@ -703,8 +703,8 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver ]/; EvenQ[Length[{x,y}]]; - -spur5LarinMVV[x__DiracGamma, y:DiracGamma[_[_,dim_],dim_], DiracGamma[5]]:= +(*Implements Eq.10 from 1506.04517 *) +spur5LarinMVVold[x__DiracGamma, y:DiracGamma[_[_,dim_],dim_], DiracGamma[5]]:= Block[{inds, epsInds, gInds, indPartitions, res, signs}, inds = First/@{x}; epsInds = Subsets[inds, {3}]; @@ -718,6 +718,22 @@ we define it is a function (traceNo5fun) so that the result can be retrieved ver fastExpand[res] ]/; EvenQ[Length[{x,y}]] && Length[{x,y}]>=4; +(*Implements Eq.11 from 1506.04517 *) +spur5LarinMVV[x__DiracGamma, y : DiracGamma[_[_, dim_], dim_], DiracGamma[5]] := +Block[{inds, epsInds, gInds, indPartitions, res, signs}, + inds = First /@ {x, y}; + epsInds = Subsets[inds, {4}]; + gInds = SelectFree[inds, #] & /@ epsInds; + indPartitions = MapThread[Join[#1, #2] &, {gInds, epsInds}]; + signs = Signature /@ (indPartitions /. Thread[Rule[inds, Range[Length[inds]]]]); + + res = + Total[MapThread[$LeviCivitaSign* + I*#2*((traceNo5Wrap @@ #1[[;; -5]]))* + Apply[Eps, #1[[-4 ;;]]] &, {indPartitions, signs}]]; + fastExpand[res] + ] /; EvenQ[Length[{x, y}]] && Length[{x, y}] >= 4; + spur5BMHVWest[x__DiracGamma, DiracGamma[5]]:= Block[{spx = {x,DiracGamma[5]},spt,res}, res = 2/(Length[spx]-5) Sum[(-1)^(i+j+1) FCUseCache[ExpandScalarProduct,{Pair[spx[[i]][[1]],spx[[j]][[1]]]},{FCI->False}] * diff --git a/FeynCalc/Documentation/Markdown/Extra/Gamma5.md b/FeynCalc/Documentation/Markdown/Extra/Gamma5.md index 8f36adc1..03a7b8bc 100644 --- a/FeynCalc/Documentation/Markdown/Extra/Gamma5.md +++ b/FeynCalc/Documentation/Markdown/Extra/Gamma5.md @@ -113,3 +113,23 @@ FeynCalc implement the so-called Moch-Vermaseren-Vogt MVV formula from [Moch:201 ```mathematica FCSetDiracGammaScheme["Larin"] ``` + +The usage of this scheme implies that all axial-vector matrices from the Feynman rules $ \gamma^\mu \gamma^5$ should be entered as +\begin{equation} +\gamma^\mu \gamma^5 \to \frac{1}{2} \left ( \gamma^\mu \gamma^5 - \gamma^5 \gamma^\mu \right ) +\end{equation} + +If the trace contains more than one $\gamma^5$, the code will insert +\begin{equation} +\gamma^\mu \gamma^5 = \frac{i}{6} \, \texttt{\$LeviCivitaSign} \, \varepsilon^{\mu \nu \rho \sigma} \gamma_\nu \gamma_\rho \gamma_\sigma +\end{equation} +for all but the right-most $\gamma^5$. Then the resulting trace will be evaluated according to Eq.(11) from [Moch:2015usa](https://arxiv.org/pdf/1506.04517.pdf) + \begin{equation} +\mathrm{Tr}(\gamma^{\mu_1} \ldots \gamma^{\mu_{2m}} \gamma^5) = 4 i \, \texttt{\$LeviCivitaSign} \, g^{\mu_1 \mu_2} \ldots g^{\mu_{2m-5} \mu_{2m-4}} \varepsilon^{\mu_{2m-3} \mu_{2m-2} \mu_{2m-1} \mu_{2m}} + \textrm{permutations of} \quad \mu_{1} \ldots {\mu_{2m}} +\end{equation} + +Notice that according to [Moch:2015usa](https://arxiv.org/pdf/1506.04517.pdf) one should distinguish between Levi-Civita tensors appearing in the calculating from traces over axial-vector matrices and those introduced e.g. via projectors. The "axial-vector" Levi-Civitas should be contracted first to avoid incorrect results. + +Since FeynCalc has no way to know the origin of $\varepsilon$-tensors in the input expression, it is advised to rename the unrelated Levi-Civitas to something else while doing the trace calculations and reintroduce them after the traces have been succesfully evaluated. + + diff --git a/Tests/Dirac/DiracTrace.test b/Tests/Dirac/DiracTrace.test index 523c23c0..378fada9 100644 --- a/Tests/Dirac/DiracTrace.test +++ b/Tests/Dirac/DiracTrace.test @@ -266,199 +266,134 @@ FCE->True]", "(-4*I)*LCD[mu1, mu2, mu3, mu4]"}, {"fcstDiracTrace-ID56", "DiracTrace[GAD[mu1,mu2,5,mu3,mu4,mu5,mu6],\ DiracTraceEvaluate->True,FCE->True]", -"(-4*I)*(LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3] - LCD[mu2, mu3, \ -mu5, mu6]*MTD[mu1, mu4] + LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5] - \ -LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu6] + LCD[mu1, mu2, mu5, \ -mu6]*MTD[mu3, mu4] - LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5] + LCD[mu1, \ -mu2, mu4, mu5]*MTD[mu3, mu6] + LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu5] \ -- LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu6] + LCD[mu1, mu2, mu3, \ -mu4]*MTD[mu5, mu6])"}, +"(-4*I)*(LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2] + +LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3] - +LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu4] + +LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5] - +LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu6] - +LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu3] + +LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4] - +LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu5] + +LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu6] + +LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu4] - +LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5] + +LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu6] + +LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu5] - +LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu6] + +LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu6])"}, {"fcstDiracTrace-ID57", "DiracTrace[GAD[mu1,mu2,mu3,mu4,mu5,mu6,5],\ DiracTraceEvaluate->True,FCE->True]", -"(-4*I)*(LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2] - LCD[mu2, mu4, \ -mu5, mu6]*MTD[mu1, mu3] + LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu4] - \ -LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5] + LCD[mu1, mu4, mu5, \ -mu6]*MTD[mu2, mu3] - LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4] + LCD[mu1, \ -mu3, mu4, mu6]*MTD[mu2, mu5] + LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu4] \ -- LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5] + LCD[mu1, mu2, mu3, \ -mu6]*MTD[mu4, mu5])"}, +"(-4*I)*(LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2] - LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3] + LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu4] - LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5] + LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu6] + LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu3] - LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4] + LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu5] - LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu6] + LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu4] - LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5] + LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu6] + LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu5] - LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu6] + LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu6])"}, {"fcstDiracTrace-ID58", "DiracTrace[GAD[mu1,mu2,mu3,mu4,mu5,mu6,mu7,mu8,5],\ DiracTraceEvaluate->True,FCE->True]", -"(-4*I)*(LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu3] - \ -LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu3] + LCD[mu4, mu5, \ -mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu3] - LCD[mu4, mu5, mu6, \ -mu8]*MTD[mu1, mu7]*MTD[mu2, mu3] - LCD[mu5, mu6, mu7, mu8]*MTD[mu1, \ -mu3]*MTD[mu2, mu4] + LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, \ -mu4] - LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu4] + LCD[mu3, \ -mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu4] + LCD[mu4, mu6, mu7, \ -mu8]*MTD[mu1, mu3]*MTD[mu2, mu5] - LCD[mu3, mu6, mu7, mu8]*MTD[mu1, \ -mu4]*MTD[mu2, mu5] + LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, \ -mu5] - LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu5] - LCD[mu4, \ -mu5, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu6] + LCD[mu3, mu5, mu7, \ -mu8]*MTD[mu1, mu4]*MTD[mu2, mu6] - LCD[mu3, mu4, mu7, mu8]*MTD[mu1, \ -mu5]*MTD[mu2, mu6] + LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu2, \ -mu6] + LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu2, mu7] - LCD[mu3, \ -mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu2, mu7] + LCD[mu3, mu4, mu6, \ -mu8]*MTD[mu1, mu5]*MTD[mu2, mu7] - LCD[mu3, mu4, mu5, mu8]*MTD[mu1, \ -mu6]*MTD[mu2, mu7] + LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, \ -mu4] - LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu4] + LCD[mu2, \ -mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu4] - LCD[mu2, mu5, mu6, \ -mu8]*MTD[mu1, mu7]*MTD[mu3, mu4] + LCD[mu1, mu6, mu7, mu8]*MTD[mu2, \ -mu5]*MTD[mu3, mu4] - LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, \ -mu4] + LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, mu4] - LCD[mu4, \ -mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu5] + LCD[mu2, mu6, mu7, \ -mu8]*MTD[mu1, mu4]*MTD[mu3, mu5] - LCD[mu2, mu4, mu7, mu8]*MTD[mu1, \ -mu6]*MTD[mu3, mu5] + LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, \ -mu5] - LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu5] + LCD[mu1, \ -mu4, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, mu5] - LCD[mu1, mu4, mu6, \ -mu8]*MTD[mu2, mu7]*MTD[mu3, mu5] + LCD[mu4, mu5, mu7, mu8]*MTD[mu1, \ -mu2]*MTD[mu3, mu6] - LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu4]*MTD[mu3, \ -mu6] + LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu6] - LCD[mu2, \ -mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu3, mu6] + LCD[mu1, mu5, mu7, \ -mu8]*MTD[mu2, mu4]*MTD[mu3, mu6] - LCD[mu1, mu4, mu7, mu8]*MTD[mu2, \ -mu5]*MTD[mu3, mu6] + LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu7]*MTD[mu3, \ -mu6] - LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu3, mu7] + LCD[mu2, \ -mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu3, mu7] - LCD[mu2, mu4, mu6, \ -mu8]*MTD[mu1, mu5]*MTD[mu3, mu7] + LCD[mu2, mu4, mu5, mu8]*MTD[mu1, \ -mu6]*MTD[mu3, mu7] - LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu4]*MTD[mu3, \ -mu7] + LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu5]*MTD[mu3, mu7] - LCD[mu1, \ -mu4, mu5, mu8]*MTD[mu2, mu6]*MTD[mu3, mu7] + LCD[mu3, mu6, mu7, \ -mu8]*MTD[mu1, mu2]*MTD[mu4, mu5] - LCD[mu2, mu6, mu7, mu8]*MTD[mu1, \ -mu3]*MTD[mu4, mu5] + LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu6]*MTD[mu4, \ -mu5] - LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu7]*MTD[mu4, mu5] + LCD[mu1, \ -mu6, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu5] - LCD[mu1, mu3, mu7, \ -mu8]*MTD[mu2, mu6]*MTD[mu4, mu5] + LCD[mu1, mu3, mu6, mu8]*MTD[mu2, \ -mu7]*MTD[mu4, mu5] + LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu6]*MTD[mu4, \ -mu5] - LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu7]*MTD[mu4, mu5] - LCD[mu3, \ -mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu4, mu6] + LCD[mu2, mu5, mu7, \ -mu8]*MTD[mu1, mu3]*MTD[mu4, mu6] - LCD[mu2, mu3, mu7, mu8]*MTD[mu1, \ -mu5]*MTD[mu4, mu6] + LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu7]*MTD[mu4, \ -mu6] - LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu6] + LCD[mu1, \ -mu3, mu7, mu8]*MTD[mu2, mu5]*MTD[mu4, mu6] - LCD[mu1, mu3, mu5, \ -mu8]*MTD[mu2, mu7]*MTD[mu4, mu6] - LCD[mu1, mu2, mu7, mu8]*MTD[mu3, \ -mu5]*MTD[mu4, mu6] + LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu7]*MTD[mu4, \ -mu6] + LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu4, mu7] - LCD[mu2, \ -mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu4, mu7] + LCD[mu2, mu3, mu6, \ -mu8]*MTD[mu1, mu5]*MTD[mu4, mu7] - LCD[mu2, mu3, mu5, mu8]*MTD[mu1, \ -mu6]*MTD[mu4, mu7] + LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu3]*MTD[mu4, \ -mu7] - LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu5]*MTD[mu4, mu7] + LCD[mu1, \ -mu3, mu5, mu8]*MTD[mu2, mu6]*MTD[mu4, mu7] + LCD[mu1, mu2, mu6, \ -mu8]*MTD[mu3, mu5]*MTD[mu4, mu7] - LCD[mu1, mu2, mu5, mu8]*MTD[mu3, \ -mu6]*MTD[mu4, mu7] + LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu2]*MTD[mu5, \ -mu6] - LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu3]*MTD[mu5, mu6] + LCD[mu2, \ -mu3, mu7, mu8]*MTD[mu1, mu4]*MTD[mu5, mu6] - LCD[mu2, mu3, mu4, \ -mu8]*MTD[mu1, mu7]*MTD[mu5, mu6] + LCD[mu1, mu4, mu7, mu8]*MTD[mu2, \ -mu3]*MTD[mu5, mu6] - LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu4]*MTD[mu5, \ -mu6] + LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu7]*MTD[mu5, mu6] + LCD[mu1, \ -mu2, mu7, mu8]*MTD[mu3, mu4]*MTD[mu5, mu6] - LCD[mu1, mu2, mu4, \ -mu8]*MTD[mu3, mu7]*MTD[mu5, mu6] + LCD[mu1, mu2, mu3, mu8]*MTD[mu4, \ -mu7]*MTD[mu5, mu6] - LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu2]*MTD[mu5, \ -mu7] + LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu3]*MTD[mu5, mu7] - LCD[mu2, \ -mu3, mu6, mu8]*MTD[mu1, mu4]*MTD[mu5, mu7] + LCD[mu2, mu3, mu4, \ -mu8]*MTD[mu1, mu6]*MTD[mu5, mu7] - LCD[mu1, mu4, mu6, mu8]*MTD[mu2, \ -mu3]*MTD[mu5, mu7] + LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu4]*MTD[mu5, \ -mu7] - LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu6]*MTD[mu5, mu7] - LCD[mu1, \ -mu2, mu6, mu8]*MTD[mu3, mu4]*MTD[mu5, mu7] + LCD[mu1, mu2, mu4, \ -mu8]*MTD[mu3, mu6]*MTD[mu5, mu7] - LCD[mu1, mu2, mu3, mu8]*MTD[mu4, \ -mu6]*MTD[mu5, mu7] + LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu2]*MTD[mu6, \ -mu7] - LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu3]*MTD[mu6, mu7] + LCD[mu2, \ -mu3, mu5, mu8]*MTD[mu1, mu4]*MTD[mu6, mu7] - LCD[mu2, mu3, mu4, \ -mu8]*MTD[mu1, mu5]*MTD[mu6, mu7] + LCD[mu1, mu4, mu5, mu8]*MTD[mu2, \ -mu3]*MTD[mu6, mu7] - LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu4]*MTD[mu6, \ -mu7] + LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu5]*MTD[mu6, mu7] + LCD[mu1, \ -mu2, mu5, mu8]*MTD[mu3, mu4]*MTD[mu6, mu7] - LCD[mu1, mu2, mu4, \ -mu8]*MTD[mu3, mu5]*MTD[mu6, mu7] + LCD[mu1, mu2, mu3, mu8]*MTD[mu4, \ -mu5]*MTD[mu6, mu7])"}, +"4*((-I)*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu3] + I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu3] - +I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu3] + I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu3] - +I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu3] + I*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu4] - +I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu4] + I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu4] - +I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu4] + I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu4] - +I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu5] + I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu5] - +I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu5] + I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu5] - +I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu5] + I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu6] - +I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu6] + I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu6] - +I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu2, mu6] + I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu2, mu6] - +I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu2, mu7] + I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu2, mu7] - +I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu5]*MTD[mu2, mu7] + I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu6]*MTD[mu2, mu7] - +I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu2, mu7] + I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu2, mu8] - +I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu2, mu8] + I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu5]*MTD[mu2, mu8] - +I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu6]*MTD[mu2, mu8] + I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu7]*MTD[mu2, mu8] - +I*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu4] + I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu4] - +I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu4] + I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, mu4] - +I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu3, mu4] - I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu5]*MTD[mu3, mu4] + +I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, mu4] - I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, mu4] + +I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu8]*MTD[mu3, mu4] + I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu5] - +I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu3, mu5] + I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu5] - +I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, mu5] + I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu8]*MTD[mu3, mu5] + +I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu5] - I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, mu5] + +I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, mu5] - I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu8]*MTD[mu3, mu5] - +I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu6] + I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu4]*MTD[mu3, mu6] - +I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu6] + I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu3, mu6] - +I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu3, mu6] - I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu6] + +I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu5]*MTD[mu3, mu6] - I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu7]*MTD[mu3, mu6] + +I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu8]*MTD[mu3, mu6] + I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu3, mu7] - +I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu3, mu7] + I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu5]*MTD[mu3, mu7] - +I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu6]*MTD[mu3, mu7] + I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu3, mu7] + +I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu4]*MTD[mu3, mu7] - I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu5]*MTD[mu3, mu7] + +I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu6]*MTD[mu3, mu7] - I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu8]*MTD[mu3, mu7] - +I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu3, mu8] + I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu3, mu8] - +I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu5]*MTD[mu3, mu8] + I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu6]*MTD[mu3, mu8] - +I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu7]*MTD[mu3, mu8] - I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu4]*MTD[mu3, mu8] + +I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu5]*MTD[mu3, mu8] - I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu6]*MTD[mu3, mu8] + +I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu7]*MTD[mu3, mu8] - I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu4, mu5] + +I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu4, mu5] - I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu6]*MTD[mu4, mu5] + +I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu7]*MTD[mu4, mu5] - I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu8]*MTD[mu4, mu5] - +I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu5] + I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu6]*MTD[mu4, mu5] - +I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu7]*MTD[mu4, mu5] + I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu8]*MTD[mu4, mu5] - +I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu6]*MTD[mu4, mu5] + I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu7]*MTD[mu4, mu5] - +I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu8]*MTD[mu4, mu5] + I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu4, mu6] - +I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu3]*MTD[mu4, mu6] + I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu5]*MTD[mu4, mu6] - +I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu7]*MTD[mu4, mu6] + I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu8]*MTD[mu4, mu6] + +I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu6] - I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu5]*MTD[mu4, mu6] + +I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu7]*MTD[mu4, mu6] - I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu8]*MTD[mu4, mu6] + +I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu5]*MTD[mu4, mu6] - I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu7]*MTD[mu4, mu6] + +I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu8]*MTD[mu4, mu6] - I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu4, mu7] + +I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu4, mu7] - I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu5]*MTD[mu4, mu7] + +I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu6]*MTD[mu4, mu7] - I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu8]*MTD[mu4, mu7] - +I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu3]*MTD[mu4, mu7] + I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu5]*MTD[mu4, mu7] - +I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu6]*MTD[mu4, mu7] + I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu8]*MTD[mu4, mu7] - +I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu5]*MTD[mu4, mu7] + I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu6]*MTD[mu4, mu7] - +I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu8]*MTD[mu4, mu7] + I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu4, mu8] - +I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu4, mu8] + I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu5]*MTD[mu4, mu8] - +I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu6]*MTD[mu4, mu8] + I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu7]*MTD[mu4, mu8] + +I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu3]*MTD[mu4, mu8] - I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu5]*MTD[mu4, mu8] + +I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu6]*MTD[mu4, mu8] - I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu7]*MTD[mu4, mu8] + +I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu5]*MTD[mu4, mu8] - I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu6]*MTD[mu4, mu8] + +I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu7]*MTD[mu4, mu8] - I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu2]*MTD[mu5, mu6] + +I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu3]*MTD[mu5, mu6] - I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu4]*MTD[mu5, mu6] + +I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu7]*MTD[mu5, mu6] - I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu8]*MTD[mu5, mu6] - +I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu3]*MTD[mu5, mu6] + I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu4]*MTD[mu5, mu6] - +I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu7]*MTD[mu5, mu6] + I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu8]*MTD[mu5, mu6] - +I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu4]*MTD[mu5, mu6] + I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu7]*MTD[mu5, mu6] - +I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu8]*MTD[mu5, mu6] - I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu7]*MTD[mu5, mu6] + +I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu8]*MTD[mu5, mu6] + I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu2]*MTD[mu5, mu7] - +I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu3]*MTD[mu5, mu7] + I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu4]*MTD[mu5, mu7] - +I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu6]*MTD[mu5, mu7] + I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu8]*MTD[mu5, mu7] + +I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu3]*MTD[mu5, mu7] - I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu4]*MTD[mu5, mu7] + +I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu6]*MTD[mu5, mu7] - I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu8]*MTD[mu5, mu7] + +I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu4]*MTD[mu5, mu7] - I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu6]*MTD[mu5, mu7] + +I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu8]*MTD[mu5, mu7] + I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu6]*MTD[mu5, mu7] - +I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu8]*MTD[mu5, mu7] - I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu2]*MTD[mu5, mu8] + +I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu3]*MTD[mu5, mu8] - I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu4]*MTD[mu5, mu8] + +I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu6]*MTD[mu5, mu8] - I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu7]*MTD[mu5, mu8] - +I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu3]*MTD[mu5, mu8] + I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu4]*MTD[mu5, mu8] - +I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu6]*MTD[mu5, mu8] + I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu7]*MTD[mu5, mu8] - +I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu4]*MTD[mu5, mu8] + I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu6]*MTD[mu5, mu8] - +I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu7]*MTD[mu5, mu8] - I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu6]*MTD[mu5, mu8] + +I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu7]*MTD[mu5, mu8] - I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu2]*MTD[mu6, mu7] + +I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu3]*MTD[mu6, mu7] - I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu4]*MTD[mu6, mu7] + +I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu5]*MTD[mu6, mu7] - I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu8]*MTD[mu6, mu7] - +I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu3]*MTD[mu6, mu7] + I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu4]*MTD[mu6, mu7] - + I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu5]*MTD[mu6, mu7] + I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu8]*MTD[mu6, mu7] - + I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu4]*MTD[mu6, mu7] + I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu5]*MTD[mu6, mu7] - + I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu8]*MTD[mu6, mu7] - I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu5]*MTD[mu6, mu7] + + I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu8]*MTD[mu6, mu7] - I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu8]*MTD[mu6, mu7] + + I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu2]*MTD[mu6, mu8] - I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu3]*MTD[mu6, mu8] + I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu4]*MTD[mu6, mu8] - + I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu5]*MTD[mu6, mu8] + I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu7]*MTD[mu6, mu8] + I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu3]*MTD[mu6, mu8] - + I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu4]*MTD[mu6, mu8] + I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu5]*MTD[mu6, mu8] - I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu7]*MTD[mu6, mu8] + + I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu4]*MTD[mu6, mu8] - I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu5]*MTD[mu6, mu8] + I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu7]*MTD[mu6, mu8] + + I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu5]*MTD[mu6, mu8] - I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu7]*MTD[mu6, mu8] + I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu7]*MTD[mu6, mu8] - + I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2]*MTD[mu7, mu8] + I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3]*MTD[mu7, mu8] - I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu4]*MTD[mu7, mu8] + + I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5]*MTD[mu7, mu8] - I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu6]*MTD[mu7, mu8] - I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu3]*MTD[mu7, mu8] + + I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4]*MTD[mu7, mu8] - I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu5]*MTD[mu7, mu8] + I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu6]*MTD[mu7, mu8] - + I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu4]*MTD[mu7, mu8] + + I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu6]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu5]*MTD[mu7, mu8] + + I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu6]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu6]*MTD[mu7, mu8])"}, {"fcstDiracTrace-ID59", "DiracTrace[GAD[mu1,mu2,mu3,mu4,mu5,5,mu6,mu7,mu8],\ DiracTraceEvaluate->True,FCE->True]", -"(4*I)*(LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu3] - \ -LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu3] + LCD[mu4, mu5, \ -mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu3] - LCD[mu4, mu5, mu6, \ -mu7]*MTD[mu1, mu8]*MTD[mu2, mu3] - LCD[mu5, mu6, mu7, mu8]*MTD[mu1, \ -mu3]*MTD[mu2, mu4] + LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, \ -mu4] - LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu4] + LCD[mu3, \ -mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu4] + LCD[mu4, mu5, mu7, \ -mu8]*MTD[mu1, mu3]*MTD[mu2, mu6] - LCD[mu3, mu5, mu7, mu8]*MTD[mu1, \ -mu4]*MTD[mu2, mu6] + LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu2, \ -mu6] - LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu2, mu6] - LCD[mu4, \ -mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu2, mu7] + LCD[mu3, mu5, mu6, \ -mu8]*MTD[mu1, mu4]*MTD[mu2, mu7] - LCD[mu3, mu4, mu5, mu8]*MTD[mu1, \ -mu6]*MTD[mu2, mu7] + LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu2, \ -mu7] + LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu2, mu8] - LCD[mu3, \ -mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu2, mu8] + LCD[mu3, mu4, mu5, \ -mu7]*MTD[mu1, mu6]*MTD[mu2, mu8] - LCD[mu3, mu4, mu5, mu6]*MTD[mu1, \ -mu7]*MTD[mu2, mu8] + LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, \ -mu4] - LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu4] + LCD[mu2, \ -mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, mu4] - LCD[mu2, mu5, mu6, \ -mu7]*MTD[mu1, mu8]*MTD[mu3, mu4] + LCD[mu1, mu5, mu7, mu8]*MTD[mu2, \ -mu6]*MTD[mu3, mu4] - LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, \ -mu4] + LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu8]*MTD[mu3, mu4] - LCD[mu4, \ -mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu6] + LCD[mu2, mu5, mu7, \ -mu8]*MTD[mu1, mu4]*MTD[mu3, mu6] - LCD[mu2, mu4, mu5, mu8]*MTD[mu1, \ -mu7]*MTD[mu3, mu6] + LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu3, \ -mu6] - LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu6] + LCD[mu1, \ -mu4, mu5, mu8]*MTD[mu2, mu7]*MTD[mu3, mu6] - LCD[mu1, mu4, mu5, \ -mu7]*MTD[mu2, mu8]*MTD[mu3, mu6] + LCD[mu4, mu5, mu6, mu8]*MTD[mu1, \ -mu2]*MTD[mu3, mu7] - LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu3, \ -mu7] + LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu6]*MTD[mu3, mu7] - LCD[mu2, \ -mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu3, mu7] + LCD[mu1, mu5, mu6, \ -mu8]*MTD[mu2, mu4]*MTD[mu3, mu7] - LCD[mu1, mu4, mu5, mu8]*MTD[mu2, \ -mu6]*MTD[mu3, mu7] + LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu8]*MTD[mu3, \ -mu7] - LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu3, mu8] + LCD[mu2, \ -mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu3, mu8] - LCD[mu2, mu4, mu5, \ -mu7]*MTD[mu1, mu6]*MTD[mu3, mu8] + LCD[mu2, mu4, mu5, mu6]*MTD[mu1, \ -mu7]*MTD[mu3, mu8] - LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu4]*MTD[mu3, \ -mu8] + LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu6]*MTD[mu3, mu8] - LCD[mu1, \ -mu4, mu5, mu6]*MTD[mu2, mu7]*MTD[mu3, mu8] + LCD[mu3, mu5, mu7, \ -mu8]*MTD[mu1, mu2]*MTD[mu4, mu6] - LCD[mu2, mu5, mu7, mu8]*MTD[mu1, \ -mu3]*MTD[mu4, mu6] + LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu7]*MTD[mu4, \ -mu6] - LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu8]*MTD[mu4, mu6] + LCD[mu1, \ -mu5, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu6] - LCD[mu1, mu3, mu5, \ -mu8]*MTD[mu2, mu7]*MTD[mu4, mu6] + LCD[mu1, mu3, mu5, mu7]*MTD[mu2, \ -mu8]*MTD[mu4, mu6] + LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu7]*MTD[mu4, \ -mu6] - LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu8]*MTD[mu4, mu6] - LCD[mu3, \ -mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu4, mu7] + LCD[mu2, mu5, mu6, \ -mu8]*MTD[mu1, mu3]*MTD[mu4, mu7] - LCD[mu2, mu3, mu5, mu8]*MTD[mu1, \ -mu6]*MTD[mu4, mu7] + LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu8]*MTD[mu4, \ -mu7] - LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu3]*MTD[mu4, mu7] + LCD[mu1, \ -mu3, mu5, mu8]*MTD[mu2, mu6]*MTD[mu4, mu7] - LCD[mu1, mu3, mu5, \ -mu6]*MTD[mu2, mu8]*MTD[mu4, mu7] - LCD[mu1, mu2, mu5, mu8]*MTD[mu3, \ -mu6]*MTD[mu4, mu7] + LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu8]*MTD[mu4, \ -mu7] + LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu4, mu8] - LCD[mu2, \ -mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu4, mu8] + LCD[mu2, mu3, mu5, \ -mu7]*MTD[mu1, mu6]*MTD[mu4, mu8] - LCD[mu2, mu3, mu5, mu6]*MTD[mu1, \ -mu7]*MTD[mu4, mu8] + LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu3]*MTD[mu4, \ -mu8] - LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu6]*MTD[mu4, mu8] + LCD[mu1, \ -mu3, mu5, mu6]*MTD[mu2, mu7]*MTD[mu4, mu8] + LCD[mu1, mu2, mu5, \ -mu7]*MTD[mu3, mu6]*MTD[mu4, mu8] - LCD[mu1, mu2, mu5, mu6]*MTD[mu3, \ -mu7]*MTD[mu4, mu8] + LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu2]*MTD[mu6, \ -mu7] - LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu3]*MTD[mu6, mu7] + LCD[mu2, \ -mu3, mu5, mu8]*MTD[mu1, mu4]*MTD[mu6, mu7] - LCD[mu2, mu3, mu4, \ -mu5]*MTD[mu1, mu8]*MTD[mu6, mu7] + LCD[mu1, mu4, mu5, mu8]*MTD[mu2, \ -mu3]*MTD[mu6, mu7] - LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu4]*MTD[mu6, \ -mu7] + LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu8]*MTD[mu6, mu7] + LCD[mu1, \ -mu2, mu5, mu8]*MTD[mu3, mu4]*MTD[mu6, mu7] - LCD[mu1, mu2, mu4, \ -mu5]*MTD[mu3, mu8]*MTD[mu6, mu7] + LCD[mu1, mu2, mu3, mu5]*MTD[mu4, \ -mu8]*MTD[mu6, mu7] - LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu2]*MTD[mu6, \ -mu8] + LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu3]*MTD[mu6, mu8] - LCD[mu2, \ -mu3, mu5, mu7]*MTD[mu1, mu4]*MTD[mu6, mu8] + LCD[mu2, mu3, mu4, \ -mu5]*MTD[mu1, mu7]*MTD[mu6, mu8] - LCD[mu1, mu4, mu5, mu7]*MTD[mu2, \ -mu3]*MTD[mu6, mu8] + LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu4]*MTD[mu6, \ -mu8] - LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu7]*MTD[mu6, mu8] - LCD[mu1, \ -mu2, mu5, mu7]*MTD[mu3, mu4]*MTD[mu6, mu8] + LCD[mu1, mu2, mu4, \ -mu5]*MTD[mu3, mu7]*MTD[mu6, mu8] - LCD[mu1, mu2, mu3, mu5]*MTD[mu4, \ -mu7]*MTD[mu6, mu8] + LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2]*MTD[mu7, \ -mu8] - LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3]*MTD[mu7, mu8] + LCD[mu2, \ -mu3, mu5, mu6]*MTD[mu1, mu4]*MTD[mu7, mu8] - LCD[mu2, mu3, mu4, \ -mu5]*MTD[mu1, mu6]*MTD[mu7, mu8] + LCD[mu1, mu4, mu5, mu6]*MTD[mu2, \ -mu3]*MTD[mu7, mu8] - LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4]*MTD[mu7, \ -mu8] + LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu6]*MTD[mu7, mu8] + LCD[mu1, \ -mu2, mu5, mu6]*MTD[mu3, mu4]*MTD[mu7, mu8] - LCD[mu1, mu2, mu4, \ -mu5]*MTD[mu3, mu6]*MTD[mu7, mu8] + LCD[mu1, mu2, mu3, mu5]*MTD[mu4, \ -mu6]*MTD[mu7, mu8])"}, +"4*(I*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu3] - I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu3] - I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu3] + I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu3] - I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu3] - I*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu4] + I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu4] + I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu4] - I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu4] + I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu4] + I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu5] - I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu5] - I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu6]*MTD[mu2, mu5] + I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu2, mu5] - I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu8]*MTD[mu2, mu5] + I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu3]*MTD[mu2, mu6] - I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu4]*MTD[mu2, mu6] + I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu5]*MTD[mu2, mu6] + I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu2, mu6] - I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu2, mu6] - I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu2, mu7] + I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu2, mu7] - I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu5]*MTD[mu2, mu7] - I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu6]*MTD[mu2, mu7] + I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu2, mu7] + I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu2, mu8] - I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu2, mu8] + I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu5]*MTD[mu2, mu8] + I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu6]*MTD[mu2, mu8] - I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu7]*MTD[mu2, mu8] + I*LCD[mu5, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu4] - I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu4] - I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu4] + I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, mu4] - I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu8]*MTD[mu3, mu4] + I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu5]*MTD[mu3, mu4] + I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, mu4] - I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, mu4] + I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu8]*MTD[mu3, mu4] - I*LCD[mu4, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu5] + I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu4]*MTD[mu3, mu5] + I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu6]*MTD[mu3, mu5] - I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu7]*MTD[mu3, mu5] + I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu8]*MTD[mu3, mu5] - I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu5] - I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu6]*MTD[mu3, mu5] + I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu7]*MTD[mu3, mu5] - I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu8]*MTD[mu3, mu5] - I*LCD[mu4, mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu3, mu6] + I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu4]*MTD[mu3, mu6] - I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu5]*MTD[mu3, mu6] - I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu7]*MTD[mu3, mu6] + I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu8]*MTD[mu3, mu6] - I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu4]*MTD[mu3, mu6] + I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu5]*MTD[mu3, mu6] + I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu7]*MTD[mu3, mu6] - I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu8]*MTD[mu3, mu6] + I*LCD[mu4, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu3, mu7] - I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu4]*MTD[mu3, mu7] + I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu5]*MTD[mu3, mu7] + I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu6]*MTD[mu3, mu7] - I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu8]*MTD[mu3, mu7] + I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu4]*MTD[mu3, mu7] - I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu5]*MTD[mu3, mu7] - I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu6]*MTD[mu3, mu7] + I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu8]*MTD[mu3, mu7] - I*LCD[mu4, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu3, mu8] + I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu4]*MTD[mu3, mu8] - I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu5]*MTD[mu3, mu8] - I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu6]*MTD[mu3, mu8] + I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu7]*MTD[mu3, mu8] - I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu4]*MTD[mu3, mu8] + I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu5]*MTD[mu3, mu8] + I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu6]*MTD[mu3, mu8] - I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu7]*MTD[mu3, mu8] + I*LCD[mu3, mu6, mu7, mu8]*MTD[mu1, mu2]*MTD[mu4, mu5] - I*LCD[mu2, mu6, mu7, mu8]*MTD[mu1, mu3]*MTD[mu4, mu5] - I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu6]*MTD[mu4, mu5] + I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu7]*MTD[mu4, mu5] - I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu8]*MTD[mu4, mu5] + I*LCD[mu1, mu6, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu5] + I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu6]*MTD[mu4, mu5] - I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu7]*MTD[mu4, mu5] + I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu8]*MTD[mu4, mu5] - I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu6]*MTD[mu4, mu5] + I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu7]*MTD[mu4, mu5] - I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu8]*MTD[mu4, mu5] + I*LCD[mu3, mu5, mu7, mu8]*MTD[mu1, mu2]*MTD[mu4, mu6] - I*LCD[mu2, mu5, mu7, mu8]*MTD[mu1, mu3]*MTD[mu4, mu6] + I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu5]*MTD[mu4, mu6] + I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu7]*MTD[mu4, mu6] - I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu8]*MTD[mu4, mu6] + I*LCD[mu1, mu5, mu7, mu8]*MTD[mu2, mu3]*MTD[mu4, mu6] - I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu5]*MTD[mu4, mu6] - I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu7]*MTD[mu4, mu6] + I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu8]*MTD[mu4, mu6] + I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu5]*MTD[mu4, mu6] + I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu7]*MTD[mu4, mu6] - I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu8]*MTD[mu4, mu6] - I*LCD[mu3, mu5, mu6, mu8]*MTD[mu1, mu2]*MTD[mu4, mu7] + I*LCD[mu2, mu5, mu6, mu8]*MTD[mu1, mu3]*MTD[mu4, mu7] - I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu5]*MTD[mu4, mu7] - I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu6]*MTD[mu4, mu7] + I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu8]*MTD[mu4, mu7] - I*LCD[mu1, mu5, mu6, mu8]*MTD[mu2, mu3]*MTD[mu4, mu7] + I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu5]*MTD[mu4, mu7] + I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu6]*MTD[mu4, mu7] - I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu8]*MTD[mu4, mu7] - I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu5]*MTD[mu4, mu7] - I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu6]*MTD[mu4, mu7] + I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu8]*MTD[mu4, mu7] + I*LCD[mu3, mu5, mu6, mu7]*MTD[mu1, mu2]*MTD[mu4, mu8] - I*LCD[mu2, mu5, mu6, mu7]*MTD[mu1, mu3]*MTD[mu4, mu8] + I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu5]*MTD[mu4, mu8] + I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu6]*MTD[mu4, mu8] - I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu7]*MTD[mu4, mu8] + I*LCD[mu1, mu5, mu6, mu7]*MTD[mu2, mu3]*MTD[mu4, mu8] - I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu5]*MTD[mu4, mu8] - I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu6]*MTD[mu4, mu8] + I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu7]*MTD[mu4, mu8] + I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu5]*MTD[mu4, mu8] + I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu6]*MTD[mu4, mu8] - I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu7]*MTD[mu4, mu8] - I*LCD[mu3, mu4, mu7, mu8]*MTD[mu1, mu2]*MTD[mu5, mu6] + I*LCD[mu2, mu4, mu7, mu8]*MTD[mu1, mu3]*MTD[mu5, mu6] - I*LCD[mu2, mu3, mu7, mu8]*MTD[mu1, mu4]*MTD[mu5, mu6] - I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu7]*MTD[mu5, mu6] + I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu8]*MTD[mu5, mu6] - I*LCD[mu1, mu4, mu7, mu8]*MTD[mu2, mu3]*MTD[mu5, mu6] + I*LCD[mu1, mu3, mu7, mu8]*MTD[mu2, mu4]*MTD[mu5, mu6] + I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu7]*MTD[mu5, mu6] - I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu8]*MTD[mu5, mu6] - I*LCD[mu1, mu2, mu7, mu8]*MTD[mu3, mu4]*MTD[mu5, mu6] - I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu7]*MTD[mu5, mu6] + I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu8]*MTD[mu5, mu6] + I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu7]*MTD[mu5, mu6] - I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu8]*MTD[mu5, mu6] + I*LCD[mu3, mu4, mu6, mu8]*MTD[mu1, mu2]*MTD[mu5, mu7] - I*LCD[mu2, mu4, mu6, mu8]*MTD[mu1, mu3]*MTD[mu5, mu7] + I*LCD[mu2, mu3, mu6, mu8]*MTD[mu1, mu4]*MTD[mu5, mu7] + I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu6]*MTD[mu5, mu7] - I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu8]*MTD[mu5, mu7] + I*LCD[mu1, mu4, mu6, mu8]*MTD[mu2, mu3]*MTD[mu5, mu7] - I*LCD[mu1, mu3, mu6, mu8]*MTD[mu2, mu4]*MTD[mu5, mu7] - I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu6]*MTD[mu5, mu7] + I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu8]*MTD[mu5, mu7] + I*LCD[mu1, mu2, mu6, mu8]*MTD[mu3, mu4]*MTD[mu5, mu7] + I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu6]*MTD[mu5, mu7] - I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu8]*MTD[mu5, mu7] - I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu6]*MTD[mu5, mu7] + I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu8]*MTD[mu5, mu7] - I*LCD[mu3, mu4, mu6, mu7]*MTD[mu1, mu2]*MTD[mu5, mu8] + I*LCD[mu2, mu4, mu6, mu7]*MTD[mu1, mu3]*MTD[mu5, mu8] - I*LCD[mu2, mu3, mu6, mu7]*MTD[mu1, mu4]*MTD[mu5, mu8] - I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu6]*MTD[mu5, mu8] + I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu7]*MTD[mu5, mu8] - I*LCD[mu1, mu4, mu6, mu7]*MTD[mu2, mu3]*MTD[mu5, mu8] + I*LCD[mu1, mu3, mu6, mu7]*MTD[mu2, mu4]*MTD[mu5, mu8] + I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu6]*MTD[mu5, mu8] - I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu7]*MTD[mu5, mu8] - I*LCD[mu1, mu2, mu6, mu7]*MTD[mu3, mu4]*MTD[mu5, mu8] - I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu6]*MTD[mu5, mu8] + I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu7]*MTD[mu5, mu8] + I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu6]*MTD[mu5, mu8] - I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu7]*MTD[mu5, mu8] + I*LCD[mu3, mu4, mu5, mu8]*MTD[mu1, mu2]*MTD[mu6, mu7] - I*LCD[mu2, mu4, mu5, mu8]*MTD[mu1, mu3]*MTD[mu6, mu7] + I*LCD[mu2, mu3, mu5, mu8]*MTD[mu1, mu4]*MTD[mu6, mu7] - I*LCD[mu2, mu3, mu4, mu8]*MTD[mu1, mu5]*MTD[mu6, mu7] - I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu8]*MTD[mu6, mu7] + I*LCD[mu1, mu4, mu5, mu8]*MTD[mu2, mu3]*MTD[mu6, mu7] - I*LCD[mu1, mu3, mu5, mu8]*MTD[mu2, mu4]*MTD[mu6, mu7] + I*LCD[mu1, mu3, mu4, mu8]*MTD[mu2, mu5]*MTD[mu6, mu7] + I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu8]*MTD[mu6, mu7] + I*LCD[mu1, mu2, mu5, mu8]*MTD[mu3, mu4]*MTD[mu6, mu7] - I*LCD[mu1, mu2, mu4, mu8]*MTD[mu3, mu5]*MTD[mu6, mu7] - I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu8]*MTD[mu6, mu7] + I*LCD[mu1, mu2, mu3, mu8]*MTD[mu4, mu5]*MTD[mu6, mu7] + I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu8]*MTD[mu6, mu7] - I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu8]*MTD[mu6, mu7] - I*LCD[mu3, mu4, mu5, mu7]*MTD[mu1, mu2]*MTD[mu6, mu8] + I*LCD[mu2, mu4, mu5, mu7]*MTD[mu1, mu3]*MTD[mu6, mu8] - I*LCD[mu2, mu3, mu5, mu7]*MTD[mu1, mu4]*MTD[mu6, mu8] + I*LCD[mu2, mu3, mu4, mu7]*MTD[mu1, mu5]*MTD[mu6, mu8] + I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu7]*MTD[mu6, mu8] - I*LCD[mu1, mu4, mu5, mu7]*MTD[mu2, mu3]*MTD[mu6, mu8] + I*LCD[mu1, mu3, mu5, mu7]*MTD[mu2, mu4]*MTD[mu6, mu8] - I*LCD[mu1, mu3, mu4, mu7]*MTD[mu2, mu5]*MTD[mu6, mu8] - I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu7]*MTD[mu6, mu8] - I*LCD[mu1, mu2, mu5, mu7]*MTD[mu3, mu4]*MTD[mu6, mu8] + I*LCD[mu1, mu2, mu4, mu7]*MTD[mu3, mu5]*MTD[mu6, mu8] + I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu7]*MTD[mu6, mu8] - I*LCD[mu1, mu2, mu3, mu7]*MTD[mu4, mu5]*MTD[mu6, mu8] - I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu7]*MTD[mu6, mu8] + I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu7]*MTD[mu6, mu8] + I*LCD[mu3, mu4, mu5, mu6]*MTD[mu1, mu2]*MTD[mu7, mu8] - I*LCD[mu2, mu4, mu5, mu6]*MTD[mu1, mu3]*MTD[mu7, mu8] + I*LCD[mu2, mu3, mu5, mu6]*MTD[mu1, mu4]*MTD[mu7, mu8] - I*LCD[mu2, mu3, mu4, mu6]*MTD[mu1, mu5]*MTD[mu7, mu8] - I*LCD[mu2, mu3, mu4, mu5]*MTD[mu1, mu6]*MTD[mu7, mu8] + I*LCD[mu1, mu4, mu5, mu6]*MTD[mu2, mu3]*MTD[mu7, mu8] - I*LCD[mu1, mu3, mu5, mu6]*MTD[mu2, mu4]*MTD[mu7, mu8] + I*LCD[mu1, mu3, mu4, mu6]*MTD[mu2, mu5]*MTD[mu7, mu8] + I*LCD[mu1, mu3, mu4, mu5]*MTD[mu2, mu6]*MTD[mu7, mu8] + I*LCD[mu1, mu2, mu5, mu6]*MTD[mu3, mu4]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu4, mu6]*MTD[mu3, mu5]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu4, mu5]*MTD[mu3, mu6]*MTD[mu7, mu8] + I*LCD[mu1, mu2, mu3, mu6]*MTD[mu4, mu5]*MTD[mu7, mu8] + I*LCD[mu1, mu2, mu3, mu5]*MTD[mu4, mu6]*MTD[mu7, mu8] - I*LCD[mu1, mu2, mu3, mu4]*MTD[mu5, mu6]*MTD[mu7, mu8]) +"}, {"fcstDiracTrace-ID60", "FCSetDiracGammaScheme[\"NDR\"];\n DiracTrace[GS[p1 + p2 + p3] . GA[i1, i2, i3] . GA[5], DiracTraceEvaluate -> True, EpsExpand -> False, FCE -> True]", "4 I LC[i1, i2, i3][p1 + p2 + p3]"}, {"fcstDiracTrace-ID61", "FCSetDiracGammaScheme[\"BMHV\"];\n DiracTrace[(GA[5] . GAD[\[Mu]] . GAD[lor1] . GAD[lorb] . GAD[lor2] . @@ -500,5 +435,33 @@ GA[5] . GSD[p1] . (1 - GA[5]) . (1 - GSD[v]) . (1 - GSD[v]), DiracTraceEvaluate -> True, EpsContract -> True, FCE->True]", "(-4*(-3 + D)*(-2 + D)*(-1 + D)*SPD[p1, v])/3"}, {"fcstDiracTrace-ID65", "FCSetDiracGammaScheme[\"Larin\"];\n DiracTrace[ GSD[p1] . (1 - GA[5]) . (1 - GSD[v]) . (1 - GSD[v]) . GA[5], -DiracTraceEvaluate -> True, EpsContract -> True]", "(-4*(-3 + D)*(-2 + D)*(-1 + D)*Pair[Momentum[p1, D], Momentum[v, D]])/3"} +DiracTraceEvaluate -> True, EpsContract -> True]", "(-4*(-3 + D)*(-2 + D)*(-1 + D)*Pair[Momentum[p1, D], Momentum[v, D]])/3"}, +{"fcstDiracTrace-ID66", "FCSetDiracGammaScheme[\"Larin\"];\n +DiracTrace[GSD[p1] . GAD[i4] . GAD[i1, i2, i3] . GSD[p2] . GAD[5], +DiracTraceEvaluate -> True, FCE -> True] /. p1 | p2 -> p3 +", "4 I (LCD[i1, i2, i3, i4] SPD[p3, p3] - +2 FVD[p3, i4] LCD[i1, i2, i3][p3] + +2 FVD[p3, i3] LCD[i1, i2, i4][p3] - +2 FVD[p3, i2] LCD[i1, i3, i4][p3] + +2 FVD[p3, i1] LCD[i2, i3, i4][p3])"}, + +{"fcstDiracTrace-ID67", "FCSetDiracGammaScheme[\"Larin\"];\n +DiracTrace[GSD[p3] . GAD[i4] . GAD[i1, i2, i3] . GSD[p3] . GAD[5], +DiracTraceEvaluate -> True, FCE -> True] +", "4 I (LCD[i1, i2, i3, i4] SPD[p3, p3] - +2 FVD[p3, i4] LCD[i1, i2, i3][p3] + +2 FVD[p3, i3] LCD[i1, i2, i4][p3] - +2 FVD[p3, i2] LCD[i1, i3, i4][p3] + +2 FVD[p3, i1] LCD[i2, i3, i4][p3])"}, +{"fcstDiracTrace-ID68", "FCSetDiracGammaScheme[\"Larin\"];\n +Factor[DiracTrace[ +GSD[p1] . DiracSigma[GAD[bb], GAD[Lor1]] . GA[5] . GSD[p2] . + GA[5] . DiracSigma[GAD[bb], GAD[Lor1]], +DiracTraceEvaluate -> True, FCE -> True] /. p1 -> p2] +", "2/3 (-5 + D) (-4 + D) (-3 + D) (-2 + D) (-1 + D) SPD[p2, p2]"}, +{"fcstDiracTrace-ID69", "Factor[DiracTrace[ +GSD[p2] . DiracSigma[GAD[bb], GAD[Lor1]] . GA[5] . GSD[p2] . +GA[5] . DiracSigma[GAD[bb], GAD[Lor1]], DiracTraceEvaluate -> True, +FCE -> True]] +", "2/3 (-5 + D) (-4 + D) (-3 + D) (-2 + D) (-1 + D) SPD[p2, p2]"} });