(* algorithm to compute the derivatives, translated from maple *)

Clear[P];
Clear[Plower];
Clear[plower];
Clear[KK];
Clear[Klower];
Clear[xv];
Clear[yv];
Clear[rv];
Clear[MM];

app[a_][w_]:= w/.X[b__]:>X[a,b];

shuf[X[a_,b___],X[c_,d___]] := app[a][shuf[X[b],X[c,d]]] + app[c][shuf[X[a,b],X[d]]];
shuf[X[b___], X[]] := X[b];
shuf[X[], X[d___]] := X[d];

OmegaSh/:Times[a___, b_OmegaSh, c_OmegaSh, d___] := Times[a,(shuf[X@@b, X@@c]//Expand)/.X->OmegaSh,d]//Expand;
OmegaSh/:Power[b_OmegaSh,n_]/;n≥2:= (shuf[X@@b, X@@b]/.X->OmegaSh)b^(n-2)//Expand;

maxorder = 4;

tuple3 = Table[Tuples[Range[1,3], i], {i, 1, maxorder}];
tuple4 = Table[Tuples[Range[1,4], i], {i, 1, maxorder}];

epsilon1 = {{1, -1, 1, -1}, {1, -1, -1, 1}, {1, 1, -1, -1}};

Phi = Pi/4;

pp = {0,0,0,0};
pp[[1]] = Exp[I Phi];
pp[[2]] = -Exp[-I Phi];
pp[[3]] = -pp[[1]];
pp[[4]] = -pp[[2]];

pp  = ExpToTrig[pp];

Print[Dynamic[{i,j, k}]]

Block[{i, j, t},
For[i = 1, i ≤ maxorder, i++,
(*Print["computing order ", i, " integrals"];*)
For[j = 1, j ≤ 4^i, j++,
t = tuple4[[i]][[j]];
Set[alpha[t], (-1)^i MPL[
Table[1, i],
 Reverse[Ratios[Join[pp[[t]], {1}]]]
]];
];
];
]

SOmega = {};
 Block[{t, s, i, j},
SOmega =Reap[For[i = 1, i ≤ maxorder, i++,
Print["computing order ", i, " integrals"];
For[j = 1, j ≤ 3^i, j++,
t = tuple3[[i]][[j]];
s = tuple4[[i]];
om = Sum[Product[epsilon1[[t[[kk]],s[[k,kk]]]], {kk, 1, i}] * alpha[s[[k]]], {k, 1, 4^i}];
Sow[Omega@@t->om];
];
]][[2,1]];
]

xv[1,0] = 1/2*(1/lambda - lambda);
xv[2,0] = -1/2*Sin[Phi]*(1/lambda + lambda);
xv[3,0] = -1/2*Cos[Phi]*(1/lambda + lambda);

For[i = 1, i<=3, i++,
yv[i,0] = xv[i,0];
];

{xv[1,0],xv[2,0],xv[3,0]}//Expand//N

rv[0] = 1;

computey[n_] := Module[{i, k},
For[i=1, i <= 3, i++,
yv[i,n] = Sum[Binomial[n,k]*rv[n-k]*xv[i,k], {k, 0, n}]
];
];

prody[d_,t_,n_] := Module[{s, k, ii}, (
If[d == 1, Return[yv[t[[1]], n]]];
s = 0;
For[k = 0, k ≤ n, k++,
s += Binomial[n,k]*prody[d-1,t[[1;;d-1]], k]*yv[t[[d]], n-k]
];
Return[s];
)];

MM[1] = {{I, 0}, {0, -I}};
MM[2] = {{0, 1},{1,0}};
MM[3] = {{0, I}, {-I, 0}};

prodM[d_,t_] := Module[{},
If[d==1, Return[MM[t[[1]]]]];
Return[prodM[d-1, t[[1;;d-1]]]. MM[t[[d]]]];
];

P[0] = {{1, 0},{0, 1}};

computePlower[n_] := Module[{s1, s2,s3, s4,  i, j, t},
s1 = 0;
For[i = 2, i ≤ n, i++,
s2 = 0;
For[j = 1, j ≤ 3^i, j++,
t = tuple3[[i,j]];
s2 += prody[i, t, n-i]*prodM[i, t] * (Omega@@t);
];

s1 += s2*n!/(n-i)!;
];

s3 = 0;
For[i = 1, i <= 3, i++,
s4 = 0;
For[j = 1, j <= n-2, j++,
s4 += Binomial[n-1,j]*rv[n-1-j]*xv[i,j]*MM[i]*Omega[i];
];
s3 += s4;
];
Plower[n] = Expand[s1 + n*s3];
];

computeP[n_] := Module[{},
If[n==1, 
P[n] = Sum[xv[ii,0]*Omega[ii]*MM[ii], {ii, 1, 3}]//Expand;,
P[n] = Plower[n] + n*Sum[(rv[n-1]*xv[ii,0] + xv[ii,n-1])*Omega[ii]*MM[ii], {ii, 1, 3} ]//Expand;
];
];

computePlower[1];

computeP[1];

P[1]//Expand//N[#, 5]&//MatrixForm

computeplower[n_] := Module[{}, 
plower[n] = Expand[Plower[n][[2,1]] - Plower[n][[1,2]] + Sum[
Binomial[n,k]*(P[k][[1,1]]*P[n-k][[2,1]]-P[k][[1,2]]*P[n-k][[2,2]]), 
{k, 1, n-1}
]];
];

KK[0] = -1;

computeKlower[n_] := Module[{k},
Klower[n]=Expand[Cos[Phi]*(1/lambda+lambda)*(xv[2,n]+xv[3,n])+Sum[Binomial[n,k]*(yv[1,k]*yv[1,n-k]-yv[2,k]*yv[2,n-k]-yv[3,k]*yv[3,n-k]),{k, 1, n-1}]+2Sum[Binomial[n,k]*rv[k](xv[1,0]*xv[1,n-k]-xv[2,0]*xv[2,n-k]-xv[3,0]*xv[3,n-k]),{k, 1, n-1}]];
];

pos1[u_] := Sum[Coefficient[u, lambda, ii] lambda^ii, {ii, 1, Exponent[u, lambda]}];
neg[u_] := Sum[Coefficient[u, lambda, ii] lambda^ii, {ii, Exponent[u, lambda, Min], -1}];
star[u_] := Sum[Coefficient[u, lambda, ii]/ lambda^ii, {ii, Exponent[u, lambda, Min], Exponent[u, lambda]}];

computex[n_] := Module[{cpos,c0, reste},
computePlower[n+1];
computeplower[n+1];
cpos = Expand[(1/(2*Pi*(n+1)))*(star[neg[plower[n+1]]] - pos1[plower[n+1]])];
c0 = Expand[-cpos-plower[n+1]/(2*Pi*(n+1))/.lambda->I];
xv[3,n]=cpos+c0;
xv[2,n]=(-1)^n*xv[3,n];
computeP[n+1];
computeKlower[n];
xv[1,n] = PolynomialQuotient[Expand[lambda*Klower[n]],lambda^2-1, lambda];
reste = PolynomialRemainder[lambda *Klower[n], lambda^2-1, lambda];
rv[n] = 1/2 * Coefficient[reste, lambda, 1];
Print["verification: ", Coefficient[reste, lambda, 0]];
computey[n];
];

For[n = 1,n <= maxorder-1, n++,
computex[n];

Print["derivatives of order ", n];
Print["a^(",n,") = ",Short[xv[1,n]//N[#,20]&]];
Print["c^(",n,") = ",Short[xv[3,n]//N[#,20]&]];
Print["r^(",n,") = ",Short[rv[n]//N[#,20]&]];
];

bv = Sum[Coefficient[xv[2,kk], lambda, 0]t^kk/kk!, {kk, 0, maxorder-1}];

bv//N[#, 20]&;

rrv = Sum[rv[kk]*t^kk/kk!, {kk, 0, maxorder-1}];

area = 1 - 2*rrv*bv*Cos[Phi];

(* Extract original formula for ar_3 *)

ar3 = -Coefficient[area, t, 3]

(* only incolcwa Pi^-3, Pi^-2, Pi^-1 *)

ar3 - Coefficient[ar3, Pi, -3]/Pi^3 - Coefficient[ar3, Pi, -2]/Pi^2-Coefficient[ar3, Pi, -1]/Pi^1//Expand

(Coefficient[ar3, Pi, -3]/Pi^3//Factor)//Factor

coeffpi3 = %/.{x:Omega[1] Omega[2]-Omega[1,2]+Omega[2,1]:>((x/.Omega->OmegaSh)/.OmegaSh->Omega)}

(Coefficient[ar3, Pi, -2]/Pi^2//Factor)/.{x:Omega[1] Omega[2]-Omega[1,2]+Omega[2,1]:>((x/.Omega->OmegaSh)/.OmegaSh->Omega2)}

%/.Omega->OmegaSh

coeffpi2 = %/.OmegaSh|Omega2->Omega/. Omega[3,3,3]->Omega[3]^3/3!

coeffpi1 = (Coefficient[ar3, Pi, -1]/Pi//Factor)/.Omega->OmegaSh/.OmegaSh->Omega//Factor

(* Apply evaluations proven below *)

coeffpi3 + coeffpi2 + coeffpi1/.{
Omega[3]:> I π,
Omega[2,1] :> -I π Log[2],
Omega[2,2,3]:> ((I (π^3))/12),
Omega[3,1,1]:>-((I (π^3))/12)+(1/2) I π ((Log[2])^2),
Omega[2,1,1,1]:>(1/12) I (π^3) Log[2]-(1/6) I π ((Log[2])^3)-(1/4) I π Zeta[3],
Omega[2,1,3,3]:>(1/4) I (π^3) Log[2]-I π Zeta[3],
Omega[2,2,2,1]:>-(1/12) I (π^3) Log[2]+(1/4) I π Zeta[3],
Omega[3,1,2,3]:>-(1/4) I (π^3) Log[2]+(13/8) I π Zeta[3],
Omega[3,3,2,1]:>(1/6) I (π^3) Log[2]-(5/8) I π Zeta[3]
}//Simplify

(* --------- *)

(* --- parity theorem, Erik Panzer, taken from supplementary maple files of the paper ---*

mpl112 = "-(Mpl([1,1,2],[1/z1,1/z2,1/z3])+Mpl([1,1,2],[z1,z2,z3]))-Mpl([4],[z2])+Mpl([1,3],[z1,z2])-7/120*Pi^4-1/6*ln(-z2*z3)*Pi^2*Mpl([1],[z1])-1/2*ln(-z2*z3)*ln(-z3)^2*Mpl([1],[z1])-ln(-z2*z3)*Mpl([2],[z3])*Mpl([1],[z1])-1/2*ln(-z3)^2*Mpl([1],[z2])*Mpl([1],[z1])-Mpl([2],[z2])*ln(-z2*z3)*Mpl([1],[z1])+1/2*Mpl([1],[z2])*ln(-z2*z3)^2*Mpl([1],[z1])-Mpl([2,2],[z1*z2,z3])-Mpl([4],[z1*z2*z3])-Mpl([1,3],[z1,z2*z3])-ln(-z1*z2*z3)*(Mpl([3],[z1*z2])+Mpl([1,2],[z1,z2])-Mpl([1],[z1])*Mpl([2],[z2]))+1/2*ln(-z1*z2*z3)^2*(Mpl([2],[z1*z2])+Mpl([1,1],[z1,z2])-Mpl([1],[z1])*Mpl([1],[z2]))+1/2*ln(-z3)^2*(-Mpl([2],[z1*z2])-Mpl([1,1],[z1,z2])+Mpl([1],[z1])*Mpl([1],[z2]))-Mpl([2],[z1])*Mpl([2],[z2])-ln(-z1*z2*z3)*(Mpl([3],[z1*z2])+Mpl([2,1],[z1,z2])-Mpl([2],[z1])*Mpl([1],[z2]))-Mpl([3],[z1])*Mpl([1],[z2])+ln(-z1*z2*z3)*(-Mpl([3],[z2*z3])-Mpl([1,2],[z2,z3])+1/2*Mpl([1],[z2])*ln(-z2*z3)^2-Mpl([2],[z2])*ln(-z2*z3)+Mpl([3],[z2])-1/2*ln(-z3)^2*Mpl([1],[z2])+ln(-z2*z3)*(-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)+2*Mpl([3],[z3])+1/3*ln(-z3)*(ln(-z3)^2+Pi^2))+1/6*Pi^2*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))+1/2*ln(-z3)^2*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))+Mpl([2],[z3])*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))+3*Mpl([4],[z1*z2])+Mpl([2,2],[z1,z2])+Mpl([3,1],[z1,z2])+3*Mpl([4],[z2*z3])+2*Mpl([1,3],[z2,z3])-3*Mpl([4],[z3])-1/8*ln(-z3)^4+Mpl([2,2],[z2,z3])+1/3*ln(-z3)*Pi^2*Mpl([1],[z2])-1/3*ln(-z2*z3)^3*Mpl([1],[z2])+1/2*ln(-z2*z3)^2*Mpl([2],[z2])-1/3*Pi^2*(ln(-z2*z3)*Mpl([1],[z2])-Mpl([2],[z2]))+1/3*ln(-z3)^3*Mpl([1],[z2])+2*ln(-z2*z3)*(Mpl([3],[z3])+1/6*ln(-z3)*(ln(-z3)^2+Pi^2))-1/4*Pi^2*ln(-z3)^2+1/2*ln(-z3)^2*Mpl([2],[z2])-(1/2*ln(-z2*z3)^2+1/6*Pi^2)*(-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)-ln(-z2*z3)*(2*Mpl([3],[z3])+1/3*ln(-z3)*(ln(-z3)^2+Pi^2))";

mpl121 = "-(Mpl([1,2,1],[1/z1,1/z2,1/z3])+Mpl([1,2,1],[z1,z2,z3]))+3*Mpl([4],[z2])-2*Mpl([1,3],[z1,z2])+7/360*Pi^4+1/6*ln(-z2*z3)*Pi^2*Mpl([1],[z1])+1/2*ln(-z2*z3)*ln(-z3)^2*Mpl([1],[z1])+ln(-z2*z3)*Mpl([2],[z3])*Mpl([1],[z1])+Mpl([2],[z2])*ln(-z2*z3)*Mpl([1],[z1])-Mpl([4],[z1*z2*z3])-Mpl([1,3],[z1,z2*z3])+ln(-z1*z2*z3)*(Mpl([3],[z1*z2])+Mpl([1,2],[z1,z2])-Mpl([1],[z1])*Mpl([2],[z2]))+Mpl([2],[z1])*Mpl([2],[z2])-1/6*Pi^2*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))-1/2*ln(-z3)^2*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))-Mpl([2],[z3])*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))-3*Mpl([4],[z1*z2])-Mpl([2,2],[z1,z2])+3*Mpl([4],[z2*z3])+Mpl([4],[z3])+1/24*ln(-z3)^4+Mpl([2,2],[z2,z3])-1/2*ln(-z2*z3)^2*Mpl([2],[z2])+2*ln(-z2*z3)*(Mpl([3],[z3])+1/6*ln(-z3)*(ln(-z3)^2+Pi^2))+1/12*Pi^2*ln(-z3)^2+1/2*ln(-z3)^2*Mpl([2],[z2])+(1/2*ln(-z2*z3)^2+1/6*Pi^2)*(-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)-ln(-z2*z3)*(2*Mpl([3],[z3])+1/3*ln(-z3)*(ln(-z3)^2+Pi^2))-Mpl([3,1],[z1*z2,z3])+2*Mpl([3,1],[z2,z3])+1/3*ln(-z2*z3)*(ln(-z2*z3)^2+Pi^2)*(Mpl([1],[z3])+ln(-z3))+ln(-z1*z2*z3)*(-Mpl([3],[z2*z3])-Mpl([2,1],[z2,z3])+Mpl([2],[z2])*ln(-z2*z3)-2*Mpl([3],[z2])-ln(-z3)*Mpl([2],[z2])-(1/2*ln(-z2*z3)^2+1/6*Pi^2)*(Mpl([1],[z3])+ln(-z3))-ln(-z2*z3)*(-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)-Mpl([3],[z3])-1/6*ln(-z3)*(ln(-z3)^2+Pi^2))+1/2*ln(-z3)*(ln(-z1*z2*z3)^2*Mpl([1],[z1])-2*ln(-z1*z2*z3)*Mpl([2],[z1])+2*Mpl([3],[z1]))+1/2*Mpl([1],[z3])*(ln(-z1*z2*z3)^2*Mpl([1],[z1])-2*ln(-z1*z2*z3)*Mpl([2],[z1])+2*Mpl([3],[z1]))+ln(-z3)*(-Mpl([3],[z1*z2])-Mpl([1,2],[z1,z2])+Mpl([1],[z1])*Mpl([2],[z2]))+2*ln(-z3)*Mpl([3],[z2])-1/2*ln(-z2*z3)^2*ln(-z3)*Mpl([1],[z1])-1/2*ln(-z2*z3)^2*Mpl([1],[z3])*Mpl([1],[z1])-ln(-z3)*Mpl([2],[z2])*Mpl([1],[z1])";

mpl211 = "-(Mpl([2,1,1],[1/z1,1/z2,1/z3])+Mpl([2,1,1],[z1,z2,z3]))-Mpl([4],[z2])+7/360*Pi^4-Mpl([4],[z1*z2*z3])+Mpl([3],[z1])*Mpl([1],[z2])-3*Mpl([4],[z1*z2])-Mpl([2,2],[z1,z2])-2*Mpl([3,1],[z1,z2])-3*Mpl([4],[z2*z3])-Mpl([1,3],[z2,z3])+Mpl([4],[z3])+1/24*ln(-z3)^4-Mpl([2,2],[z2,z3])-1/6*ln(-z3)*Pi^2*Mpl([1],[z2])+1/6*ln(-z2*z3)^3*Mpl([1],[z2])+1/6*Pi^2*(ln(-z2*z3)*Mpl([1],[z2])-Mpl([2],[z2]))-1/6*ln(-z3)^3*Mpl([1],[z2])-2*ln(-z2*z3)*(Mpl([3],[z3])+1/6*ln(-z3)*(ln(-z3)^2+Pi^2))+1/12*Pi^2*ln(-z3)^2-1/2*ln(-z3)^2*Mpl([2],[z2])+ln(-z2*z3)*(2*Mpl([3],[z3])+1/3*ln(-z3)*(ln(-z3)^2+Pi^2))-Mpl([3,1],[z1*z2,z3])-Mpl([3,1],[z2,z3])-1/6*ln(-z2*z3)*(ln(-z2*z3)^2+Pi^2)*(Mpl([1],[z3])+ln(-z3))-ln(-z3)*Mpl([3],[z2])+ln(-z1*z2*z3)*Mpl([3],[z1*z2])+ln(-z1*z2*z3)*Mpl([2,1],[z1,z2])-ln(-z3)*Mpl([3],[z1])-Mpl([1],[z3])*Mpl([3],[z1])-ln(-z3)*Mpl([3],[z1*z2])-ln(-z3)*Mpl([2,1],[z1,z2])-(1/2*ln(-z1*z2*z3)^2+1/6*Pi^2)*(Mpl([2],[z2*z3])+Mpl([1,1],[z2,z3])-ln(-z2*z3)*Mpl([1],[z2])+Mpl([2],[z2])+ln(-z3)*Mpl([1],[z2])+ln(-z2*z3)*(Mpl([1],[z3])+ln(-z3))-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)-ln(-z1*z2*z3)*(-2*Mpl([3],[z2*z3])-Mpl([1,2],[z2,z3])+1/2*Mpl([1],[z2])*ln(-z2*z3)^2-Mpl([3],[z2])-1/2*ln(-z3)^2*Mpl([1],[z2])+Mpl([3],[z3])+1/6*ln(-z3)*(ln(-z3)^2+Pi^2)-Mpl([2,1],[z2,z3])-ln(-z3)*Mpl([2],[z2])-(1/2*ln(-z2*z3)^2+1/6*Pi^2)*(Mpl([1],[z3])+ln(-z3)))+Mpl([1],[z3])*(ln(-z1*z2*z3)*Mpl([2],[z1])-Mpl([3],[z1]))-Mpl([1],[z2])*(ln(-z1*z2*z3)*Mpl([2],[z1])-Mpl([3],[z1]))+ln(-z3)*(ln(-z1*z2*z3)*Mpl([2],[z1])-Mpl([3],[z1]))-Mpl([2,2],[z1,z2*z3])-ln(-z2*z3)*ln(-z3)*Mpl([2],[z1])-ln(-z2*z3)*Mpl([1],[z3])*Mpl([2],[z1])+ln(-z2*z3)*Mpl([1],[z2])*Mpl([2],[z1])";

mpl1111 = "-(Mpl([1,1,1,1],[1/z1,1/z2,1/z3,1/z4])-Mpl([1,1,1,1],[z1,z2,z3,z4]))-1/2*ln(-z4)^2*Mpl([1],[z3])*Mpl([1],[z2])+1/2*Mpl([1],[z3])*ln(-z3*z4)^2*Mpl([1],[z2])+1/6*ln(-z4)*Pi^2*Mpl([1],[z3])+1/6*ln(-z3*z4)*(ln(-z3*z4)^2+Pi^2)*(Mpl([1],[z4])+ln(-z4))-1/2*ln(-z3*z4)^2*ln(-z4)*Mpl([1],[z2])-1/2*ln(-z3*z4)^2*Mpl([1],[z4])*Mpl([1],[z2])-ln(-z4)*Mpl([2],[z3])*Mpl([1],[z2])-ln(-z3*z4)*ln(-z4)*Mpl([2],[z2])-ln(-z3*z4)*Mpl([1],[z4])*Mpl([2],[z2])+ln(-z3*z4)*Mpl([1],[z3])*Mpl([2],[z2])+Mpl([2,1,1],[z1*z2,z3,z4])+Mpl([2,2],[z1*z2,z3*z4])+Mpl([1,1,2],[z1,z2,z3*z4])+Mpl([4],[z1*z2*z3*z4])+Mpl([1,3],[z1,z2*z3*z4])+Mpl([3,1],[z1*z2*z3,z4])+Mpl([1,2,1],[z1,z2*z3,z4])-7/360*Pi^4+Mpl([2,2],[z1*z2,z3])+3*Mpl([4],[z1*z2*z3])+2*Mpl([1,3],[z1,z2*z3])+Mpl([1,2,1],[z1,z2,z3])+Mpl([1,1,2],[z1,z2,z3])+ln(-z2*z3*z4)*(-Mpl([3],[z3*z4])-Mpl([2,1],[z3,z4])+Mpl([2],[z3])*ln(-z3*z4)-2*Mpl([3],[z3])-ln(-z4)*Mpl([2],[z3])-(1/2*ln(-z3*z4)^2+1/6*Pi^2)*(Mpl([1],[z4])+ln(-z4))-ln(-z3*z4)*(-Mpl([2],[z4])-1/2*ln(-z4)^2-1/6*Pi^2)-Mpl([3],[z4])-1/6*ln(-z4)*(ln(-z4)^2+Pi^2))+1/2*ln(-z4)*(ln(-z2*z3*z4)^2*Mpl([1],[z2])-2*ln(-z2*z3*z4)*Mpl([2],[z2])+2*Mpl([3],[z2]))+1/2*Mpl([1],[z4])*(ln(-z2*z3*z4)^2*Mpl([1],[z2])-2*ln(-z2*z3*z4)*Mpl([2],[z2])+2*Mpl([3],[z2]))+ln(-z4)*(-Mpl([3],[z2*z3])-Mpl([1,2],[z2,z3])+Mpl([1],[z2])*Mpl([2],[z3]))+ln(-z4)*Mpl([3],[z3])+ln(-z2*z3*z4)*Mpl([3],[z2*z3])+ln(-z2*z3*z4)*Mpl([2,1],[z2,z3])-ln(-z4)*Mpl([3],[z2])-Mpl([1],[z4])*Mpl([3],[z2])-ln(-z4)*Mpl([3],[z2*z3])-ln(-z4)*Mpl([2,1],[z2,z3])-(1/2*ln(-z2*z3*z4)^2+1/6*Pi^2)*(Mpl([2],[z3*z4])+Mpl([1,1],[z3,z4])-ln(-z3*z4)*Mpl([1],[z3])+Mpl([2],[z3])+ln(-z4)*Mpl([1],[z3])+ln(-z3*z4)*(Mpl([1],[z4])+ln(-z4))-Mpl([2],[z4])-1/2*ln(-z4)^2-1/6*Pi^2)-ln(-z2*z3*z4)*(-2*Mpl([3],[z3*z4])-Mpl([1,2],[z3,z4])+1/2*Mpl([1],[z3])*ln(-z3*z4)^2-Mpl([3],[z3])-1/2*ln(-z4)^2*Mpl([1],[z3])+Mpl([3],[z4])+1/6*ln(-z4)*(ln(-z4)^2+Pi^2)-Mpl([2,1],[z3,z4])-ln(-z4)*Mpl([2],[z3])-(1/2*ln(-z3*z4)^2+1/6*Pi^2)*(Mpl([1],[z4])+ln(-z4)))+Mpl([1],[z4])*(ln(-z2*z3*z4)*Mpl([2],[z2])-Mpl([3],[z2]))-Mpl([1],[z3])*(ln(-z2*z3*z4)*Mpl([2],[z2])-Mpl([3],[z2]))+ln(-z4)*(ln(-z2*z3*z4)*Mpl([2],[z2])-Mpl([3],[z2]))+1/2*ln(-z2*z3*z4)^2*(Mpl([2],[z2*z3])+Mpl([1,1],[z2,z3])-Mpl([1],[z2])*Mpl([1],[z3]))+1/2*ln(-z4)^2*(-Mpl([2],[z2*z3])-Mpl([1,1],[z2,z3])+Mpl([1],[z2])*Mpl([1],[z3]))-ln(-z2*z3*z4)*(Mpl([3],[z2*z3])+Mpl([2,1],[z2,z3])-Mpl([2],[z2])*Mpl([1],[z3]))+ln(-z2*z3*z4)*(-Mpl([3],[z3*z4])-Mpl([1,2],[z3,z4])+1/2*Mpl([1],[z3])*ln(-z3*z4)^2-Mpl([2],[z3])*ln(-z3*z4)+Mpl([3],[z3])-1/2*ln(-z4)^2*Mpl([1],[z3])+ln(-z3*z4)*(-Mpl([2],[z4])-1/2*ln(-z4)^2-1/6*Pi^2)+2*Mpl([3],[z4])+1/3*ln(-z4)*(ln(-z4)^2+Pi^2))-1/6*ln(-z3*z4)^3*Mpl([1],[z3])-1/6*Pi^2*(ln(-z3*z4)*Mpl([1],[z3])-Mpl([2],[z3]))+1/6*ln(-z4)^3*Mpl([1],[z3])+2*ln(-z3*z4)*(Mpl([3],[z4])+1/6*ln(-z4)*(ln(-z4)^2+Pi^2))-1/12*Pi^2*ln(-z4)^2+1/2*ln(-z4)^2*Mpl([2],[z3])-ln(-z3*z4)*(2*Mpl([3],[z4])+1/3*ln(-z4)*(ln(-z4)^2+Pi^2))+ln(-z4)*Mpl([2],[z2*z3])*Mpl([1],[z1])+Mpl([1],[z4])*Mpl([2],[z2])*Mpl([1],[z1])+ln(-z4)*Mpl([2],[z2])*Mpl([1],[z1])-1/6*ln(-z2*z3*z4)*Pi^2*Mpl([1],[z1])-1/2*ln(-z2*z3*z4)*ln(-z4)^2*Mpl([1],[z1])-ln(-z2*z3*z4)*Mpl([2],[z4])*Mpl([1],[z1])+ln(-z2*z3*z4)*Mpl([2],[z3])*Mpl([1],[z1])+ln(-z2*z3*z4)*Mpl([1,1],[z3,z4])*Mpl([1],[z1])+ln(-z2*z3*z4)*Mpl([2],[z3*z4])*Mpl([1],[z1])-Mpl([2],[z2])*Mpl([1],[z3])*Mpl([1],[z1])+ln(-z4)*Mpl([1,1],[z2,z3])*Mpl([1],[z1])-ln(-z2*z3*z4)*Mpl([2],[z2*z3])*Mpl([1],[z1])-ln(-z2*z3*z4)*Mpl([1,1],[z2,z3])*Mpl([1],[z1])-ln(-z3*z4)*ln(-z4)*(-Mpl([2],[z1*z2])-Mpl([1,1],[z1,z2])+Mpl([1],[z1])*Mpl([1],[z2]))-ln(-z3*z4)*Mpl([1],[z4])*(-Mpl([2],[z1*z2])-Mpl([1,1],[z1,z2])+Mpl([1],[z1])*Mpl([1],[z2]))+ln(-z3*z4)*Mpl([1],[z3])*(-Mpl([2],[z1*z2])-Mpl([1,1],[z1,z2])+Mpl([1],[z1])*Mpl([1],[z2]))+ln(-z3*z4)*Mpl([1],[z3])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-ln(-z4)*Mpl([1],[z3])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-ln(-z3*z4)*Mpl([1],[z4])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-ln(-z3*z4)*ln(-z4)*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-3*Mpl([4],[z2*z3])-Mpl([1,3],[z2,z3])+Mpl([4],[z3])-Mpl([2,2],[z2,z3])+2*Mpl([3,1],[z1*z2,z3])+Mpl([2,1,1],[z1,z2,z3])-ln(-z1*z2*z3*z4)*(Mpl([3],[z1*z2*z3])+Mpl([1,2],[z1,z2*z3])-Mpl([1],[z1])*Mpl([2],[z2*z3]))-Mpl([2],[z1])*Mpl([1,1],[z2,z3])-Mpl([2],[z1])*Mpl([2],[z2*z3])-ln(-z4)*(-Mpl([2,1],[z1*z2,z3])-Mpl([1,1,1],[z1,z2,z3])+Mpl([1],[z1])*Mpl([1,1],[z2,z3]))-ln(-z4)*(-Mpl([3],[z1*z2*z3])-Mpl([1,2],[z1,z2*z3])+Mpl([1],[z1])*Mpl([2],[z2*z3]))-Mpl([1],[z4])*(-Mpl([3],[z1*z2])-Mpl([1,2],[z1,z2])+Mpl([1],[z1])*Mpl([2],[z2]))-ln(-z4)*(-Mpl([3],[z1*z2])-Mpl([1,2],[z1,z2])+Mpl([1],[z1])*Mpl([2],[z2]))+1/6*Pi^2*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))+1/2*ln(-z4)^2*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))+Mpl([2],[z4])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-Mpl([2],[z3])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-Mpl([1,1],[z3,z4])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))-Mpl([2],[z3*z4])*(ln(-z1*z2*z3*z4)*Mpl([1],[z1])-Mpl([2],[z1]))+Mpl([1],[z3])*(-Mpl([3],[z1*z2])-Mpl([1,2],[z1,z2])+Mpl([1],[z1])*Mpl([2],[z2]))-Mpl([1],[z3])*(-ln(-z1*z2*z3*z4)*(Mpl([2],[z1*z2])+Mpl([1,1],[z1,z2])-Mpl([1],[z1])*Mpl([1],[z2]))+Mpl([3],[z1*z2])+Mpl([2,1],[z1,z2])-Mpl([2],[z1])*Mpl([1],[z2]))+Mpl([1],[z4])*(-ln(-z1*z2*z3*z4)*(Mpl([2],[z1*z2])+Mpl([1,1],[z1,z2])-Mpl([1],[z1])*Mpl([1],[z2]))+Mpl([3],[z1*z2])+Mpl([2,1],[z1,z2])-Mpl([2],[z1])*Mpl([1],[z2]))+ln(-z4)*(-ln(-z1*z2*z3*z4)*(Mpl([2],[z1*z2])+Mpl([1,1],[z1,z2])-Mpl([1],[z1])*Mpl([1],[z2]))+Mpl([3],[z1*z2])+Mpl([2,1],[z1,z2])-Mpl([2],[z1])*Mpl([1],[z2]))+ln(-z1*z2*z3*z4)*(Mpl([2,1],[z2,z3])+2*Mpl([3],[z2*z3])+Mpl([1,2],[z2,z3])-Mpl([3],[z3])+1/2*Mpl([1],[z3])*ln(-z3*z4)^2-1/2*ln(-z4)^2*Mpl([1],[z3])+1/6*ln(-z4)*(ln(-z4)^2+Pi^2)-ln(-z4)*Mpl([2],[z3])-(1/2*ln(-z3*z4)^2+1/6*Pi^2)*(Mpl([1],[z4])+ln(-z4))+ln(-z2*z3*z4)*(Mpl([2],[z3*z4])+Mpl([1,1],[z3,z4])-ln(-z3*z4)*Mpl([1],[z3])+Mpl([2],[z3])+ln(-z4)*Mpl([1],[z3])+ln(-z3*z4)*(Mpl([1],[z4])+ln(-z4))-Mpl([2],[z4])-1/2*ln(-z4)^2-1/6*Pi^2)-ln(-z4)*(ln(-z2*z3*z4)*Mpl([1],[z2])-Mpl([2],[z2]))-Mpl([1],[z4])*(ln(-z2*z3*z4)*Mpl([1],[z2])-Mpl([2],[z2]))-ln(-z4)*(-Mpl([2],[z2*z3])-Mpl([1,1],[z2,z3])+Mpl([1],[z2])*Mpl([1],[z3]))-ln(-z2*z3*z4)*(Mpl([2],[z2*z3])+Mpl([1,1],[z2,z3])-Mpl([1],[z2])*Mpl([1],[z3]))-Mpl([2],[z2])*Mpl([1],[z3])-Mpl([2,1],[z3,z4])-2*Mpl([3],[z3*z4])-Mpl([1,2],[z3,z4])+Mpl([3],[z4])+Mpl([2,1],[z2*z3,z4])+Mpl([3],[z2*z3*z4])+Mpl([1,2],[z2,z3*z4])+Mpl([1,1,1],[z2,z3,z4])+ln(-z3*z4)*ln(-z4)*Mpl([1],[z2])+ln(-z3*z4)*Mpl([1],[z4])*Mpl([1],[z2])+ln(-z4)*Mpl([1],[z3])*Mpl([1],[z2])-ln(-z3*z4)*Mpl([1],[z3])*Mpl([1],[z2]))-ln(-z1*z2*z3*z4)*(Mpl([2,1],[z1*z2,z3])+Mpl([1,1,1],[z1,z2,z3])-Mpl([1],[z1])*Mpl([1,1],[z2,z3]))-Mpl([3,1],[z2,z3])+ln(-z2*z3*z4)*ln(-z4)*Mpl([1],[z3])*Mpl([1],[z1])+ln(-z2*z3*z4)*Mpl([1],[z2])*Mpl([1],[z3])*Mpl([1],[z1])-Mpl([1],[z4])*ln(-z2*z3*z4)*Mpl([1],[z2])*Mpl([1],[z1])-ln(-z2*z3*z4)*ln(-z3*z4)*Mpl([1],[z3])*Mpl([1],[z1])-ln(-z3*z4)*Mpl([1],[z3])*Mpl([1],[z2])*Mpl([1],[z1])-ln(-z4)*ln(-z2*z3*z4)*Mpl([1],[z2])*Mpl([1],[z1])+ln(-z2*z3*z4)*ln(-z3*z4)*ln(-z4)*Mpl([1],[z1])+ln(-z2*z3*z4)*ln(-z3*z4)*Mpl([1],[z4])*Mpl([1],[z1])+ln(-z3*z4)*ln(-z4)*Mpl([1],[z2])*Mpl([1],[z1])+ln(-z3*z4)*Mpl([1],[z4])*Mpl([1],[z2])*Mpl([1],[z1])-Mpl([2,1,1],[z2,z3,z4])-Mpl([2,2],[z2,z3*z4])-2*Mpl([3,1],[z2*z3,z4])+Mpl([3,1],[z3,z4])-Mpl([1,2,1],[z2,z3,z4])-2*Mpl([1,3],[z2,z3*z4])-Mpl([1,1,2],[z2,z3,z4])+3*Mpl([4],[z3*z4])+Mpl([1,3],[z3,z4])-Mpl([4],[z4])-1/24*ln(-z4)^4+Mpl([2,2],[z3,z4])-Mpl([2,2],[z2*z3,z4])-3*Mpl([4],[z2*z3*z4])+Mpl([2,2],[z1,z2*z3])";

mpl1="-(Mpl([1],[1/z1])-Mpl([1],[z1])) + (ln(-z1))";

mpl2="-(Mpl([2],[1/z1])+Mpl([2],[z1])) + (-1/2*ln(-z1)^2-1/6*Pi^2)";

mpl11="-(Mpl([1, 1],[1/z1, 1/z2])-Mpl([1, 1],[z1, z2])) + (Mpl([2],[z1*z2])-ln(-z1*z2)*Mpl([1],[z1])+Mpl([2],[z1])+ln(-z2)*Mpl([1],[z1])+ln(-z1*z2)*(Mpl([1],[z2])+ln(-z2))-Mpl([2],[z2])-1/2*ln(-z2)^2-1/6*Pi^2)";

mpl3="-(Mpl([3],[1/z1])-Mpl([3],[z1])) + (1/6*ln(-z1)*(ln(-z1)^2+Pi^2))";

mpl12="-(Mpl([1, 2],[1/z1, 1/z2])+Mpl([1, 2],[z1, z2])) + (-Mpl([3],[z1*z2])+1/2*Mpl([1],[z1])*ln(-z1*z2)^2-Mpl([2],[z1])*ln(-z1*z2)+Mpl([3],[z1])-1/2*ln(-z2)^2*Mpl([1],[z1])+ln(-z1*z2)*(-Mpl([2],[z2])-1/2*ln(-z2)^2-1/6*Pi^2)+2*Mpl([3],[z2])+1/3*ln(-z2)*(ln(-z2)^2+Pi^2))";

mpl21="-(Mpl([2, 1],[1/z1, 1/z2])+Mpl([2, 1],[z1, z2])) + (-Mpl([3],[z1*z2])+Mpl([2],[z1])*ln(-z1*z2)-2*Mpl([3],[z1])-ln(-z2)*Mpl([2],[z1])-(1/2*ln(-z1*z2)^2+1/6*Pi^2)*(Mpl([1],[z2])+ln(-z2))-ln(-z1*z2)*(-Mpl([2],[z2])-1/2*ln(-z2)^2-1/6*Pi^2)-Mpl([3],[z2])-1/6*ln(-z2)*(ln(-z2)^2+Pi^2))";

mpl111="-(Mpl([1, 1, 1],[1/z1, 1/z2, 1/z3])-Mpl([1, 1, 1],[z1, z2, z3])) + (Mpl([1, 2],[z1, z2])+2*Mpl([3],[z1*z2])-Mpl([3],[z2])+Mpl([2, 1],[z1*z2, z3])+Mpl([3],[z1*z2*z3])+Mpl([1, 2],[z1, z2*z3])+ln(-z1*z2*z3)*(Mpl([2],[z2*z3])+Mpl([1, 1],[z2, z3])-ln(-z2*z3)*Mpl([1],[z2])+Mpl([2],[z2])+ln(-z3)*Mpl([1],[z2])+ln(-z2*z3)*(Mpl([1],[z3])+ln(-z3))-Mpl([2],[z3])-1/2*ln(-z3)^2-1/6*Pi^2)-ln(-z3)*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))-Mpl([1],[z3])*(ln(-z1*z2*z3)*Mpl([1],[z1])-Mpl([2],[z1]))-ln(-z3)*(-Mpl([2],[z1*z2])-Mpl([1, 1],[z1, z2])+Mpl([1],[z1])*Mpl([1],[z2]))-ln(-z1*z2*z3)*(Mpl([2],[z1*z2])+Mpl([1, 1],[z1, z2])-Mpl([1],[z1])*Mpl([1],[z2]))-Mpl([2],[z1])*Mpl([1],[z2])+ln(-z2*z3)*ln(-z3)*Mpl([1],[z1])+ln(-z2*z3)*Mpl([1],[z3])*Mpl([1],[z1])+ln(-z3)*Mpl([1],[z2])*Mpl([1],[z1])-ln(-z2*z3)*Mpl([1],[z2])*Mpl([1],[z1])-Mpl([2, 1],[z2, z3])-2*Mpl([3],[z2*z3])-Mpl([1, 2],[z2, z3])+Mpl([3],[z3])+1/2*Mpl([1],[z2])*ln(-z2*z3)^2-1/2*ln(-z3)^2*Mpl([1],[z2])+1/6*ln(-z3)*(ln(-z3)^2+Pi^2)-ln(-z3)*Mpl([2],[z2])-(1/2*ln(-z2*z3)^2+1/6*Pi^2)*(Mpl([1],[z3])+ln(-z3))+Mpl([2, 1],[z1, z2]))";

mpl4="-(Mpl([4],[1/z1])+Mpl([4],[z1])) + (-1/24*ln(-z1)^4-1/12*Pi^2*ln(-z1)^2-7/360*Pi^4)";

mpl13="-(Mpl([1, 3],[1/z1, 1/z2])-Mpl([1, 3],[z1, z2])) + (Mpl([4],[z1*z2])-1/6*ln(-z1*z2)^3*Mpl([1],[z1])+1/2*ln(-z1*z2)^2*Mpl([2],[z1])-ln(-z1*z2)*Mpl([3],[z1])+Mpl([4],[z1])-1/6*Pi^2*(ln(-z1*z2)*Mpl([1],[z1])-Mpl([2],[z1]))+1/6*ln(-z2)^3*Mpl([1],[z1])+1/6*ln(-z2)*Pi^2*Mpl([1],[z1])+ln(-z1*z2)*(Mpl([3],[z2])+1/6*ln(-z2)*(ln(-z2)^2+Pi^2))-3*Mpl([4],[z2])-1/8*ln(-z2)^4-1/4*Pi^2*ln(-z2)^2-7/120*Pi^4)";

mpl22="-(Mpl([2, 2],[1/z1, 1/z2])-Mpl([2, 2],[z1, z2])) + (Mpl([4],[z1*z2])-1/2*ln(-z1*z2)^2*Mpl([2],[z1])+2*ln(-z1*z2)*Mpl([3],[z1])-3*Mpl([4],[z1])+1/2*ln(-z2)^2*Mpl([2],[z1])-(1/2*ln(-z1*z2)^2+1/6*Pi^2)*(-Mpl([2],[z2])-1/2*ln(-z2)^2-1/6*Pi^2)-ln(-z1*z2)*(2*Mpl([3],[z2])+1/3*ln(-z2)*(ln(-z2)^2+Pi^2))+3*Mpl([4],[z2])+1/8*ln(-z2)^4+1/4*Pi^2*ln(-z2)^2+7/120*Pi^4)";

mpl31="-(Mpl([3, 1],[1/z1, 1/z2])-Mpl([3, 1],[z1, z2])) + (-Mpl([4],[z2])-1/24*ln(-z2)^4-7/360*Pi^4+ln(-z1*z2)*(Mpl([3],[z2])+1/6*ln(-z2)*(ln(-z2)^2+Pi^2))+ln(-z2)*Mpl([3],[z1])-1/12*Pi^2*ln(-z2)^2+1/6*ln(-z1*z2)*(ln(-z1*z2)^2+Pi^2)*(Mpl([1],[z2])+ln(-z2))+(1/2*ln(-z1*z2)^2+1/6*Pi^2)*(-Mpl([2],[z2])-1/2*ln(-z2)^2-1/6*Pi^2)-ln(-z1*z2)*Mpl([3],[z1])+3*Mpl([4],[z1])+Mpl([4],[z1*z2]))";

expr1111 = ToExpression[StringReplace[mpl1111,{"["->"{","]"->"}"}], TraditionalForm];
expr211 = ToExpression[StringReplace[mpl211,{"["->"{","]"->"}"}], TraditionalForm];
expr121 = ToExpression[StringReplace[mpl121,{"["->"{","]"->"}"}], TraditionalForm];
expr112 = ToExpression[StringReplace[mpl112,{"["->"{","]"->"}"}], TraditionalForm];

expr2 = ToExpression[StringReplace[mpl2,{"["->"{","]"->"}"}], TraditionalForm];
expr11 = ToExpression[StringReplace[mpl11,{"["->"{","]"->"}"}], TraditionalForm];
expr3 = ToExpression[StringReplace[mpl3,{"["->"{","]"->"}"}], TraditionalForm];
expr12 = ToExpression[StringReplace[mpl12,{"["->"{","]"->"}"}], TraditionalForm];
expr21 = ToExpression[StringReplace[mpl21,{"["->"{","]"->"}"}], TraditionalForm];
expr111 = ToExpression[StringReplace[mpl111,{"["->"{","]"->"}"}], TraditionalForm];


expr4 = ToExpression[StringReplace[mpl4,{"["->"{","]"->"}"}], TraditionalForm];
expr31 = ToExpression[StringReplace[mpl31,{"["->"{","]"->"}"}], TraditionalForm];
expr22 = ToExpression[StringReplace[mpl22,{"["->"{","]"->"}"}], TraditionalForm];
expr13 = ToExpression[StringReplace[mpl13,{"["->"{","]"->"}"}], TraditionalForm];

expr1 = ToExpression[StringReplace[mpl1,{"["->"{","]"->"}"}], TraditionalForm];

(* --- stuffle regularisation, to make sense of limit MPL[(1,1,1}, {x, y, z}] as z -> 1 --- *)

Clear[mplSt];
Clear[mplSt2];
mplSt[p_, q_] := mplSt2[Transpose[p],Transpose[q]];
mplSt2[p_, q:{{a_,b_}}] := Sum[Mpli@@Transpose[Join[p[[1;;i]], q, p[[i+1;;All]]]], {i,0, Length[p]}] + Sum[Mpli@@Transpose[Join[p[[1;;i-1]], {{p[[i,1]] + a,p[[i,2]]*b}}, p[[i+1;;All]]]], {i, 1, Length[p]}]

Clear[mplReg];
mplReg[{1},{1}] = 0;
mplReg[{a___, b_},{c___,d_}]/;b=!= 1|| d =!= 1 := Mpl[{a,b},{c,d}];
mplReg[{a___,b:1...,1}, {c___,d:1..., 1}] :=mplReg[{a,b,1},{c,d,1}] = Expand[(Mpli[{a, b,1},{c,d,1}] -  1/(1+Min[Length[{b}],Length[{d}]]) (mplSt[{{a,b},{c,d}},{{1},{1}}]  - Mpli[{a,b},{c,d}]Mpli[{1},{1}])//Expand)/.{Mpli->mplReg}];

parity4 =(#/.x:Mpl[{1,1,1,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr1111/.{z1->a[[1]],z2->a[[2]],z3->a[[3]],z4->a[[4]]}]/.Mpl->mplReg)

/.x:Mpl[{1,1,2},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr112/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}]/.Mpl->mplReg)
/.x:Mpl[{1,2,1},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr121/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}]/.Mpl->mplReg)
/.x:Mpl[{2,1,1},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr211/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}]/.Mpl->mplReg)

/.x:Mpl[{3,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr31/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)
/.x:Mpl[{2,2},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr22/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)
/.x:Mpl[{1,3},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr13/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)

/.x:Mpl[{4},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr4/.{z1->a[[1]]}]/.Mpl->mplReg)//Expand)&;

red4 = (#/.x:Mpl[{1,1,2},a_]:>(x + If[a== 1/a, 1/2* expr112/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]},0 ]/.Mpl->mplReg)
/.x:Mpl[{1,2,1},a_]:>(x + If[a== 1/a, 1/2* expr121/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}, 0]/.Mpl->mplReg)
/.x:Mpl[{2,1,1},a_]:>(x + If[a== 1/a, 1/2* expr211/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}, 0]/.Mpl->mplReg)

/.x:Mpl[{4},a_]:>(x + If[a== 1/a, 1/2* expr4/.{z1->a[[1]]}, 0]/.Mpl->mplReg)//Expand)&;

parity3 = (#/.x:Mpl[{1,1,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr111/.{z1->a[[1]],z2->a[[2]],z3->a[[3]]}]/.Mpl->mplReg)
/.x:Mpl[{1,2},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr12/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)
/.x:Mpl[{2,1},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr21/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)
/.x:Mpl[{3},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr3/.{z1->a[[1]]}]/.Mpl->mplReg)//Expand)&;

red3 = (#/.x:Mpl[{1,2},a_]:>(x + If[a== 1/a, 1/2* expr12/.{z1->a[[1]],z2->a[[2]]},0 ]/.Mpl->mplReg)
/.x:Mpl[{2,1},a_]:>(x + If[a== 1/a, 1/2* expr21/.{z1->a[[1]],z2->a[[2]]}, 0]/.Mpl->mplReg)//Expand)&;

parity2 = (#/.x:Mpl[{1,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr11/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg)
/.x:Mpl[{2},a_]:>(x + If[OrderedQ[{a, 1/a}], 0, expr2/.{z1->a[[1]]}]/.Mpl->mplReg)//Expand)&;

red2 = (#/.x:Mpl[{2},a_]:>(x + If[a== 1/a, 1/2* expr2/.{z1->a[[1]]}, 0]/.Mpl->mplReg)//Expand)&;

parity1 =(#/.x:Mpl[{1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr1/.{z1->a[[1]]}]/.Mpl->mplReg)//Expand)&;

(* ---- *)

litog[inds_List, z_List] :=Join@@Table[{ (1/(Times@@z[[i0;;All]])), Sequence@@Table[0, inds[[i0]]-1]}, {i0, 1, Length[z]}];

IIxtoMPL[a_] := Module[{pos, rat}, (
pos = Position[Join[a,{1}], Except[0], 1,Heads->False]//Flatten;
rat = Ratios[Join[a,{1}][[pos]]];
Mpl[Differences[pos], rat]
)];

MplSt/:Times[a___, MplSt[p_,q_], MplSt[r_, s_], b___] := a (stX[{p, q}, {r, s}] /.Mpl->MplSt//Expand)b//Expand;
MplSt/:Power[MplSt[p_,q_],n_Integer]/;n≥2 := ( stX[{p,q},{p,q}]/.Mpl->MplSt//Expand) MplSt[p,q]^(n-2)//Expand;

appSt[a_,b_][expr_] := expr/.Mpl[{alpha___},{beta___}] :> Mpl[{a, alpha}, {b, beta}];
stX[{{a0_, a___}, {b0_, b___}}, {{c0_, c___}, {d0_, d___}}]:=(appSt[a0, b0]@stX[{{a}, {b}}, {{c0, c}, {d0, d}}]) + (appSt[c0, d0]@stX[{{a0,a}, {b0,b}}, {{ c}, {d}}]) + (appSt[a0 + c0, b0*d0]@stX[{{a}, {b}}, {{c}, {d}}]);
stX[{{},{}}, p_] := Mpl@@p;
stX[p_,{{},{}}] := Mpl@@p;

MplSh/:Times[a___, MplSh[p_,q_], MplSh[r_, s_], b___] := a( shX[litog[p, q],litog[ r, s]]/.IIx->IIxtoMPL/.Mpl->MplSh//Expand) b//Expand;
MplSh/:Power[MplSh[p_,q_],n_Integer]/;n≥2 := ( shX[litog[p, q],litog[p,q]]/.IIx->IIxtoMPL/.Mpl->MplSh//Expand) MplSh[p,q]^(n-2)//Expand;

appSh[a_][expr_] := expr/.IIx[{alpha___}]:>IIx[{a, alpha}];
shX[{a0_, a___}, {c0_, c___}]:=(appSh[a0]@shX[{a},{c0,c}]) + (appSh[c0]@shX[{a0,a},{c}])
shX[{},p_] := IIx[p];
shX[p_,{}] := IIx[p];

omega2mpl = (#/.SOmega/.MPL[a_,b_]:>Mpl[Reverse[a],Reverse[b]])&;

Mplev[{1},{-(1+I)/Sqrt[2]}] := -((I π)/8)-((Log[2])/4)-(1/2) Log[1+(Sqrt[2])];
Mplev[{1},{-(1-I)/Sqrt[2]}] := +((I π)/8)-((Log[2])/4)-(1/2) Log[1+(Sqrt[2])];

Mplev[{1},{(1-I)/Sqrt[2]}] := -((3 I π)/8)-((Log[2])/4)+(1/2) Log[1+(Sqrt[2])];
Mplev[{1},{(1+I)/Sqrt[2]}] := ((3 I π)/8)-((Log[2])/4)+(1/2) Log[1+(Sqrt[2])];

Mplev[{1},{-1}] := -Log[2];

Mplev[{1},{I}] := ((I π)/4)-((Log[2])/2);
Mplev[{1},{-I}] := -((I π)/4)-((Log[2])/2);

(* ---- *)

Mplev[{2},{1}] := Zeta[2];

Mplev[{2},{-1}]  := -(1/2)Zeta[2];

(Subscript[Omega, 3])

Omega[3]//omega2mpl

%/.Mpl->Mplev

OmegaEv[3] = %;

(Subscript[Omega, 2,1])

Omega[2,1]//omega2mpl

%//parity2

%/.Mpl->Mplev//Expand

OmegaEv[2,1] = %;

(Subscript[Omega, 2,2,3])

(* shuffle identity *)

MplSh[{1,1},{1,-1}] - MplSh[{1},{-1}]^2/2!

Mplev[{1,1},{1,-1}] = Mplev[{1},{-1}]^2/2!;

(* ---- *)

(* stuffle identtiy *)

id1 = Mpl[{1},{-1}]Mpl[{1},{-I}] - Mpl[{1,1},{-I,-1}] -Mpl[{1,1},{-1,-I}]- Mpl[{2},{I}];

id1/.Mpl->MplSt

Omega[2,2,3]//omega2mpl

%//parity3

%//red3

%//parity2

%//red2

% - 2 Pi I id1//Expand

%//parity2

%/.Mpl->Mplev//Expand

OmegaEv[2,2,3] = %;

(Subscript[Omega, 3,1,1])

(* --------- *)

Mpl[{1},{-I}] Mpl[{1},{I}]-Mpl[{1,1},{-1,-I}]-Mpl[{1,1},{-1,I}]/.Mpl->MplSh

(Mpl[{1},{-I}] Mpl[{1},{I}]-Mpl[{1,1},{-1,-I}]-Mpl[{1,1},{-1,I}])/2//parity2

Mplev[{1,1},{-1,-I}] := ((π^2)/8)-(1/2) I π Mpl[{1},{-1}]+(1/4) I π Mpl[{1},{I}]+(1/2) Mpl[{1},{-I}] Mpl[{1},{I}]+(1/2) Mpl[{2},{-1}]+Mpl[{2},{-I}]

Mplev[{1,1},{-1,I}]:= Mpl[{1},{-I}] Mpl[{1},{I}]-Mpl[{1,1},{-1,-I}]

Mpl[{1},{-1}] Mpl[{1},{-I}]-Mpl[{1,1},{-1,-I}]-Mpl[{1,1},{-I,-1}]- Mpl[{2},{I}]/.Mpl->MplSt

Mplev[{1,1},{-I,-1}]:= Mpl[{1},{-1}] Mpl[{1},{-I}]-Mpl[{1,1},{-1,-I}]- Mpl[{2},{I}]

(* ---- *)

Mpl[{1},{-((1+I)/(Sqrt[2]))}] Mpl[{1},{-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,-((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{I,-((1-I)/(Sqrt[2]))}]/.Mpl->MplSh

(Mpl[{1},{-((1+I)/(Sqrt[2]))}] Mpl[{1},{-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,-((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{I,-((1-I)/(Sqrt[2]))}])/2//parity2

Mplev[{1,1},{-I,-((1+I)/(Sqrt[2]))}] := ((π^2)/96)-(1/4) I π Mpl[{1},{I}]+(1/8) I π Mpl[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) Mpl[{1},{-((1+I)/(Sqrt[2]))}] Mpl[{1},{-((1-I)/(Sqrt[2]))}]-(1/2) Mpl[{2},{-I}]+Mpl[{2},{-((1+I)/(Sqrt[2]))}]

(* --------- *)

Mpl[{1},{((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{I,((1-I)/(Sqrt[2]))}]/.Mpl->MplSh

(Mpl[{1},{((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{I,((1-I)/(Sqrt[2]))}])/2//parity2

Mplev[{1,1},{-I,((1+I)/(Sqrt[2]))}]:= ((3 (π^2))/8)+(3/4) I π Mpl[{1},{I}]-(3/8) I π Mpl[{1},{((1-I)/(Sqrt[2]))}]+(1/2) Mpl[{1},{((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]-(1/2) Mpl[{2},{-I}]-Mpl[{2},{((1-I)/(Sqrt[2]))}]

(* --------- *)

1/2! ((Mpl[{1},{-((1+I)/(Sqrt[2]))}])^2)- Mpl[{1,1},{1,-((1+I)/(Sqrt[2]))}]/.Mpl->MplSh

Mplev[{1,1},{1,-((1+I)/(Sqrt[2]))}]:=1/2! ((Mpl[{1},{-((1+I)/(Sqrt[2]))}])^2)

(* --------- *)

(1/2) Mpl[{1},{-I}]^2-(1/2) Mpl[{2},{-1}]-Mpl[{1,1},{-I,-I}]/.Mpl->MplSt//Expand

Mplev[{1,1},{-I,-I}] := (1/2) ((Mpl[{1},{-I}])^2)-(1/2) Mpl[{2},{-1}]

(* --------- *)

1/2Mpl[{1},{1/I}]^2 - Mpl[{1,1},{1, -I}]/.Mpl->MplSh//Expand

Mplev[{1,1},{1, -I}] := 1/2! Mpl[{1},{1/I}]^2

(* --------- *)

Mpl[{1,1},{1,((1-I)/(Sqrt[2]))}] - 1/2! Mpl[{1},{((1-I)/(Sqrt[2]))}]^2

Mplev[{1,1},{1,((1-I)/(Sqrt[2]))}] := 1/2! Mpl[{1},{((1-I)/(Sqrt[2]))}]^2;

(* --------- *)

Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,((1-I)/(Sqrt[2]))}]/.Mpl->MplSh

(Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,((1-I)/(Sqrt[2]))}]/.x:Mpl[{1,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr11/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg))//Expand

rule1 = Mpl[{1,1},{-1,((1-I)/(Sqrt[2]))}] :> ((5 (π^2))/96)-I π Mpl[{1},{-1}]+(3/4) I π Mpl[{1},{-((1-I)/(Sqrt[2]))}]+Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1-I)/(Sqrt[2]))}]+Mpl[{2},{-1}]-Mpl[{2},{-((1-I)/(Sqrt[2]))}]+Mpl[{2},{((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,-((1+I)/(Sqrt[2]))}]

Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{I,((1+I)/(Sqrt[2]))}]/.Mpl->MplSh

(Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{I,((1+I)/(Sqrt[2]))}]/.x:Mpl[{1,1},a_]:>(x - If[OrderedQ[{a, 1/a}], 0, expr11/.{z1->a[[1]],z2->a[[2]]}]/.Mpl->mplReg))//Expand

rule2 = Mpl[{1,1},{-I,((1-I)/(Sqrt[2]))}]:> -((7 (π^2))/96)-(1/2) I π Mpl[{1},{I}]-(1/4) I π Mpl[{1},{((1+I)/(Sqrt[2]))}]+Mpl[{1},{-((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]+Mpl[{2},{I}]+Mpl[{2},{-((1-I)/(Sqrt[2]))}]-Mpl[{2},{((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-I,-((1-I)/(Sqrt[2]))}];

(* -- *)

Omega[3,1,1]//omega2mpl

%//parity3

%//red3

%//parity2

%//red2

%/.{rule1, rule2}//Expand

%//parity2

%//red2

%//.Mpl->Mplev//Expand

%/.Mplev->Mpl

%//parity2

OmegaEv[3,1,1] = %;

(Subscript[Omega, 2,1,1,1])

comb1 =-4 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+4 MplShi[{1},{-1}] ((MplShi[{1},{-I}])^2)-(4/3) ((MplShi[{1},{-I}])^3)+4 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]-2 ((MplShi[{1},{-I}])^2) MplShi[{1},{I}]-2 MplShi[{1},{-I}] ((MplShi[{1},{I}])^2)+4 MplShi[{1},{-I}] MplShi[{2},{-1}]-8 MplShi[{1},{-I}] MplShi[{2},{-I}]+2 MplShi[{1},{-I}] MplShi[{2},{I}]+4 MplShi[{1},{-I}] MplShi[{2},{1}]+2 MplShi[{1},{I}] MplShi[{2},{1}]+4 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]-4 MplShi[{1},{-1}] MplShi[{1,1},{-1,-I}]-4 MplShi[{1},{-I}] MplShi[{1,1},{-1,I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-I,-1}]+2 MplShi[{1},{I}] MplShi[{1,1},{-I,-1}]+4 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]-4 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]-10 MplShi[{1},{-I}] MplShi[{1,1},{I,-1}]-4 MplShi[{1},{I}] MplShi[{1,1},{I,-1}]+(1/3) ((MplSti[{1},{-1}])^3)+3 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]-2 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)+((MplSti[{1},{-I}])^2) MplSti[{1},{I}]+2 MplSti[{1},{-1}] ((MplSti[{1},{I}])^2)-2 MplSti[{1},{-I}] MplSti[{2},{-1}]-5 MplSti[{1},{I}] MplSti[{2},{-1}]-2 MplSti[{1},{-1}] MplSti[{2},{-I}]+2 MplSti[{1},{-I}] MplSti[{2},{-I}]-4 MplSti[{1},{I}] MplSti[{2},{-I}]-8 MplSti[{1},{-1}] MplSti[{2},{I}]-MplSti[{1},{-1}] MplSti[{2},{1}]+6 MplSti[{1},{-I}] MplSti[{2},{1}]-2 MplSti[{1},{I}] MplSti[{2},{1}]+2 MplSti[{1},{-1}] MplSti[{1,1},{-1,I}]-6 MplSti[{1},{-1}] MplSti[{1,1},{-I,-1}]+4 MplSti[{1},{-I}] MplSti[{1,1},{-I,-1}]-4 MplSti[{1},{I}] MplSti[{1,1},{I,-1}]+8 MplSti[{1},{I}] MplSti[{1,1},{1,-1}]+4 MplSti[{1},{-1}] MplSti[{1,1},{1,I}];

rhs1 = (comb1/.MplSti->MplSt/.MplShi->MplSh//Expand)/.MplSt|MplSh->Mpl

lhs1 = comb1/.MplSti|MplShi->Mpl

id2111wt3 = rhs1 - lhs1

Mpl[{1,1},{-1,-1}] - 1/2 Mpl[{1},{-1}]^2 + 1/2 Mpl[{2},{1}]/.Mpl->MplSt//Expand

Mplev[{1,1},{-1,-1}]:= -( - 1/2 Mpl[{1},{-1}]^2 + 1/2 Mpl[{2},{1}]);

(* --- *)

Mpl[{1},{((1+I)/(Sqrt[2]))}]Mpl[{1},{-((1+I)/(Sqrt[2]))}]-MplSh[{1,1},{-1,-((1+I)/(Sqrt[2]))}]-MplSh[{1,1},{-1,((1+I)/(Sqrt[2]))}]/.Mpl->MplSh

Mplev[{1,1},{-1,-((1+I)/(Sqrt[2]))}]:=Mpl[{1},{((1+I)/(Sqrt[2]))}]Mpl[{1},{-((1+I)/(Sqrt[2]))}]-Mpl[{1,1},{-1,((1+I)/(Sqrt[2]))}];

Mpl[{1,1},{-I,((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{I,-((1+I)/(Sqrt[2]))}]- Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1-I)/(Sqrt[2]))}]/.Mpl->MplSh

Mplev[{1,1},{-I,((1-I)/(Sqrt[2]))}]:=-(+Mpl[{1,1},{I,-((1+I)/(Sqrt[2]))}]- Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1-I)/(Sqrt[2]))}])

(* ---- *)

Mpl[{1},{I}]Mpl[{1},{-I}]/.Mpl->MplSt

Mpl[{2},{1}]+Mpl[{1,1},{-I,I}]+Mpl[{1,1},{I,-I}] - Mpl[{1},{I}]Mpl[{1},{-I}]/.Mpl->MplSt

-(Mpl[{2},{1}]+Mpl[{1,1},{-I,I}]+Mpl[{1,1},{I,-I}] - Mpl[{1},{I}]Mpl[{1},{-I}])/2//parity2

Mplev[{1,1},{-I,I}]:=-((7 (π^2))/24)+(1/2) I π Mpl[{1},{-I}]-(1/4) I π Mpl[{1},{I}]+(1/2) Mpl[{1},{-I}] Mpl[{1},{I}]-Mpl[{2},{-I}]

Mplev[{1,1},{I,-I}]:= -(Mpl[{2},{1}]+Mpl[{1,1},{-I,I}] - Mpl[{1},{I}]Mpl[{1},{-I}]);

(* ---- *)

(* distribution *)

Mplev[{3},{1}] := Zeta[3];

Mpl[{3},{1}] + Mpl[{3},{-1}] - 1/4 Mpl[{3},{1}]/.Mpl[{a_},{b_}]:>PolyLog[a,b]//FunctionExpand

Mplev[{3},{-1}] := -3/4Mpl[{3},{1}]

Mpl[{3},{I}] + Mpl[{3},{-I}] - 1/4 Mpl[{3},{-1}]/.Mpl[{a_},{b_}]:>PolyLog[a,b]//FunctionExpand

1/2(Mpl[{3},{I}] + Mpl[{3},{-I}] - 1/4 Mpl[{3},{-1}])//parity3

Mplev[{3},{-I}] := -(((I (π^3))/32)-(1/8) Mpl[{3},{-1}])

Mplev[{3},{I}] := -(-(1/4) Mpl[{3},{-1}]+ Mpl[{3},{-I}]);

Mpl[{3},{I}]//.Mpl->Mplev

(* --- *)

Omega[2,1,1,1]//omega2mpl

%//parity4;

%//red4;

%//parity3;

%//red3;

%//parity2;

%//red2;

% - (I Pi )id2111wt3//Expand

%//parity3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity2;

%//red2;

%

%/.Mpl->Mplev//Expand

OmegaEv[2,1,1,1] = %;

(Subscript[Omega, 2,1,3,3])

comb2 =-(2/3) ((MplShi[{1},{-1}])^3)+4 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+2 MplShi[{1},{-1}] ((MplShi[{1},{-I}])^2)-(4/3) ((MplShi[{1},{-I}])^3)+2 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]+8 MplShi[{1},{-1}] MplShi[{2},{-I}]+2 MplShi[{1},{-I}] MplShi[{2},{-I}]+6 MplShi[{1},{I}] MplShi[{2},{-I}]+2 MplShi[{1},{-1}] MplShi[{2},{I}]+3 MplShi[{1},{-1}] MplShi[{2},{1}]+2 MplShi[{1},{-I}] MplShi[{2},{1}]-8 MplShi[{1},{I}] MplShi[{2},{1}]-12 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]-12 MplShi[{1},{I}] MplShi[{1,1},{-1,-1}]+4 MplShi[{1},{-I}] MplShi[{1,1},{-1,I}]+2 MplShi[{1},{-1}] MplShi[{1,1},{-I,-1}]-6 MplShi[{1},{-I}] MplShi[{1,1},{-I,-1}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]+2 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]-8 MplShi[{1},{-I}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{I}] MplShi[{1,1},{-I,I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{I,-1}]-2 MplShi[{1},{I}] MplShi[{1,1},{I,-1}]+2 MplShi[{1},{-1}] MplShi[{1,1},{I,-I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{I,-I}]-2 MplShi[{1},{I}] MplShi[{1,1},{I,-I}]-(1/3) ((MplSti[{1},{-1}])^3)-3 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]+5 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)+(1/3) ((MplSti[{1},{-I}])^3)-2 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{I}]-3 ((MplSti[{1},{-I}])^2) MplSti[{1},{I}]+5 MplSti[{1},{-1}] ((MplSti[{1},{I}])^2)+MplSti[{1},{-I}] ((MplSti[{1},{I}])^2)-13 MplSti[{1},{-1}] MplSti[{2},{-1}]+2 MplSti[{1},{-I}] MplSti[{2},{-1}]-5 MplSti[{1},{I}] MplSti[{2},{-1}]-4 MplSti[{1},{-1}] MplSti[{2},{-I}]-12 MplSti[{1},{I}] MplSti[{2},{-I}]+10 MplSti[{1},{-1}] MplSti[{1,1},{-I,-1}]+6 MplSti[{1},{-I}] MplSti[{1,1},{-I,I}]+6 MplSti[{1},{-1}] MplSti[{1,1},{I,-1}]-8 MplSti[{1},{I}] MplSti[{1,1},{1,-1}]-4 MplSti[{1},{I}] MplSti[{1,1},{1,-I}]+4 MplSti[{1},{-I}] MplSti[{1,1},{1,I}];

lhs2 = (comb2)/.MplSti|MplShi->Mpl

rhs2 = (comb2/.{MplSti->MplSt,MplShi->MplSh}//Expand)/.MplSt|MplSh->Mpl

id2133wt3 = rhs2 - lhs2

(* === *)

Mpl[{3},{1}]+Mpl[{1,2},{-I,I}]+Mpl[{2,1},{I,-I}] - Mpl[{2},{I}]Mpl[{1},{-I}]/.Mpl->MplSt

Mplev[{1,2},{-I,I}]:= -(Mpl[{3},{1}]+Mpl[{2,1},{I,-I}] - Mpl[{2},{I}]Mpl[{1},{-I}])

Mpl[{3},{-1}]+Mpl[{1,2},{-I,-I}]+Mpl[{2,1},{-I,-I}] - Mpl[{2},{-I}]Mpl[{1},{-I}]/.Mpl->MplSt

Mplev[{1,2},{-I,-I}]:= -(Mpl[{3},{-1}]+Mpl[{2,1},{-I,-I}] - Mpl[{2},{-I}]Mpl[{1},{-I}]);

-Mpl[{1},{I}] Mpl[{2},{-1}]+Mpl[{1},{-1}] Mpl[{2},{I}]-Mpl[{2,1},{-I,-1}]+Mpl[{2,1},{I,I}]/.Mpl->MplSh

Mplev[{2,1},{-I,-1}]:=-Mpl[{1},{I}] Mpl[{2},{-1}]+Mpl[{1},{-1}] Mpl[{2},{I}]+Mpl[{2,1},{I,I}];

(* --- *)

2 Mpl[{1,2},{1,-I}]+Mpl[{2,1},{1,-I}] - Mpl[{2},{-I}]Mpl[{1},{-I}]/.Mpl->MplSh

Mplev[{2,1},{1,-I}]:=-(2 Mpl[{1,2},{1,-I}] - Mpl[{2},{-I}]Mpl[{1},{-I}]);

Mpl[{3},{-I}]+Mpl[{1,2},{1,-I}]+Mpl[{2,1},{-I,1}]- Mpl[{2},{-I}]Mpl[{1},{1}]/.Mpl->MplSt/.MplSt->Mpl

Mplev[{1,2},{1,-I}]:= -(Mpl[{3},{-I}]+Mpl[{2,1},{-I,1}]- Mpl[{2},{-I}]Mpl[{1},{1}]);

Mpl[{1},{1}] Mpl[{2},{-I}]-Mpl[{1},{-I}] Mpl[{2},{1}]-Mpl[{2,1},{-I,1}]+Mpl[{2,1},{I,-I}]/.Mpl->MplSh

Mplev[{2,1},{-I,1}] := Mpl[{1},{1}] Mpl[{2},{-I}]-Mpl[{1},{-I}] Mpl[{2},{1}]+Mpl[{2,1},{I,-I}]

(* --- *)

Omega[2,1,3,3]//omega2mpl

%//parity4;

%//red4;

%//parity3;

%//red3;

%//parity2;

%//red2;

% -  Pi I id2133wt3//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

OmegaEv[2,1,3,3] = %;

(Subscript[Omega, 2,2,2,1])

comb3 = (4/3) ((MplShi[{1},{-1}])^3)-2 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+2 MplShi[{1},{-1}] ((MplShi[{1},{-I}])^2)-6 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]-2 ((MplShi[{1},{-I}])^2) MplShi[{1},{I}]-2 MplShi[{1},{-I}] MplShi[{2},{-I}]-6 MplShi[{1},{I}] MplShi[{2},{-I}]-2 MplShi[{1},{-1}] MplShi[{2},{I}]-MplShi[{1},{-1}] MplShi[{2},{1}]+10 MplShi[{1},{-I}] MplShi[{2},{1}]+2 MplShi[{1},{I}] MplShi[{2},{1}]+12 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]+8 MplShi[{1},{I}] MplShi[{1,1},{-1,-1}]+4 MplShi[{1},{-1}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-I,-1}]+2 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]+10 MplShi[{1},{-I}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{I}] MplShi[{1,1},{-I,I}]-4 MplShi[{1},{-I}] MplShi[{1,1},{I,-1}]+6 MplShi[{1},{I}] MplShi[{1,1},{I,-1}]-2 MplShi[{1},{-1}] MplShi[{1,1},{I,-I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{I,-I}]-2 MplShi[{1},{I}] MplShi[{1,1},{I,-I}]-(1/3) ((MplSti[{1},{-1}])^3)+3 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]-5 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)+2 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{I}]-3 MplSti[{1},{-1}] ((MplSti[{1},{I}])^2)+MplSti[{1},{-I}] ((MplSti[{1},{I}])^2)+9 MplSti[{1},{-1}] MplSti[{2},{-1}]-MplSti[{1},{-I}] MplSti[{2},{-1}]-2 MplSti[{1},{I}] MplSti[{2},{-I}]+4 MplSti[{1},{-I}] MplSti[{2},{I}]-8 MplSti[{1},{-1}] MplSti[{1,1},{-I,-1}]+2 MplSti[{1},{-I}] MplSti[{1,1},{-I,-1}]-4 MplSti[{1},{-I}] MplSti[{1,1},{-I,I}]-4 MplSti[{1},{-1}] MplSti[{1,1},{I,-1}]-2 MplSti[{1},{I}] MplSti[{1,1},{I,-1}]+4 MplSti[{1},{I}] MplSti[{1,1},{1,-1}]-4 MplSti[{1},{I}] MplSti[{1,1},{1,-I}]+4 MplSti[{1},{-I}] MplSti[{1,1},{1,I}];

rhs3 = (comb3/.{MplSti->MplSt,MplShi->MplSh}//Expand)/.MplSt|MplSh->Mpl

lhs3= comb3/.MplSti|MplShi->Mpl

id2221wt3 = rhs3 - lhs3

(* -- *)

Mpl[{4},{-1}]+Mpl[{1,3},{-1,1}]+Mpl[{3,1},{1,-1}]- Mpl[{1},{-1}]Mpl[{3},{1}]/.Mpl->MplSt

Mplev[{1,3},{-1,1}]:=-(Mpl[{4},{-1}]+Mpl[{3,1},{1,-1}]- Mpl[{1},{-1}]Mpl[{3},{1}])

(* ---- *)

-Mpl[{1},{I}] Mpl[{2},{-I}]+Mpl[{1},{-I}] Mpl[{2},{I}]-Mpl[{2,1},{-1,-I}]+Mpl[{2,1},{-1,I}]/.Mpl->MplSh

(-Mpl[{1},{I}] Mpl[{2},{-I}]+Mpl[{1},{-I}] Mpl[{2},{I}]-Mpl[{2,1},{-1,-I}]+Mpl[{2,1},{-1,I}])/2//parity3

Mplev[{2,1},{-1,-I}]:= ((I (π^3))/48)-(1/48) (π^2) Mpl[{1},{I}]+(1/2) I π Mpl[{2},{-1}]-(1/2) Mpl[{1},{I}] Mpl[{2},{-I}]+(1/4) I π Mpl[{2},{I}]+(1/2) Mpl[{1},{-I}] Mpl[{2},{I}]-Mpl[{3},{-1}]-Mpl[{3},{-I}]

(* --- *)

Mplev[{4},{1}] := Zeta[4];

PolyLog[4,1] + PolyLog[4,-1] - 1/8 PolyLog[4,1]//FunctionExpand

Mplev[{4},{-1}] := -7/8 Mpl[{4},{1}];

(* --- *)

Omega[2,2,2,1]//omega2mpl

%//parity4;

%//red4;

%//parity3;

%//red3;

%//parity2;

%//red2;

%  - Pi I id2221wt3//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity3

%//red3

%//parity2

%//red2

%//.Mpl->Mplev//Expand

OmegaEv[2,2,2,1] = %;

(Subscript[Omega, 3,1,2,3])

comb4 = -(2/3) ((MplShi[{1},{-1}])^3)-2 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+(2/3) ((MplShi[{1},{-I}])^3)+4 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]+2 ((MplShi[{1},{-I}])^2) MplShi[{1},{I}]+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-((1+I)/(Sqrt[2]))}] ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-3 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1+I)/(Sqrt[2]))}])^2)+(21/2) MplShi[{1},{-I}] MplShi[{2},{-1}]-7 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]-7 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]-16 MplShi[{1},{-1}] MplShi[{2},{-I}]+4 MplShi[{1},{-I}] MplShi[{2},{-I}]+(5/2) MplShi[{1},{I}] MplShi[{2},{-I}]-(15/2) MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]-(19/2) MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]+3 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-I}]-5 MplShi[{1},{-I}] MplShi[{2},{1}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+18 MplShi[{1},{-1}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]-(7/2) MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+9 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+18 MplShi[{1},{-1}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+8 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+17 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]-(19/2) MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]+2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-I,-I}]-9 MplShi[{1},{I}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-16 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]-6 MplShi[{1},{-I}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]+6 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]+6 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-3 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-(1/3) ((MplSti[{1},{-1}])^3)-3 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]+6 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)-(1/6) ((MplSti[{1},{-I}])^3)+8 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{I}]+((MplSti[{1},{-1}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^3)+((MplSti[{1},{-1}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-MplSti[{1},{-((1-I)/(Sqrt[2]))}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^3)-6 MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1+I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]+MplSti[{1},{-1}] MplSti[{2},{-I}]-(19/2) MplSti[{1},{-I}] MplSti[{2},{-I}]+9 MplSti[{1},{I}] MplSti[{2},{-I}]+3 MplSti[{1},{-I}] MplSti[{2},{1}]-3 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-3 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-6 MplSti[{1},{-1}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+MplSti[{1},{-I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+(11/2) MplSti[{1},{I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+7 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-1}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+(17/2) MplSti[{1},{I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-5 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+8 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{I}] MplSti[{1,1},{-I,-1}]+2 MplSti[{1},{-I}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]+4 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-I}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),I}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-I}]-14 par[{1,2},{-1,-1}]-(11/2) par[{1,2},{-1,-I}]+(41/2) par[{1,2},{-1,-((1-I)/(Sqrt[2]))}]+13 par[{1,2},{-1,((1-I)/(Sqrt[2]))}]-(21/2) par[{1,2},{-I,-1}]+11 par[{1,2},{-I,-I}]+8 par[{1,2},{-I,I}]+(3/2) par[{1,2},{-I,-((1+I)/(Sqrt[2]))}]+12 par[{1,2},{-I,-((1-I)/(Sqrt[2]))}]+3 par[{1,2},{-I,((1-I)/(Sqrt[2]))}]-(7/2) par[{1,2},{-I,((1+I)/(Sqrt[2]))}]+2 par[{1,2},{1,-1}]+4 par[{1,2},{1,-I}]-2 par[{1,2},{1,-((1-I)/(Sqrt[2]))}]-2 par[{1,2},{1,((1-I)/(Sqrt[2]))}]+(17/2) par[{1,2},{-((1-I)/(Sqrt[2])),-1}]+par[{1,2},{-((1-I)/(Sqrt[2])),-I}]-(15/2) par[{1,2},{-((1-I)/(Sqrt[2])),I}]-(3/2) par[{1,2},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+par[{1,2},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-par[{1,2},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(5/2) par[{1,2},{((1-I)/(Sqrt[2])),-1}]+par[{1,2},{((1-I)/(Sqrt[2])),-I}]-(19/2) par[{1,2},{((1-I)/(Sqrt[2])),I}]-3 par[{1,2},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{1,2},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-10 par[{1,2},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-4 par[{2,1},{-1,-1}]-(5/2) par[{2,1},{-1,-I}]+(39/2) par[{2,1},{-1,-((1-I)/(Sqrt[2]))}]+6 par[{2,1},{-1,((1-I)/(Sqrt[2]))}]-23 par[{2,1},{-I,-1}]+30 par[{2,1},{-I,-I}]+3 par[{2,1},{-I,I}]+(7/2) par[{2,1},{-I,-((1+I)/(Sqrt[2]))}]+3 par[{2,1},{-I,-((1-I)/(Sqrt[2]))}]-7 par[{2,1},{-I,((1-I)/(Sqrt[2]))}]-(5/2) par[{2,1},{-I,((1+I)/(Sqrt[2]))}]+(9/2) par[{2,1},{1,-1}]+2 par[{2,1},{1,-I}]-4 par[{2,1},{1,-((1-I)/(Sqrt[2]))}]+(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),-1}]+2 par[{2,1},{-((1-I)/(Sqrt[2])),-I}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),I}]-(19/2) par[{2,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{2,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(11/2) par[{2,1},{((1-I)/(Sqrt[2])),-1}]-2 par[{2,1},{((1-I)/(Sqrt[2])),I}]-21 par[{2,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{2,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{2,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 par[{2,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-1,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-1,-I,-1}]-16 par[{1,1,1},{-1,-I,-I}]+8 par[{1,1,1},{-1,-I,I}]-5 par[{1,1,1},{-1,-I,-((1+I)/(Sqrt[2]))}]+5 par[{1,1,1},{-1,-I,-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-1,-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{-1,-I,((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-1,1,-((1-I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-1,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),I}]-(9/2) par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,((1-I)/(Sqrt[2])),I}]-8 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-4 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{-I,-1,-I}]+3 par[{1,1,1},{-I,-1,I}]-2 par[{1,1,1},{-I,-1,-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-I,-1,((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,-I,-1}]+4 par[{1,1,1},{-I,-I,-I}]+2 par[{1,1,1},{-I,-I,-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-I,-I,((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,I,-1}]+2 par[{1,1,1},{-I,I,I}]+2 par[{1,1,1},{-I,I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,I,((1+I)/(Sqrt[2]))}]-4 par[{1,1,1},{-I,1,-1}]+2 par[{1,1,1},{-I,1,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,1,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,1,((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-1}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-I}]+2 par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-1}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{1,-1,-I}]-2 par[{1,1,1},{1,-1,-((1-I)/(Sqrt[2]))}]-2 par[{1,1,1},{1,-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{1,1,-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-1}]-par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]-3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,I}]-4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]+(3/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+(1/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-1}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1-I)/(Sqrt[2]))}]-3 par[{1,1,1},{((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]-8 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-1}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-I}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}];

comb4 = -(2/3) ((MplShi[{1},{-1}])^3)-2 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+(2/3) ((MplShi[{1},{-I}])^3)+4 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]+2 ((MplShi[{1},{-I}])^2) MplShi[{1},{I}]+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-((1+I)/(Sqrt[2]))}] ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-3 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1+I)/(Sqrt[2]))}])^2)+(21/2) MplShi[{1},{-I}] MplShi[{2},{-1}]-7 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]-7 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]-16 MplShi[{1},{-1}] MplShi[{2},{-I}]+7 MplShi[{1},{-I}] MplShi[{2},{-I}]+(5/2) MplShi[{1},{I}] MplShi[{2},{-I}]-(15/2) MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]-(19/2) MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]+3 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-I}]-2 MplShi[{1},{-I}] MplShi[{2},{1}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+18 MplShi[{1},{-1}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]-(7/2) MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+9 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+18 MplShi[{1},{-1}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+8 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+17 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]-(19/2) MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]+2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-I,-I}]-9 MplShi[{1},{I}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-16 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]-6 MplShi[{1},{-I}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]+6 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]+6 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-3 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-(1/3) ((MplSti[{1},{-1}])^3)-3 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]+6 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)-(1/6) ((MplSti[{1},{-I}])^3)+8 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{I}]+((MplSti[{1},{-1}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^3)+((MplSti[{1},{-1}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-MplSti[{1},{-((1-I)/(Sqrt[2]))}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^3)-6 MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1+I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]+MplSti[{1},{-1}] MplSti[{2},{-I}]-(19/2) MplSti[{1},{-I}] MplSti[{2},{-I}]+6 MplSti[{1},{I}] MplSti[{2},{-I}]-3 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-3 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-6 MplSti[{1},{-1}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+MplSti[{1},{-I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+(11/2) MplSti[{1},{I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+7 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-1}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+(17/2) MplSti[{1},{I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-5 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+8 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{I}] MplSti[{1,1},{-I,-1}]+2 MplSti[{1},{-I}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]+4 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-I}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),I}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-I}]-14 par[{1,2},{-1,-1}]-(11/2) par[{1,2},{-1,-I}]+(41/2) par[{1,2},{-1,-((1-I)/(Sqrt[2]))}]+13 par[{1,2},{-1,((1-I)/(Sqrt[2]))}]-(21/2) par[{1,2},{-I,-1}]+11 par[{1,2},{-I,-I}]+8 par[{1,2},{-I,I}]+(3/2) par[{1,2},{-I,-((1+I)/(Sqrt[2]))}]+12 par[{1,2},{-I,-((1-I)/(Sqrt[2]))}]+3 par[{1,2},{-I,((1-I)/(Sqrt[2]))}]-(7/2) par[{1,2},{-I,((1+I)/(Sqrt[2]))}]+2 par[{1,2},{1,-1}]+4 par[{1,2},{1,-I}]-2 par[{1,2},{1,-((1-I)/(Sqrt[2]))}]-2 par[{1,2},{1,((1-I)/(Sqrt[2]))}]+(17/2) par[{1,2},{-((1-I)/(Sqrt[2])),-1}]+par[{1,2},{-((1-I)/(Sqrt[2])),-I}]-(15/2) par[{1,2},{-((1-I)/(Sqrt[2])),I}]-(3/2) par[{1,2},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+par[{1,2},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-par[{1,2},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(5/2) par[{1,2},{((1-I)/(Sqrt[2])),-1}]+par[{1,2},{((1-I)/(Sqrt[2])),-I}]-(19/2) par[{1,2},{((1-I)/(Sqrt[2])),I}]-3 par[{1,2},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{1,2},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-10 par[{1,2},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-4 par[{2,1},{-1,-1}]-(5/2) par[{2,1},{-1,-I}]+(39/2) par[{2,1},{-1,-((1-I)/(Sqrt[2]))}]+6 par[{2,1},{-1,((1-I)/(Sqrt[2]))}]-23 par[{2,1},{-I,-1}]+30 par[{2,1},{-I,-I}]+(7/2) par[{2,1},{-I,-((1+I)/(Sqrt[2]))}]+3 par[{2,1},{-I,-((1-I)/(Sqrt[2]))}]-7 par[{2,1},{-I,((1-I)/(Sqrt[2]))}]-(5/2) par[{2,1},{-I,((1+I)/(Sqrt[2]))}]+(9/2) par[{2,1},{1,-1}]+2 par[{2,1},{1,-I}]-4 par[{2,1},{1,-((1-I)/(Sqrt[2]))}]+(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),-1}]+2 par[{2,1},{-((1-I)/(Sqrt[2])),-I}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),I}]-(19/2) par[{2,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{2,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(11/2) par[{2,1},{((1-I)/(Sqrt[2])),-1}]-2 par[{2,1},{((1-I)/(Sqrt[2])),I}]-21 par[{2,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{2,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{2,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 par[{2,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-1,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-1,-I,-1}]-16 par[{1,1,1},{-1,-I,-I}]+8 par[{1,1,1},{-1,-I,I}]-5 par[{1,1,1},{-1,-I,-((1+I)/(Sqrt[2]))}]+5 par[{1,1,1},{-1,-I,-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-1,-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{-1,-I,((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-1,1,-((1-I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-1,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),I}]-(9/2) par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,((1-I)/(Sqrt[2])),I}]-8 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-4 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{-I,-1,-I}]+3 par[{1,1,1},{-I,-1,I}]-2 par[{1,1,1},{-I,-1,-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-I,-1,((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,-I,-1}]+4 par[{1,1,1},{-I,-I,-I}]+2 par[{1,1,1},{-I,-I,-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-I,-I,((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,I,-1}]+2 par[{1,1,1},{-I,I,I}]+2 par[{1,1,1},{-I,I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,I,((1+I)/(Sqrt[2]))}]-4 par[{1,1,1},{-I,1,-1}]+2 par[{1,1,1},{-I,1,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,1,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,1,((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-1}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-I}]+2 par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-1}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{1,-1,-I}]-2 par[{1,1,1},{1,-1,-((1-I)/(Sqrt[2]))}]-2 par[{1,1,1},{1,-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{1,1,-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-1}]-par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]-3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,I}]-4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]+(3/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+(1/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-1}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1-I)/(Sqrt[2]))}]-3 par[{1,1,1},{((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]-8 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-1}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-I}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}];

rhs4 = (comb4/.{MplSti->MplSt,MplShi->MplSh}//Expand)/.MplSh|MplSt->Mpl/.par[{1,1,1},{a_,b_,c_}]:> ((expr111/. {z1->a,z2->b,z3->c}/. Mpl->mplReg)//Expand)/.par[{2,1},{a_,b_}]:> ((expr21/. {z1->a,z2->b}/. Mpl->mplReg)//Expand)/.par[{1,2},{a_,b_}]:> ((expr12/. {z1->a,z2->b}/. Mpl->mplReg)//Expand);

lhs4 = (comb4/.MplSti|MplShi->Mpl)/.par->(0&);

id3123wt3 = rhs4 - lhs4//Expand;

(* ---- *)

(* distribution *)

Mpl[{3},{-((1+I)/(Sqrt[2]))}] + Mpl[{3},{((1+I)/(Sqrt[2]))}] -1/4Mpl[{3},{I}]  /.Mpl[{a_},{b_}]:>PolyLog[a,b]//FunctionExpand//Expand

Mplev[{3},{-((1+I)/(Sqrt[2]))}]:=-( + Mpl[{3},{((1+I)/(Sqrt[2]))}] -1/4Mpl[{3},{I}]  );

Mpl[{2},{-((1+I)/(Sqrt[2]))}] + Mpl[{2},{((1+I)/(Sqrt[2]))}] -1/2Mpl[{2},{I}]  /.Mpl[{a_},{b_}]:>PolyLog[a,b]//FunctionExpand//Expand

Mpl[{2},{-I}] + Mpl[{2},{I}] -1/2Mpl[{2},{-1}]  /.Mpl[{a_},{b_}]:>PolyLog[a,b]//FunctionExpand//Expand

Mplev[{2},{-((1+I)/(Sqrt[2]))}]:=-( + Mpl[{2},{((1+I)/(Sqrt[2]))}] -1/2Mpl[{2},{I}]  );

Mplev[{2},{-I}]:=-( + Mpl[{2},{I}] -1/2Mpl[{2},{-1}] );

(* shuffle *)

Mplev[{1,1},{((1-I)/(Sqrt[2])),-1}]:=-(Mpl[{1,1},{((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-Mpl[{1},{1/-1}]Mpl[{1},{1/-((1+I)/(Sqrt[2]))}]);

Mplev[{1,1},{-((1+I)/(Sqrt[2])),-1}]:=-(+Mpl[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-Mpl[{1},{1/-1}]Mpl[{1},{1/((1-I)/(Sqrt[2]))}]);

Mplev[{1,1},{((1-I)/(Sqrt[2])),I}]:=-(+Mpl[{1,1},{((1+I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-Mpl[{1},{1/-I}]Mpl[{1},{1/((1-I)/(Sqrt[2]))}]);

Mplev[{1,1},{-((1+I)/(Sqrt[2])),-I}]:=-Mpl[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+Mpl[{1},{1/-((1+I)/(Sqrt[2]))}]Mpl[{1},{1/I}]

Mplev[{1,1},{-((1+I)/(Sqrt[2])),I}]:=-(+Mpl[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-Mpl[{1},{1/((1+I)/(Sqrt[2]))}]Mpl[{1},{1/-I}]);

Mplev[{1,1},{((1-I)/(Sqrt[2])),-I}]:=-(+Mpl[{1,1},{((1+I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{-I}]);

Mpl[{2},{-((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{-1,((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-1}]-Mpl[{1},{-1}]Mpl[{1},{((1-I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl

Mplev[{1,1},{-1,((1-I)/(Sqrt[2]))}]:=-(Mpl[{2},{-((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-1}]-Mpl[{1},{-1}]Mpl[{1},{((1-I)/(Sqrt[2]))}]);

Mpl[{2},{((1+I)/(Sqrt[2]))}]+Mpl[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{-((1-I)/(Sqrt[2])),-I}]-Mpl[{1},{-I}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl

Mplev[{1,1},{-I,-((1-I)/(Sqrt[2]))}]:=-(Mpl[{2},{((1+I)/(Sqrt[2]))}]+Mpl[{1,1},{-((1-I)/(Sqrt[2])),-I}]-Mpl[{1},{-I}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]);

-Mpl[{2},{I}]-Mpl[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl

Mplev[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]:=-Mpl[{2},{I}]-Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]

%//parity2

Mpl[{2},{-1}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{-((1+I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl//Expand

Mplev[{1,1},{-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]:=-(Mpl[{2},{-1}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{-((1+I)/(Sqrt[2]))}]);

Mpl[{2},{-1}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1-I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl//Expand

Mplev[{1,1},{-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]:=-(Mpl[{2},{-1}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1-I)/(Sqrt[2]))}]);

Mpl[{2},{-I}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+Mpl[{1,1},{((1+I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]- Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1+I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl//Expand

Mplev[{1,1},{-((1+I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]:=-(Mpl[{2},{-I}]+Mpl[{1,1},{((1+I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]- Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{((1+I)/(Sqrt[2]))}]);

(1/2) Mpl[{2},{-I}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]- 1/2Mpl[{1},{((1-I)/(Sqrt[2]))}]^2/.Mpl->MplSt//Expand

Mplev[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]:=-((1/2) Mpl[{2},{-I}]+- 1/2Mpl[{1},{((1-I)/(Sqrt[2]))}]^2)

(1/2) Mpl[{2},{I}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]- 1/2Mpl[{1},{-((1+I)/(Sqrt[2]))}]^2/.Mpl->MplSt//Expand

Mplev[{1,1},{-((1+I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]:=-((1/2) Mpl[{2},{I}]- 1/2Mpl[{1},{-((1+I)/(Sqrt[2]))}]^2);

Mpl[{2},{1}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}] - Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]/.Mpl->MplSt

(Mpl[{2},{1}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+Mpl[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}] - Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{-((1-I)/(Sqrt[2]))}])/2//parity2

Mplev[{1,1},{-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]:=-(((25 (π^2))/96)-(1/2) I π Mpl[{1},{-((1+I)/(Sqrt[2]))}]+(3/8) I π Mpl[{1},{-((1-I)/(Sqrt[2]))}]-(1/2) Mpl[{1},{-((1+I)/(Sqrt[2]))}] Mpl[{1},{-((1-I)/(Sqrt[2]))}]+Mpl[{2},{-((1+I)/(Sqrt[2]))}]);

Mplev[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]:=-(Mpl[{2},{1}]+Mpl[{1,1},{-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}] - Mpl[{1},{-((1+I)/(Sqrt[2]))}]Mpl[{1},{-((1-I)/(Sqrt[2]))}]);

Mpl[{2},{1}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+Mpl[{1,1},{((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{((1+I)/(Sqrt[2]))}]/.Mpl->MplSt/.MplSt->Mpl

(Mpl[{2},{1}]+Mpl[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+Mpl[{1,1},{((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-Mpl[{1},{((1-I)/(Sqrt[2]))}]Mpl[{1},{((1+I)/(Sqrt[2]))}])/2//parity2

Mplev[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]:=-(((25 (π^2))/96)-(1/2) I π Mpl[{1},{((1-I)/(Sqrt[2]))}]+(1/8) I π Mpl[{1},{((1+I)/(Sqrt[2]))}]-(1/2) Mpl[{1},{((1-I)/(Sqrt[2]))}] Mpl[{1},{((1+I)/(Sqrt[2]))}]+Mpl[{2},{((1-I)/(Sqrt[2]))}]);

(* ------ *)

Omega[3,1,2,3]//omega2mpl;

%//parity4;

%//red4;

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand;

% - I Pi id3123wt3//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

OmegaEv[3,1,2,3] = %;

(Subscript[Omega, 3,3,2,1])

comb5 = (4/3) ((MplShi[{1},{-1}])^3)+2 ((MplShi[{1},{-1}])^2) MplShi[{1},{-I}]+2 MplShi[{1},{-1}] ((MplShi[{1},{-I}])^2)+(2/3) ((MplShi[{1},{-I}])^3)-3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{I}]+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}]+MplShi[{1},{-((1+I)/(Sqrt[2]))}] ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-1}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-I}] MplShi[{1},{I}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}]-((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/3) ((MplShi[{1},{((1-I)/(Sqrt[2]))}])^3)+3 MplShi[{1},{-1}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+((MplShi[{1},{-((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]+(1/2) MplShi[{1},{-1}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-I}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1},{((1+I)/(Sqrt[2]))}]+((MplShi[{1},{((1-I)/(Sqrt[2]))}])^2) MplShi[{1},{((1+I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] ((MplShi[{1},{((1+I)/(Sqrt[2]))}])^2)+(7/2) MplShi[{1},{-I}] MplShi[{2},{-1}]-7 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]-7 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-1}]+2 MplShi[{1},{-1}] MplShi[{2},{-I}]-7 MplShi[{1},{-I}] MplShi[{2},{-I}]-(5/2) MplShi[{1},{I}] MplShi[{2},{-I}]-(15/2) MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]-(19/2) MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-I}]+3 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-I}]-10 MplShi[{1},{-I}] MplShi[{2},{1}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{1}]+18 MplShi[{1},{-1}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+3 MplShi[{1},{I}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]-(7/2) MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+9 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]-5 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{-((1-I)/(Sqrt[2]))}]+18 MplShi[{1},{-1}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]+13 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]-(11/2) MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{2},{((1-I)/(Sqrt[2]))}]-6 MplShi[{1},{-I}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-1}]-2 MplShi[{1},{-I}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-1,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-I,-I}]-4 MplShi[{1},{-I}] MplShi[{1,1},{-I,-I}]+3 MplShi[{1},{I}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-I}]-10 MplShi[{1},{-1}] MplShi[{1,1},{-I,I}]-8 MplShi[{1},{-I}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]+4 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,I}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1+I)/(Sqrt[2]))}]+MplShi[{1},{-I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{I}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-I,-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-I}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-I,((1+I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-3 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-MplShi[{1},{((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-2 MplShi[{1},{((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+8 MplShi[{1},{-1}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{-I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+2 MplShi[{1},{I}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1+I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplShi[{1},{-((1-I)/(Sqrt[2]))}] MplShi[{1,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-(1/3) ((MplSti[{1},{-1}])^3)+2 ((MplSti[{1},{-1}])^2) MplSti[{1},{-I}]+8 MplSti[{1},{-1}] ((MplSti[{1},{-I}])^2)+(5/6) ((MplSti[{1},{-I}])^3)+5 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{I}]-((MplSti[{1},{-I}])^2) MplSti[{1},{I}]+((MplSti[{1},{-1}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{-((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^3)+((MplSti[{1},{-1}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-3 MplSti[{1},{-1}] MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-(3/2) ((MplSti[{1},{-I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+2 MplSti[{1},{-I}] MplSti[{1},{I}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) ((MplSti[{1},{I}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]-MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]+MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1-I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1-I)/(Sqrt[2]))}]+(1/2) MplSti[{1},{-1}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-(1/2) MplSti[{1},{-I}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)-MplSti[{1},{-((1-I)/(Sqrt[2]))}] ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^2)+(1/3) ((MplSti[{1},{((1-I)/(Sqrt[2]))}])^3)-6 MplSti[{1},{-1}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{-I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-MplSti[{1},{I}] MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-((MplSti[{1},{-((1-I)/(Sqrt[2]))}])^2) MplSti[{1},{((1+I)/(Sqrt[2]))}]-4 MplSti[{1},{-1}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-2 MplSti[{1},{-I}] MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1},{((1+I)/(Sqrt[2]))}]-8 MplSti[{1},{-1}] MplSti[{2},{-I}]-(7/2) MplSti[{1},{-I}] MplSti[{2},{-I}]+2 MplSti[{1},{I}] MplSti[{2},{-I}]-MplSti[{1},{-I}] MplSti[{2},{1}]-3 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-3 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{1}]-6 MplSti[{1},{-1}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+MplSti[{1},{-I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+(11/2) MplSti[{1},{I}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]+7 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{2},{-((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{-1}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{-I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+(17/2) MplSti[{1},{I}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-5 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-9 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]+8 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{2},{((1-I)/(Sqrt[2]))}]-6 MplSti[{1},{I}] MplSti[{1,1},{-I,-1}]+4 MplSti[{1},{-I}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{-((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]-6 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-I,I}]+4 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),-I}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),I}]+2 MplSti[{1},{-((1+I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 MplSti[{1},{((1-I)/(Sqrt[2]))}] MplSti[{1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-1}]+2 MplSti[{1},{((1+I)/(Sqrt[2]))}] MplSti[{1,1},{((1-I)/(Sqrt[2])),-I}]-10 par[{1,2},{-1,-1}]-(19/2) par[{1,2},{-1,-I}]+(35/2) par[{1,2},{-1,-((1-I)/(Sqrt[2]))}]+5 par[{1,2},{-1,((1-I)/(Sqrt[2]))}]+(5/2) par[{1,2},{-I,-1}]+12 par[{1,2},{-I,-I}]-4 par[{1,2},{-I,I}]+(3/2) par[{1,2},{-I,-((1+I)/(Sqrt[2]))}]+8 par[{1,2},{-I,-((1-I)/(Sqrt[2]))}]-5 par[{1,2},{-I,((1-I)/(Sqrt[2]))}]+(1/2) par[{1,2},{-I,((1+I)/(Sqrt[2]))}]+4 par[{1,2},{1,-I}]+2 par[{1,2},{1,-((1-I)/(Sqrt[2]))}]-2 par[{1,2},{1,((1-I)/(Sqrt[2]))}]+(17/2) par[{1,2},{-((1-I)/(Sqrt[2])),-1}]+par[{1,2},{-((1-I)/(Sqrt[2])),-I}]-(15/2) par[{1,2},{-((1-I)/(Sqrt[2])),I}]-(13/2) par[{1,2},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+par[{1,2},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-par[{1,2},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(5/2) par[{1,2},{((1-I)/(Sqrt[2])),-1}]+par[{1,2},{((1-I)/(Sqrt[2])),-I}]-(19/2) par[{1,2},{((1-I)/(Sqrt[2])),I}]-3 par[{1,2},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{1,2},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-10 par[{1,2},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-8 par[{2,1},{-1,-1}]-(17/2) par[{2,1},{-1,-I}]+(33/2) par[{2,1},{-1,-((1-I)/(Sqrt[2]))}]+6 par[{2,1},{-1,((1-I)/(Sqrt[2]))}]+par[{2,1},{-I,-1}]+18 par[{2,1},{-I,-I}]-4 par[{2,1},{-I,I}]-(1/2) par[{2,1},{-I,-((1+I)/(Sqrt[2]))}]+7 par[{2,1},{-I,-((1-I)/(Sqrt[2]))}]-11 par[{2,1},{-I,((1-I)/(Sqrt[2]))}]-(5/2) par[{2,1},{-I,((1+I)/(Sqrt[2]))}]-(5/2) par[{2,1},{1,-1}]-2 par[{2,1},{1,-I}]+(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),-1}]+2 par[{2,1},{-((1-I)/(Sqrt[2])),-I}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),I}]-(29/2) par[{2,1},{-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-3 par[{2,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{2,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-(17/2) par[{2,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+(11/2) par[{2,1},{((1-I)/(Sqrt[2])),-1}]-2 par[{2,1},{((1-I)/(Sqrt[2])),I}]-16 par[{2,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{2,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-par[{2,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]-4 par[{2,1},{((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-1,-((1-I)/(Sqrt[2]))}]-3 par[{1,1,1},{-1,-I,-1}]-10 par[{1,1,1},{-1,-I,-I}]+5 par[{1,1,1},{-1,-I,I}]-par[{1,1,1},{-1,-I,-((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-1,-I,-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-1,-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{-1,-I,((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,1,-((1-I)/(Sqrt[2]))}]+(9/2) par[{1,1,1},{-1,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),I}]+(1/2) par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-1,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-I}]+par[{1,1,1},{-1,((1-I)/(Sqrt[2])),I}]-8 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-4 par[{1,1,1},{-1,((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]-8 par[{1,1,1},{-I,-1,-I}]+5 par[{1,1,1},{-I,-1,I}]+2 par[{1,1,1},{-I,-1,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,-1,((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{-I,-I,-1}]-3 par[{1,1,1},{-I,-I,-I}]+2 par[{1,1,1},{-I,-I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,-I,((1+I)/(Sqrt[2]))}]-par[{1,1,1},{-I,I,-1}]-2 par[{1,1,1},{-I,I,I}]+2 par[{1,1,1},{-I,I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,I,((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,1,-1}]+2 par[{1,1,1},{-I,1,-((1+I)/(Sqrt[2]))}]-2 par[{1,1,1},{-I,1,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,1,((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-1}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-I}]+2 par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{-I,-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-1}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-I,((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{1,-1,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{1,-I,-1}]+2 par[{1,1,1},{1,-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{1,1,-((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{-((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-1}]-par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]-3 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,I}]-4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]+(3/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+(1/2) par[{1,1,1},{-((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]-2 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-1}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{-((1-I)/(Sqrt[2])),((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-1,I}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,-((1+I)/(Sqrt[2]))}]-6 par[{1,1,1},{((1-I)/(Sqrt[2])),-1,((1+I)/(Sqrt[2]))}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-1}]+par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1+I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,-((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1-I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-I,((1+I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-1}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,-I}]-2 par[{1,1,1},{((1-I)/(Sqrt[2])),I,I}]+par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1+I)/(Sqrt[2]))}]-(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),I,-((1-I)/(Sqrt[2]))}]-3 par[{1,1,1},{((1-I)/(Sqrt[2])),I,((1+I)/(Sqrt[2]))}]-8 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-1}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-I}]-par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),I}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),-((1-I)/(Sqrt[2]))}]+2 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+4 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),-I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),I}]+3 par[{1,1,1},{((1-I)/(Sqrt[2])),-((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}]+par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-I}]+(1/2) par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),-((1+I)/(Sqrt[2]))}]-par[{1,1,1},{((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2])),((1-I)/(Sqrt[2]))}];

rhs5= (comb5/.{MplSti->MplSt,MplShi->MplSh}//Expand)/.MplSh|MplSt->Mpl/.par[{1,1,1},{a_,b_,c_}]:> ((expr111/. {z1->a,z2->b,z3->c}/. Mpl->mplReg)//Expand)/.par[{2,1},{a_,b_}]:> ((expr21/. {z1->a,z2->b}/. Mpl->mplReg)//Expand)/.par[{1,2},{a_,b_}]:> ((expr12/. {z1->a,z2->b}/. Mpl->mplReg)//Expand);

lhs5 = (comb5/.MplSti|MplShi->Mpl)/.par->(0&);

id3321wt3 = rhs5 - lhs5//Expand;

(* ------ *)

Omega[3,3,2,1]//omega2mpl

%//parity4;

%//red4;

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

% - I Pi id3321wt3//Expand

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity3;

%//red3;

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

%//parity2;

%//red2;

%//.Mpl->Mplev/.Mplev->Mpl//Expand

OmegaEv[3,3,2,1] = %;

(Subscript[Ω, Sequence@@#])==OmegaEv@@#&/@{
{3},{2,1},{2,2,3},{3,1,1},{2,1,1,1},{2,1,3,3},{2,2,2,1},{3,1,2,3},{3,3,2,1}
}//Column

(* Apply the evaluations again to ar3 *)

coeffpi3 + coeffpi2 + coeffpi1/.Omega->OmegaEv//Simplify