<<PolylogTools`

I41[x_,y_] := G[y, 0, 0, 0, x, 1];

bloch[n_, x_] := -(CiTi[1-x, Sequence@@Table[x, {n-1}]] - CiTi[x, 1-x, Sequence@@Table[x, {n-2}]])

bloch[n_, x_, y_] := -(CiTi[1-x, Sequence@@Table[x, {n-1}], y] - CiTi[x, 1-x, Sequence@@Table[x, {n-2}],y])

bloch[n_, x_, y_,z_] := -(CiTi[1-x, Sequence@@Table[x, {n-1}], y,z] - CiTi[x, 1-x, Sequence@@Table[x, {n-2}],y,z])

bloch[4,x] - 4*sh@CreateTensor[-G[0, 0, 0, 1/x, 1]]//Expand

bloch[5,x]/5 - sh@CreateTensor[-G[0, 0, 0,0, 1/x, 1]]//Expand

myexpr = -3bloch[5, x/y] - bloch[5,x] - bloch[5,y] +
+ bloch[4,x/y, (1-x)/(1-y)] + bloch[4,x,1-y] + bloch[4,y,1-x] +
-(bloch[3,1-x,x/y,x/y]+bloch[3,1-y,x/y,x/y]-bloch[3,(1-x)/(1-y),x/y,x/y]+bloch[3,(1-1/x)/(1-1/y),x/y,x/y])+
+(bloch[3,x,1-y,x/y]-bloch[3,y,1-x,x/y]+bloch[3,x/y,(1-x)/(1-y),x/y])//ReduceTensorProduct//flatTensor//Expand;

realexpr = 5*CreateTensor[I41[x,y]]//sh//flatTensor//Expand;

myexpr-realexpr

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

modsh = (#//CreateTensor//sh//flatTensor//Expand)&;

wedges = (-TensWedge[Li[{2},{x}]//modsh, Li[{3},{y}]//modsh] + TensWedge[Li[{3},{x}]//modsh, Li[{2},{y}]//modsh])/.CiTi[w___]:>Tens@@(ElTens/@{w});

i41 = I41[x,y]//CreateTensor//del//Expand;

wedges - i41

wedges1oy = (-TensWedge[Li[{2},{x}]//modsh, Li[{3},{y}]//modsh] - TensWedge[Li[{3},{x}]//modsh, Li[{2},{y}]//modsh])/.CiTi[w___]:>Tens@@(ElTens/@{w});

i411oy = I41[x,1/y]//CreateTensor//del//Expand;

wedges1oy-i411oy

Li[{2},{x}]//modsh

Li[{2},{1/x}]//modsh

I31[x_,y_] := G[y, 0, 0, x, 1];

(I31[x,y]//CreateTensor//del//Expand) - ((-TensWedge[Li[{2},{x}]//modsh, Li[{2},{y}]//modsh])/.CiTi[w___]:>Tens@@(ElTens/@{w}))