Pensieve header: AutoAd for ZeroCo.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\OneCo-1604\\Zero"];
<< ZeroLocal.m

AutoAd[B_, x_][y_] := Module[{pows, states, i, s, seq,sh=5, dseq, sf1, sf2, sf, t1, n},
pows = NestList[B[x,#]&, y, 20];
states = Union[Cases[pows, s_β|s_a :> ReplacePart[s, 1->_], ∞]];
UU@Sum[
seq=Cases[{#},states[[i]], ∞]& /@ pows;
seq=Replace[seq,{{_[f_,___]}:>f, {}->0}, {1}];
dseq=Drop[seq, sh];
If[Union[Length[MonomialList[#]]& /@ dseq]==={1}∧Union[Length[FactorTermsList[#]]& /@ dseq]==={2},
sf1 = FindSequenceFunction[FactorTermsList[#][[1]]& /@ dseq];
sf2 = FindSequenceFunction[FactorTermsList[#][[2]]& /@ dseq];
sf = (sf1[#]sf2[#]&),
(*Else*) sf=FindSequenceFunction[dseq, FunctionSpace->{"ConstantRecursive","HolonomicSequence", "Polynomial", "RationalFunction","HypergeometricTerm"}]];
ReplacePart[states[[i]], 1 ->FullSimplify[ (∑_(n=0)^(sh-1))((seq[[n+1]])/(n!))+ (∑_(n=sh)^∞)((sf[n+1-sh])/(n!))]],
{i,Length@states}] ];

AutoAd[bb[j,k],UU@a[1,j,k]][UU@a[1,0,j]]

AutoAd[bb[j,k],UU@a[1,j,k]][UU@a[1,0,k]]

AutoAd[bb[j,k],UU@a[t,j,k]][UU@a[1,j,∞]]

AutoAd[bb[1,2],UU@a[1,1,2]][UU@a[1,1,0]]

AutoAd[bb[j,k],UU@a[t,j,k]][UU@a[1,k,∞]]

AutoAd[bb[1,2],UU@a[1,1,2]][UU@a[1,2,0]]

AutoAd[bb[i,j],UU@a[1,i,j]][UU@a[1,k,j]]

AutoAd[bb[i,j],UU@a[1,i,j]][UU@a[1,k,i]]

AutoAd[bb[i,j],UU@a[1,i,j]][UU@a[1,j,k]]

AutoAd[bb[i,j],UU@a[1,i,j]][UU@a[1,j,i]]