HYMNS.nb
The HYMNs for GR(2,2) and GR(4,4) as in arXiv:XXXX.XXXXX [hep-th]
Complete Check of GR(2,2), random check of GR(4,4)

$RecursionLimit=Infinity

Import the Adinkra package

<<Adinkra`

BuildDate[Adinkra]

Function Lists

FunctionList[Adinkra]

Elements of BC2

HPerm1[a] := (OverBar[a])  with a = 0, 1      where ((OverBar[1]))  =   (({{-1, 0}, {0, 1}})),  ((OverBar[0])) := ()= Identity
H1[[a]] := (H^a) = { (), ((OverBar[1]))}   (* //First probably needs to be added if HPerm1, S2Perm, etc. are saved in a .m file *)

HPerm1[0] = (({{1, 0}, {0, 1}}));
HPerm1[1] = (({{-1, 0}, {0, 1}}));
HPerm1MatrixForm[ai_]:=HPerm1[ai]//MatrixForm

HPerm1MatrixForm[0]

H1List = {0,1};

H1 = Table[HPerm1[H1List[[ai]]],{ai,1,2}]

H1[[1]]

H1MatrixForm = Table[H1[[ai]]//MatrixForm,{ai,1,2}]

S2Perm[μ] := (μ)  two element permutation group,  μ =  0, 12   with (0) := ()
S2[[μ]] := (Subscript[S, 2]^μ) = {(), (12)}

S2Perm[0] = (({{1, 0}, {0, 1}}));
S2Perm[12] =  (({{0, 1}, {1, 0}}));

S2PermMatrixForm[mu_]:=S2Perm[mu]//MatrixForm;

S2PermMatrixForm[0]

S2List = {0,12};

S2 = Table[S2Perm[S2List[[mu]]],{mu,1,2}]

S2[[2]]//MatrixForm

S2MatrixForm = Table[S2[[mu]]//MatrixForm,{mu,1,2}]

BC2[[n,a,μ]] := (((-))^n)((Subscript[((Subscript[H, 1]^a)), I])^K)((Subscript[((Subscript[S, 2]^μ)), K])^J), n = 1,2; a = 1,2; μ = 1,2
BC2Perm[n,a,μ][[I,J]] = (((-))^n)((Subscript[((OverBar[a])), I])^K)((Subscript[(μ), K])^J), n = integers;  a = 0,1; μ =0,12

BC2Perm[ni_,ai_,mu_] := (((-1))^ni)HPerm1[ai].S2Perm[mu]
BC2PermMatrixForm[ni_,ai_,mu_] := BC2Perm[ni,ai,mu]//MatrixForm

BC2 = Table[BC2Perm[ni,H1List[[ai]],S2List[[mu]]],{ni,1,2},{ai,1,2},{mu,1,2}];
BC2MatrixForm = Table[BC2[[ni,ai,mu]]//MatrixForm,{ni,1,2},{ai,1,2},{mu,1,2}];

BC2Color[n,a,μ][L]:= Flips and Flops the colors of the adinkra matrices L according to BC2[[n,a,μ]]
BC2ColorPerm[n,a,μ]:= Flips and Flops the colors of the adinkra matrices L according to BC2Perm[n,a,μ] (permutation notation)

BC2Color[ni_,ai_,mu_][L_]:= Table[Sum[BC2[[If[EvenQ[ni],2,1],ai,mu]][[Ii,Ji]]L[[Ji,ii,jhat]],{Ji,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

BC2ColorPerm[ni_,ai_,mu_][L_]:= Table[Sum[BC2Perm[ni,ai,mu][[Ii,Ji]]L[[Ji,ii,jhat]],{Ji,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

BC2Boson[n,a,μ][L]:= Flips and Flops the bosons of the adinkra matrices L according to BC2[[n,a,μ]]
BC2BosonPerm[n,a,μ]:= Flips and Flops the bosons of the adinkra matrices L according to BC2Perm[n,a,μ] (permutation notation)

BC2Boson[ni_,ai_,mu_][L_]:= Table[Sum[BC2[[If[EvenQ[ni],2,1],ai,mu]][[ii,ji]]L[[Ii,ji,jhat]],{ji,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

BC2BosonPerm[ni_,ai_,mu_][L_]:= Table[Sum[BC2Perm[ni,ai,mu][[ii,ji]]L[[Ii,ji,jhat]],{ji,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

BC2Fermion[n,a,μ,A][L]:= Flips and Flops the fermions of the adinkra matrices L according to BC2[[n,a,μ,A]]
BC2FermionPerm[n,a,μ,A]:= Flips and Flops the fermions of the adinkra matrices L according to BC2Perm[n,a,μ,A] (permutation notation)

BC2Fermion[ni_,ai_,mu_][L_]:= Table[Sum[BC2[[If[EvenQ[ni],2,1],ai,mu]][[jhat,khat]]L[[Ii,ii,khat]],{khat,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

BC2FermionPerm[ni_,ai_,mu_][L_]:= Table[Sum[BC2Perm[ni,ai,mu][[jhat,khat]]L[[Ii,ii,khat]],{khat,1,2}],{Ii,1,2},{ii,1,2},{jhat,1,2}]

L[RepNumber][[i,jhat]]:=((Subscript[((Subscript[L, I]^(saμν))), i])^(OverHat[j]))= (((-))^n)((Subscript[((Subscript[H, 1]^a)), i])^j)((Subscript[((Subscript[S, 2]^μ)), j])^k)((Subscript[((Subscript[S, 2]^ν)), I])^J)((Subscript[((Subscript[L, J]^((0)))), k])^(OverHat[j]))
L[GR220]:=((Subscript[((Subscript[L, J]^((0)))), k])^(OverHat[j])) = {(({{1, 0}, {0, 1}})),(({{0, -1}, {1, 0}}))}
RepNumber = saμν, s = ±1; a , μ,ν=1,2;  n= 1 for s = -1, 2 for s=+1

L[GR220]={{{1,0},{0,1}},{{0,-1},{1,0}}};

FillL2[RepNumber_] := BC2Boson[NegToOnePosToTwo[RepNumber],Digit[Abs[RepNumber],2],Digit[Abs[RepNumber],1]][BC2Color[2,1,Digit[Abs[RepNumber],0]][L[GR220]]]

RepNumberList = {111,112,121,122,211,212,221,222,-111,-112,-121,-122,-211,-212,-221,-222};

Do[L[RepNumber] = FillL2[RepNumber],{RepNumber,{111,112,121,122,211,212,221,222,-111,-112,-121,-122,-211,-212,-221,-222}}];

Do[R[RepNumber]= Table[Transpose[L[RepNumber][[II]]],{II,1,2}],{RepNumber,{111,112,121,122,211,212,221,222,-111,-112,-121,-122,-211,-212,-221,-222}}];

GenerateAdinkraData[111]

AdinkraReport[111,8]

V[111][[1,2]]

Some Tests of L[RepNumber]: seems to be working

L[111]==L[GR220]

L[-111] == - L[GR220]

HPerm1[1]

L[-221]== Table[-HPerm1[1].S2Perm[12].L[GR220][[II]],{II,1,2}]

L[212]== Table[HPerm1[1].S2Perm[0].Sum[S2Perm[12][[II,JJ]]L[GR220][[JJ]],{JJ,1,2}],{II,1,2}]

L[-111111]

HYMNS, LRaised[Node][Rep][[I]] := M (Subscript[L, I]),  RRaised[Node][Rep][[II]]:=  (Subscript[R, I])(M^(-1))
LRaised and RRaised satisfy GR(2,2)

Raising Operator: RaiseOpM[m,word]

RaiseOpM[m_,word_]:= (({{(m^(IntegerDigits[word,2,2][[2]])), 0}, {0, (m^(IntegerDigits[word,2,2][[1]]))}}))

LRaised[Rep_][m_,word_]:=Table[ RaiseOpM[m,word].L[Rep][[II]],{II,1,2}]
RRaised[Rep_][mu_,word_] :=Table[ R[Rep][[II]].Inverse[RaiseOpM[mu,word]],{II,1,2}]

RRaised[-212][μ,1][[2]]

GATest[LRaised[-212][m,3],RRaised[-212][m,3]]

GATest[LRaised[-212][m,3],RRaised[-212][m/ρ,3]]

%/.ρ-> 1

Use Yangrui’s definitions: B1 = L1*R1, B2 = L2*R1, B3 = R1*L1, B4 = R1*L2, B5 = R2*L1, B6 = R2*L2

B[1][Rep_][word_]:= LRaised[Rep][m,word][[1]].RRaised[Rep][m/ρ,word][[1]]
B[2][Rep_][word_]:= LRaised[Rep][m,word][[2]].RRaised[Rep][m/ρ,word][[1]]
B[3][Rep_][word_]:= RRaised[Rep][m/ρ,word][[1]].LRaised[Rep][m,word][[1]]
B[4][Rep_][word_]:= RRaised[Rep][m/ρ,word][[1]].LRaised[Rep][m,word][[2]]
B[5][Rep_][word_]:= RRaised[Rep][m/ρ,word][[2]].LRaised[Rep][m,word][[1]]
B[6][Rep_][word_]:= RRaised[Rep][m/ρ,word][[2]].LRaised[Rep][m,word][[2]]

zero nodes raised: w = 0

LocalWord = 0; (*Valise *)
BEigens[1][LocalWord,2,2] = Table[{1,1},{RepCounter,1,16}];
BEigens[2][LocalWord,2,2] = Table[{I,-I},{RepCounter,1,16}];
BEigens[3][LocalWord,2,2] = Table[{1,1},{RepCounter,1,16}];
BEigens[4][LocalWord,2,2] = Table[{I,-I},{RepCounter,1,16}];
BEigens[5][LocalWord,2,2] = Table[{I,-I},{RepCounter,1,16}];
BEigens[6][LocalWord,2,2] = Table[{1,1},{RepCounter,1,16}];

LocalBEigens = Table[Eigenvalues[B[Bindex][RepNumberList[[RepNo]]][LocalWord]],{Bindex,1,6},{RepNo,1,16}]
LocalBEigens == Table[BEigens[Bindex][LocalWord,2,2],{Bindex,1,6}]
LocalWord
Clear[LocalBEigens,LocalWord]

node one raised: w =1

LocalWord = 1; 
BEigens[1][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];
BEigens[2][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[3][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];
BEigens[4][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[5][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[6][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];

LocalBEigens = Table[Eigenvalues[B[Bindex][RepNumberList[[RepNo]]][LocalWord]],{Bindex,1,6},{RepNo,1,16}]
LocalBEigens == Table[BEigens[Bindex][LocalWord,2,2],{Bindex,1,6}]
LocalWord
Clear[LocalBEigens,LocalWord]

node two raised: w =2

LocalWord = 2;
BEigens[1][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];
BEigens[2][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[3][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];
BEigens[4][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[5][LocalWord,2,2] = Table[{-I(Sqrt[ρ]),I(Sqrt[ρ])},{RepCounter,1,16}];
BEigens[6][LocalWord,2,2] = Table[{1,ρ},{RepCounter,1,16}];

LocalBEigens = Table[Eigenvalues[B[Bindex][RepNumberList[[RepNo]]][LocalWord]],{Bindex,1,6},{RepNo,1,16}]
LocalBEigens == Table[BEigens[Bindex][LocalWord,2,2],{Bindex,1,6}]
LocalWord
Clear[LocalBEigens,LocalWord]

both nodes raised: w =3

LocalWord = 3;
BEigens[1][LocalWord,2,2] = Table[{ρ,ρ},{RepCounter,1,16}];
BEigens[2][LocalWord,2,2] = Table[{I ρ,-I ρ},{RepCounter,1,16}];
BEigens[3][LocalWord,2,2] = Table[{ρ,ρ},{RepCounter,1,16}];
BEigens[4][LocalWord,2,2] = Table[{I ρ,-I ρ},{RepCounter,1,16}];
BEigens[5][LocalWord,2,2] = Table[{I ρ,-I ρ},{RepCounter,1,16}];
BEigens[6][LocalWord,2,2] = Table[{ρ,ρ},{RepCounter,1,16}];

LocalBEigens = Table[Eigenvalues[B[Bindex][RepNumberList[[RepNo]]][LocalWord]],{Bindex,1,6},{RepNo,1,16}]
LocalBEigens == Table[BEigens[Bindex][LocalWord,2,2],{Bindex,1,6}]
LocalWord
Clear[LocalBEigens,LocalWord]

GR(4,4)
Checking Yangrui’s Python results by selecting 100 random reps to save time. For full check over all 36,864, change LocalRandomRepList -> 1 to 36864

Explaining the Rep Code

GraphAdinkra[Q]
PrintAllL[Q]

LocalRep = -111751;

GraphAdinkra[LocalRep]
PrintAllL[LocalRep]

LocalRep = -441751;
GraphAdinkra[LocalRep]
PrintAllL[LocalRep]
Clear[LocalRep]

LocalRep = -442751;
GraphAdinkra[LocalRep]
PrintAllL[LocalRep]
Clear[LocalRep]

Raising Operator: RaiseOpM4[m,word]

RaiseOpM4[m_,word_]:=(({{(m^(IntegerDigits[word,2,4][[4]])), 0, 0, 0}, {0, (m^(IntegerDigits[word,2,4][[3]])), 0, 0}, {0, 0, (m^(IntegerDigits[word,2,4][[2]])), 0}, {0, 0, 0, (m^(IntegerDigits[word,2,4][[1]]))}}))

Table[RaiseOpM4[m,wordnum]//MatrixForm,{wordnum,0,15}]

LRaised4[Rep_][m_,word_]:=Table[ RaiseOpM4[m,word].L[Rep][[II]],{II,1,4}]
RRaised4[Rep_][mu_,word_] :=Table[ Transpose[L[Rep][[II]]].Inverse[RaiseOpM4[mu,word]],{II,1,4}]

Test on the Rep = -864861

LocalRep = -864861;

RRaised4[LocalRep][m/ρ,1][[2]]

LRaised4[LocalRep][m,1][[2]]//MatrixForm

GATest[LRaised4[LocalRep][m,3],RRaised4[LocalRep][m,3]]

GATest[LRaised4[LocalRep][m,3],RRaised4[LocalRep][m/ρ,3]]/.ρ-> 1

Clear[LocalRep]

BL = L4.R3.L2.R1 and BR = R4.L3.R2.L1

B[L][Rep_][word_]:= LRaised4[Rep][m,word][[4]].RRaised4[Rep][m/ρ,word][[3]].LRaised4[Rep][m,word][[2]].RRaised4[Rep][m/ρ,word][[1]]
B[R][Rep_][word_]:= RRaised4[Rep][m/ρ,word][[4]].LRaised4[Rep][m,word][[3]].RRaised4[Rep][m/ρ,word][[2]].LRaised4[Rep][m,word][[1]]

χ0[Rep_] :=CalculateChi0[L[Rep],RO[Rep]] (* Calculation of chi0 without need of generating R matrices, assumes orthogonal adinkra matrices L = R^T*)

GR44RepList = Table[(((-1))^p1)*(aa*(10^5)+mu*(10^4)+AA*(10^3)+bb*(10^2)+nu*(10^1)+tt),{p1,0,1},{aa,1,8},{mu,1,6},{AA,1,4},{bb,1,8},{nu,1,6},{tt,1,2}]//Flatten;  (* List of all Rep Codes for the GR44 valise adinkras as in *)

Dimensions[GR44RepList]

B[L][-111111][1]

χ0[-111111]

RepNo = 5891
χ0[GR44RepList[[RepNo]]]Eigenvalues[B[R][GR44RepList[[RepNo]]][15]]
Clear[RepNo]

zero nodes raised: w = 0
Prints True/False whether the eigenvalues of (Subscript[B, L]) are correct or not and True/False whether the eigenvalues of (Subscript[B, R]) are correct or not

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 0; (*Valise *)
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{1,1,1,1},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-1,-1,-1,-1},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

One Nodes Raised: w = 1,2,4,8
Prints True/False whether the eigenvalues of (Subscript[B, L]) are correct or not and True/False whether the eigenvalues of (Subscript[B, R]) are correct or not

one node raised: w = 1

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 1; (* First node raised *)
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{1,1,ρ,ρ},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-1,-1,-ρ,-ρ},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

one node raised: w = 2

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 2; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{1,1,ρ,ρ},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-1,-1,-ρ,-ρ},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

one node raised: w = 4

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 4; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{1,1,ρ,ρ},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-1,-1,-ρ,-ρ},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

one node raised: w = 8

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 8; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{1,1,ρ,ρ},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-1,-1,-ρ,-ρ},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

Two Nodes Raised, (w,15-w) = (3,12),(5,10),(6,9) Prints a singleTrue/False if the Eigenvalue Equivalence Classes are paired as (w,15-w) or not and if they fall into one of the three Eigenvalue Equivalence classes for (Subscript[B, L]) and (Subscript[B, R]) or not

BEigensPair[1][L][Rep_]:= χ0[Rep]*{ρ,ρ,ρ,ρ}
BEigensPair[1][R][Rep_]:= χ0[Rep]*{-1,-1,-(ρ^2),-(ρ^2)}
BEigensPair[2][L][Rep_]:= χ0[Rep]*{1,1,(ρ^2),(ρ^2)}
BEigensPair[2][R][Rep_]:= χ0[Rep]*{-ρ,-ρ,-ρ,-ρ}
BEigensPair[3][L][Rep_]:= χ0[Rep]*{ρ,ρ,ρ,ρ}
BEigensPair[3][R][Rep_]:= χ0[Rep]*{-ρ,-ρ,-ρ,-ρ}

two nodes raised: (w,15-w) = (3,12)

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 3; 
Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[L][GR44RepList[[RepNo]]][15-LocalWord]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[R][GR44RepList[[RepNo]]][15-LocalWord]]&&((Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][R][GR44RepList[[RepNo]]])),{RepNo,LocalRandomRepList}]==Table[True,{RepNo,LocalRandomRepList}]
Print[StringJoin["Equivalence Word Pair = (", ToString[LocalWord]], ", ", ToString[15-LocalWord], ")"]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

two nodes raised: (w,15-w) = (5,10)

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 5; 
Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[L][GR44RepList[[RepNo]]][15-LocalWord]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[R][GR44RepList[[RepNo]]][15-LocalWord]]&&((Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][R][GR44RepList[[RepNo]]])),{RepNo,LocalRandomRepList}]==Table[True,{RepNo,LocalRandomRepList}]
Print[StringJoin["Equivalence Word Pair = (", ToString[LocalWord]], ", ", ToString[15-LocalWord], ")"]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

two nodes raised: (w,15-w) = (6,9)

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 6; 
Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[L][GR44RepList[[RepNo]]][15-LocalWord]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==Eigenvalues[B[R][GR44RepList[[RepNo]]][15-LocalWord]]&&((Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[1][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[2][R][GR44RepList[[RepNo]]])||(Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][L][GR44RepList[[RepNo]]]&&Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]]==BEigensPair[3][R][GR44RepList[[RepNo]]])),{RepNo,LocalRandomRepList}]==Table[True,{RepNo,LocalRandomRepList}]
Print[StringJoin["Equivalence Word Pair = (", ToString[LocalWord]], ", ", ToString[15-LocalWord], ")"]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

three nodes raised: w = 7,11,13,14
Prints True/False whether the eigenvalues of (Subscript[B, L]) are correct or not and True/False whether the eigenvalues of (Subscript[B, R]) are correct or not

three nodes raised: w = 7

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord = 7; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{ρ,ρ,(ρ^2),(ρ^2)},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-ρ,-ρ,-(ρ^2),-(ρ^2)},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

three nodes raised: w = 11

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord =11; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{ρ,ρ,(ρ^2),(ρ^2)},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-ρ,-ρ,-(ρ^2),-(ρ^2)},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

three nodes raised: w = 13

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord =13; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{ρ,ρ,(ρ^2),(ρ^2)},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-ρ,-ρ,-(ρ^2),-(ρ^2)},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

three nodes raised: w = 14

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord =14; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{ρ,ρ,(ρ^2),(ρ^2)},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-ρ,-ρ,-(ρ^2),-(ρ^2)},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]

all four nodes raised: w = 15
Prints True/False whether the eigenvalues of (Subscript[B, L]) are correct or not and True/False whether the eigenvalues of (Subscript[B, R]) are correct or not

LocalNumReps = 100;
LocalRandomRepList =RandomInteger[{1,36864},LocalNumReps];
LocalWord =15; 
BEigens[L][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{(ρ^2),(ρ^2),(ρ^2),(ρ^2)},{RepNo,LocalRandomRepList}];
BEigens[R][LocalWord,4,4] =Table[χ0[GR44RepList[[RepNo]]]*{-(ρ^2),-(ρ^2),-(ρ^2),-(ρ^2)},{RepNo,LocalRandomRepList}];BEigens[L][LocalWord,4,4]==Table[Eigenvalues[B[L][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
BEigens[R][LocalWord,4,4]==Table[Eigenvalues[B[R][GR44RepList[[RepNo]]][LocalWord]],{RepNo,LocalRandomRepList}]
Print[StringJoin["Word = ", ToString[LocalWord]]]
Print[StringJoin["Reps Randomly Checked  are ", ToString[LocalRandomRepList]]]
Clear[LocalWord,LocalRandomRepList,LocalNumReps]