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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData["\<\"IndexRange[AdinkraEssentials][Index], Index = p1, II, \
ReportLevel, or pm\\n\\n***IMPORTANT****: Default Settings are VScaleFactor = \
VtildeScaleFactor = -I, VsoNScaleFactor = -I/(2 VsoNScaleFactor), \
VtildesoNScaleFactor = -I/(2 VtildesoNScaleFactor)\\n\\nReports: \
AdinkraReport[Rep,ReportLevel], AdinkraPreliminaryReport[L,R], \
AdinkraPreliminaryReport[Rep], AdinkraPreliminaryReportO[Rep], \
AdinkraHoloMonoReport[Rep], AdinkraSummaryReport[Rep], AdinkraFullReport[Rep]\
\\n\\nBasic Functions: nMatrices[Matrices], nRows[Matrices], \
nColumns[Matrices], Commute[Matrix1,Matrix2], NColors[Rep], NColors[L,R], \
dmin[N], dbosons[Rep], dbosons[L,R], dfermions[Rep], dfermions[L,R], \
WordW[{p1,p2,...,pN}]\\n\\nIntense Calculations: Gadget[Rep1,Rep2], \
BosonGadget[Rep1,Rep2], ListOfIdenticalMonoOrHolo[MonoOrHolo,Rep], \
NumDistinctHoloOrMono[HoloOrMono,Rep]\\n\\nPrint Functions: PrintL[Rep][II], \
PrintR[Rep][II], PrintGALR[Rep][II,JJ], PrintGARL[Rep][II,JJ], \
PrintV[Rep][II,JJ], PrintVtilde[Rep][II,JJ], PrintZetaGen[Rep][II], \
PrintHoloraumy[Rep][{p1,p2,...,pN}], \
PrintMonodromy[Rep][{p1,p2,...,pN}],PrintZetatildeGen[Rep][II], \
PrintHoloraumytilde[Rep][{p1,p2,...,pN}], \
PrintMonodromytilde[Rep][{p1,p2,...,pN}], PrintVtildePM[pm][Rep][II,JJ], \
PrintVtildePM[pm][Rep][II,JJ], PrintAllL[Rep], PrintAllR[Rep], \
PrintAllGALR[Rep], PrintAllGARL[Rep], PrintAllV[Rep], PrintAllVtilde[Rep], \
PrintAllZetaGen[Rep], PrintAllHoloraumy[Rep], \
PrintAllMonodromy[Rep],PrintAllZetatildeGen[Rep], \
PrintAllHoloraumytilde[Rep], PrintAllMonodromytilde[Rep], \
PrintAllVtildePM[pm][Rep], PrintAllVtildePM[pm][Rep], \
,PrintSigmaProduct[Matrix], PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\\n\\nTest Functions: CorrectDimensions[Rep], \
CorrectDimensions[L,R], TransposeTest[Rep], TransposeTest[L,R], \
InverseTest[Rep], InverseTest[L,R], RO[Rep], Chi0Report[L,R], GATest[Rep], \
GATest[L,R], soNTest[Matrices], su2Test[MgenPM[pm]][Rep], \
MutuallyCommuteTest[M1,M2], LinearlyIndependent[Mgen]\\n\\nData generated by \
GenerateAdinkraData[Rep], GenerateAdinkraData[Rep,Orthogonal], \
GenerateAdinkraDataO[Rep], GenerateAdinkraData[Rep,L], or \
GenerateAdinkraData[Rep,L,R]:\\nL[Rep], R[Rep], GALR[Rep], GARL[Rep], \
chi0[Rep], ncis[Rep], ntrans[Rep], V[Rep], Vtilde[Rep], VsoN[Rep], \
VtildesoN[Rep], ZetaGen[Rep], Holoraumy[Rep], Monodromy[Rep], \
ZetatildeGen[Rep], Holoraumytilde[Rep], Monodromytilde[Rep], VPM[pm][Rep], \
VtildePM[pm][Rep], VsoNPM[pm][Rep], VtildesoNPM[pm][Rep] cSoln[V[Rep]], \
cSoln[Vtilde[Rep]]\\n\\n******************************************************\
**********************************\\n*****************************************\
***********************************************\"\>"], "Output",
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Cell[BoxData["\<\"IndexRange[BasisDecomposition][Index], Index = mu, ahat, a, \
d, or n\\n\\nGeneral Matrix Tools:\\nsigma[mu], \[Alpha]matrix[ahat], \
\[Beta]matrix[ahat], SigmaProduct[mu1,mu2,...,mun], \
SigmaProductMF[mu1,mu2,...,mun], SigmaMatrixProduct[mu,AnyMatrix], \
\[Rho]matrix[mu,nu], \[Omega]matrix[n][a], Basis[d][a,mu,nu], TestOrthogonal\
\[Sigma], Test\[Rho]Orthogonal, Test\[Omega]Orthogonal[n], \
TestBasisOrthogonal[d], Coeffs[d][Matrix][a,mu,nu]\\n\\nGenerateCoeffs[Rep] \
generates adinkra representation specific functions:\\nLCoeffs[Rep][II], \
CheckLCoeffs[Rep], RCoeffs[Rep][II], CheckRCoeffs[Rep], VCoeffs[Rep][II,JJ], \
CheckVCoeffs[Rep], VtildeCoeffs[Rep][II,JJ], CheckVtildeCoeffs[Rep], \
VPMCoeffs[pm][Rep][II,JJ], CheckVPMCoeffs[pm][Rep], \
VtildePMCoeffs[pm][Rep][II,JJ], CheckVtildePMCoeffs[pm][Rep], \
NumberNonZero[LCoeffsMat], CoeffsSummaryReport[Rep], CoeffsFullReport[Rep], \
CMessage[Rep][mi,si]\\n\\nPrint Functions:\\n PrintSigmaProduct[Matrix], \
PrintBasis[Matrix], PrintLBasis[Rep][II], PrintRBasis[Rep][II], \
PrintGALRBasis[Rep][II,JJ], PrintGARLBasis[Rep][II,JJ], \
PrintVBasis[Rep][II,JJ], PrintVtildeBasis[Rep][II,JJ], \
PrintVPMBasis[pm][Rep][II,JJ], PrintVtildePMBasis[pm][Rep][II,JJ], \
PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\\n\\n*************************************************\
***************************************\\n************************************\
****************************************************\"\>"], "Output",
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Cell[BoxData["\<\"\\nIndexRange[BC4Tools][Index], Index = n, a, \[Mu], A, II, \
or tt\\n\\nFunctions: \\nHPerm[a], H[[a]], S3Perm[\[Mu]], S3[[\[Mu]]], \
VierPerm[A], Vier[[A]], BC4[[n,a,\[Mu],A,II,JJ]] , \
BC4Perm[n,a,\[Mu],A][[II,JJ]], QuaternionTestIJK[Quat], \
QuaternionTestKJI[Quat], Digit[Num,Pow], ell[Rep][tt,a][II,JJ], \
kappa[Rep][ti,a][II,JJ], IellABColor[Rep][[a]], PrintIell[Rep][[a]], \
IellABCode[Rep][[a]], AntisymmetryCheck[Object1], BC4Color[n,a,\[Mu],A][L], \
BC4ColorPerm[n,a,\[Mu],A][L],BC4Boson[n,a,\[Mu],A][L],BC4BosonPerm[n,a,\[Mu],\
A][L], HList,S3List,VierList,PrintBC4Perm[n,a,\[Mu],A],PrintBC4BosonPerm[n,a,\
\[Mu],A],PrintBC4FermionPerm[n,a,\[Mu],A],PrintBC4ColorPerm[n,a,\[Mu],A],L[Q],\
L[Qtilde],L[RepCode]\\n\\n****************************************************\
************************************\\n***************************************\
*************************************************\"\>"], "Output",
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Cell[CellGroupData[{

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Cell[BoxData["\<\"IndexRange[GraphingTools][list]\\n\\n AdinkraGreen, \
AdinkraViolet, AdinkraOrange, AdinkraRed, padLmatrix[L], \
adjacencyToEdge[mat,col], buildrules[list], Valise, GraphAdinkra[Rep], \
GraphAdinkra[Rep,BuildRules[list], \
ExportAdinkra[Rep,BuildRules[list],filename]\\n\\n****************************\
************************************************************\\n***************\
*************************************************************************\"\>\
"], "Output",
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   3.7567347804945383`*^9, 3.7567348670172853`*^9, 3.7567432250897255`*^9, 
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Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "Adinkra", "]"}]], "Input",
 CellChangeTimes->{{3.7424465936653976`*^9, 3.742446599983512*^9}},
 CellLabel->"In[10]:=",ExpressionUUID->"157db393-0dff-4169-adae-289b23a3d1a9"],

Cell[BoxData["\<\"SpaceTime:\\nIndexRange[SpaceTime][Index], Index = mu, a, \
or RaiseCode\\n\\ncoordinates, \[CapitalStigma][mu], \[Eta][mu,nu], \
Cmetric[[a,b]], InverseCmetric[[a,b]], UD[Field,\[CapitalStigma][mu]] , \
Lap[Field], UP, DOWN, \
RaiseSTIndex[Field,RaiseCode1,RaiseCode2,...,RaiseCoden], \
RaiseFermionIndex[Field]\\n\\n************************************************\
****************************************\\n***********************************\
*****************************************************\\n\\nGenerateLandR:\\\
nNColors[D,Phi,Psi], LTable[DColor,Phi,Psi], \
RTable[DColor,Phi,Psi],GenerateLandR[DColor,Phi,Psi,Rep]\\n\\n****************\
************************************************************************\\n***\
******************************************************************************\
*******\\n\\nAdinkraEssentials:\\nIndexRange[AdinkraEssentials][Index], Index \
= p1, II, ReportLevel, or pm\\n\\n***IMPORTANT****: Default Settings are \
VScaleFactor = VtildeScaleFactor = -I, VsoNScaleFactor = -I/(2 \
VsoNScaleFactor), VtildesoNScaleFactor = -I/(2 \
VtildesoNScaleFactor)\\n\\nReports: AdinkraReport[Rep,ReportLevel], \
AdinkraPreliminaryReport[L,R], AdinkraPreliminaryReport[Rep], \
AdinkraPreliminaryReportO[Rep], AdinkraHoloMonoReport[Rep], \
AdinkraSummaryReport[Rep], AdinkraFullReport[Rep]\\n\\nBasic Functions: \
nMatrices[Matrices], nRows[Matrices], nColumns[Matrices], \
Commute[Matrix1,Matrix2], NColors[Rep], NColors[L,R], dmin[N], dbosons[Rep], \
dbosons[L,R], dfermions[Rep], dfermions[L,R], \
WordW[{p1,p2,...,pN}]\\n\\nIntense Calculations: Gadget[Rep1,Rep2], \
BosonGadget[Rep1,Rep2], ListOfIdenticalMonoOrHolo[MonoOrHolo,Rep], \
NumDistinctHoloOrMono[HoloOrMono,Rep]\\n\\nPrint Functions: PrintL[Rep][II], \
PrintR[Rep][II], PrintGALR[Rep][II,JJ], PrintGARL[Rep][II,JJ], \
PrintV[Rep][II,JJ], PrintVtilde[Rep][II,JJ], PrintZetaGen[Rep][II], \
PrintHoloraumy[Rep][{p1,p2,...,pN}], \
PrintMonodromy[Rep][{p1,p2,...,pN}],PrintZetatildeGen[Rep][II], \
PrintHoloraumytilde[Rep][{p1,p2,...,pN}], \
PrintMonodromytilde[Rep][{p1,p2,...,pN}], PrintVtildePM[pm][Rep][II,JJ], \
PrintVtildePM[pm][Rep][II,JJ], PrintAllL[Rep], PrintAllR[Rep], \
PrintAllGALR[Rep], PrintAllGARL[Rep], PrintAllV[Rep], PrintAllVtilde[Rep], \
PrintAllZetaGen[Rep], PrintAllHoloraumy[Rep], \
PrintAllMonodromy[Rep],PrintAllZetatildeGen[Rep], \
PrintAllHoloraumytilde[Rep], PrintAllMonodromytilde[Rep], \
PrintAllVtildePM[pm][Rep], PrintAllVtildePM[pm][Rep], \
,PrintSigmaProduct[Matrix], PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\\n\\nTest Functions: CorrectDimensions[Rep], \
CorrectDimensions[L,R], TransposeTest[Rep], TransposeTest[L,R], \
InverseTest[Rep], InverseTest[L,R], RO[Rep], Chi0Report[L,R], GATest[Rep], \
GATest[L,R], soNTest[Matrices], su2Test[MgenPM[pm]][Rep], \
MutuallyCommuteTest[M1,M2], LinearlyIndependent[Mgen]\\n\\nData generated by \
GenerateAdinkraData[Rep], GenerateAdinkraData[Rep,Orthogonal], \
GenerateAdinkraDataO[Rep], GenerateAdinkraData[Rep,L], or \
GenerateAdinkraData[Rep,L,R]:\\nL[Rep], R[Rep], GALR[Rep], GARL[Rep], \
chi0[Rep], ncis[Rep], ntrans[Rep], V[Rep], Vtilde[Rep], VsoN[Rep], \
VtildesoN[Rep], ZetaGen[Rep], Holoraumy[Rep], Monodromy[Rep], \
ZetatildeGen[Rep], Holoraumytilde[Rep], Monodromytilde[Rep], VPM[pm][Rep], \
VtildePM[pm][Rep], VsoNPM[pm][Rep], VtildesoNPM[pm][Rep] cSoln[V[Rep]], \
cSoln[Vtilde[Rep]]\\n\\n******************************************************\
**********************************\\n*****************************************\
***********************************************\\n\\nBasisDecomposition:\\\
nIndexRange[BasisDecomposition][Index], Index = mu, ahat, a, d, or \
n\\n\\nGeneral Matrix Tools:\\nsigma[mu], \[Alpha]matrix[ahat], \
\[Beta]matrix[ahat], SigmaProduct[mu1,mu2,...,mun], \
SigmaProductMF[mu1,mu2,...,mun], SigmaMatrixProduct[mu,AnyMatrix], \
\[Rho]matrix[mu,nu], \[Omega]matrix[n][a], Basis[d][a,mu,nu], TestOrthogonal\
\[Sigma], Test\[Rho]Orthogonal, Test\[Omega]Orthogonal[n], \
TestBasisOrthogonal[d], Coeffs[d][Matrix][a,mu,nu]\\n\\nGenerateCoeffs[Rep] \
generates adinkra representation specific functions:\\nLCoeffs[Rep][II], \
CheckLCoeffs[Rep], RCoeffs[Rep][II], CheckRCoeffs[Rep], VCoeffs[Rep][II,JJ], \
CheckVCoeffs[Rep], VtildeCoeffs[Rep][II,JJ], CheckVtildeCoeffs[Rep], \
VPMCoeffs[pm][Rep][II,JJ], CheckVPMCoeffs[pm][Rep], \
VtildePMCoeffs[pm][Rep][II,JJ], CheckVtildePMCoeffs[pm][Rep], \
NumberNonZero[LCoeffsMat], CoeffsSummaryReport[Rep], CoeffsFullReport[Rep], \
CMessage[Rep][mi,si]\\n\\nPrint Functions:\\n PrintSigmaProduct[Matrix], \
PrintBasis[Matrix], PrintLBasis[Rep][II], PrintRBasis[Rep][II], \
PrintGALRBasis[Rep][II,JJ], PrintGARLBasis[Rep][II,JJ], \
PrintVBasis[Rep][II,JJ], PrintVtildeBasis[Rep][II,JJ], \
PrintVPMBasis[pm][Rep][II,JJ], PrintVtildePMBasis[pm][Rep][II,JJ], \
PrintLSigmaProduct[Rep], \
PrintRSigmaProduct[Rep]\\n\\n*************************************************\
***************************************\\n************************************\
****************************************************\\n\\nBC4Tools:\\n\\\
nIndexRange[BC4Tools][Index], Index = n, a, \[Mu], A, II, or \
tt\\n\\nFunctions: \\nHPerm[a], H[[a]], S3Perm[\[Mu]], S3[[\[Mu]]], \
VierPerm[A], Vier[[A]], BC4[[n,a,\[Mu],A,II,JJ]] , \
BC4Perm[n,a,\[Mu],A][[II,JJ]], QuaternionTestIJK[Quat], \
QuaternionTestKJI[Quat], Digit[Num,Pow], ell[Rep][tt,a][II,JJ], \
kappa[Rep][ti,a][II,JJ], IellABColor[Rep][[a]], PrintIell[Rep][[a]], \
IellABCode[Rep][[a]], AntisymmetryCheck[Object1], BC4Color[n,a,\[Mu],A][L], \
BC4ColorPerm[n,a,\[Mu],A][L],BC4Boson[n,a,\[Mu],A][L],BC4BosonPerm[n,a,\[Mu],\
A][L], HList,S3List,VierList,PrintBC4Perm[n,a,\[Mu],A],PrintBC4BosonPerm[n,a,\
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************************************\\n***************************************\
*************************************************\\n\\nGraphingTools:\\\
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************************************************************\\n***************\
*************************************************************************\"\>\
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When the LinearlyIndependent function does not give True, the output below is \
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VPM[-1][CM][[2,3]] + VPM[-1][CM][[1,4]]   =  0   =>   VPM[-1][CM][[2,3]] = - \
VPM[-1][CM][[1,4]] 
VPM[-1][CM][[2,4]] -  VPM[-1][CM][[1,3]]  =  0   =>     VPM[-1][CM][[2,4]] = \
VPM[-1][CM][[1,3]]
VPM[-1][CM][[3,4]] + VPM[-1][CM][[1,2]]  =  0   =>     VPM[-1][CM][[3,4]] = - \
VPM[-1][CM][[1,2]] \
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Here we are using the BC4Tools package, so lets display the function list to \
see what we have to use\
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1 and 4 and 2 and 3:  (14)(23)\nthen flopping color 1 to 2 to 3 to 1:  (123)\n\
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orange stays orange\nthe flipping (switching the sign of) colors 3 and 4 \
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