(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 11.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 834393, 20040] NotebookOptionsPosition[ 800327, 19424] NotebookOutlinePosition[ 800896, 19445] CellTagsIndexPosition[ 800805, 19440] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Compare20x20Reps.nb Loads dWvH.m, OS.m, and nmSG.m, demonstrates their holoraumy and calculates \ their gadgets, etc. as explained in the paper\ \>", "Section", CellChangeTimes->{{3.7110191735260987`*^9, 3.7110192147454567`*^9}, { 3.7118614273209577`*^9, 3.711861430347131*^9}, {3.712105052705511*^9, 3.712105057153765*^9}, {3.7123570726801944`*^9, 3.7123570767084246`*^9}, { 3.7512257881886787`*^9, 3.7512257907056446`*^9}, {3.753924186928907*^9, 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"Subsection", CellChangeTimes->{{3.746556066750236*^9, 3.746556069037942*^9}},ExpressionUUID->"c9f594d7-ce81-46bf-93df-\ 7f228d40cace"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FunctionList", "[", "Adinkra", "]"}]], "Input", CellChangeTimes->{{3.7424465936653976`*^9, 3.742446599983512*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"85edeaa8-6f06-4b4c-906d-ad6a466ed3d0"], 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,\ \[Mu],A],PrintBC4FermionPerm[n,a,\[Mu],A],PrintBC4ColorPerm[n,a,\[Mu],A],L[Q],\ L[Qtilde],L[RepCode]\\n\\n****************************************************\ ************************************\\n***************************************\ *************************************************\\n\\nGraphingTools:\\\ nIndexRange[GraphingTools][list]\\n\\n AdinkraGreen, AdinkraViolet, \ AdinkraOrange, AdinkraRed, padLmatrix[L], adjacencyToEdge[mat,col], \ buildrules[list], Valise, GraphAdinkra[L], GraphAdinkra[L,BuildRules[list], \ ExportAdinkra[L,BuildRules[list],filename]\\n\\n******************************\ **********************************************************\\n*****************\ ***********************************************************************\"\>"],\ "Output", 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VCoeffs, VtildeCoeffs, VPMCoeffs, \ VtildePMCoeffs, ncis, ntrans, chi0, and nzvalue for Rep = dWvH are \ loaded\"\>"], "Output", CellChangeTimes->{3.7539252544902835`*^9, 3.7539264582569637`*^9, 3.754070849511589*^9, 3.756839056994997*^9, 3.7568394135299206`*^9, 3.7568440833081236`*^9, 3.760729100424308*^9, 3.760729964176014*^9}, CellLabel->"Out[6]=",ExpressionUUID->"83910f67-7a68-4aab-a642-50cf1d374b5b"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.71150063575192*^9, 3.7115006395731387`*^9}, { 3.711657367639683*^9, 3.711657367720688*^9}, {3.71186146547114*^9, 3.7118614655411434`*^9}, {3.7121050707415423`*^9, 3.712105070813546*^9}, { 3.7123570951014767`*^9, 3.712357095895522*^9}, {3.7505403174489098`*^9, 3.7505403175915723`*^9}, 3.753924254674737*^9}, CellLabel->"In[7]:=",ExpressionUUID->"d40b380f-cad4-4c79-a3b1-4f6945c648a9"], Cell[BoxData["\<\"L, R, GALR, GARL, V, Vtilde, VPM, VtildePM, LCoeffs, \ RCoeffs, GALRCoeffs, GARLCoeffs, VCoeffs, VtildeCoeffs, VPMCoeffs, \ VtildePMCoeffs, ncis, ntrans, chi0, and nzvalue for Rep = nmSG are \ loaded\"\>"], "Output", CellChangeTimes->{3.7539264585342307`*^9, 3.7540708497372355`*^9, 3.756839057207279*^9, 3.7568394137555914`*^9, 3.756844083518428*^9, 3.760729100651311*^9, 3.7607299643936615`*^9}, CellLabel->"Out[7]=",ExpressionUUID->"377bf213-cae4-42c6-a61d-a821bc903964"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.71150063575192*^9, 3.7115006395731387`*^9}, { 3.711657367639683*^9, 3.711657367720688*^9}, {3.71186146547114*^9, 3.7118614655411434`*^9}, {3.712022939443369*^9, 3.7120229397383857`*^9}, { 3.7121050733816934`*^9, 3.712105073461698*^9}, {3.7503381508987045`*^9, 3.750338151023546*^9}, 3.753924258249699*^9}, CellLabel->"In[8]:=",ExpressionUUID->"d34a10bf-6117-4b61-a0c4-254b5f59c784"], Cell[BoxData["\<\"L, R, GALR, GARL, V, Vtilde, VPM, VtildePM, LCoeffs, \ RCoeffs, GALRCoeffs, GARLCoeffs, VCoeffs, VtildeCoeffs, VPMCoeffs, \ VtildePMCoeffs, ncis, ntrans, chi0, and nzvalue for Rep = OS are \ loaded\"\>"], "Output", CellChangeTimes->{3.753925257773507*^9, 3.7539264587426558`*^9, 3.754070849886773*^9, 3.756839057347151*^9, 3.7568394139044113`*^9, 3.7568440836632595`*^9, 3.7607291008020654`*^9, 3.760729964540593*^9}, CellLabel->"Out[8]=",ExpressionUUID->"bc6827e9-8a84-4973-9fbf-50094ccf6eaa"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.711015329985261*^9, 3.7110153299942613`*^9}, { 3.7110153816732173`*^9, 3.711015388684618*^9}, {3.711015433021154*^9, 3.7110154367103653`*^9}, {3.7110162679929113`*^9, 3.7110162751733227`*^9}, {3.7110192934459577`*^9, 3.7110192974371862`*^9}, 3.7118614493492174`*^9, {3.7121050682053976`*^9, 3.712105068294402*^9}, { 3.7503381526178474`*^9, 3.7503381527115517`*^9}, {3.753920099361403*^9, 3.753920099528503*^9}, {3.756839402738104*^9, 3.7568394031381283`*^9}}, CellLabel->"In[9]:=",ExpressionUUID->"e0f3965f-d1bf-40b8-be6e-7ad4c054e20e"], Cell[BoxData["\<\"L, R, V, Vtilde, VPM, VtildePM, LCoeffs, RCoeffs, VCoeffs, \ VtildeCoeffs, VPMCoeffs, VtildePMCoeffs, ncis, ntrans, chi0, PrintLBasis, \ PrintRBasis, PrintVBasis, PrintVtildeBasis, PrintVPMBasis, \ PrintVtildePMBasis, and nzvalue for Rep = dWvHprime are loaded\"\>"], "Output", CellChangeTimes->{3.7539252544902835`*^9, 3.7539264582569637`*^9, 3.754070849511589*^9, 3.756839056994997*^9, 3.7568394139763193`*^9, 3.756844083734686*^9, 3.7607291008818135`*^9, 3.7607299646339407`*^9}, CellLabel->"Out[9]=",ExpressionUUID->"41ef0e98-90e4-4f5c-95cf-c24f8d0abdfc"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.71150063575192*^9, 3.7115006395731387`*^9}, { 3.711657367639683*^9, 3.711657367720688*^9}, {3.71186146547114*^9, 3.7118614655411434`*^9}, {3.7121050707415423`*^9, 3.712105070813546*^9}, { 3.7123570951014767`*^9, 3.712357095895522*^9}, {3.7505403174489098`*^9, 3.7505403175915723`*^9}, 3.753924254674737*^9, {3.7568394056661353`*^9, 3.7568394060575542`*^9}}, CellLabel->"In[10]:=",ExpressionUUID->"6e7ab65a-56f2-408e-8305-25556ece3b01"], Cell[BoxData["\<\"L, R, V, Vtilde, VPM, VtildePM, ZetaGen, ZetatildeGen, \ LCoeffs, RCoeffs, VCoeffs, VtildeCoeffs, VPMCoeffs, VtildePMCoeffs, ncis, \ ntrans, chi0, and nzvalue for Rep = nmSGprime are loaded, Holoraumy and \ Monodromy not generated\"\>"], "Output", CellChangeTimes->{3.7539264585342307`*^9, 3.7540708497372355`*^9, 3.756839057207279*^9, 3.75683941411372*^9, 3.756844083952924*^9, 3.760729101035035*^9, 3.7607299647794843`*^9}, CellLabel->"Out[10]=",ExpressionUUID->"c6e564cb-3496-463a-bfe4-7dd4c79d6c1f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Get", "[", "\"\\"", "]"}]], "Input", CellChangeTimes->{{3.71150063575192*^9, 3.7115006395731387`*^9}, { 3.711657367639683*^9, 3.711657367720688*^9}, {3.71186146547114*^9, 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