(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.2' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     90277,       2193]
NotebookOptionsPosition[     77893,       1872]
NotebookOutlinePosition[     78413,       1892]
CellTagsIndexPosition[     78370,       1889]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["4DTools.nb", "Title",
 CellChangeTimes->{{3.431643447359375*^9, 3.43164348528125*^9}, {
   3.4332803471875*^9, 3.4332803938125*^9}, {3.439841647921875*^9, 
   3.439841676265625*^9}, {3.4399946617855*^9, 3.43999466687925*^9}, {
   3.44088192175*^9, 3.440881923578125*^9}, {3.4423479416875*^9, 
   3.442347948953125*^9}, {3.442980454609375*^9, 3.442980483234375*^9}, {
   3.443704482140625*^9, 3.443704510671875*^9}, {3.443704683796875*^9, 
   3.443704691203125*^9}, {3.44372638084375*^9, 3.443726451640625*^9}, {
   3.45355300203125*^9, 3.453553002890625*^9}, {3.454246287921875*^9, 
   3.454246303546875*^9}, {3.454246379453125*^9, 3.4542464184375*^9}, {
   3.454246473484375*^9, 3.454246483109375*^9}, {3.4544147554375*^9, 
   3.454414815859375*^9}, {3.454852671*^9, 3.4548527046875*^9}, {
   3.454856728203125*^9, 3.45485673075*^9}, {3.454926202984375*^9, 
   3.454926295546875*^9}, {3.455015384*^9, 3.455015392609375*^9}, {
   3.455015444671875*^9, 3.455015446890625*^9}, {3.455015517421875*^9, 
   3.455015519890625*^9}, {3.4550155711875*^9, 3.455015606859375*^9}, {
   3.455016320453125*^9, 3.45501632865625*^9}, {3.455042848390625*^9, 
   3.455042857671875*^9}, {3.455043636234375*^9, 3.4550436771875*^9}, {
   3.511555277628312*^9, 3.5115553207117767`*^9}, {3.511625771375633*^9, 
   3.5116258752865763`*^9}, {3.5116411679872684`*^9, 3.511641221284317*^9}, {
   3.5199454008058896`*^9, 3.5199454666306543`*^9}, {3.5199455739987955`*^9, 
   3.519945622294558*^9}, {3.5206458956356697`*^9, 3.520645943704419*^9}, {
   3.523718893836775*^9, 3.523718923873493*^9}, {3.536715674278531*^9, 
   3.5367157073544226`*^9}, {3.53853389765368*^9, 3.538533899967812*^9}, {
   3.538942345864266*^9, 3.538942357964958*^9}, {3.5389474299050565`*^9, 
   3.538947485150216*^9}, {3.5390845827297893`*^9, 3.5390846106083837`*^9}, {
   3.53908510341057*^9, 3.5390851199535165`*^9}, {3.539086064745556*^9, 
   3.5390861577368746`*^9}, {3.5451459061807747`*^9, 3.545145907619857*^9}, {
   3.54514596135293*^9, 3.5451460262956448`*^9}, {3.548677365614721*^9, 
   3.548677420252846*^9}, {3.5486904482318554`*^9, 3.5486904831498528`*^9}, {
   3.5507964280028415`*^9, 3.550796434750227*^9}, {3.5516981864105062`*^9, 
   3.5516981873125577`*^9}, {3.5517063670611444`*^9, 3.551706375990655*^9}, {
   3.5517143798937216`*^9, 3.5517143832039113`*^9}, {3.5517286202182903`*^9, 
   3.5517286597495513`*^9}, {3.5517928905442033`*^9, 3.551792917464743*^9}, {
   3.5521354453831377`*^9, 3.5521354853424234`*^9}, {3.552135534200218*^9, 
   3.552135558024581*^9}, {3.5521356059203205`*^9, 3.552135681027616*^9}, {
   3.5521357231810274`*^9, 3.5521357548318377`*^9}, {3.55231422706569*^9, 
   3.5523142637937903`*^9}, {3.552314318528921*^9, 3.552314318928944*^9}, {
   3.552314384905718*^9, 3.552314430815344*^9}, {3.552314502398438*^9, 
   3.5523146413143835`*^9}, {3.552473196132519*^9, 3.5524732208799343`*^9}, 
   3.5528371122703466`*^9, 3.5528444571634464`*^9, {3.5528449407701073`*^9, 
   3.5528450003105125`*^9}, {3.552866910465884*^9, 3.5528670764143763`*^9}, {
   3.5528755049588575`*^9, 3.552875669883291*^9}, {3.5528757974815893`*^9, 
   3.5528759485802317`*^9}, {3.552876032727044*^9, 3.5528760646078677`*^9}, 
   3.5528770280839753`*^9, {3.552905728992181*^9, 3.5529057870398817`*^9}, {
   3.552924313800542*^9, 3.552924357451039*^9}, {3.5529244139042673`*^9, 
   3.5529245023153243`*^9}, {3.5529245516931486`*^9, 3.552924613397678*^9}, {
   3.552928164005761*^9, 3.552928186311037*^9}, {3.5529298153452125`*^9, 
   3.5529298409716783`*^9}, {3.5532932040039682`*^9, 
   3.5532932496185775`*^9}, {3.553293282659467*^9, 3.553293292302019*^9}, {
   3.553293383011207*^9, 3.553293411333827*^9}, {3.5532981370511494`*^9, 
   3.553298408108653*^9}, {3.553298441734576*^9, 3.5532987180763826`*^9}, {
   3.5532987757606816`*^9, 3.5532988306618223`*^9}, {3.5533029743948298`*^9, 
   3.5533030195604134`*^9}, {3.553306886924614*^9, 3.5533068932679768`*^9}, {
   3.553311679995762*^9, 3.553311730478649*^9}, {3.553311805864961*^9, 
   3.5533118710006866`*^9}, {3.5533120465167255`*^9, 3.553312046787741*^9}, {
   3.5533122428069525`*^9, 3.5533122428069525`*^9}, {3.553312319318329*^9, 
   3.553312332850103*^9}, {3.5533123656929817`*^9, 3.5533123938585925`*^9}, 
   3.5533125753399725`*^9, {3.5533162583976316`*^9, 3.5533162749975805`*^9}, 
   3.5533163117066803`*^9, {3.5533163518819785`*^9, 3.5533164029468994`*^9}, {
   3.553357870429034*^9, 3.55335793120451*^9}, {3.553360423158042*^9, 
   3.553360477275137*^9}, {3.5533605162343655`*^9, 3.553360605248457*^9}, {
   3.55336064149253*^9, 3.5533607117395477`*^9}, {3.553360769712864*^9, 
   3.553360790017025*^9}, {3.553360827712181*^9, 3.5533608685515165`*^9}, {
   3.5533609116069794`*^9, 3.553360984719161*^9}, {3.553361035631073*^9, 
   3.5533610708610888`*^9}, {3.5533611506446514`*^9, 3.553361152577762*^9}, {
   3.553361571282711*^9, 3.553361617443351*^9}, {3.553362021762477*^9, 
   3.5533621970635033`*^9}, {3.55336225609488*^9, 3.553362258462015*^9}, {
   3.553362402136233*^9, 3.5533624518330755`*^9}, {3.553362520950029*^9, 
   3.5533625853667135`*^9}, {3.5533635314808273`*^9, 
   3.5533635853299074`*^9}, {3.553363685328627*^9, 3.553363698002352*^9}, {
   3.553363909535451*^9, 3.5533639144157305`*^9}, 3.553364219200163*^9, 
   3.5533644938708735`*^9, {3.553364575184524*^9, 3.553364599654924*^9}, {
   3.55336466183048*^9, 3.5533646655966954`*^9}, {3.553365137488686*^9, 
   3.553365145141124*^9}, {3.5533656688530784`*^9, 3.5533657248882837`*^9}, 
   3.553366821643014*^9, {3.5533671012070045`*^9, 3.5533671132246914`*^9}, {
   3.553367256017859*^9, 3.5533672954111123`*^9}, {3.5533673936717324`*^9, 
   3.553367442797542*^9}, {3.553393155762641*^9, 3.5533933527619085`*^9}, {
   3.5533934025587573`*^9, 3.55339343250747*^9}, {3.553393466195397*^9, 
   3.5533934799451838`*^9}, {3.5533936057913814`*^9, 3.553393621924304*^9}, {
   3.5533936651637774`*^9, 3.553393696448567*^9}, {3.5533938357385335`*^9, 
   3.5533938415228643`*^9}, {3.55339396837212*^9, 3.553393970315231*^9}, {
   3.553394007223342*^9, 3.5533940655636787`*^9}, {3.5533948267242146`*^9, 
   3.553394871172757*^9}, 3.5533949827821407`*^9, {3.553395879210414*^9, 
   3.55339590415384*^9}, {3.5533960192464232`*^9, 3.553396052167306*^9}, {
   3.5534453110074387`*^9, 3.5534453210730143`*^9}, {3.5543978769816384`*^9, 
   3.5543979153068304`*^9}, {3.5543979522839456`*^9, 3.554398051165597*^9}, {
   3.559413579039064*^9, 3.559414031602949*^9}, {3.5594140643608227`*^9, 
   3.559414824354292*^9}, {3.5594148673047485`*^9, 3.5594148697598886`*^9}, 
   3.559434854871258*^9, {3.5594361459001007`*^9, 3.5594361488202677`*^9}, {
   3.5594362074236193`*^9, 3.5594362074236193`*^9}, {3.5594413332417994`*^9, 
   3.559441339224142*^9}, {3.5594800125024767`*^9, 3.5594800206869445`*^9}, 
   3.55949611087125*^9, {3.5594961446901846`*^9, 3.5594963728392344`*^9}, {
   3.5594967272045026`*^9, 3.559496732893828*^9}, {3.559496827283227*^9, 
   3.559496972989561*^9}, {3.559498343667959*^9, 3.5594984776456223`*^9}, {
   3.5594985619584446`*^9, 3.5594986885086827`*^9}, {3.559504207814369*^9, 
   3.5595043347686305`*^9}, {3.5610849081423254`*^9, 3.561084919991003*^9}, {
   3.674997609869558*^9, 3.6749976403446026`*^9}, {3.7095691177887754`*^9, 
   3.7095692232638083`*^9}, {3.709569416628868*^9, 3.709569447700645*^9}, {
   3.709570025775709*^9, 3.7095700822929416`*^9}, {3.7095701212661705`*^9, 
   3.7095701302756863`*^9}, {3.7095701635905914`*^9, 
   3.7095701953544083`*^9}, {3.709570238234861*^9, 3.7095703996370926`*^9}, {
   3.7095705169488025`*^9, 3.709570536260907*^9}, {3.709570570671875*^9, 
   3.7095707000022726`*^9}, {3.7095707414556437`*^9, 3.709570911927394*^9}, {
   3.7095709420471168`*^9, 3.7095709556628957`*^9}, {3.709571091599671*^9, 
   3.7095711396634197`*^9}, {3.7095711775595875`*^9, 3.709571198140764*^9}, {
   3.709573470067711*^9, 3.7095735804760265`*^9}, {3.70957367197526*^9, 
   3.709573673761362*^9}, {3.709575309022894*^9, 3.7095753967389107`*^9}, {
   3.7108085535310116`*^9, 3.710808698160284*^9}, {3.7117169877149534`*^9, 
   3.71171700584299*^9}, {3.711843921222666*^9, 3.711843950188323*^9}, {
   3.7120954091535835`*^9, 3.712095410524662*^9}, {3.737153557144597*^9, 
   3.7371535573632975`*^9}, {3.737153660538913*^9, 3.737153677384055*^9}, {
   3.737289276440363*^9, 3.7372892764413633`*^9}, {3.7379791370084977`*^9, 
   3.7379791561145906`*^9}, {3.7379792255395613`*^9, 3.737979267044935*^9}, {
   3.738580160531347*^9, 3.7385801752121863`*^9}, {3.7422187903728733`*^9, 
   3.742218794232212*^9}, {3.74239600783539*^9, 3.742396031273322*^9}, {
   3.742396076391885*^9, 3.7423960771785297`*^9}, {3.74244271196679*^9, 
   3.74244273700751*^9}, {3.742443757095769*^9, 3.742443769730857*^9}, {
   3.7474009412101183`*^9, 3.7474009449538765`*^9}, {3.75700357550987*^9, 
   3.757003581134755*^9}},ExpressionUUID->"dfab12f3-523a-4891-ab6d-\
6353bcfa0aa5"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"$RecursionLimit", "=", "Infinity"}]], "Input",ExpressionUUID->"65e9b759-d921-4a12-9e52-b3e8b17f8777"],

Cell[BoxData["\[Infinity]"], "Output",
 CellChangeTimes->{
  3.75000980146104*^9, 3.750013814734825*^9, 3.7500138991313705`*^9, 
   3.750013955464712*^9, 3.750017992642973*^9, 3.7500183270220547`*^9, 
   3.7501575184969435`*^9, 3.7503401677111044`*^9, 3.750375395139457*^9, {
   3.750375531335409*^9, 3.7503755526374416`*^9}, 3.750375767846264*^9, 
   3.750376418753233*^9, 3.7503767284595356`*^9, 3.750377366066451*^9, 
   3.750377518685463*^9, 3.7503775713806267`*^9, 3.750377994341915*^9, 
   3.7506852649086094`*^9, 3.752425226183292*^9, 3.7525149478152847`*^9, 
   3.752519673386527*^9, 3.7525197282480564`*^9, 3.7525200520073175`*^9, 
   3.752520461359535*^9, 3.752520511125148*^9, 3.7525206938160768`*^9, 
   3.752586920158411*^9, 3.7525871649052706`*^9, 3.7525874602936306`*^9, 
   3.7525884157214108`*^9, 3.7525888345725064`*^9, 3.7525900270455775`*^9, 
   3.7539142033886743`*^9, 3.7543340494756317`*^9, 
   3.757003548960999*^9},ExpressionUUID->"6c7b3753-5f27-4f2b-a073-\
60a98bdbcd4c"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Import Adinkra package", "Section",
 CellChangeTimes->{{3.7108088373262444`*^9, 3.7108088416734924`*^9}, {
  3.742443794211779*^9, 3.7424437981540127`*^9}, {3.742447582747436*^9, 
  3.742447583928364*^9}, {3.7567334737765293`*^9, 
  3.7567334765110493`*^9}},ExpressionUUID->"8ce62cfa-2467-4484-bfab-\
5a2bb7149ea5"],

Cell[BoxData[
 RowBox[{"<<", "Adinkra`"}]], "Input",
 CellChangeTimes->{{3.742443803362287*^9, 3.742443804715487*^9}, {
  3.742446558681669*^9, 3.742446563370216*^9}, {3.756733429820123*^9, 
  3.7567334324120774`*^9}},ExpressionUUID->"3ce86a4c-e50b-42b6-b6ba-\
cfca0898781a"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"BuildDate", "[", "Adinkra", "]"}]], "Input",
 CellChangeTimes->{{3.746549445600609*^9, 
  3.746549448047648*^9}},ExpressionUUID->"335154d1-1580-4631-8a3e-\
4170890b8e5c"],

Cell[BoxData["181216"], "Output",
 CellChangeTimes->{
  3.750003189196753*^9, 3.7500098016448317`*^9, 3.750013814908918*^9, 
   3.75001389921817*^9, 3.750013955565403*^9, 3.7500179927402325`*^9, 
   3.750018331921175*^9, 3.7501575186621485`*^9, 3.750340167867319*^9, 
   3.750375395294075*^9, {3.7503755315168867`*^9, 3.750375552798994*^9}, 
   3.7503757680556803`*^9, 3.750376418895879*^9, 3.750376728596168*^9, 
   3.750377366258939*^9, 3.750377518843042*^9, 3.750377571592062*^9, 
   3.7503779945404234`*^9, 3.7506852650941105`*^9, 3.752425233016388*^9, 
   3.752514947948928*^9, 3.7525196735692577`*^9, 3.7525197283786964`*^9, 
   3.752520052204206*^9, 3.752520461494176*^9, 3.7525205112508554`*^9, 
   3.752520694045436*^9, {3.752586924711528*^9, 3.752586934194687*^9}, 
   3.7525871650227795`*^9, 3.7525874604261837`*^9, 3.7525884159278603`*^9, 
   3.7525888347989383`*^9, 3.7525900272108307`*^9, 3.7539142355958705`*^9, 
   3.754334049631844*^9, {3.7567334173087854`*^9, 3.7567334461477823`*^9}, 
   3.757003549322824*^9},ExpressionUUID->"a3ded3b2-b7a9-4dfb-a777-\
239928c8e844"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Function Lists", "Subsection",
 CellChangeTimes->{{3.746556066750236*^9, 
  3.746556069037942*^9}},ExpressionUUID->"9032bd95-7de1-4377-8cd7-\
b7fd291e0e1f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "SpaceTime", "]"}]], "Input",
 CellChangeTimes->{{3.7113871307973413`*^9, 3.7113871345915585`*^9}, {
   3.737153856684306*^9, 3.7371538843584447`*^9}, 3.737153921314643*^9, 
   3.74240099428962*^9},ExpressionUUID->"433cc145-fb86-450b-9648-\
f7c5cbb57d74"],

Cell[BoxData["\<\"IndexRange[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***********************************\
*****************************************************\"\>"], "Output",
 CellChangeTimes->{
  3.750009801786179*^9, 3.7500138149342546`*^9, 3.7500138992479305`*^9, 
   3.7500139555887327`*^9, 3.7500179927804065`*^9, 3.750018331968354*^9, 
   3.7501575186974063`*^9, 3.7503401679141855`*^9, 3.7503753953349686`*^9, {
   3.7503755315618215`*^9, 3.75037555284092*^9}, 3.750375768112529*^9, 
   3.750376418950735*^9, 3.7503767292444353`*^9, 3.75037736628088*^9, 
   3.750377518871966*^9, 3.750377571621002*^9, 3.75037799457335*^9, 
   3.750685265138276*^9, 3.752425239693218*^9, 3.75251494798088*^9, 
   3.752519673586209*^9, 3.7525197283966484`*^9, 3.752520052225191*^9, 
   3.752520461518112*^9, 3.7525205112688055`*^9, 3.752520694062445*^9, {
   3.7525869247929115`*^9, 3.75258693421083*^9}, 3.75258716505398*^9, 
   3.7525874604666224`*^9, 3.7525884159926853`*^9, 3.752588834853798*^9, 
   3.752590027253207*^9, 3.7539142502379885`*^9, {3.7543340444270935`*^9, 
   3.754334049647436*^9}, 
   3.757003549440843*^9},ExpressionUUID->"df972d6d-37f5-42d8-94b0-\
ea46625ec3fa"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "GenerateLandR", "]"}]], "Input",
 CellChangeTimes->{{3.711385162397755*^9, 3.711385168130083*^9}, 
   3.737162730827726*^9, 
   3.742400996260387*^9},ExpressionUUID->"5ab02646-7eb8-4bc6-9cc6-\
8c4ac39583d4"],

Cell[BoxData["\<\"NColors[D,Phi,Psi], LTable[DColor,Phi,Psi], \
RTable[DColor,Phi,Psi],GenerateLandR[DColor,Phi,Psi,Rep]\\n\\n****************\
************************************************************************\\n***\
******************************************************************************\
*******\"\>"], "Output",
 CellChangeTimes->{
  3.750009801905787*^9, 3.7500138149466596`*^9, 3.750013899264798*^9, 
   3.750013955600634*^9, 3.7500179928017387`*^9, 3.7500183319975586`*^9, 
   3.7501575187151823`*^9, 3.750340167929804*^9, 3.750375395352887*^9, {
   3.7503755315857334`*^9, 3.750375552859831*^9}, 3.7503757681394634`*^9, 
   3.7503764189746404`*^9, 3.7503767292683716`*^9, 3.7503773662908525`*^9, 
   3.750377518884977*^9, 3.7503775716329217`*^9, 3.7503779945873213`*^9, 
   3.750685265154149*^9, 3.752425239757814*^9, 3.75251494801182*^9, 
   3.752519673609151*^9, 3.7525197284126034`*^9, 3.75252005225607*^9, 
   3.7525204615370607`*^9, 3.7525205112847676`*^9, 3.752520694094326*^9, {
   3.752586924827161*^9, 3.752586934247032*^9}, 3.7525871650696373`*^9, 
   3.7525874604822693`*^9, 3.752588416012754*^9, 3.7525888348776903`*^9, 
   3.7525900272736697`*^9, 3.7539142502692013`*^9, 3.754334049663089*^9, 
   3.757003549504363*^9},ExpressionUUID->"f261176c-3908-4028-aa59-\
1684a3766102"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "AdinkraEssentials", "]"}]], "Input",
 CellChangeTimes->{{3.7108090604950085`*^9, 
  3.710809067253395*^9}},ExpressionUUID->"f2152041-3457-4816-9e34-\
ccfb12c93d8a"],

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",
 CellChangeTimes->{
  3.750009801970381*^9, 3.7500138149615355`*^9, 3.7500138992806654`*^9, 
   3.7500139556205807`*^9, 3.75001799282302*^9, 3.7500183320129957`*^9, 
   3.750157518735022*^9, 3.7503401679453945`*^9, 3.7503753953708725`*^9, {
   3.750375531604685*^9, 3.750375552882778*^9}, 3.750375768162423*^9, 
   3.7503764189956193`*^9, 3.750376729290313*^9, 3.7503773663008275`*^9, 
   3.7503775188979397`*^9, 3.750377571644926*^9, 3.750377994601222*^9, 
   3.750685265169029*^9, 3.75242523978398*^9, 3.7525149480337396`*^9, 
   3.7525196736261096`*^9, 3.752519728428563*^9, 3.7525200522711067`*^9, 
   3.7525204615699744`*^9, 3.752520511300723*^9, 3.752520694110281*^9, {
   3.7525869248533316`*^9, 3.752586934279681*^9}, 3.7525871650852227`*^9, 
   3.7525874604978805`*^9, 3.7525884160537853`*^9, 3.7525888349046583`*^9, 
   3.7525900272757683`*^9, 3.7539142502692013`*^9, 3.754334049663089*^9, 
   3.757003549568965*^9},ExpressionUUID->"9a82b3ca-5a2e-4f79-b1c1-\
bb5c10d4d3a2"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "BasisDecomposition", "]"}]], "Input",
 CellChangeTimes->{{3.7108090693605156`*^9, 3.710809079103073*^9}, {
   3.738580277883059*^9, 3.738580278195077*^9}, 
   3.7465494655188327`*^9},ExpressionUUID->"cd131f93-6eb8-4ba3-b71c-\
6c9265945b1e"],

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_]\\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",
 CellChangeTimes->{
  3.7500098020361147`*^9, 3.7500138149783974`*^9, 3.7500138992925706`*^9, 
   3.750013955629508*^9, 3.7500179928493567`*^9, 3.7500183320347586`*^9, 
   3.750157518760458*^9, 3.750340167976637*^9, 3.7503753953927803`*^9, {
   3.750375531625595*^9, 3.750375552900722*^9}, 3.7503757681883574`*^9, 
   3.7503764190195208`*^9, 3.75037672931326*^9, 3.7503773663098125`*^9, 
   3.750377518910918*^9, 3.7503775716568923`*^9, 3.7503779946161823`*^9, 
   3.750685265185398*^9, 3.752425239838821*^9, 3.752514948063665*^9, 
   3.7525196736430597`*^9, 3.7525197284455175`*^9, 3.7525200522900515`*^9, 
   3.7525204615849333`*^9, 3.752520511316683*^9, 3.7525206941302643`*^9, {
   3.7525869248689504`*^9, 3.752586934304495*^9}, 3.7525871651184587`*^9, 
   3.7525874605291185`*^9, 3.7525884160737314`*^9, 3.752588834925612*^9, 
   3.7525900273070145`*^9, 3.7539142502848067`*^9, 3.754334049678707*^9, 
   3.757003549633306*^9},ExpressionUUID->"fdecae43-67d0-48ee-8642-\
103702327116"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "BC4Tools", "]"}]], "Input",
 CellChangeTimes->{{3.7108090693605156`*^9, 3.710809079103073*^9}, {
  3.738580277883059*^9, 3.738580278195077*^9}, {3.7423962019662447`*^9, 
  3.742396207751975*^9}},ExpressionUUID->"5cf8981a-5985-4a6c-861a-\
8b771458a158"],

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",
 CellChangeTimes->{
  3.75000980210111*^9, 3.7500138149947767`*^9, 3.750013899313898*^9, 
   3.7500139556484213`*^9, 3.750017992871176*^9, 3.750018332065054*^9, 
   3.7501575187807837`*^9, 3.7503401679922633`*^9, 3.750375395415719*^9, {
   3.750375531645573*^9, 3.7503755529206696`*^9}, 3.75037576821329*^9, 
   3.7503764190464487`*^9, 3.75037672933619*^9, 3.750377366320773*^9, 
   3.7503775189228287`*^9, 3.7503775716698236`*^9, 3.7503779946302032`*^9, 
   3.750685265204742*^9, 3.752425239888069*^9, 3.752514948089549*^9, 
   3.7525196736599607`*^9, 3.752519728461475*^9, 3.752520052318905*^9, 
   3.7525204616038823`*^9, 3.7525205113316393`*^9, 3.7525206941561956`*^9, {
   3.7525869249088345`*^9, 3.752586934320157*^9}, 3.7525871651395087`*^9, 
   3.7525874605447397`*^9, 3.7525884161098127`*^9, 3.7525888349555674`*^9, 
   3.752590027322673*^9, 3.7539142503004117`*^9, 3.75433404969433*^9, 
   3.757003549696796*^9},ExpressionUUID->"21e82ba8-0f11-4fdb-b7b4-\
b2b8b2a23494"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "GraphingTools", "]"}]], "Input",
 CellChangeTimes->{{3.7108090693605156`*^9, 3.710809079103073*^9}, {
  3.738580277883059*^9, 3.738580278195077*^9}, {3.7423962019662447`*^9, 
  3.742396232829598*^9}},ExpressionUUID->"8a453f50-9c25-4910-84fc-\
5bfae4aaeae8"],

Cell[BoxData["\<\"IndexRange[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",
 CellChangeTimes->{
  3.750009802500476*^9, 3.7500138150111*^9, 3.7500138993262973`*^9, 
   3.750013955664786*^9, 3.7500179928954735`*^9, 3.7500183320838623`*^9, 
   3.750157518800626*^9, 3.750340168007908*^9, 3.750375395433671*^9, {
   3.750375531664525*^9, 3.7503755529416122`*^9}, 3.750375768238224*^9, 
   3.750376419617952*^9, 3.750376729363118*^9, 3.75037736632975*^9, 
   3.750377518936838*^9, 3.750377571685807*^9, 3.7503779946471367`*^9, 
   3.7506852652210875`*^9, 3.752425239939026*^9, 3.752514948112524*^9, 
   3.7525196736769605`*^9, 3.7525197284784293`*^9, 3.7525200523348913`*^9, 
   3.752520461636795*^9, 3.752520511347597*^9, 3.752520694176916*^9, {
   3.752586924933112*^9, 3.752586934343094*^9}, 3.7525871651551676`*^9, 
   3.7525874605603557`*^9, 3.752588416134202*^9, 3.7525888349868526`*^9, 
   3.752590027338292*^9, 3.7539142503004117`*^9, 3.75433404969433*^9, 
   3.757003549760112*^9},ExpressionUUID->"b92ef2fb-c027-4947-951a-\
d09e9f77f3ef"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "Adinkra", "]"}]], "Input",
 CellChangeTimes->{{3.7424465936653976`*^9, 
  3.742446599983512*^9}},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_]\\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",
 CellChangeTimes->{
  3.750003234323081*^9, 3.75000980275079*^9, 3.7500138150289526`*^9, 
   3.750013899349115*^9, 3.750013955681652*^9, 3.750017992917305*^9, 
   3.7500183321126304`*^9, 3.7501575188215227`*^9, 3.750340168039153*^9, 
   3.7503753954526205`*^9, {3.750375531686447*^9, 3.7503755529615936`*^9}, 
   3.750375768264124*^9, 3.7503764196398926`*^9, 3.7503767293890715`*^9, 
   3.7503773663397207`*^9, 3.750377518948786*^9, 3.750377571702735*^9, 
   3.7503779946630898`*^9, 3.750685265233983*^9, 3.752425239986079*^9, 
   3.7525149481414127`*^9, 3.7525196736938677`*^9, 3.7525197284963818`*^9, 
   3.752520052353868*^9, 3.752520461651754*^9, 3.7525205113635545`*^9, 
   3.7525206942038417`*^9, {3.7525869249628134`*^9, 3.752586934363202*^9}, 
   3.752587165170752*^9, 3.7525874605759697`*^9, 3.7525884161571417`*^9, 
   3.752588835011074*^9, 3.7525900273539147`*^9, 3.753914250316063*^9, 
   3.7543340497099547`*^9, 
   3.7570035498240643`*^9},ExpressionUUID->"ef5d28a2-0b94-4b1f-8eca-\
b39cf62bf18c"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Introduction to some of these functions", "Subsection",
 CellChangeTimes->{{3.750007903453146*^9, 
  3.750007917274867*^9}},ExpressionUUID->"d2a6411a-95d2-4892-9744-\
45cbf8b5fc2e"],

Cell[CellGroupData[{

Cell["Within FunctionList[SpaceTime]", "Subsubsection",
 CellChangeTimes->{{3.7500079523883343`*^9, 
  3.750007982323703*^9}},ExpressionUUID->"6d43e65b-1220-4dd0-ac77-\
fbe7c15c929c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{" ", 
  RowBox[{"\[Eta]", "[", 
   RowBox[{"1", ",", "1"}], "]"}]}]], "Input",
 CellChangeTimes->{{3.750003335953824*^9, 
  3.750003350132477*^9}},ExpressionUUID->"696619bb-4bda-4abd-a3d7-\
6c21086107ae"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{{3.750003343025764*^9, 3.7500033508829517`*^9}, 
   3.750009802862823*^9, 3.75001381504631*^9, 3.750013899363499*^9, 
   3.750013955696086*^9, 3.7500179929415627`*^9, {3.7500183321349883`*^9, 
   3.75001835178246*^9}, 3.750157518845323*^9, 3.7503401680547748`*^9, 
   3.750375395471613*^9, {3.750375531705413*^9, 3.7503755529845285`*^9}, 
   3.7503757682920485`*^9, 3.750376419665824*^9, 3.750376729416974*^9, 
   3.7503773663516903`*^9, 3.7503775189617386`*^9, 3.750377571716712*^9, 
   3.7503779946780186`*^9, 3.7506852652538233`*^9, 3.7524252400330143`*^9, 
   3.752514948165385*^9, 3.7525196737118225`*^9, 3.7525197285143337`*^9, 
   3.7525200523737955`*^9, 3.7525204616717014`*^9, 3.7525205113785377`*^9, 
   3.7525206942277355`*^9, {3.7525869249850807`*^9, 3.7525869343988266`*^9}, 
   3.752587165189828*^9, 3.7525874605915937`*^9, 3.7525884161930447`*^9, 
   3.752588835060896*^9, 3.7525900273695655`*^9, 3.753914250316063*^9, 
   3.757003549887417*^9},ExpressionUUID->"b39135be-78cf-4577-985e-\
885e9cc9c2b1"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["Cmetric"], "Input",
 CellChangeTimes->{{3.750003357600115*^9, 
  3.750003358566908*^9}},ExpressionUUID->"da336974-8655-41e2-a289-\
74fb778d736c"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"-", "1"}], ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.750003365689596*^9, 3.750009802939212*^9, 3.750013815078054*^9, 
   3.7500138993758984`*^9, 3.7500139557158766`*^9, 3.7500179929638824`*^9, {
   3.750018332165206*^9, 3.7500183518988466`*^9}, 3.7501575188740916`*^9, 
   3.750340168086319*^9, 3.750375395491563*^9, {3.750375531726327*^9, 
   3.750375553004445*^9}, 3.750375768314019*^9, 3.75037641968777*^9, 
   3.7503767294399433`*^9, 3.7503773663616624`*^9, 3.750377518974719*^9, 
   3.7503775717316575`*^9, 3.750377994694973*^9, 3.7506852652687025`*^9, 
   3.752425240066082*^9, 3.752514948195306*^9, 3.7525196737298193`*^9, 
   3.752519728531288*^9, 3.752520052399719*^9, 3.752520461703616*^9, 
   3.7525205113944755`*^9, 3.752520694244728*^9, {3.75258692499885*^9, 
   3.7525869344144855`*^9}, 3.7525871652087803`*^9, 3.75258746060723*^9, 
   3.7525884162148633`*^9, 3.752588835081374*^9, 3.7525900274008017`*^9, 
   3.7539142503316793`*^9, 
   3.7570035499507847`*^9},ExpressionUUID->"fa15472b-0555-45d9-ab93-\
c0a798162a70"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Lap", "[", 
  RowBox[{"SomeField", "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.7500034669181023`*^9, 
  3.750003479050886*^9}},ExpressionUUID->"61551fc0-f96c-4eff-a43f-\
a97ce806d229"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SuperscriptBox["SomeField", 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "0", ",", "2"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox["SomeField", 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "2", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox["SomeField", 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "2", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "-", 
  RowBox[{
   SuperscriptBox["SomeField", 
    TagBox[
     RowBox[{"(", 
      RowBox[{"2", ",", "0", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}]}]], "Output",
 CellChangeTimes->{
  3.750003488229455*^9, 3.750009803018718*^9, 3.7500138151365843`*^9, 
   3.75001389939882*^9, 3.7500139557327404`*^9, 3.750017992986738*^9, {
   3.7500183321830654`*^9, 3.7500183519211645`*^9}, 3.7501575189375515`*^9, 
   3.750340168101942*^9, 3.750375395563324*^9, {3.75037553174531*^9, 
   3.7503755530253887`*^9}, 3.750375768338923*^9, 3.750376419709677*^9, 
   3.750376729467882*^9, 3.7503773663756285`*^9, 3.7503775189886513`*^9, 
   3.750377571745674*^9, 3.7503779947119412`*^9, 3.750685265302696*^9, 
   3.75242524010464*^9, 3.752514948224227*^9, 3.75251967375497*^9, 
   3.7525197285552254`*^9, 3.7525200524226227`*^9, 3.75252046172057*^9, 
   3.7525205114113965`*^9, 3.752520694270265*^9, {3.75258692501451*^9, 
   3.7525869344300747`*^9}, 3.752587165217142*^9, 3.7525874606384573`*^9, 
   3.7525884162350707`*^9, 3.7525888351027527`*^9, 3.752590027416399*^9, 
   3.7539142503472767`*^9, 
   3.757003550016671*^9},ExpressionUUID->"1e784759-e386-4e45-8c30-\
dd6e74661796"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Lap", "[", 
  RowBox[{
   RowBox[{"A", "[", "2", "]"}], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.7500035060951433`*^9, 3.750003529986573*^9}, {
  3.7500035602709618`*^9, 
  3.7500035666779737`*^9}},ExpressionUUID->"a623415f-9142-4544-adfe-\
1e00582a4797"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SuperscriptBox[
    RowBox[{"A", "[", "2", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "0", ",", "2"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"A", "[", "2", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "2", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"A", "[", "2", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "2", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "-", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"A", "[", "2", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"2", ",", "0", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}]}]], "Output",
 CellChangeTimes->{{3.750003537354557*^9, 3.750003567032598*^9}, 
   3.750009803085595*^9, 3.750013815158944*^9, 3.750013899410226*^9, 
   3.7500139557446423`*^9, 3.7500179930120573`*^9, {3.7500183322049456`*^9, 
   3.75001835194501*^9}, 3.750157518964362*^9, 3.75034016813321*^9, 
   3.7503753955823183`*^9, {3.7503755323097973`*^9, 3.750375553047329*^9}, 
   3.750375768362888*^9, 3.750376419732647*^9, 3.7503767294937677`*^9, 
   3.7503773663875947`*^9, 3.7503775190016184`*^9, 3.75037757176061*^9, 
   3.750377994731873*^9, 3.750685265320287*^9, 3.752425240152581*^9, 
   3.752514948246206*^9, 3.7525196737759123`*^9, 3.7525197285761685`*^9, 
   3.7525200524386196`*^9, 3.752520461737526*^9, 3.75252051142739*^9, 
   3.7525206942872205`*^9, {3.752586925030137*^9, 3.752586934474908*^9}, 
   3.7525871652469015`*^9, 3.75258746065409*^9, 3.752588416256015*^9, 
   3.7525888351246524`*^9, 3.752590027432023*^9, 3.7539142503629274`*^9, 
   3.757003550162416*^9},ExpressionUUID->"3caf3019-b351-46d5-85f5-\
d17e91717d45"]
}, Open  ]]
}, Closed]],

Cell[CellGroupData[{

Cell["Within FunctionList[AdinkraEssentials]", "Subsubsection",
 CellChangeTimes->{{3.7500079523883343`*^9, 3.750007982323703*^9}, {
  3.750375799279215*^9, 
  3.750375803055151*^9}},ExpressionUUID->"9e6f5328-f24c-43bd-9942-\
c8f1da8f8655"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"IndexRange", "[", "AdinkraEssentials", "]"}], "[", "ReportLevel", 
  "]"}]], "Input",
 CellChangeTimes->{{3.7503756086626616`*^9, 3.750375645171093*^9}, {
  3.7503757778285875`*^9, 
  3.750375781507756*^9}},ExpressionUUID->"5fb3bfd5-b3f1-4920-94ac-\
b5a0e529a661"],

Cell[BoxData["\<\"1, 2, 3, 4, 5, 6, 7, 8\"\>"], "Output",
 CellChangeTimes->{{3.7503756176127295`*^9, 3.7503756456637745`*^9}, {
   3.750375768386795*^9, 3.750375782018355*^9}, 3.7503764197545867`*^9, 
   3.750376729610488*^9, 3.750377366396571*^9, 3.7503775190146165`*^9, 
   3.7503775717745743`*^9, 3.750377994748828*^9, 3.7506852653366575`*^9, 
   3.752425240204514*^9, 3.7525149482671585`*^9, 3.752519673793867*^9, 
   3.7525197285941205`*^9, 3.752520052469499*^9, 3.7525204617525234`*^9, 
   3.7525205114443045`*^9, 3.7525206943031874`*^9, {3.7525869250457535`*^9, 
   3.7525869344938946`*^9}, 3.752587165781597*^9, 3.7525874606697006`*^9, 
   3.752588416276959*^9, 3.7525888351466293`*^9, 3.7525900274476433`*^9, 
   3.7539142503629274`*^9, 
   3.757003550164966*^9},ExpressionUUID->"5d9baa36-af56-4ff0-bd28-\
c94f3f359c6b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FunctionList", "[", "AdinkraEssentials", "]"}]], "Input",
 CellChangeTimes->{{3.750375653396105*^9, 
  3.750375660115147*^9}},ExpressionUUID->"d3176023-b48b-47c7-a647-\
5e2098481ea2"],

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",
 CellChangeTimes->{
  3.750375660705533*^9, 3.7503757684137545`*^9, 3.75037641977853*^9, 
   3.7503767296364317`*^9, 3.750377366405547*^9, 3.750377519027564*^9, 
   3.7503775717934923`*^9, 3.7503779947637873`*^9, 3.7506852653515344`*^9, 
   3.752425240252656*^9, 3.752514948286109*^9, 3.7525196738107758`*^9, 
   3.7525197286111193`*^9, 3.7525200524854927`*^9, 3.752520461767445*^9, 
   3.752520511461256*^9, 3.75252069431817*^9, {3.7525869250770087`*^9, 
   3.7525869345130053`*^9}, 3.7525871658128376`*^9, 3.7525874612771053`*^9, 
   3.7525884162969055`*^9, 3.752588835166541*^9, 3.7525900274632635`*^9, 
   3.753914250378519*^9, 
   3.75700355022816*^9},ExpressionUUID->"d2168833-9b97-4758-a932-\
524859c138af"]
}, Open  ]]
}, Closed]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["Testing 4D space-time", "Section",
 CellChangeTimes->{{3.742447433567292*^9, 
  3.742447441559691*^9}},ExpressionUUID->"867351f9-5484-4126-a47d-\
d94d902b177f"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[Gamma]5\[Gamma]", "[", "0", "]"}]], "Input",
 CellChangeTimes->{{3.742447443968371*^9, 
  3.742447464250478*^9}},ExpressionUUID->"c96a094c-792b-4f3b-b88a-\
257150e53b4d"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "\[ImaginaryI]", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", "\[ImaginaryI]"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0", ",", "0", ",", "0"}], "}"}], 
   ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0", ",", "0"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.7500178883983603`*^9, 3.7500180391567507`*^9, 
  3.7539143168200808`*^9, 
  3.757003550291526*^9},ExpressionUUID->"c6033bed-7f4b-4775-bbf3-\
6a985c273449"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]5", ".", 
   RowBox[{"CommuteGammastdownstupdown", "[", 
    RowBox[{"0", ",", "1"}], "]"}]}], "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.742447474748006*^9, 
  3.742447501328562*^9}},ExpressionUUID->"a4728552-95a4-4d02-ad9f-\
2afcc771ffe9"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", "0", 
      RowBox[{"2", " ", "\[ImaginaryI]"}], "0"},
     {"0", "0", "0", 
      RowBox[{
       RowBox[{"-", "2"}], " ", "\[ImaginaryI]"}]},
     {
      RowBox[{"2", " ", "\[ImaginaryI]"}], "0", "0", "0"},
     {"0", 
      RowBox[{
       RowBox[{"-", "2"}], " ", "\[ImaginaryI]"}], "0", "0"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.750017888430106*^9, 3.750018039183539*^9, 
  3.753914316835702*^9, 
  3.757003550360318*^9},ExpressionUUID->"16045a56-a303-4014-800c-\
71c496e9df59"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Cmetric", "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.7424475072807207`*^9, 
  3.742447518890211*^9}},ExpressionUUID->"bfc853bc-7a80-4bb2-a9bb-\
b155863bcc13"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", 
      RowBox[{"-", "1"}], "0", "0"},
     {"1", "0", "0", "0"},
     {"0", "0", "0", "1"},
     {"0", "0", 
      RowBox[{"-", "1"}], "0"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.750017888452923*^9, 3.750018039200981*^9, 
  3.753914316867279*^9, 
  3.7570035504258127`*^9},ExpressionUUID->"30a46528-1fab-49db-8b49-\
7ec8ee5a6356"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"UD", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"\[Psi]", "[", "1", "]"}], "[", 
    RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], ",", "t"}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.742447525747052*^9, 
  3.742447549380886*^9}},ExpressionUUID->"6c686fac-1ff8-4172-a22d-\
fb357e80d4bd"],

Cell[BoxData[
 RowBox[{"-", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "1", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"1", ",", "0", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}]}]], "Output",
 CellChangeTimes->{3.750017888480817*^9, 3.7500180392218127`*^9, 
  3.753914316882896*^9, 
  3.7570035504913473`*^9},ExpressionUUID->"942c64d0-fbcb-474f-8502-\
96704f5fd475"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Lap", "[", 
  RowBox[{
   RowBox[{"\[Psi]", "[", "1", "]"}], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.74244753811308*^9, 
  3.742447556028775*^9}},ExpressionUUID->"21a4a468-1f8e-47b4-bdd3-\
f2f33af9260e"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "1", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "0", ",", "2"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "1", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "0", ",", "2", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "+", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "1", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"0", ",", "2", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}], "-", 
  RowBox[{
   SuperscriptBox[
    RowBox[{"\[Psi]", "[", "1", "]"}], 
    TagBox[
     RowBox[{"(", 
      RowBox[{"2", ",", "0", ",", "0", ",", "0"}], ")"}],
     Derivative],
    MultilineFunction->None], "[", 
   RowBox[{"t", ",", "x", ",", "y", ",", "z"}], "]"}]}]], "Output",
 CellChangeTimes->{3.750017888504695*^9, 3.750018039255045*^9, 
  3.7539143169141383`*^9, 
  3.757003550557507*^9},ExpressionUUID->"89582e00-2a79-4be5-868b-\
63aa145c6e3d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Table", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"\[Alpha]matrix", "[", "ahat", "]"}], "//", "MatrixForm"}], ",", 
   RowBox[{"{", 
    RowBox[{"ahat", ",", "1", ",", "3"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7465532875418015`*^9, 
  3.74655330581242*^9}},ExpressionUUID->"8caf2543-ffc1-4d3e-9df4-\
54fd14da029f"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {"0", "0", "0", 
        RowBox[{"-", "\[ImaginaryI]"}]},
       {"0", "0", 
        RowBox[{"-", "\[ImaginaryI]"}], "0"},
       {"0", "\[ImaginaryI]", "0", "0"},
       {"\[ImaginaryI]", "0", "0", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {"0", 
        RowBox[{"-", "\[ImaginaryI]"}], "0", "0"},
       {"\[ImaginaryI]", "0", "0", "0"},
       {"0", "0", "0", 
        RowBox[{"-", "\[ImaginaryI]"}]},
       {"0", "0", "\[ImaginaryI]", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]], ",", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {"0", "0", 
        RowBox[{"-", "\[ImaginaryI]"}], "0"},
       {"0", "0", "0", "\[ImaginaryI]"},
       {"\[ImaginaryI]", "0", "0", "0"},
       {"0", 
        RowBox[{"-", "\[ImaginaryI]"}], "0", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}], "}"}]], "Output",
 CellChangeTimes->{3.7500178885291276`*^9, 3.7500180392738924`*^9, 
  3.7539143169297924`*^9, 
  3.757003550625422*^9},ExpressionUUID->"41ee4176-ae58-4c53-9423-\
7ebd96ebff0b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"\[Gamma]", "[", "2", "]"}], ".", 
   RowBox[{"\[Gamma]", "[", "3", "]"}]}], "\[Equal]", 
  RowBox[{"I", " ", 
   RowBox[{"\[Alpha]matrix", "[", "1", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.746553271891163*^9, 
  3.746553326863762*^9}},ExpressionUUID->"5274f2db-86e4-43eb-a73b-\
f53200b8d399"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888549961*^9, 3.7500180393220415`*^9, 
  3.7539143169610033`*^9, 
  3.757003550695016*^9},ExpressionUUID->"ddfda764-7922-4aa7-af9b-\
8ed0ebb618a9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"\[Gamma]", "[", "3", "]"}], ".", 
   RowBox[{"\[Gamma]", "[", "1", "]"}]}], "\[Equal]", 
  RowBox[{"I", " ", 
   RowBox[{"\[Alpha]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7465533358248234`*^9, 
  3.746553347618163*^9}},ExpressionUUID->"b8ae2771-fb67-4561-8e3b-\
579c20e20adf"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.75001788857228*^9, 3.750018039338373*^9, 
  3.753914316976641*^9, 
  3.7570035507630243`*^9},ExpressionUUID->"9ab7fc1e-df6e-4a6a-99cf-\
fc0b0626eafd"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"\[Gamma]", "[", "1", "]"}], ".", 
   RowBox[{"\[Gamma]", "[", "2", "]"}]}], " ", "\[Equal]", " ", 
  RowBox[{"I", " ", 
   RowBox[{"\[Alpha]matrix", "[", "3", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.746553349802328*^9, 
  3.746553359755376*^9}},ExpressionUUID->"a149c725-3af3-4104-8fa6-\
7b2cf6150a28"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888600552*^9, 3.7500180393592043`*^9, 
  3.7539143169922757`*^9, 
  3.757003550830512*^9},ExpressionUUID->"76980bc6-76f8-423e-b4f2-\
38e178163228"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "0", "]"}], "\[Equal]", 
  RowBox[{"I", " ", 
   RowBox[{"\[Beta]matrix", "[", "3", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.7465533698404846`*^9, 3.746553380109207*^9}, {
  3.746553415042225*^9, 
  3.7465534539419336`*^9}},ExpressionUUID->"9c39496b-3e3f-4eef-b547-\
02d2378c0c24"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888628691*^9, 3.7500180393880177`*^9, 
  3.753914317023488*^9, 
  3.757003550898526*^9},ExpressionUUID->"04859b1e-ba22-4214-bbf5-\
dde812f6baee"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData["\[Gamma]5"], "Input",
 CellChangeTimes->{{3.7465535251987753`*^9, 
  3.7465535257683296`*^9}},ExpressionUUID->"883fb1e8-7e4c-4dd5-ad61-\
591e4577dcfa"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", "\[ImaginaryI]"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "\[ImaginaryI]", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0", ",", "0", ",", "0"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.75001788865047*^9, 3.7500180394043407`*^9, 
  3.7539143170391407`*^9, 
  3.757003550968227*^9},ExpressionUUID->"f409b919-0ed4-4e50-a7a1-\
1dc975c9ac20"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[Gamma]5", " ", "\[Equal]", " ", 
  RowBox[{"-", 
   RowBox[{"\[Beta]matrix", "[", "1", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.746553461783628*^9, 3.746553496803726*^9}, {
  3.7465535463352723`*^9, 
  3.74655356213838*^9}},ExpressionUUID->"9e894f20-26c5-41a7-938c-\
5eeb0c8ef40e"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.7500178886732874`*^9, 3.750018039424181*^9, 
  3.7539143170391407`*^9, 
  3.7570035510376177`*^9},ExpressionUUID->"049eef8c-2ed6-4351-bc24-\
51bccbd96138"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"\[Gamma]", "[", "0", "]"}], ".", "\[Gamma]5"}], " ", "\[Equal]", 
  " ", 
  RowBox[{"\[Beta]matrix", "[", "2", "]"}]}]], "Input",
 CellChangeTimes->{{3.746553581046234*^9, 
  3.746553596891637*^9}},ExpressionUUID->"cf4d0370-c174-456e-8b40-\
c9ceb56bae7f"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888700566*^9, 3.750018039449973*^9, 
  3.7539143170547547`*^9, 
  3.757003551234029*^9},ExpressionUUID->"f0794985-65ff-4f23-8958-\
7f9d578bc9c4"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"su2matrix", "[", 
  RowBox[{"1", ",", "1"}], "]"}]], "Input",
 CellChangeTimes->{{3.709237241493265*^9, 
  3.7092372437973967`*^9}},ExpressionUUID->"17e1c53e-a51c-42df-a1f6-\
ec76bc17dcc4"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "\[ImaginaryI]", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[ImaginaryI]", ",", "0", ",", "0", ",", "0"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.750017888722887*^9, 3.7500180394688206`*^9, 
  3.7539143170547547`*^9, 
  3.7570035512849617`*^9},ExpressionUUID->"476c68a8-a9ac-4c98-ada0-\
969167e1557a"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[Alpha]matrix", "[", "1", "]"}]], "Input",
 CellChangeTimes->{{3.7092372459275184`*^9, 
  3.709237247628616*^9}},ExpressionUUID->"82b5b273-9d7b-4fbe-b2a4-\
0bdca6a9309a"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", "\[ImaginaryI]"}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "\[ImaginaryI]", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[ImaginaryI]", ",", "0", ",", "0", ",", "0"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.750017888754675*^9, 3.750018039489652*^9, 
  3.753914317070376*^9, 
  3.7570035514127703`*^9},ExpressionUUID->"c527580b-27f1-4e14-b446-\
f5e55d1a0f45"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AntiCommuteGamma", "[", 
  RowBox[{"2", ",", "2"}], "]"}]], "Input",
 CellChangeTimes->{{3.5744657884825735`*^9, 
  3.574465807701807*^9}},ExpressionUUID->"c99bfc8b-bca3-4464-b0fc-\
b05befb48c8c"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"2", ",", "0", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "2", ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "2", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", "2"}], "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.7500178887839346`*^9, 3.750018039516437*^9, 
  3.753914317070376*^9, 
  3.757003551521551*^9},ExpressionUUID->"622c6274-3f8d-4800-ad3b-\
b16c3768eb74"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "5", "]"}], " ", "==", " ", 
  RowBox[{"(", 
   RowBox[{"-", 
    RowBox[{"TwoTensor", "[", 
     RowBox[{"1", ",", "2"}], "]"}]}], ")"}]}]], "Input",
 CellChangeTimes->{{3.5744658375134597`*^9, 
  3.5744658573878946`*^9}},ExpressionUUID->"a30636f3-1032-4db1-80a6-\
5d8033af4392"],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "5", "]"}], "\[Equal]", 
  RowBox[{"-", 
   RowBox[{"TwoTensor", "[", 
    RowBox[{"1", ",", "2"}], "]"}]}]}]], "Output",
 CellChangeTimes->{3.7500178888067093`*^9, 3.7500180395388064`*^9, 
  3.7539143170860014`*^9, 
  3.757003551615337*^9},ExpressionUUID->"6bb80ef7-97f2-461e-b6f5-\
6da44fcc217b"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"1", ",", "2"}], "]"}], " ", "=", " ", 
  RowBox[{
   RowBox[{"-", " ", "I"}], " ", 
   FractionBox["1", "2"], 
   RowBox[{
    RowBox[{"\[Gamma]", "[", "1", "]"}], ".", 
    RowBox[{"\[Gamma]", "[", "2", "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"2", ",", "3"}], "]"}], " ", "=", " ", 
  RowBox[{
   RowBox[{"-", "I"}], " ", 
   FractionBox["1", "2"], 
   RowBox[{
    RowBox[{"\[Gamma]", "[", "2", "]"}], ".", 
    RowBox[{"\[Gamma]", "[", "3", "]"}]}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"3", ",", "1"}], "]"}], " ", "=", " ", 
  RowBox[{
   RowBox[{"-", "I"}], " ", 
   FractionBox["1", "2"], 
   RowBox[{
    RowBox[{"\[Gamma]", "[", "3", "]"}], ".", 
    RowBox[{"\[Gamma]", "[", "1", "]"}]}]}]}]}], "Input",
 CellChangeTimes->{{3.574465865733909*^9, 
  3.5744659064499807`*^9}},ExpressionUUID->"0955fa9e-d286-4100-b7ce-\
41ef90bd0b58"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", 
     FractionBox["\[ImaginaryI]", "2"]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0", ",", "0"}], "}"}],
    ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}], ",", "0", ",", "0"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.7500178888325515`*^9, 3.750018039557109*^9, 
  3.7539143171172256`*^9, 
  3.757003551709156*^9},ExpressionUUID->"76d3f120-3f82-46d7-b609-\
a2b64c3cd284"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}], ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", 
     FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0", ",", "0"}], 
    "}"}]}], "}"}]], "Output",
 CellChangeTimes->{3.7500178888325515`*^9, 3.750018039557109*^9, 
  3.7539143171172256`*^9, 
  3.757003551710479*^9},ExpressionUUID->"67638c6b-f418-4ecc-adfd-\
a5e7289d4c47"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}], ",", "0", ",", "0"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0", ",", "0"}], "}"}],
    ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", "0", ",", 
     RowBox[{"-", 
      FractionBox["\[ImaginaryI]", "2"]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"0", ",", "0", ",", 
     FractionBox["\[ImaginaryI]", "2"], ",", "0"}], "}"}]}], "}"}]], "Output",\

 CellChangeTimes->{3.7500178888325515`*^9, 3.750018039557109*^9, 
  3.7539143171172256`*^9, 
  3.757003551711507*^9},ExpressionUUID->"6e77d381-6567-46b6-b7b8-\
9fe5f4dfbae6"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "0", "]"}], " ", "\[Equal]", " ", 
  RowBox[{"I", " ", 
   RowBox[{"\[Beta]matrix", "[", "3", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5744659455592494`*^9, 
  3.5744659526104617`*^9}},ExpressionUUID->"05309d17-70a0-41fe-bc88-\
bffbf00b4967"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.7500178888588467`*^9, 3.7500180395930343`*^9, 
  3.7539143171328373`*^9, 
  3.75700355180838*^9},ExpressionUUID->"eb6bd596-1c0d-4394-8e3a-d0243e264b58"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "1", "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   RowBox[{"\[Alpha]matrix", "[", "1", "]"}], ".", 
   RowBox[{"\[Beta]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.574465954576065*^9, 
  3.574465974809301*^9}},ExpressionUUID->"92ff637e-9a92-4d25-8ecb-\
2014ee0dd28f"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888876646*^9, 3.750018039622299*^9, 
  3.7539143171328373`*^9, 
  3.7570035518920717`*^9},ExpressionUUID->"f21c1b64-ae67-4f62-becd-\
4d9a4a791f74"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "2", "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   RowBox[{"\[Alpha]matrix", "[", "2", "]"}], ".", 
   RowBox[{"\[Beta]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.574465978085306*^9, 
  3.574465986509321*^9}},ExpressionUUID->"c7d0aea9-b659-45b4-bf5e-\
42c77570b423"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.7500178888949976`*^9, 3.750018039639164*^9, 
  3.75391431714849*^9, 
  3.7570035519886703`*^9},ExpressionUUID->"e78f239f-6579-493d-9738-\
1b658ea3ffae"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "3", "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   RowBox[{"\[Alpha]matrix", "[", "3", "]"}], ".", 
   RowBox[{"\[Beta]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.574465989800927*^9, 
  3.5744659983341417`*^9}},ExpressionUUID->"5bca0d8d-df29-485c-bf87-\
7dfd120487f2"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888913847*^9, 3.7500180396601057`*^9, 
  3.75391431714849*^9, 
  3.75700355205827*^9},ExpressionUUID->"b43219b2-6b18-4c09-9f7c-e81a1c6ed7b5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"1", ",", "2"}], "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Alpha]matrix", "[", "3", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5744660048393536`*^9, 
  3.5744660143397703`*^9}},ExpressionUUID->"aeec6083-d8a5-434f-94d2-\
608ca41c27e2"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.7500178889336853`*^9, 3.750018039686328*^9, 
  3.7539143171640806`*^9, 
  3.757003552207355*^9},ExpressionUUID->"34ac6088-8f6a-4757-a5b4-\
bba39816b09e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"2", ",", "3"}], "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Alpha]matrix", "[", "1", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5744660171945753`*^9, 
  3.5744660254469895`*^9}},ExpressionUUID->"adc5e456-2849-4fe9-b839-\
30751fb2c4c0"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017888953528*^9, 3.7500180397071595`*^9, 
  3.7539143171797028`*^9, 
  3.75700355222444*^9},ExpressionUUID->"c395e4e3-3832-4260-a561-3964c79abb2e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Sig", "[", 
   RowBox[{"3", ",", "1"}], "]"}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Alpha]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.574466028364195*^9, 
  3.5744660366946096`*^9}},ExpressionUUID->"d1248931-0bcd-432f-a3b7-\
c213060bf5ea"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.75001788897287*^9, 3.750018039734439*^9, 
  3.7539143171953325`*^9, 
  3.7570035522921867`*^9},ExpressionUUID->"be374169-4849-4c07-be5f-\
9b7dda1df037"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "5", "]"}], " ", "\[Equal]", " ", 
  RowBox[{"-", " ", 
   RowBox[{"\[Beta]matrix", "[", "1", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.57446604865983*^9, 
  3.574466055165042*^9}},ExpressionUUID->"0e85c406-eb86-4fa9-b535-\
02113968e8e4"],

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Gamma]", "[", "5", "]"}], "\[Equal]", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "0", ",", "\[ImaginaryI]"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", 
      RowBox[{"-", "\[ImaginaryI]"}], ",", "0"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "\[ImaginaryI]", ",", "0", ",", "0"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], ",", "0", ",", "0", ",", "0"}], "}"}]}],
    "}"}]}]], "Output",
 CellChangeTimes->{3.7500178889922523`*^9, 3.7500180397563066`*^9, 
  3.7539143172265673`*^9, 
  3.75700355236185*^9},ExpressionUUID->"e0de5854-1a88-4d04-b751-14642b0cef33"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "I"}], " ", 
   FractionBox["1", "2"], 
   RowBox[{"\[Gamma]", "[", "0", "]"}]}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Beta]matrix", "[", "3", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5744660650086594`*^9, 
  3.57446608224669*^9}},ExpressionUUID->"38bbcc65-9f61-4711-9543-\
7389979f2041"],

Cell[BoxData["True"], "Output",
 CellChangeTimes->{3.750017889011103*^9, 3.7500180397841015`*^9, 
  3.7539143172421865`*^9, 
  3.757003552430799*^9},ExpressionUUID->"76aa9ae8-d380-4d62-94e5-\
6c84906ad757"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   FractionBox[
    RowBox[{"-", "1"}], "2"], 
   RowBox[{"\[Gamma]", "[", "5", "]"}]}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Beta]matrix", "[", "1", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.5744660850078945`*^9, 
  3.5744660952727127`*^9}},ExpressionUUID->"6606803d-38e9-4702-8331-\
3899340c9527"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   FractionBox[
    RowBox[{"\[Gamma]", "[", "5", "]"}], "2"]}], "\[Equal]", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "0", ",", 
      RowBox[{"-", 
       FractionBox["\[ImaginaryI]", "2"]}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", 
      FractionBox["\[ImaginaryI]", "2"], ",", "0"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", 
      RowBox[{"-", 
       FractionBox["\[ImaginaryI]", "2"]}], ",", "0", ",", "0"}], "}"}], ",", 
    
    RowBox[{"{", 
     RowBox[{
      FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0", ",", "0"}], 
     "}"}]}], "}"}]}]], "Output",
 CellChangeTimes->{3.750017889031399*^9, 3.750018039802413*^9, 
  3.75391431727343*^9, 
  3.757003552499475*^9},ExpressionUUID->"a6e5604e-4f73-457c-a8a6-\
a8c7620e0b9d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{
    RowBox[{"\[Gamma]", "[", "0", "]"}], ".", 
    RowBox[{"\[Gamma]", "[", "5", "]"}]}]}], " ", "\[Equal]", " ", 
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"\[Beta]matrix", "[", "2", "]"}]}]}]], "Input",
 CellChangeTimes->{{3.574466098798319*^9, 
  3.5744661104827394`*^9}},ExpressionUUID->"1d457f2e-cfbe-4e62-b6a5-\
f3d147c6784a"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   FractionBox["1", "2"], " ", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"-", "1"}], ",", "0", ",", "0", ",", "0"}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "0", ",", 
        RowBox[{"-", "1"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}]}], "}"}], ".", 
    RowBox[{"\[Gamma]", "[", "5", "]"}]}]}], "\[Equal]", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", 
      RowBox[{"-", 
       FractionBox["\[ImaginaryI]", "2"]}], ",", "0"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "0", ",", 
      RowBox[{"-", 
       FractionBox["\[ImaginaryI]", "2"]}]}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{
      FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0", ",", "0"}], 
     "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"0", ",", 
      FractionBox["\[ImaginaryI]", "2"], ",", "0", ",", "0"}], "}"}]}], 
   "}"}]}]], "Output",
 CellChangeTimes->{3.7500178890532236`*^9, 3.7500180398262863`*^9, 
  3.753914317304734*^9, 
  3.757003552568692*^9},ExpressionUUID->"8f31f05e-eebc-4dae-8c42-\
dc14da55b737"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"\[Beta]matrix", "[", "2", "]"}], "//", "MatrixForm"}]], "Input",
 CellChangeTimes->{{3.574466315296499*^9, 
  3.5744663243289146`*^9}},ExpressionUUID->"b803c677-ffb6-408a-b191-\
fa965c007516"],

Cell[BoxData[
 TagBox[
  RowBox[{"(", "\[NoBreak]", GridBox[{
     {"0", "0", 
      RowBox[{"-", "\[ImaginaryI]"}], "0"},
     {"0", "0", "0", 
      RowBox[{"-", "\[ImaginaryI]"}]},
     {"\[ImaginaryI]", "0", "0", "0"},
     {"0", "\[ImaginaryI]", "0", "0"}
    },
    GridBoxAlignment->{
     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
      "RowsIndexed" -> {}},
    GridBoxSpacings->{"Columns" -> {
        Offset[0.27999999999999997`], {
         Offset[0.7]}, 
        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
        Offset[0.2], {
         Offset[0.4]}, 
        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
  Function[BoxForm`e$, 
   MatrixForm[BoxForm`e$]]]], "Output",
 CellChangeTimes->{3.7500178890745955`*^9, 3.7500180398545866`*^9, 
  3.7539143173202934`*^9, 
  3.757003552637351*^9},ExpressionUUID->"90aaf2a2-7e67-4fb5-a4ca-\
c300c488366f"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1920, 997},
WindowMargins->{{Automatic, 0}, {Automatic, -13}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
ShowSelection->True,
CellContext->Notebook,
FrontEndVersion->"11.1 for Linux x86 (64-bit) (April 18, 2017)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 8889, 120, 94, "Title", "ExpressionUUID" -> \
"dfab12f3-523a-4891-ab6d-6353bcfa0aa5"],
Cell[CellGroupData[{
Cell[9494, 146, 125, 1, 33, "Input", "ExpressionUUID" -> \
"65e9b759-d921-4a12-9e52-b3e8b17f8777"],
Cell[9622, 149, 997, 15, 33, "Output", "ExpressionUUID" -> \
"6c7b3753-5f27-4f2b-a073-60a98bdbcd4c"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10656, 169, 321, 5, 66, "Section", "ExpressionUUID" -> \
"8ce62cfa-2467-4484-bfab-5a2bb7149ea5"],
Cell[10980, 176, 275, 5, 33, "Input", "ExpressionUUID" -> \
"3ce86a4c-e50b-42b6-b6ba-cfca0898781a"],
Cell[CellGroupData[{
Cell[11280, 185, 194, 4, 33, "Input", "ExpressionUUID" -> \
"335154d1-1580-4631-8a3e-4170890b8e5c"],
Cell[11477, 191, 1086, 16, 33, "Output", "ExpressionUUID" -> \
"a3ded3b2-b7a9-4dfb-a777-239928c8e844"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12600, 212, 162, 3, 46, "Subsection", "ExpressionUUID" -> \
"9032bd95-7de1-4377-8cd7-b7fd291e0e1f"],
Cell[CellGroupData[{
Cell[12787, 219, 299, 5, 33, "Input", "ExpressionUUID" -> \
"433cc145-fb86-450b-9648-f7c5cbb57d74"],
Cell[13089, 226, 1523, 23, 70, "Output", "ExpressionUUID" -> \
"df972d6d-37f5-42d8-94b0-ea46625ec3fa"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14649, 254, 252, 5, 33, "Input", "ExpressionUUID" -> \
"5ab02646-7eb8-4bc6-9cc6-8c4ac39583d4"],
Cell[14904, 261, 1310, 19, 70, "Output", "ExpressionUUID" -> \
"f261176c-3908-4028-aa59-1684a3766102"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16251, 285, 209, 4, 33, "Input", "ExpressionUUID" -> \
"f2152041-3457-4816-9e34-ccfb12c93d8a"],
Cell[16463, 291, 3740, 55, 70, "Output", "ExpressionUUID" -> \
"9a82b3ca-5a2e-4f79-b1c1-bb5c10d4d3a2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[20240, 351, 285, 5, 33, "Input", "ExpressionUUID" -> \
"cd131f93-6eb8-4ba3-b71c-6c9265945b1e"],
Cell[20528, 358, 2462, 36, 70, "Output", "ExpressionUUID" -> \
"fdecae43-67d0-48ee-8642-103702327116"]
}, Open  ]],
Cell[CellGroupData[{
Cell[23027, 399, 297, 5, 33, "Input", "ExpressionUUID" -> \
"5cf8981a-5985-4a6c-861a-8b771458a158"],
Cell[23327, 406, 1923, 27, 70, "Output", "ExpressionUUID" -> \
"21e82ba8-0f11-4fdb-b7b4-b2b8b2a23494"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25287, 438, 302, 5, 33, "Input", "ExpressionUUID" -> \
"8a453f50-9c25-4910-84fc-5bfae4aaeae8"],
Cell[25592, 445, 1455, 22, 70, "Output", "ExpressionUUID" -> \
"b92ef2fb-c027-4947-951a-d09e9f77f3ef"]
}, Open  ]],
Cell[CellGroupData[{
Cell[27084, 472, 199, 4, 33, "Input", "ExpressionUUID" -> \
"157db393-0dff-4169-adae-289b23a3d1a9"],
Cell[27286, 478, 7486, 111, 70, "Output", "ExpressionUUID" -> \
"ef5d28a2-0b94-4b1f-8eca-b39cf62bf18c"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[34821, 595, 187, 3, 38, "Subsection", "ExpressionUUID" -> \
"d2a6411a-95d2-4892-9744-45cbf8b5fc2e"],
Cell[CellGroupData[{
Cell[35033, 602, 183, 3, 70, "Subsubsection", "ExpressionUUID" -> \
"6d43e65b-1220-4dd0-ac77-fbe7c15c929c"],
Cell[CellGroupData[{
Cell[35241, 609, 227, 6, 70, "Input", "ExpressionUUID" -> \
"696619bb-4bda-4abd-a3d7-6c21086107ae"],
Cell[35471, 617, 1065, 15, 70, "Output", "ExpressionUUID" -> \
"b39135be-78cf-4577-985e-885e9cc9c2b1"]
}, Open  ]],
Cell[CellGroupData[{
Cell[36573, 637, 159, 3, 70, "Input", "ExpressionUUID" -> \
"da336974-8655-41e2-a289-74fb778d736c"],
Cell[36735, 642, 1416, 28, 70, "Output", "ExpressionUUID" -> \
"fa15472b-0555-45d9-ab93-c0a798162a70"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38188, 675, 264, 6, 70, "Input", "ExpressionUUID" -> \
"61551fc0-f96c-4eff-a43f-a97ce806d229"],
Cell[38455, 683, 2020, 49, 70, "Output", "ExpressionUUID" -> \
"1e784759-e386-4e45-8c30-dd6e74661796"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40512, 737, 338, 8, 70, "Input", "ExpressionUUID" -> \
"a623415f-9142-4544-adfe-1e00582a4797"],
Cell[40853, 747, 2126, 52, 70, "Output", "ExpressionUUID" -> \
"3caf3019-b351-46d5-85f5-d17e91717d45"]
}, Open  ]]
}, Closed]],
Cell[CellGroupData[{
Cell[43028, 805, 240, 4, 70, "Subsubsection", "ExpressionUUID" -> \
"9e6f5328-f24c-43bd-9942-c8f1da8f8655"],
Cell[CellGroupData[{
Cell[43293, 813, 299, 7, 70, "Input", "ExpressionUUID" -> \
"5fb3bfd5-b3f1-4920-94ac-b5a0e529a661"],
Cell[43595, 822, 830, 12, 70, "Output", "ExpressionUUID" -> \
"5d9baa36-af56-4ff0-bd28-c94f3f359c6b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[44462, 839, 207, 4, 70, "Input", "ExpressionUUID" -> \
"d3176023-b48b-47c7-a647-5e2098481ea2"],
Cell[44672, 845, 3471, 52, 70, "Output", "ExpressionUUID" -> \
"d2168833-9b97-4758-a932-524859c138af"]
}, Open  ]]
}, Closed]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[48216, 905, 166, 3, 66, "Section", "ExpressionUUID" -> \
"867351f9-5484-4126-a47d-d94d902b177f"],
Cell[CellGroupData[{
Cell[48407, 912, 196, 4, 33, "Input", "ExpressionUUID" -> \
"c96a094c-792b-4f3b-b88a-257150e53b4d"],
Cell[48606, 918, 643, 18, 35, "Output", "ExpressionUUID" -> \
"c6033bed-7f4b-4775-bbf3-6a985c273449"]
}, Open  ]],
Cell[CellGroupData[{
Cell[49286, 941, 295, 7, 35, "Input", "ExpressionUUID" -> \
"a4728552-95a4-4d02-ad9f-2afcc771ffe9"],
Cell[49584, 950, 1032, 29, 104, "Output", "ExpressionUUID" -> \
"16045a56-a303-4014-800c-71c496e9df59"]
}, Open  ]],
Cell[CellGroupData[{
Cell[50653, 984, 193, 4, 33, "Input", "ExpressionUUID" -> \
"bfc853bc-7a80-4bb2-a9bb-b155863bcc13"],
Cell[50849, 990, 876, 25, 104, "Output", "ExpressionUUID" -> \
"30a46528-1fab-49db-8b49-7ec8ee5a6356"]
}, Open  ]],
Cell[CellGroupData[{
Cell[51762, 1020, 316, 9, 35, "Input", "ExpressionUUID" -> \
"6c686fac-1ff8-4172-a22d-fb357e80d4bd"],
Cell[52081, 1031, 484, 14, 35, "Output", "ExpressionUUID" -> \
"942c64d0-fbcb-474f-8502-96704f5fd475"]
}, Open  ]],
Cell[CellGroupData[{
Cell[52602, 1050, 287, 7, 35, "Input", "ExpressionUUID" -> \
"21a4a468-1f8e-47b4-bdd3-f2f33af9260e"],
Cell[52892, 1059, 1299, 41, 35, "Output", "ExpressionUUID" -> \
"89582e00-2a79-4be5-868b-63aa145c6e3d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[54228, 1105, 350, 9, 35, "Input", "ExpressionUUID" -> \
"8caf2543-ffc1-4d3e-9df4-54fd14da029f"],
Cell[54581, 1116, 2555, 69, 88, "Output", "ExpressionUUID" -> \
"41ee4176-ae58-4c53-9423-7ebd96ebff0b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[57173, 1190, 342, 9, 33, "Input", "ExpressionUUID" -> \
"5274f2db-86e4-43eb-a73b-f53200b8d399"],
Cell[57518, 1201, 206, 4, 33, "Output", "ExpressionUUID" -> \
"ddfda764-7922-4aa7-af9b-8ed0ebb618a9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[57761, 1210, 344, 9, 33, "Input", "ExpressionUUID" -> \
"b8ae2771-fb67-4561-8e3b-579c20e20adf"],
Cell[58108, 1221, 203, 4, 33, "Output", "ExpressionUUID" -> \
"9ab7fc1e-df6e-4a6a-99cf-fc0b0626eafd"]
}, Open  ]],
Cell[CellGroupData[{
Cell[58348, 1230, 352, 9, 33, "Input", "ExpressionUUID" -> \
"a149c725-3af3-4104-8fa6-7b2cf6150a28"],
Cell[58703, 1241, 206, 4, 33, "Output", "ExpressionUUID" -> \
"76980bc6-76f8-423e-b4f2-38e178163228"]
}, Open  ]],
Cell[CellGroupData[{
Cell[58946, 1250, 334, 8, 33, "Input", "ExpressionUUID" -> \
"9c39496b-3e3f-4eef-b547-02d2378c0c24"],
Cell[59283, 1260, 204, 4, 33, "Output", "ExpressionUUID" -> \
"04859b1e-ba22-4214-bbf5-dde812f6baee"]
}, Open  ]],
Cell[CellGroupData[{
Cell[59524, 1269, 165, 3, 33, "Input", "ExpressionUUID" -> \
"883fb1e8-7e4c-4dd5-ad61-591e4577dcfa"],
Cell[59692, 1274, 636, 17, 35, "Output", "ExpressionUUID" -> \
"f409b919-0ed4-4e50-a7a1-1dc975c9ac20"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60365, 1296, 309, 7, 33, "Input", "ExpressionUUID" -> \
"9e894f20-26c5-41a7-938c-5eeb0c8ef40e"],
Cell[60677, 1305, 208, 4, 33, "Output", "ExpressionUUID" -> \
"049eef8c-2ed6-4351-bc24-51bccbd96138"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60922, 1314, 302, 8, 33, "Input", "ExpressionUUID" -> \
"cf4d0370-c174-456e-8b40-c9ceb56bae7f"],
Cell[61227, 1324, 204, 4, 33, "Output", "ExpressionUUID" -> \
"f0794985-65ff-4f23-8958-7f9d578bc9c4"]
}, Open  ]],
Cell[CellGroupData[{
Cell[61468, 1333, 213, 5, 35, "Input", "ExpressionUUID" -> \
"17e1c53e-a51c-42df-a1f6-ec76bc17dcc4"],
Cell[61684, 1340, 639, 17, 35, "Output", "ExpressionUUID" -> \
"476c68a8-a9ac-4c98-ada0-969167e1557a"]
}, Open  ]],
Cell[CellGroupData[{
Cell[62360, 1362, 195, 4, 33, "Input", "ExpressionUUID" -> \
"82b5b273-9d7b-4fbe-b2a4-0bdca6a9309a"],
Cell[62558, 1368, 635, 17, 35, "Output", "ExpressionUUID" -> \
"c527580b-27f1-4e14-b446-f5e55d1a0f45"]
}, Open  ]],
Cell[CellGroupData[{
Cell[63230, 1390, 220, 5, 35, "Input", "ExpressionUUID" -> \
"c99bfc8b-bca3-4464-b0fc-b05befb48c8c"],
Cell[63453, 1397, 542, 14, 35, "Output", "ExpressionUUID" -> \
"622c6274-3f8d-4800-ad3b-b16c3768eb74"]
}, Open  ]],
Cell[CellGroupData[{
Cell[64032, 1416, 331, 9, 35, "Input", "ExpressionUUID" -> \
"a30636f3-1032-4db1-80a6-5d8033af4392"],
Cell[64366, 1427, 349, 9, 35, "Output", "ExpressionUUID" -> \
"6bb80ef7-97f2-461e-b6f5-6da44fcc217b"]
}, Open  ]],
Cell[CellGroupData[{
Cell[64752, 1441, 977, 30, 133, "Input", "ExpressionUUID" -> \
"0955fa9e-d286-4100-b7ce-41ef90bd0b58"],
Cell[65732, 1473, 739, 22, 52, "Output", "ExpressionUUID" -> \
"76d3f120-3f82-46d7-b609-a2b64c3cd284"],
Cell[66474, 1497, 737, 21, 52, "Output", "ExpressionUUID" -> \
"67638c6b-f418-4ecc-adfd-a5e7289d4c47"],
Cell[67214, 1520, 738, 22, 52, "Output", "ExpressionUUID" -> \
"6e77d381-6567-46b6-b7b8-9fe5f4dfbae6"]
}, Open  ]],
Cell[CellGroupData[{
Cell[67989, 1547, 295, 7, 33, "Input", "ExpressionUUID" -> \
"05309d17-70a0-41fe-bc88-bffbf00b4967"],
Cell[68287, 1556, 205, 3, 33, "Output", "ExpressionUUID" -> \
"eb6bd596-1c0d-4394-8e3a-d0243e264b58"]
}, Open  ]],
Cell[CellGroupData[{
Cell[68529, 1564, 333, 8, 33, "Input", "ExpressionUUID" -> \
"92ff637e-9a92-4d25-8ecb-2014ee0dd28f"],
Cell[68865, 1574, 206, 4, 33, "Output", "ExpressionUUID" -> \
"f21c1b64-ae67-4f62-becd-4d9a4a791f74"]
}, Open  ]],
Cell[CellGroupData[{
Cell[69108, 1583, 333, 8, 33, "Input", "ExpressionUUID" -> \
"c7d0aea9-b659-45b4-bf5e-42c77570b423"],
Cell[69444, 1593, 205, 4, 33, "Output", "ExpressionUUID" -> \
"e78f239f-6579-493d-9738-1b658ea3ffae"]
}, Open  ]],
Cell[CellGroupData[{
Cell[69686, 1602, 335, 8, 33, "Input", "ExpressionUUID" -> \
"5bca0d8d-df29-485c-bf87-7dfd120487f2"],
Cell[70024, 1612, 200, 3, 33, "Output", "ExpressionUUID" -> \
"b43219b2-6b18-4c09-9f7c-e81a1c6ed7b5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[70261, 1620, 332, 9, 51, "Input", "ExpressionUUID" -> \
"aeec6083-d8a5-434f-94d2-608ca41c27e2"],
Cell[70596, 1631, 206, 4, 33, "Output", "ExpressionUUID" -> \
"34ac6088-8f6a-4757-a5b4-bba39816b09e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[70839, 1640, 332, 9, 51, "Input", "ExpressionUUID" -> \
"adc5e456-2849-4fe9-b839-30751fb2c4c0"],
Cell[71174, 1651, 203, 3, 33, "Output", "ExpressionUUID" -> \
"c395e4e3-3832-4260-a561-3964c79abb2e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[71414, 1659, 330, 9, 51, "Input", "ExpressionUUID" -> \
"d1248931-0bcd-432f-a3b7-c213060bf5ea"],
Cell[71747, 1670, 205, 4, 33, "Output", "ExpressionUUID" -> \
"be374169-4849-4c07-be5f-9b7dda1df037"]
}, Open  ]],
Cell[CellGroupData[{
Cell[71989, 1679, 290, 7, 33, "Input", "ExpressionUUID" -> \
"0e85c406-eb86-4fa9-b535-02113968e8e4"],
Cell[72282, 1688, 713, 18, 35, "Output", "ExpressionUUID" -> \
"e0de5854-1a88-4d04-b751-14642b0cef33"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73032, 1711, 379, 11, 51, "Input", "ExpressionUUID" -> \
"38bbcc65-9f61-4711-9543-7389979f2041"],
Cell[73414, 1724, 206, 4, 33, "Output", "ExpressionUUID" -> \
"76aa9ae8-d380-4d62-94e5-6c84906ad757"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73657, 1733, 373, 11, 51, "Input", "ExpressionUUID" -> \
"6606803d-38e9-4702-8331-3899340c9527"],
Cell[74033, 1746, 860, 26, 52, "Output", "ExpressionUUID" -> \
"a6e5604e-4f73-457c-a8a6-a8c7620e0b9d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[74930, 1777, 413, 12, 51, "Input", "ExpressionUUID" -> \
"1d457f2e-cfbe-4e62-b6a5-f3d147c6784a"],
Cell[75346, 1791, 1312, 39, 52, "Output", "ExpressionUUID" -> \
"8f31f05e-eebc-4dae-8c42-dc14da55b737"]
}, Open  ]],
Cell[CellGroupData[{
Cell[76695, 1835, 227, 5, 33, "Input", "ExpressionUUID" -> \
"b803c677-ffb6-408a-b191-fa965c007516"],
Cell[76925, 1842, 928, 25, 161, "Output", "ExpressionUUID" -> \
"90aaf2a2-7e67-4fb5-a4ca-c300c488366f"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)