(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 812995, 29286] NotebookOptionsPosition[ 673766, 26112] NotebookOutlinePosition[ 794909, 28683] CellTagsIndexPosition[ 794369, 28665] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ \[LightBulb]\[LightBulb]\[LightBulb] DYNAMO 2x2 \[LightBulb]\[LightBulb]\ \[LightBulb] Diagrams for Evolutionary Game Dynamics\ \>", "Title", CellFrame->True, CellChangeTimes->{{3.4825041879508667`*^9, 3.482504191510717*^9}}, TextAlignment->Center, FontSize->32, FontColor->GrayLevel[1], Background->RGBColor[0, 0, 0.500008]], Cell[CellGroupData[{ Cell["User-defined Parameters", "Subtitle", CellDingbat->None], Cell[CellGroupData[{ Cell["\<\ When you have finished specifying parameters, click on the rightmost vertical \ bar and press Enter (or Shift-Enter) to run the program.\ \>", "Text", Evaluatable->False, FontFamily->"Palatino", FontSize->14], Cell[BoxData[ RowBox[{ RowBox[{"Off", "[", " ", RowBox[{"General", "::", "spell1"}], " ", "]"}], " ", ";", " ", RowBox[{"Off", "[", " ", RowBox[{"General", "::", "spell"}], "]"}], " ", ";"}]], "Input", CellOpen->False, InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Specification of the game", "Section"]], "Section", Evaluatable->False, CellChangeTimes->{{3.482504087953454*^9, 3.482504092321219*^9}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Functional form", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, 3.482504095097822*^9}], Cell[TextData[{ "The population game F[x_] is initially defined via matching in a normal \ form game with payoff matrices (A, B). Pressing the button marked ", StyleBox["General Linear ", FontWeight->"Bold"], "redefines F[x_] appropriately; pressing ", StyleBox["Normal Form", FontWeight->"Bold"], " restores the original definition. Payoff parameters are specified in the \ next subsection." }], "Text", Evaluatable->False, CellChangeTimes->{{3.481416137684971*^9, 3.481416148370336*^9}, { 3.481416185764106*^9, 3.481416344882907*^9}, 3.481416391519968*^9, { 3.481815812928955*^9, 3.481815825497027*^9}, {3.481815888277301*^9, 3.4818160139780493`*^9}, {3.4818888098052845`*^9, 3.481888810716595*^9}, 3.481894204638324*^9, {3.482097423467162*^9, 3.4820974505891705`*^9}, { 3.482235952026026*^9, 3.482236034835099*^9}, {3.482236706550979*^9, 3.482237005120301*^9}, {3.4822370356341777`*^9, 3.482237097382968*^9}, 3.4822822749032927`*^9, {3.4825038058100452`*^9, 3.482503911303746*^9}, { 3.482503958850415*^9, 3.4825039650826283`*^9}, {3.482504125164016*^9, 3.4825041252031813`*^9}}, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "textsl", ",", "valuesl", ",", "names", " ", ",", "texts", ",", "values", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "rowt", ",", "rowv", ",", "name", ",", "text", ",", "value", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", " ", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"textsl", " ", "=", " ", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ "\"\\"", ",", "\[IndentingNewLine]", "\"\\""}], "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"valuesl", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"Join", "[", RowBox[{"rowt", ",", RowBox[{"{", RowBox[{"textsl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"Join", "[", RowBox[{"rowv", ",", RowBox[{"{", RowBox[{"valuesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"Join", "[", RowBox[{"texts", ",", RowBox[{"{", "rowt", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"Join", "[", RowBox[{"values", ",", RowBox[{"{", "rowv", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{ RowBox[{"Column", "[", RowBox[{ RowBox[{"{", "name", "}"}], ",", RowBox[{"Alignment", "\[Rule]", RowBox[{"{", "Center", "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "NotebookLocate", "[", "\"\\"", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", RowBox[{"RowBox", "[", RowBox[{"{", "text", "}"}], "]"}], ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"120", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{ "ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], " ", "/.", RowBox[{"text", "->", RowBox[{ RowBox[{"texts", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"value", "->", RowBox[{ RowBox[{"values", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", " ", "[", " ", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "3", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, {3.481736647042942*^9, 3.481736703093539*^9}, 3.4817375426908207`*^9, {3.4818119966889615`*^9, 3.481812002957976*^9}, {3.481812105737727*^9, 3.481812272981318*^9}, { 3.4818124484235916`*^9, 3.481812457366451*^9}, {3.481812498485577*^9, 3.481812523040886*^9}, {3.4818125683860893`*^9, 3.4818125706493435`*^9}, { 3.481812612139003*^9, 3.481812639708646*^9}, {3.4818128485990157`*^9, 3.481812864662113*^9}, {3.4818129721767116`*^9, 3.4818130553963757`*^9}, { 3.4818132379588876`*^9, 3.4818133245333757`*^9}, {3.481813355407771*^9, 3.4818133663935676`*^9}, 3.4818134196132183`*^9, {3.4818134879827776`*^9, 3.481813489202236*^9}, {3.4818136452104654`*^9, 3.481813661273563*^9}, { 3.4818137634451456`*^9, 3.481813778596933*^9}, {3.4818140028480997`*^9, 3.481814031477353*^9}, {3.481814092975784*^9, 3.4818141259632177`*^9}, { 3.4818141856590557`*^9, 3.4818141929395247`*^9}, {3.4818142536968894`*^9, 3.481814383273211*^9}, {3.4818144211176286`*^9, 3.4818145387768145`*^9}, { 3.4818146624446397`*^9, 3.4818146646778507`*^9}, {3.48181469749504*^9, 3.4818147106439466`*^9}, {3.4818888661262703`*^9, 3.481888873416754*^9}, { 3.481893160246562*^9, 3.481893161117815*^9}, {3.4818932673806133`*^9, 3.481893309060546*^9}, {3.481893407021407*^9, 3.481893454229288*^9}, 3.4818939490808496`*^9, {3.4822350584911857`*^9, 3.4822350683253264`*^9}, 3.482235885069747*^9, {3.482236280027669*^9, 3.482236334385832*^9}, { 3.4822363787396097`*^9, 3.482236401442254*^9}, {3.482236463531534*^9, 3.4822364679078274`*^9}}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Normal Form\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payofffunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"F1[x_,y_]:=A.y;\nF2[x_,y_]:=Transpose[B].x;"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"General Linear\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payofffunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"F1[x_,y_]:=M[[1,1]].x+M[[1,2]].y;\nF2[x_,y_]:=M[[2,1]].x \ +M[[2,2]].y;"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]]], "Output", CellChangeTimes->{3.48223634359908*^9, 3.4822364032248173`*^9, 3.482236472905013*^9}, CellTags->"buttoncell"] }, {2}]], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"A", ".", "y"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{"Transpose", "[", "B", "]"}], ".", "x"}]}], ";"}]}], "Input", CellChangeTimes->{ 3.482235510180683*^9, {3.4822360750829725`*^9, 3.4822360953521185`*^9}, { 3.482236346783659*^9, 3.4822363697667074`*^9}, {3.482236405978778*^9, 3.482236411296424*^9}, {3.482236474266971*^9, 3.4822364894387875`*^9}, { 3.4822366463243775`*^9, 3.482236680132992*^9}, {3.4822371029309454`*^9, 3.482237106496072*^9}, {3.482237462287675*^9, 3.4822374633692303`*^9}, 3.482245939657696*^9}, CellTags->"payofffunction"] }, Closed]], Cell[CellGroupData[{ Cell["Payoff parameters", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.481816053845376*^9, 3.4818160546865854`*^9}, {3.4818162696456814`*^9, 3.4818162731507215`*^9}, {3.481891966159549*^9, 3.4818919684127893`*^9}, 3.482504100426029*^9}], Cell[CellGroupData[{ Cell["Normal form games", "Subsubsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.481816053845376*^9, 3.4818160546865854`*^9}, {3.4818162696456814`*^9, 3.4818162731507215`*^9}, {3.48250405931177*^9, 3.482504065671825*^9}}], Cell[TextData[{ "The bimatrix ", StyleBox["U", FontWeight->"Bold"], " is the normal form game to be analyzed. Edit its entries directly, or \ choose a payoff matrix by pressing a button in the cell below." }], "Text", Evaluatable->False, CellChangeTimes->{ 3.481573292434955*^9, {3.4825039492276278`*^9, 3.482503955756072*^9}, { 3.4825041397004557`*^9, 3.482504153004982*^9}}, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "matsl", ",", "names", " ", ",", "mats", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "rowm", ",", "name", ",", "mat", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", " ", RowBox[{"{", RowBox[{ "\"\<12 Coordination\>\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"matsl", " ", "=", " ", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}]}], "}"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "3"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"3", ",", "0"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"5", ",", "5"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "4"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"4", ",", "0"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "4"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "4"}], "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"-", "4"}], ",", RowBox[{"-", "4"}]}], "}"}], "}"}]}], "}"}]}], "}"}]}], "\[IndentingNewLine]", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"mats", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowm", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowm", "=", RowBox[{"Join", "[", RowBox[{"rowm", ",", RowBox[{"{", RowBox[{"matsl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"mats", "=", RowBox[{"Join", "[", RowBox[{"mats", ",", RowBox[{"{", "rowm", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowm", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{ RowBox[{"Column", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"MatrixForm", "[", "mat", "]"}], ",", "name"}], "}"}], ",", RowBox[{"Alignment", "\[Rule]", RowBox[{"{", "Center", "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"NotebookLocate", "[", "\"\\"", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", RowBox[{"RowBox", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"ToBoxes", "[", RowBox[{"MatrixForm", "[", "mat", "]"}], "]"}], ",", "\"\<;\>\""}], "}"}], "]"}], ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"150", ",", "80"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{ "ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], " ", "/.", RowBox[{"mat", "->", RowBox[{ RowBox[{"mats", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", "[", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "8", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, {3.481736647042942*^9, 3.481736703093539*^9}, 3.4817375426908207`*^9, {3.4818122976768284`*^9, 3.481812298417894*^9}, {3.481812350362587*^9, 3.481812357372667*^9}, { 3.4818128664446764`*^9, 3.481812875197262*^9}, {3.4818129301963468`*^9, 3.4818129355740795`*^9}, {3.4818143148348017`*^9, 3.4818143212440176`*^9}, {3.481814414818571*^9, 3.481814415068931*^9}, { 3.4820969728582077`*^9, 3.482096984803899*^9}, 3.4820971576124716`*^9}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2"} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"12 Coordination\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{1, 1}}, {{0, 0}}}, {{{0, 0}}, {{2, 2}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"Pure Coordination\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{1, 1}}, {{0, 0}}}, {{{0, 0}}, {{1, 1}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}]} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "1"}], "1"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "1"}], "1"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}]} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"Matching Pennies\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{1, -1}}, {{-1, 1}}}, {{{-1, 1}}, {{1, -1}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "3"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"3", "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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1"} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"Prisoner's Dilemma\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{2, 2}}, {{0, 3}}}, {{{3, 0}}, {{1, 1}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "5"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "4"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"4", "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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2"} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"Stag Hunt\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{5, 5}}, {{0, 4}}}, {{{4, 0}}, {{2, 2}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ { TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "4"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "4"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"-", "4"}], RowBox[{"-", "4"}]} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}, {"\<\"Chain Store\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "payoffmatrix", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"U=", ToBoxes[ MatrixForm[{{{{0, 4}}, {{0, 4}}}, {{{2, 2}}, {{-4, -4}}}}]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]]], "Output", CellChangeTimes->{3.482096986883875*^9, 3.4820971585279574`*^9, 3.4820976860193357`*^9}, CellTags->"buttoncell"] }, {2}]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"U", "=", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "5"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "4"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"4", "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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2"} }, 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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}], ";"}]], "Input", CellChangeTimes->{ 3.481575155063283*^9, 3.481820467992608*^9, 3.481820990273611*^9, { 3.4820970026672316`*^9, 3.4820970070099688`*^9}, {3.4820971592769914`*^9, 3.4820971677698846`*^9}, 3.48209764606188*^9, 3.482097687321208*^9, { 3.4822361018514643`*^9, 3.4822361220104513`*^9}, {3.482237129899725*^9, 3.4822371331544046`*^9}, {3.482246029076274*^9, 3.4822460352751875`*^9}, 3.4825059221386538`*^9, 3.482505992831841*^9}, CellTags->"payoffmatrix"], Cell[TextData[{ "These cells define the payoff matrices ", StyleBox["(A, B) ", FontWeight->"Bold"], "in terms of the bimatrix ", StyleBox["U", FontWeight->"Bold"], "." }], "Text", Evaluatable->False, CellChangeTimes->{ 3.481573292434955*^9, {3.4825039492276278`*^9, 3.482503955756072*^9}, { 3.4825040173907146`*^9, 3.482504044150907*^9}}, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{ RowBox[{"A", "=", RowBox[{"(", GridBox[{ { RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}], RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}, { RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"2", ",", "1", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}], RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"2", ",", "2", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]} }], ")"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"B", "=", RowBox[{"(", GridBox[{ { RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1", ",", "1", ",", "2"}], "\[RightDoubleBracket]"}], RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2", ",", "1", ",", "2"}], "\[RightDoubleBracket]"}]}, { RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"2", ",", "1", ",", "1", ",", "2"}], "\[RightDoubleBracket]"}], RowBox[{"U", "\[LeftDoubleBracket]", RowBox[{"2", ",", "2", ",", "1", ",", "2"}], "\[RightDoubleBracket]"}]} }], ")"}]}], " ", ";"}]}], "Input", CellChangeTimes->{ 3.481575155063283*^9, 3.481820467992608*^9, 3.481820990273611*^9, { 3.4820970026672316`*^9, 3.4820970070099688`*^9}, {3.4820971592769914`*^9, 3.4820971677698846`*^9}, 3.48209764606188*^9, 3.482097687321208*^9, { 3.4822361018514643`*^9, 3.4822361220104513`*^9}, {3.4822366494488707`*^9, 3.482236673122912*^9}, {3.482237448968523*^9, 3.4822374523333616`*^9}, { 3.482245944033989*^9, 3.4822459485805264`*^9}}, CellTags->"payoffmatrix"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["General linear games", "Subsubsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.481816053845376*^9, 3.4818160546865854`*^9}, {3.4818162696456814`*^9, 3.4818162731507215`*^9}, {3.4822352575374002`*^9, 3.4822352601010866`*^9}, 3.4822371446909933`*^9, {3.4825040709683313`*^9, 3.4825040824488993`*^9}}], Cell[TextData[{ "The matrix ", StyleBox["M", FontWeight->"Bold"], " specifies the payoffs for the two-population linear game ", StyleBox["F[x_]=Mx", FontWeight->"Bold"], "." }], "Text", Evaluatable->False, CellChangeTimes->{ 3.481573292434955*^9, {3.4822365091971984`*^9, 3.4822365104289694`*^9}, { 3.4822371514907713`*^9, 3.4822373800394077`*^9}, {3.482504219672345*^9, 3.482504264618704*^9}}, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[ RowBox[{ RowBox[{"M", "=", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0"}, {"0", "2"} }, 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]", ")"}]}, { RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0"}, {"0", "2"} }, 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]", ")"}], RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "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]", ")"}]} }, 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$, MatrixForm[BoxForm`e$]]]}], ";"}]], "Input", CellChangeTimes->{ 3.481575155063283*^9, 3.481820467992608*^9, 3.481820990273611*^9, { 3.4820970026672316`*^9, 3.4820970070099688`*^9}, {3.4820971592769914`*^9, 3.4820971677698846`*^9}, 3.48209764606188*^9, 3.482097687321208*^9, { 3.482236514264485*^9, 3.4822365793280416`*^9}}, CellTags->"payoffmatrix"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Names of strategies", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.4818160457537403`*^9, 3.48181605160215*^9}, {3.4818162757043934`*^9, 3.481816305417118*^9}, { 3.4818185096266155`*^9, 3.48181851273108*^9}, 3.482504161893372*^9}], Cell[TextData[{ "Give the strategies one-character names to be printed on the phase diagram. \ ", StyleBox["strategy[1]", FontWeight->"Bold"], " and ", StyleBox["strategy[2] ", FontWeight->"Bold"], "are population 1's strategies. ", StyleBox["strategy[3]", FontWeight->"Bold"], " and ", StyleBox["strategy[4] ", FontWeight->"Bold"], "are population 2's strategies." }], "Text", CellChangeTimes->{{3.4825042746191893`*^9, 3.482504325094503*^9}}, FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"strategy", "[", "1", "]"}], "=", "\"\\""}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"strategy", "[", "2", "]"}], "=", "\"\\""}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"strategy", "[", "3", "]"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"strategy", "[", "4", "]"}], "=", "\"\\""}], " ", ";"}]}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Finding Nash equilibria", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.4818160457537403`*^9, 3.48181605160215*^9}, {3.4818162757043934`*^9, 3.481816305417118*^9}, { 3.4818185317784686`*^9, 3.481818537646907*^9}, {3.482504113138597*^9, 3.482504113722337*^9}, 3.482504165205385*^9}], Cell[TextData[{ "If ", StyleBox["findnashequilibria", FontWeight->"Bold"], " = 1, Dynamo will use a fixed point search from a grid of initial \ conditions to find the Nash equilibria of F. If F has a nonsingleton \ component of Nash equilibria, Dynamo will find a random subset of this \ component. To skip the computation of the Nash equilibria, set ", StyleBox["findnashequilibria", FontWeight->"Bold"], " = 0." }], "Text", CellChangeTimes->{3.4825043448331223`*^9}, FontFamily->"Palatino"], Cell[BoxData[ RowBox[{ RowBox[{"findnashequilibria", "=", "1"}], " ", ";"}]], "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Choice of dynamic", "Section", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Choosing the evolutionary dynamic", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.4818160457537403`*^9, 3.48181605160215*^9}, {3.4818162757043934`*^9, 3.481816305417118*^9}, { 3.4818185317784686`*^9, 3.481818537646907*^9}, {3.481901544248423*^9, 3.4819015490471973`*^9}, {3.4819031937608747`*^9, 3.481903194040564*^9}, { 3.481903249254183*^9, 3.481903251787709*^9}, {3.481903451311884*^9, 3.48190346767138*^9}}], Cell[TextData[{ "The variable ", StyleBox["dyn", FontWeight->"Bold"], " represents the evolutionary dynamic to be considered. Press a button in \ one of the cells below specifies the value of ", StyleBox["dyn", FontWeight->"Bold"], ". Parameters for the dynamics that require them are specified in \ \"Parameters for parameterized dynamics\". (To approximate the best response \ dynamic, choose Logit[\[Eta]] with \[Eta] = .001.) The definitions of the \ evolutionary dynamics can be found in the final subsection." }], "Text", CellChangeTimes->{{3.481903502754609*^9, 3.481903613823289*^9}, { 3.481903649322209*^9, 3.481903788064867*^9}, {3.481903915937501*^9, 3.481903918001616*^9}}, FontFamily->"Palatino"], Cell[CellGroupData[{ Cell["Some standard dynamics", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "matsl", ",", "names", " ", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "name", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", " ", RowBox[{"{", RowBox[{"Replicator", ",", RowBox[{"Defer", "[", RowBox[{"Logit", "[", "\[Eta]", "]"}], "]"}], ",", "BNN", ",", "MSReplicator", ",", "\"\< \>\"", " ", ",", "Smith", ",", RowBox[{"Defer", "[", RowBox[{"ILogit", "[", "\[Eta]", "]"}], "]"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{"name", ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"NotebookLocate", "[", "\"\\"", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", RowBox[{"RowBox", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"ToBoxes", "[", "name", "]"}], ",", "\"\<;\>\""}], "}"}], "]"}], ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"100", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{"ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"ToString", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}], "]"}], "==", " ", "\"\< \>\""}], ",", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "\"\<\>\"", "}"}]}], "]"}]}], ",", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", "[", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "3", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, 3.481735615579771*^9, { 3.481735646874771*^9, 3.4817356922600317`*^9}, 3.4817357345808864`*^9, 3.4817357949476895`*^9, {3.481735861463334*^9, 3.4817358750528755`*^9}, { 3.4817359228315773`*^9, 3.481735925495408*^9}, {3.4817374335538893`*^9, 3.4817374686543617`*^9}, {3.4817375128579235`*^9, 3.4817375183257856`*^9}, {3.481812891450633*^9, 3.481812899642412*^9}, 3.481812942794462*^9, 3.4818349201208076`*^9, {3.482098335573349*^9, 3.4820984073565683`*^9}, 3.482098474973797*^9}, CellTags->"buttoncell"], Cell[BoxData[ InterpretationBox[GridBox[{ { StyleBox[ ButtonBox["Replicator", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Replicator], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ RowBox[{"Logit", "[", "\[Eta]", "]"}], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[ Defer[ $CellContext`Logit[$CellContext`\[Eta]]]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox["BNN", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`BNN], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]}, { StyleBox[ ButtonBox["MSReplicator", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`MSReplicator], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], "\<\"\"\>", StyleBox[ ButtonBox["Smith", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Smith], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]}, { StyleBox[ ButtonBox[ RowBox[{"ILogit", "[", "\[Eta]", "]"}], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[ Defer[ $CellContext`ILogit[$CellContext`\[Eta]]]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], "\<\"\"\>", "\<\"\"\>"} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], TableForm[{{ Style[ Button[$CellContext`Replicator, NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Replicator], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"], Style[ Button[ Defer[ $CellContext`Logit[$CellContext`\[Eta]]], NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[ Defer[ $CellContext`Logit[$CellContext`\[Eta]]]], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"], Style[ Button[$CellContext`BNN, NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`BNN], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"]}, { Style[ Button[$CellContext`MSReplicator, NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`MSReplicator], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"], "", Style[ Button[$CellContext`Smith, NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Smith], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"]}, { Style[ Button[ Defer[ $CellContext`ILogit[$CellContext`\[Eta]]], NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[ Defer[ $CellContext`ILogit[$CellContext`\[Eta]]]], ";"}], AutoScroll -> False]; Null], ControlsRendering -> "Generic"]}}, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]], "Output", CellChangeTimes->{3.4820984461323247`*^9, 3.482098478809312*^9}, CellTags->"buttoncell"] }, {2}]] }, Open ]], Cell[CellGroupData[{ Cell["More dynamics", "SmallText", CellChangeTimes->{{3.481894707891967*^9, 3.4818947086630754`*^9}, { 3.4818947430525255`*^9, 3.4818947437935905`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "matsl", ",", "names", " ", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "name", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", " ", RowBox[{"{", RowBox[{"ExcessPayoff", ",", "PairwiseComparison", StyleBox[",", FontWeight->"Plain"], "projection", StyleBox[",", FontWeight->"Plain"], "Combined", StyleBox[",", FontWeight->"Plain"], "Other"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{"name", ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"NotebookLocate", "[", "\"\\"", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", RowBox[{"RowBox", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"ToBoxes", "[", "name", "]"}], ",", "\"\<;\>\""}], "}"}], "]"}], ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"100", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{"ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"ToString", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}], "]"}], "==", " ", "\"\< \>\""}], ",", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "\"\<\>\"", "}"}]}], "]"}]}], ",", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", "[", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "5", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, 3.481735615579771*^9, { 3.481735646874771*^9, 3.4817356922600317`*^9}, 3.4817357345808864`*^9, 3.4817357949476895`*^9, {3.481735861463334*^9, 3.4817358750528755`*^9}, { 3.4817359228315773`*^9, 3.481735925495408*^9}, {3.4817374335538893`*^9, 3.4817374686543617`*^9}, {3.4817375128579235`*^9, 3.4817375183257856`*^9}, {3.481812891450633*^9, 3.481812899642412*^9}, 3.481812942794462*^9, 3.4818349201208076`*^9, {3.482098335573349*^9, 3.4820984073565683`*^9}, 3.482098474973797*^9, {3.4820986565548973`*^9, 3.4820986625635376`*^9}}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ ButtonBox["ExcessPayoff", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`ExcessPayoff], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox["PairwiseComparison", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`PairwiseComparison], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox["projection", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`projection], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox["Combined", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Combined], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox["Other", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "meandynamic", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"dyn:=", ToBoxes[$CellContext`Other], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]]], "Output", CellChangeTimes->{3.482098663675136*^9, 3.4820988196894736`*^9}, CellTags->"buttoncell"] }, {2}]] }, Closed]], Cell[BoxData[ RowBox[{ RowBox[{"dyn", ":=", "Replicator"}], ";"}]], "Input", CellChangeTimes->{ 3.474407443638883*^9, 3.480869840070631*^9, 3.48088757527647*^9, 3.4815704923586435`*^9, {3.4815706634646816`*^9, 3.4815706780656767`*^9}, 3.4820980948472013`*^9, {3.4820986679012127`*^9, 3.4820986848656063`*^9}, 3.482098822833995*^9, 3.482102135667616*^9}, CellTags->"meandynamic"], Cell[CellGroupData[{ Cell["Parameters for parameterized dynamics", "SmallText", CellChangeTimes->{{3.481903127062379*^9, 3.4819031341334057`*^9}}], Cell[CellGroupData[{ Cell["Noise level for the logit and i-logit dynamics", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"\[Eta]", " ", "=", " ", ".01"}], " ", ";"}]], "Input"] }, Closed]] }, Closed]], Cell[BoxData[ RowBox[{ RowBox[{"dyn", "=", "dyn"}], ";"}]], "Input", CellOpen->False, CellChangeTimes->{{3.4818348627583246`*^9, 3.481834865722587*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Finding rest points", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.4818160457537403`*^9, 3.48181605160215*^9}, {3.4818162757043934`*^9, 3.481816305417118*^9}, { 3.4818185317784686`*^9, 3.481818537646907*^9}, {3.481901544248423*^9, 3.4819015490471973`*^9}, {3.4819031937608747`*^9, 3.481903194040564*^9}, { 3.481903249254183*^9, 3.481903251787709*^9}, {3.4819055118698387`*^9, 3.481905514021892*^9}}], Cell[TextData[{ "If ", StyleBox["findrestpoints", FontWeight->"Bold"], " = 1, Dynamo will use a fixed point search from a grid of initial \ conditions to find the rest points of F. If F has a nonsingleton component \ of rest points, Dynamo will find a random subset of this component. To skip \ the computation of the rest points, set ", StyleBox["findrestpoints", FontWeight->"Bold"], " = 0." }], "Text", CellChangeTimes->{{3.481903835445944*^9, 3.481903847574621*^9}, { 3.482504504090583*^9, 3.4825045181045103`*^9}}, FontFamily->"Palatino"], Cell[BoxData[ RowBox[{ RowBox[{"findrestpoints", "=", "1"}], ";"}]], "Input", CellChangeTimes->{{3.474407608145432*^9, 3.474407608576051*^9}, { 3.4750248928902655`*^9, 3.4750248937715325`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Definitions of dynamics", "Subsection", CellChangeTimes->{ 3.4816700476457615`*^9, {3.4818116260860605`*^9, 3.481811629100395*^9}, { 3.4818152985993853`*^9, 3.481815299991387*^9}, {3.4818160457537403`*^9, 3.48181605160215*^9}, {3.4818162757043934`*^9, 3.481816305417118*^9}, { 3.4818185317784686`*^9, 3.481818537646907*^9}, {3.481901544248423*^9, 3.4819015490471973`*^9}, {3.4819031937608747`*^9, 3.481903194040564*^9}, { 3.481903256420993*^9, 3.481903261596171*^9}, 3.48190551650214*^9}], Cell[CellGroupData[{ Cell[TextData[StyleBox["Payoff-related definitions", FontSlant->"Italic"]], "SmallText"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", "F", "]"}], ";", RowBox[{"Clear", "[", "Fbar", "]"}], " ", ";", " ", RowBox[{"Clear", "[", "Fhat", "]"}], " ", ";", " ", RowBox[{"Clear", "[", "Fhatplus", "]"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{{3.482235534225258*^9, 3.4822355372896643`*^9}}], Cell[CellGroupData[{ Cell["The populations payoffs", "Text", InitializationCell->True, CellChangeTimes->{{3.4822356365223536`*^9, 3.4822356551090803`*^9}, { 3.482504773110115*^9, 3.482504775702202*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"F", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], ",", RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}]}], "}"}]}], " ", ";"}]], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["The populations' average payoffs", "Text", InitializationCell->True, CellChangeTimes->{{3.482504766645734*^9, 3.4825047699418793`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fbar", "[", "1", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_"}], "]"}], ":=", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fbar", "[", "2", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F2_"}], "]"}], ":=", " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["Excess payoff vectors", "Text", InitializationCell->True, CellChangeTimes->{3.482504763509513*^9}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_"}], "]"}], ":=", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], " ", "-", " ", RowBox[{ RowBox[{"Fbar", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F2_"}], "]"}], ":=", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], " ", "-", " ", RowBox[{ RowBox[{"Fbar", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["Vectors of positive parts of excess payoffs", "Text", InitializationCell->True, CellChangeTimes->{3.482504762222719*^9}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_"}], "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "]"}]}], "}"}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F2_"}], "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "]"}]}], "}"}]}], " ", ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["Projected payoff vector", "Text"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"PhiF", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "2"}], ",", RowBox[{"1", "/", "2"}]}], "}"}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "[", RowBox[{"[", "i", "]"}], "]"}]}]}]}], ",", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "/", "2"}], ",", RowBox[{"1", "/", "2"}]}], "}"}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "[", RowBox[{"[", "i", "]"}], "]"}]}]}]}]}], " ", "}"}], ",", "1"}], "]"}]}], ";"}]], "Input", InitializationCell->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definition of combination of two dynamics", FontSlant->"Italic"]], "SmallText"], Cell["\<\ To define a combination of two dynamics, specify the two dynamics to be \ combined, the weights on the dynamics, and the characterization of the rest \ points of combined dynamic. Nash is the default setting for the set or rest \ points. This is correct, for example, with combinations of the replicator \ dynamic and an excess payoff dynamic like the BNN dynamic. If the rest \ points aren't identical to the Nash equilibria for the dynamics you have \ specified, you can replace Nash with Automatic if the combined dynamic is \ smooth. (If the combined dynamic isn't smooth, you're on your own!) The \ last line of code formally defines the combined dynamic according to your \ specificcations.\ \>", "Text", FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"dyn", "[", "1", "]"}], "=", "Replicator"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"dyn", "[", "2", "]"}], "=", "BNN"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"weight", "[", "1", "]"}], "=", ".9"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"weight", "[", "2", "]"}], "=", ".1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "Combined", "]"}], "=", "Nash"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Combined", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"weight", "[", "1", "]"}], " ", RowBox[{ RowBox[{"dyn", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}]}], "+", RowBox[{ RowBox[{"weight", "[", "2", "]"}], " ", RowBox[{ RowBox[{"dyn", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}]}]}]}], ";"}]}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definitions of dynamics", FontSlant->"Italic"]], "SmallText", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Clear", "[", "Replicator", "]"}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "BNN", "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "Logit", "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "rho", "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Clear", "[", "Smith", "]"}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Clear", "[", "rho1", "]"}], " ", ";"}]}], "Input", CellOpen->False, InitializationCell->True, CellChangeTimes->{ 3.4815705464263887`*^9, {3.482504797936713*^9, 3.482504799496624*^9}}, CellTags->"dynamicslibrary"], Cell[CellGroupData[{ Cell["Replicator dynamic", "Text", InitializationCell->True, CellChangeTimes->{3.482504874587615*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Replicator", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}]}], " ", ";"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "Replicator", "]"}], "=", "Automatic"}], " ", ";"}], "\[IndentingNewLine]"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Maynard Smith replicator dynamic", "Text", InitializationCell->True, CellChangeTimes->{{3.482504871803585*^9, 3.4825048735716343`*^9}}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"MSReplicator", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ FractionBox["1", RowBox[{ RowBox[{"Fbar", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}]], RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"Fbar", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}]], RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"Fbar", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}]], RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox["1", RowBox[{ RowBox[{"Fbar", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}]], RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}]}], " ", ";"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "MSReplicator", "]"}], "=", "Automatic"}], " ", ";"}], "\[IndentingNewLine]"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Imitative logit dynamic", "Text", InitializationCell->True, CellChangeTimes->{{3.4825048641963587`*^9, 3.482504868459486*^9}}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"ILogit", "[", "\[Eta]_", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Eta]"]]}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]}]], " ", "-", RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[Eta]"]]}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]}]], "-", RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Eta]"]]}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]}]], " ", "-", RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[Eta]"]]}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]}]], "-", RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}]}], " ", ";"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", RowBox[{"ILogit", "[", "_", "]"}], "]"}], "=", "Automatic"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.480869985023756*^9}, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Logit dynamic", "Text", InitializationCell->True, CellChangeTimes->{3.482504869883338*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Logit", "[", "\[Eta]_", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ FractionBox[ SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Eta]"]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]], "-", RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[Eta]"]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]], "-", RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Eta]"]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]], "-", RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ FractionBox[ SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[Eta]"]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}]], "-", RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}]}], " ", ";"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", RowBox[{"Logit", "[", "_", "]"}], "]"}], "=", "Automatic"}], " ", ";"}], "\[IndentingNewLine]"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Brown-von Neumann-Nash dynamic", "Text", InitializationCell->True, CellChangeTimes->{3.482504861764662*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"BNN", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}]}], "}"}]}], " ", ";"}]], "Input",\ InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "BNN", "]"}], "=", "Nash"}], " ", ";"}], "\[IndentingNewLine]"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Smith dynamic", "Text", InitializationCell->True, CellChangeTimes->{{3.482282954410376*^9, 3.4822829553717585`*^9}, 3.482504852330421*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"rho", "[", "1", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ",", "0"}], "}"}]}], "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"rho", "[", "2", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ",", "0"}], "}"}]}], "}"}]}], " ", ";"}]}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Smith", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", RowBox[{ RowBox[{"rho", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "]"}], ".", " ", "x"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ "x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "}"}], ".", RowBox[{ RowBox[{"rho", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"Flatten", "[", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", RowBox[{ RowBox[{"rho", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "]"}], ".", " ", "y"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "}"}], ".", RowBox[{ RowBox[{"rho", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}], "]"}]}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.481570547457872*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "Smith", "]"}], "=", "Nash"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4815705483491535`*^9}, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Excess payoff dynamic", "Text", InitializationCell->True, CellChangeTimes->{3.48250485333042*^9, 3.4825049012222643`*^9}], Cell[TextData[{ "Here one specifies the vector field sigmatilde that defines an excess \ payoff dynamic. This definition should be stated in terms of the excess \ payoff vector Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "], which is defined as Fhat[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "] = F", StyleBox["i", FontSlant->"Italic"], "[x,y] - Fbar[", StyleBox["i", FontSlant->"Italic"], "][x,y,F", StyleBox["i", FontSlant->"Italic"], "], for each population ", StyleBox["i ", FontSlant->"Italic"], "= 1, 2. (", StyleBox["Mathematica", FontSlant->"Italic"], " subtracts the scalar from the vector correctly.) When computing rest \ points, the program assumes that sigmatilde is acute, so that the rest points \ of the dynamic are the Nash equilibria of the underlying game." }], "Text", InitializationCell->True, FontFamily->"Palatino"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", " ", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "]"}], ")"}], "^", "2"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "]"}], ")"}], "^", "2"}], ",", RowBox[{ RowBox[{"(", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "]"}], ")"}], "^", "2"}], ",", RowBox[{ RowBox[{"(", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "]"}], ")"}], "^", "2"}]}], "}"}]}], ";"}]], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ExcessPayoff", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "3"}], "4"], RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}], ",", RowBox[{ RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "3"}], "4"], RowBox[{ RowBox[{"sigmatilde", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}]}]}]}], "}"}]}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.481570566034584*^9}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "ExcessPayoff", "]"}], "=", "Nash"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.481570567636888*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Pairwise comparison dynamic", "Text", InitializationCell->True, CellChangeTimes->{{3.482504849306291*^9, 3.482504851082426*^9}, 3.4825049019170513`*^9}], Cell["\<\ Here one specifies the vector field rho that defines an excess payoff \ dynamic. When computing rest points, the program assumes that rho is \ separable and sign-preserving, so that the rest points of the dynamic are the \ Nash equilibria of the underlying game.\ \>", "Text", InitializationCell->True], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"rho1", "[", "1", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F1_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ",", "0"}], "}"}]}], "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"rho1", "[", "2", "]"}], "[", RowBox[{"x_", ",", "y_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ",", "0"}], "}"}]}], "}"}]}], " ", ";"}]}], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"PairwiseComparison", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"Flatten", "[", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", RowBox[{ RowBox[{"rho1", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "]"}], ".", " ", "x"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ "x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "}"}], ".", RowBox[{ RowBox[{"rho1", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"Flatten", "[", RowBox[{ RowBox[{ RowBox[{"Transpose", "[", RowBox[{ RowBox[{"rho1", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "]"}], ".", " ", "y"}], "-", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "}"}], ".", RowBox[{ RowBox[{"rho1", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], ".", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}], "]"}]}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4815706171080236`*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "PairwiseComparison", "]"}], "=", "Nash"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4815706202024736`*^9}, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Projection dynamic", "Text", InitializationCell->True, CellChangeTimes->{3.4825048470833693`*^9}, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{"closetozero", "=", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "7"}], ")"}]}]}], " ", ";"}]], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"projection", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[GreaterEqual]", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ")"}]}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ "x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{"(", RowBox[{ FractionBox["1", "2"], RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}]}], ",", "0"}], "]"}], ",", "0"}], "]"}], "]"}], ",", RowBox[{"Evaluate", "[", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ")"}]}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ "x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ")"}]}], ",", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{"(", RowBox[{ FractionBox["1", "2"], RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}]}], ",", "0"}], "]"}], ",", "0"}], "]"}], "]"}], ",", RowBox[{"Evaluate", "[", RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[GreaterEqual]", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}], " ", ",", RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}], ",", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "-", RowBox[{"(", RowBox[{ FractionBox["1", "2"], RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}]}], ",", "0"}], "]"}], ",", "0"}], "]"}], "]"}], ",", RowBox[{"Evaluate", "[", RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ">", "closetozero"}], " ", "||", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[GreaterEqual]", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}], " ", ",", RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], "-", RowBox[{"(", RowBox[{ FractionBox["1", "2"], RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}]}], ")"}]}], ")"}]}], ",", "0"}], "]"}], ",", "0"}], "]"}], "]"}]}], " ", "}"}]}], " ", ";"}]], "Input",\ InitializationCell->True, CellChangeTimes->{3.475004689175253*^9}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "projection", "]"}], "=", "Nash"}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4750046960351167`*^9}, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell["Other (for user-defined dynamics)", "Text", InitializationCell->True, CellChangeTimes->{3.48250484468371*^9}, CellTags->"dynamicslibrary"], Cell["\<\ Define any other dynamic you want to use. When defining be sure you follow \ same style with previously defined dynamics. Otherwise, you may need to do \ major changes in the program.\ \>", "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Other", "[", RowBox[{"x_", ",", "y_", ",", "F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], " ", RowBox[{ RowBox[{ RowBox[{"Fhat", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}]}], ";"}]], "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "Other", "]"}], "=", "Automatic"}], " ", ";"}]], "Input", InitializationCell->True] }, Closed]] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Specifications for the phase diagram", "Section", Evaluatable->False, CellChangeTimes->{3.4825050002041397`*^9}, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["Basic options", "Subsection", CellChangeTimes->{{3.481670096105443*^9, 3.4816701004717216`*^9}, { 3.4818952324462385`*^9, 3.481895257672512*^9}, {3.482505060358889*^9, 3.482505063965598*^9}}], Cell[TextData[{ StyleBox["phasediagram", FontWeight->"Bold"], " = 1 creates a phase diagram on the simplex.\n", StyleBox["ppoints", FontWeight->"Bold"], " determines how many points will be used when drawing the solution \ trajectories. \n\n", StyleBox["includecontourplot", FontWeight->"Bold"], " = 1 draws the phase diagram on top of a contour plot.\n", StyleBox["color", FontWeight->"Bold"], " = 1 generates color output; color = 0 generates black and white. The \ scales used are drawn below.\n", StyleBox["numberofcontours", FontWeight->"Bold"], " specifies the number of contour levels shown in the contour plots.\n", StyleBox["plotprecision", FontWeight->"Bold"], " specifies the number of points sampled in each dimension when drawing the \ contour plots. This option typically determines the program's running time. \ Settings between 50 and 200 are accurate enough for most purposes. For fast \ drafts a setting of 20 is adequate.\n" }], "Text", CellChangeTimes->{{3.480779243193115*^9, 3.4807792961292334`*^9}, 3.4807794713011184`*^9, {3.480779514703528*^9, 3.4807795412717314`*^9}, { 3.4807797587995887`*^9, 3.4807799035777693`*^9}, {3.4807799399500704`*^9, 3.4807799407712507`*^9}, {3.480780151674515*^9, 3.4807801526859694`*^9}, { 3.481756068394542*^9, 3.48175606959627*^9}, {3.4818061451898513`*^9, 3.481806188842621*^9}, {3.4818062519032974`*^9, 3.4818062577016354`*^9}, { 3.4825050676805897`*^9, 3.482505080279986*^9}, 3.482505368873185*^9}], Cell[BoxData[Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .10844 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.47619 0.00258189 0.47619 [ [ 0 0 0 0 ] [ 1 .10844 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .10844 L 0 .10844 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00258189 0.477324 0.105858 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.942951 0.0337105 0.942951 [ [ 0 0 0 0 ] [ 1 .22772 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .22772 L 0 .22772 L closepath clip newpath 0 .1 1 r .02381 .03371 m .02381 .2223 L .03324 .2223 L .03324 .03371 L F 0 .145 1 r .03324 .03371 m .03324 .2223 L .04267 .2223 L .04267 .03371 L F 0 .19 1 r .04267 .03371 m .04267 .2223 L .0521 .2223 L .0521 .03371 L F 0 .235 1 r .0521 .03371 m .0521 .2223 L .06153 .2223 L .06153 .03371 L F 0 .28 1 r .06153 .03371 m .06153 .2223 L .07096 .2223 L .07096 .03371 L F 0 .325 1 r .07096 .03371 m .07096 .2223 L .08039 .2223 L .08039 .03371 L F 0 .37 1 r .08039 .03371 m .08039 .2223 L .08982 .2223 L .08982 .03371 L F 0 .415 1 r .08982 .03371 m .08982 .2223 L .09925 .2223 L .09925 .03371 L F 0 .46 1 r .09925 .03371 m .09925 .2223 L .10868 .2223 L .10868 .03371 L F 0 .505 1 r .10868 .03371 m .10868 .2223 L .1181 .2223 L .1181 .03371 L F 0 .55 1 r .1181 .03371 m .1181 .2223 L .12753 .2223 L .12753 .03371 L F 0 .595 1 r .12753 .03371 m .12753 .2223 L .13696 .2223 L .13696 .03371 L F 0 .64 1 r .13696 .03371 m .13696 .2223 L .14639 .2223 L .14639 .03371 L F 0 .685 1 r .14639 .03371 m .14639 .2223 L .15582 .2223 L .15582 .03371 L F 0 .73 1 r .15582 .03371 m .15582 .2223 L .16525 .2223 L .16525 .03371 L F 0 .775 1 r .16525 .03371 m .16525 .2223 L .17468 .2223 L .17468 .03371 L F 0 .82 1 r .17468 .03371 m .17468 .2223 L .18411 .2223 L .18411 .03371 L F 0 .865 1 r .18411 .03371 m .18411 .2223 L .19354 .2223 L .19354 .03371 L F 0 .91 1 r .19354 .03371 m .19354 .2223 L .20297 .2223 L .20297 .03371 L F 0 .955 1 r .20297 .03371 m .20297 .2223 L .2124 .2223 L .2124 .03371 L F 0 1 1 r .2124 .03371 m .2124 .2223 L .22183 .2223 L .22183 .03371 L F 0 1 .955 r .22183 .03371 m .22183 .2223 L .23126 .2223 L .23126 .03371 L F 0 1 .91 r .23126 .03371 m .23126 .2223 L .24069 .2223 L .24069 .03371 L F 0 1 .865 r .24069 .03371 m .24069 .2223 L .25012 .2223 L .25012 .03371 L F 0 1 .82 r .25012 .03371 m .25012 .2223 L .25955 .2223 L .25955 .03371 L F 0 1 .775 r .25955 .03371 m .25955 .2223 L .26898 .2223 L .26898 .03371 L F 0 1 .73 r .26898 .03371 m .26898 .2223 L .27841 .2223 L .27841 .03371 L F 0 1 .685 r .27841 .03371 m .27841 .2223 L .28784 .2223 L .28784 .03371 L F 0 1 .64 r .28784 .03371 m .28784 .2223 L .29727 .2223 L .29727 .03371 L F 0 1 .595 r .29727 .03371 m .29727 .2223 L .30669 .2223 L .30669 .03371 L F 0 1 .55 r .30669 .03371 m .30669 .2223 L .31612 .2223 L .31612 .03371 L F 0 1 .505 r .31612 .03371 m .31612 .2223 L .32555 .2223 L .32555 .03371 L F 0 1 .46 r .32555 .03371 m .32555 .2223 L .33498 .2223 L .33498 .03371 L F 0 1 .415 r .33498 .03371 m .33498 .2223 L .34441 .2223 L .34441 .03371 L F 0 1 .352 r .34441 .03371 m .34441 .2223 L .35384 .2223 L .35384 .03371 L F 0 1 .28 r .35384 .03371 m .35384 .2223 L .36327 .2223 L .36327 .03371 L F 0 1 .208 r .36327 .03371 m .36327 .2223 L .3727 .2223 L .3727 .03371 L F 0 1 .136 r .3727 .03371 m .3727 .2223 L .38213 .2223 L .38213 .03371 L F 0 1 .064 r .38213 .03371 m .38213 .2223 L .39156 .2223 L .39156 .03371 L F .008 1 0 r .39156 .03371 m .39156 .2223 L .40099 .2223 L .40099 .03371 L F .08 1 0 r .40099 .03371 m .40099 .2223 L .41042 .2223 L .41042 .03371 L F .152 1 0 r .41042 .03371 m .41042 .2223 L .41985 .2223 L .41985 .03371 L F .224 1 0 r .41985 .03371 m .41985 .2223 L .42928 .2223 L .42928 .03371 L F .296 1 0 r .42928 .03371 m .42928 .2223 L .43871 .2223 L .43871 .03371 L F .368 1 0 r .43871 .03371 m .43871 .2223 L .44814 .2223 L .44814 .03371 L F .44 1 0 r .44814 .03371 m .44814 .2223 L .45757 .2223 L .45757 .03371 L F .512 1 0 r .45757 .03371 m .45757 .2223 L .467 .2223 L .467 .03371 L F .584 1 0 r .467 .03371 m .467 .2223 L .47643 .2223 L .47643 .03371 L F .656 1 0 r .47643 .03371 m .47643 .2223 L .48586 .2223 L .48586 .03371 L F .728 1 0 r .48586 .03371 m .48586 .2223 L .49529 .2223 L .49529 .03371 L F .8 1 0 r .49529 .03371 m .49529 .2223 L .50471 .2223 L .50471 .03371 L F .824 1 0 r .50471 .03371 m .50471 .2223 L .51414 .2223 L .51414 .03371 L F .848 1 0 r .51414 .03371 m .51414 .2223 L .52357 .2223 L .52357 .03371 L F .872 1 0 r .52357 .03371 m .52357 .2223 L .533 .2223 L .533 .03371 L F .896 1 0 r .533 .03371 m .533 .2223 L .54243 .2223 L .54243 .03371 L F .92 1 0 r .54243 .03371 m .54243 .2223 L .55186 .2223 L .55186 .03371 L F .944 1 0 r .55186 .03371 m .55186 .2223 L .56129 .2223 L .56129 .03371 L F .968 1 0 r .56129 .03371 m .56129 .2223 L .57072 .2223 L .57072 .03371 L F .992 1 0 r .57072 .03371 m .57072 .2223 L .58015 .2223 L .58015 .03371 L F 1 .984 0 r .58015 .03371 m .58015 .2223 L .58958 .2223 L .58958 .03371 L F 1 .96 0 r .58958 .03371 m .58958 .2223 L .59901 .2223 L .59901 .03371 L F 1 .936 0 r .59901 .03371 m .59901 .2223 L .60844 .2223 L .60844 .03371 L F 1 .912 0 r .60844 .03371 m .60844 .2223 L .61787 .2223 L .61787 .03371 L F 1 .888 0 r .61787 .03371 m .61787 .2223 L .6273 .2223 L .6273 .03371 L F 1 .864 0 r .6273 .03371 m .6273 .2223 L .63673 .2223 L .63673 .03371 L F 1 .84 0 r .63673 .03371 m .63673 .2223 L .64616 .2223 L .64616 .03371 L F 1 .816 0 r .64616 .03371 m .64616 .2223 L .65559 .2223 L .65559 .03371 L F 1 .792 0 r .65559 .03371 m .65559 .2223 L .66502 .2223 L .66502 .03371 L F 1 .768 0 r .66502 .03371 m .66502 .2223 L .67445 .2223 L .67445 .03371 L F 1 .744 0 r .67445 .03371 m .67445 .2223 L .68388 .2223 L .68388 .03371 L F 1 .72 0 r .68388 .03371 m .68388 .2223 L .69331 .2223 L .69331 .03371 L F 1 .696 0 r .69331 .03371 m .69331 .2223 L .70273 .2223 L .70273 .03371 L F 1 .672 0 r .70273 .03371 m .70273 .2223 L .71216 .2223 L .71216 .03371 L F 1 .648 0 r .71216 .03371 m .71216 .2223 L .72159 .2223 L .72159 .03371 L F 1 .624 0 r .72159 .03371 m .72159 .2223 L .73102 .2223 L .73102 .03371 L F 1 .6 0 r .73102 .03371 m .73102 .2223 L .74045 .2223 L .74045 .03371 L F 1 .576 0 r .74045 .03371 m .74045 .2223 L .74988 .2223 L .74988 .03371 L F 1 .552 0 r .74988 .03371 m .74988 .2223 L .75931 .2223 L .75931 .03371 L F 1 .528 0 r .75931 .03371 m .75931 .2223 L .76874 .2223 L .76874 .03371 L F 1 .504 0 r .76874 .03371 m .76874 .2223 L .77817 .2223 L .77817 .03371 L F 1 .48 0 r .77817 .03371 m .77817 .2223 L .7876 .2223 L .7876 .03371 L F 1 .456 0 r .7876 .03371 m .7876 .2223 L .79703 .2223 L .79703 .03371 L F 1 .432 0 r .79703 .03371 m .79703 .2223 L .80646 .2223 L .80646 .03371 L F 1 .408 0 r .80646 .03371 m .80646 .2223 L .81589 .2223 L .81589 .03371 L F 1 .384 0 r .81589 .03371 m .81589 .2223 L .82532 .2223 L .82532 .03371 L F 1 .36 0 r .82532 .03371 m .82532 .2223 L .83475 .2223 L .83475 .03371 L F 1 .336 0 r .83475 .03371 m .83475 .2223 L .84418 .2223 L .84418 .03371 L F 1 .312 0 r .84418 .03371 m .84418 .2223 L .85361 .2223 L .85361 .03371 L F 1 .288 0 r .85361 .03371 m .85361 .2223 L .86304 .2223 L .86304 .03371 L F 1 .264 0 r .86304 .03371 m .86304 .2223 L .87247 .2223 L .87247 .03371 L F 1 .24 0 r .87247 .03371 m .87247 .2223 L .8819 .2223 L .8819 .03371 L F 1 .216 0 r .8819 .03371 m .8819 .2223 L .89132 .2223 L .89132 .03371 L F 1 .192 0 r .89132 .03371 m .89132 .2223 L .90075 .2223 L .90075 .03371 L F 1 .168 0 r .90075 .03371 m .90075 .2223 L .91018 .2223 L .91018 .03371 L F 1 .144 0 r .91018 .03371 m .91018 .2223 L .91961 .2223 L .91961 .03371 L F 1 .12 0 r .91961 .03371 m .91961 .2223 L .92904 .2223 L .92904 .03371 L F 1 .096 0 r .92904 .03371 m .92904 .2223 L .93847 .2223 L .93847 .03371 L F 1 .072 0 r .93847 .03371 m .93847 .2223 L .9479 .2223 L .9479 .03371 L F 1 .048 0 r .9479 .03371 m .9479 .2223 L .95733 .2223 L .95733 .03371 L F 1 .024 0 r .95733 .03371 m .95733 .2223 L .96676 .2223 L .96676 .03371 L F 1 0 0 r .96676 .03371 m .96676 .2223 L .97619 .2223 L .97619 .03371 L F 0 g .5 Mabswid [ ] 0 setdash .02381 .03371 m .02381 .04785 L s .1181 .03371 m .1181 .04785 L s .2124 .03371 m .2124 .04785 L s .30669 .03371 m .30669 .04785 L s .40099 .03371 m .40099 .04785 L s .49529 .03371 m .49529 .04785 L s .58958 .03371 m .58958 .04785 L s .68388 .03371 m .68388 .04785 L s .77817 .03371 m .77817 .04785 L s .87247 .03371 m .87247 .04785 L s .96676 .03371 m .96676 .04785 L s .49529 .03371 m .49529 .06671 L s .02381 .03371 m .02381 .06671 L s .96676 .03371 m .96676 .06671 L s gsave .02381 .00542 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .96676 .00542 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.522676 0.00258189 0.97619 0.105858 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.942951 0.0337105 0.942951 [ [ 0 0 0 0 ] [ 1 .22772 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .22772 L 0 .22772 L closepath clip newpath .295 g .02381 .03371 m .02381 .2223 L .03324 .2223 L .03324 .03371 L F .301 g .03324 .03371 m .03324 .2223 L .04267 .2223 L .04267 .03371 L F .308 g .04267 .03371 m .04267 .2223 L .0521 .2223 L .0521 .03371 L F .314 g .0521 .03371 m .0521 .2223 L .06153 .2223 L .06153 .03371 L F .321 g .06153 .03371 m .06153 .2223 L .07096 .2223 L .07096 .03371 L F .328 g .07096 .03371 m .07096 .2223 L .08039 .2223 L .08039 .03371 L F .334 g .08039 .03371 m .08039 .2223 L .08982 .2223 L .08982 .03371 L F .341 g .08982 .03371 m .08982 .2223 L .09925 .2223 L .09925 .03371 L F .347 g .09925 .03371 m .09925 .2223 L .10868 .2223 L .10868 .03371 L F .354 g .10868 .03371 m .10868 .2223 L .1181 .2223 L .1181 .03371 L F .36 g .1181 .03371 m .1181 .2223 L .12753 .2223 L .12753 .03371 L F .367 g .12753 .03371 m .12753 .2223 L .13696 .2223 L .13696 .03371 L F .373 g .13696 .03371 m .13696 .2223 L .14639 .2223 L .14639 .03371 L F .38 g .14639 .03371 m .14639 .2223 L .15582 .2223 L .15582 .03371 L F .387 g .15582 .03371 m .15582 .2223 L .16525 .2223 L .16525 .03371 L F .393 g .16525 .03371 m .16525 .2223 L .17468 .2223 L .17468 .03371 L F .4 g .17468 .03371 m .17468 .2223 L .18411 .2223 L .18411 .03371 L F .406 g .18411 .03371 m .18411 .2223 L .19354 .2223 L .19354 .03371 L F .413 g .19354 .03371 m .19354 .2223 L .20297 .2223 L .20297 .03371 L F .419 g .20297 .03371 m .20297 .2223 L .2124 .2223 L .2124 .03371 L F .426 g .2124 .03371 m .2124 .2223 L .22183 .2223 L .22183 .03371 L F .432 g .22183 .03371 m .22183 .2223 L .23126 .2223 L .23126 .03371 L F .439 g .23126 .03371 m .23126 .2223 L .24069 .2223 L .24069 .03371 L F .446 g .24069 .03371 m .24069 .2223 L .25012 .2223 L .25012 .03371 L F .452 g .25012 .03371 m .25012 .2223 L .25955 .2223 L .25955 .03371 L F .459 g .25955 .03371 m .25955 .2223 L .26898 .2223 L .26898 .03371 L F .465 g .26898 .03371 m .26898 .2223 L .27841 .2223 L .27841 .03371 L F .472 g .27841 .03371 m .27841 .2223 L .28784 .2223 L .28784 .03371 L F .478 g .28784 .03371 m .28784 .2223 L .29727 .2223 L .29727 .03371 L F .485 g .29727 .03371 m .29727 .2223 L .30669 .2223 L .30669 .03371 L F .491 g .30669 .03371 m .30669 .2223 L .31612 .2223 L .31612 .03371 L F .498 g .31612 .03371 m .31612 .2223 L .32555 .2223 L .32555 .03371 L F .504 g .32555 .03371 m .32555 .2223 L .33498 .2223 L .33498 .03371 L F .511 g .33498 .03371 m .33498 .2223 L .34441 .2223 L .34441 .03371 L F .518 g .34441 .03371 m .34441 .2223 L .35384 .2223 L .35384 .03371 L F .524 g .35384 .03371 m .35384 .2223 L .36327 .2223 L .36327 .03371 L F .531 g .36327 .03371 m .36327 .2223 L .3727 .2223 L .3727 .03371 L F .537 g .3727 .03371 m .3727 .2223 L .38213 .2223 L .38213 .03371 L F .544 g .38213 .03371 m .38213 .2223 L .39156 .2223 L .39156 .03371 L F .55 g .39156 .03371 m .39156 .2223 L .40099 .2223 L .40099 .03371 L F .557 g .40099 .03371 m .40099 .2223 L .41042 .2223 L .41042 .03371 L F .563 g .41042 .03371 m .41042 .2223 L .41985 .2223 L .41985 .03371 L F .57 g .41985 .03371 m .41985 .2223 L .42928 .2223 L .42928 .03371 L F .577 g .42928 .03371 m .42928 .2223 L .43871 .2223 L .43871 .03371 L F .583 g .43871 .03371 m .43871 .2223 L .44814 .2223 L .44814 .03371 L F .59 g .44814 .03371 m .44814 .2223 L .45757 .2223 L .45757 .03371 L F .596 g .45757 .03371 m .45757 .2223 L .467 .2223 L .467 .03371 L F .603 g .467 .03371 m .467 .2223 L .47643 .2223 L .47643 .03371 L F .609 g .47643 .03371 m .47643 .2223 L .48586 .2223 L .48586 .03371 L F .616 g .48586 .03371 m .48586 .2223 L .49529 .2223 L .49529 .03371 L F .622 g .49529 .03371 m .49529 .2223 L .50471 .2223 L .50471 .03371 L F .629 g .50471 .03371 m .50471 .2223 L .51414 .2223 L .51414 .03371 L F .636 g .51414 .03371 m .51414 .2223 L .52357 .2223 L .52357 .03371 L F .642 g .52357 .03371 m .52357 .2223 L .533 .2223 L .533 .03371 L F .649 g .533 .03371 m .533 .2223 L .54243 .2223 L .54243 .03371 L F .655 g .54243 .03371 m .54243 .2223 L .55186 .2223 L .55186 .03371 L F .662 g .55186 .03371 m .55186 .2223 L .56129 .2223 L .56129 .03371 L F .668 g .56129 .03371 m .56129 .2223 L .57072 .2223 L .57072 .03371 L F .675 g .57072 .03371 m .57072 .2223 L .58015 .2223 L .58015 .03371 L F .681 g .58015 .03371 m .58015 .2223 L .58958 .2223 L .58958 .03371 L F .688 g .58958 .03371 m .58958 .2223 L .59901 .2223 L .59901 .03371 L F .694 g .59901 .03371 m .59901 .2223 L .60844 .2223 L .60844 .03371 L F .701 g .60844 .03371 m .60844 .2223 L .61787 .2223 L .61787 .03371 L F .708 g .61787 .03371 m .61787 .2223 L .6273 .2223 L .6273 .03371 L F .714 g .6273 .03371 m .6273 .2223 L .63673 .2223 L .63673 .03371 L F .721 g .63673 .03371 m .63673 .2223 L .64616 .2223 L .64616 .03371 L F .727 g .64616 .03371 m .64616 .2223 L .65559 .2223 L .65559 .03371 L F .734 g .65559 .03371 m .65559 .2223 L .66502 .2223 L .66502 .03371 L F .74 g .66502 .03371 m .66502 .2223 L .67445 .2223 L .67445 .03371 L F .747 g .67445 .03371 m .67445 .2223 L .68388 .2223 L .68388 .03371 L F .753 g .68388 .03371 m .68388 .2223 L .69331 .2223 L .69331 .03371 L F .76 g .69331 .03371 m .69331 .2223 L .70273 .2223 L .70273 .03371 L F .767 g .70273 .03371 m .70273 .2223 L .71216 .2223 L .71216 .03371 L F .773 g .71216 .03371 m .71216 .2223 L .72159 .2223 L .72159 .03371 L F .78 g .72159 .03371 m .72159 .2223 L .73102 .2223 L .73102 .03371 L F .786 g .73102 .03371 m .73102 .2223 L .74045 .2223 L .74045 .03371 L F .793 g .74045 .03371 m .74045 .2223 L .74988 .2223 L .74988 .03371 L F .799 g .74988 .03371 m .74988 .2223 L .75931 .2223 L .75931 .03371 L F .806 g .75931 .03371 m .75931 .2223 L .76874 .2223 L .76874 .03371 L F .812 g .76874 .03371 m .76874 .2223 L .77817 .2223 L .77817 .03371 L F .819 g .77817 .03371 m .77817 .2223 L .7876 .2223 L .7876 .03371 L F .826 g .7876 .03371 m .7876 .2223 L .79703 .2223 L .79703 .03371 L F .832 g .79703 .03371 m .79703 .2223 L .80646 .2223 L .80646 .03371 L F .839 g .80646 .03371 m .80646 .2223 L .81589 .2223 L .81589 .03371 L F .845 g .81589 .03371 m .81589 .2223 L .82532 .2223 L .82532 .03371 L F .852 g .82532 .03371 m .82532 .2223 L .83475 .2223 L .83475 .03371 L F .858 g .83475 .03371 m .83475 .2223 L .84418 .2223 L .84418 .03371 L F .865 g .84418 .03371 m .84418 .2223 L .85361 .2223 L .85361 .03371 L F .871 g .85361 .03371 m .85361 .2223 L .86304 .2223 L .86304 .03371 L F .878 g .86304 .03371 m .86304 .2223 L .87247 .2223 L .87247 .03371 L F .884 g .87247 .03371 m .87247 .2223 L .8819 .2223 L .8819 .03371 L F .891 g .8819 .03371 m .8819 .2223 L .89132 .2223 L .89132 .03371 L F .898 g .89132 .03371 m .89132 .2223 L .90075 .2223 L .90075 .03371 L F .904 g .90075 .03371 m .90075 .2223 L .91018 .2223 L .91018 .03371 L F .911 g .91018 .03371 m .91018 .2223 L .91961 .2223 L .91961 .03371 L F .917 g .91961 .03371 m .91961 .2223 L .92904 .2223 L .92904 .03371 L F .924 g .92904 .03371 m .92904 .2223 L .93847 .2223 L .93847 .03371 L F .93 g .93847 .03371 m .93847 .2223 L .9479 .2223 L .9479 .03371 L F .937 g .9479 .03371 m .9479 .2223 L .95733 .2223 L .95733 .03371 L F .943 g .95733 .03371 m .95733 .2223 L .96676 .2223 L .96676 .03371 L F .95 g .96676 .03371 m .96676 .2223 L .97619 .2223 L .97619 .03371 L F .2 0 1 r .5 Mabswid [ ] 0 setdash .02381 .03371 m .02381 .04785 L s .1181 .03371 m .1181 .04785 L s .2124 .03371 m .2124 .04785 L s .30669 .03371 m .30669 .04785 L s .40099 .03371 m .40099 .04785 L s .49529 .03371 m .49529 .04785 L s .58958 .03371 m .58958 .04785 L s .68388 .03371 m .68388 .04785 L s .77817 .03371 m .77817 .04785 L s .87247 .03371 m .87247 .04785 L s .96676 .03371 m .96676 .04785 L s .49529 .03371 m .49529 .06671 L s .02381 .03371 m .02381 .06671 L s .96676 .03371 m .96676 .06671 L s 0 g gsave .02381 .00542 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .96676 .00542 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", GeneratedCell->False, CellAutoOverwrite->False, ImageSize->{507.438, 55}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJzt2V9InWUcB/DH77u66iLcWutmWVQ33RQRI6iroBFDE8UcYpOTy80Nl/gH hyhyTJThSRIRTRHJ2USUzRqKHDFDdLIUzTmWKWeJJZsmirjoYoun7/t6RDg3 ntFWYN+H5/s+7/O+v/Och/ecjxeeeF/B6U9yfAXZmb64o3m+3NPZmflx732a x0tOjDEx940xRw4ZnlueeXHbA2brdOvsAI/gzRscn+D4fMT8oFe13z3u217D XWzGHZydK4d3rfg/rLT9NGfC4wsR80MRT/+ZiFViI+b7d7m/2/xhX79bfZw3 fyM83a7fmcfuMn/Y+n/6+oM7T9n99Mxz1rzsdpjXmLetY45yTGZOMGeYQsYf rg5Y0+h2x1zk1StMkLnGTDMh5i7v3QtX8z3sPXYYe5cJMdPMNSboGHuF40Wm MVwdMNbPziuFzBkmjVVHOb7JvMg8DXDzbvUBa17xuvOWNTjGnGBymc+YeqaD CbLa/awmrNsNbvDaz8wvzBLzO7PB/Ml1/uJo72+tbv8wdt3tsMvMr0yI+ck4 9keOPzAjzHfh6n5jv3U7bDcrvubYynzJ1DGfM1WMf2svttjYAu6FB9hzzGnm Yyad+ZD5gHmf67wbXv0dY4+4HfZ15lXmJeYww79lNpbjU8yT4dW9L+bOt/KY 1wzi4+ORkJCAxMREJCUlITk5GSkpKUhNTXWOHz+OtLQ0s4/16enpH3kNGRkZ 8Pl8yMzMxMmTJ52srCycOnUK2dnZOHv2rFedk5NzzmvIzc1FXl6ek5+fj8LC QhQVFeH8+fMoLi5GSUmJt5fS0tKysjIDHuD3+1FeXo6KigpUVlaiqqoKFy5c QHV1tRMIBLzVa2pqvvAaamtrUVdXh/r6ejQ0NKCxsdFpampCc3MzWlpavOrW 1tavvIa2tja0t7fj0qVLTkdHBzo7O9HV1YXu7m5cvnzZq+7p6fnGa87Vq1fR 29uLvr4+9Pf3IxgMYmBgAIODgxgaGvJ2/r3XDIaHhzEyMoLR0VGMjY3h+vXr GB8fx8TEhDM5OYmpqSlv9enp6Rmv4ebNm7h16xZmZ2cxNzfnzM/PIxQK4fbt 21hYWPCqFxcXf/MalpaWnDt37mB5eRkrKytYXV3F2toa1tfXsbGx4e1lc3NT juVYjuVYjuVYjuVYjuVYjv9bx6BhRCGY2tzsapcJIAq1oFg8Bq+gVUQhFVSK KIyCPp0obIIu8S+oBEUiCo+gRUQhEVToRCEQ1IdHbg90hyjUOeQWjTZQGqJw BhqDhEmYhEmYhEmYhEmYhEnYIxQG6sIesOUQ1V4w5f6ryP0V3yGivWAI9IM9 oAeU86zUSI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3U SI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3U SI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USI3U SI3USI3USI3USI3USI3USI3USI3USI3USI3USI3USM1jU8ODfRBxZmL+BnC0 SyI=\ \>"], ImageRangeCache->{{{0, 506.438}, {54, 0}} -> {-0.0678623, -0.00542311, 0.00421716, 0.00421716}, {{16.0625, 241.875}, {52.6875, 1.25}} -> {-0.100692, -0.0419516, 0.00469642, 0.00469642}, {{264.5, 490.313}, {52.6875, 1.25}} -> {-1.26746, -0.0419516, 0.00469642, 0.00469642}}]], "Text"], Cell[BoxData[{ RowBox[{ RowBox[{"phasediagram", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ppoints", "=", "50"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"includecontourplot", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"color", "=", "1"}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"numberofcontours", "=", "100"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"plotprecision", "=", "50"}], " ", ";"}]}], "Input", CellChangeTimes->{{3.481806280424309*^9, 3.481806282507304*^9}, { 3.4818063574951315`*^9, 3.4818063682706256`*^9}, {3.4818908249685974`*^9, 3.48189083860821*^9}, 3.482101394782275*^9, 3.4825053412471323`*^9, { 3.4825053732170773`*^9, 3.4825053779199543`*^9}, {3.482505974827471*^9, 3.482505978424987*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Choice of contour function", "Subsection", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "The variable ", StyleBox["ContourFunction", FontWeight->"Bold"], " specifies the function plotted behind the solution trajectories in the \ phase diagram. If you choose ", StyleBox["StableGameLyapunov[dyn]", FontWeight->"Bold"], ", Dynamo uses the Lyapunov function that is appropriate for the dynamic ", StyleBox["dyn", FontWeight->"Bold"], ", provided that one is known. " }], "Text", CellChangeTimes->{3.4744074747135663`*^9, 3.4815704923987007`*^9, 3.481572990450723*^9, 3.4820980948672304`*^9, 3.4825052782755404`*^9}, FontFamily->"Palatino"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "names", " ", ",", "buttons", ",", "col", ",", "colbut", ",", "name", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", " ", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Speed", ",", "L1Speed"}], "}"}], ",", RowBox[{"{", "NormalFormPotential", "}"}], ",", RowBox[{"{", RowBox[{"Defer", "[", RowBox[{"StableGameLyapunov", "[", "dyn", "]"}], "]"}], "}"}], ",", RowBox[{"{", "Other", "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"col", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"col", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"colbut", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "col", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{"name", ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ "NotebookLocate", "[", "\"\\"", "]"}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", RowBox[{"RowBox", "[", RowBox[{"{", RowBox[{"\"\\"", ",", RowBox[{"ToBoxes", "[", "name", "]"}], ",", "\"\<;\>\""}], "}"}], "]"}], ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"250", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{"ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "col", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"colbut", "=", RowBox[{"Join", "[", RowBox[{"colbut", ",", RowBox[{"{", "button", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", RowBox[{"Column", "[", "colbut", "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"col", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", "[", RowBox[{ RowBox[{"{", "buttons", "}"}], ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Center", ",", "Top"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Row", "[", RowBox[{"buttons", ",", RowBox[{"Alignment", "->", RowBox[{"{", "Top", "}"}]}]}], "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, {3.4816740331466303`*^9, 3.481674065713459*^9}, { 3.481674238521946*^9, 3.4816742890345793`*^9}, {3.481674331806082*^9, 3.481674340829056*^9}, {3.4816743915620065`*^9, 3.4816744212947598`*^9}, { 3.4816747202947006`*^9, 3.481674733964357*^9}, {3.4816747804011297`*^9, 3.481674900724146*^9}, 3.481735482883896*^9, {3.4817380541162148`*^9, 3.48173807889184*^9}, {3.48173811685643*^9, 3.4817381399496365`*^9}, { 3.48173818204016*^9, 3.4817381861360493`*^9}, 3.481805509315509*^9, { 3.4818056125139008`*^9, 3.4818056395427666`*^9}, {3.4818129093764095`*^9, 3.4818129153650208`*^9}, 3.482099075387149*^9}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { TagBox[GridBox[{ { StyleBox[ ButtonBox["Speed", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "contourfunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"ContourFunction=", ToBoxes[$CellContext`Speed], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]}, { StyleBox[ ButtonBox["L1Speed", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "contourfunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"ContourFunction=", ToBoxes[$CellContext`L1Speed], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], TagBox[GridBox[{ { StyleBox[ ButtonBox["NormalFormPotential", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "contourfunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"ContourFunction=", ToBoxes[$CellContext`NormalFormPotential], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], TagBox[GridBox[{ { StyleBox[ ButtonBox[ RowBox[{"StableGameLyapunov", "[", "dyn", "]"}], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "contourfunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"ContourFunction=", ToBoxes[ Defer[ $CellContext`StableGameLyapunov[$CellContext`dyn]]], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], TagBox[GridBox[{ { StyleBox[ ButtonBox["Other", Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "contourfunction", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], RowBox[{"ContourFunction=", ToBoxes[$CellContext`Other], ";"}], AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[BoxForm`e$, TableAlignments -> {Center, Top}]]]], "Output", CellChangeTimes->{3.482099083508827*^9}, CellTags->"buttoncell"] }, {2}]], Cell[BoxData[ RowBox[{ RowBox[{"ContourFunction", "=", "Speed"}], ";"}]], "Input", CellChangeTimes->{{3.4815710103434687`*^9, 3.4815710181747293`*^9}, { 3.482098236460832*^9, 3.48209823666112*^9}, 3.48209898048068*^9, { 3.4820990951355457`*^9, 3.482099109536253*^9}}, CellTags->"contourfunction"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Definitions of contour functions", FontSlant->"Italic"]], "SmallText", InitializationCell->True, CellTags->"contourfunctions"], Cell[CellGroupData[{ Cell["Speed functions", "Subsubsection", CellTags->"contourfunctions"], Cell["\<\ Speed is the standard (Euclidean) speed on the simplex. L1Speed is \ self-explanatory. \ \>", "Text", Evaluatable->False, InitializationCell->True, CellChangeTimes->{{3.482505409282015*^9, 3.482505409920401*^9}}, FontFamily->"Palatino", CellTags->"contourfunctions"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Speed", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"If", "[", RowBox[{ RowBox[{"dyn", "===", " ", "projection"}], ",", RowBox[{"Sqrt", "[", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "4"], SuperscriptBox[ RowBox[{ RowBox[{"PhiF", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "2"]}], "]"}], " ", ",", RowBox[{"Sqrt", "[", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "4"], SuperscriptBox[ RowBox[{ RowBox[{"dyn", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "2"]}], "]"}]}], " ", "]"}]}], ";"}]], "Input", InitializationCell->True, CellChangeTimes->{{3.474407477367382*^9, 3.474407479210032*^9}, 3.475004701022288*^9, {3.4815704924087152`*^9, 3.4815704924087152`*^9}, { 3.482098094907288*^9, 3.482098094917302*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"L1Speed", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "4"], RowBox[{"Abs", "[", RowBox[{ RowBox[{"dyn", "[", RowBox[{"x", ",", "y", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "]"}]}]}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.474407479961112*^9, 3.48157049241873*^9, 3.4820980949473457`*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Potential functions", "Subsubsection", CellTags->"contourfunctions"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"NormalFormPotential", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"x", ".", RowBox[{"(", RowBox[{"A", ".", "y"}], " ", ")"}]}]}], " ", ";"}]], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Lyapunov functions ", "Subsubsection", CellTags->"contourfunctions"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"NEQ", "=", RowBox[{"If", "[", RowBox[{ RowBox[{"findnashequilibria", "\[Equal]", "1"}], ",", RowBox[{"NashEq", "[", RowBox[{"F1", ",", "F2"}], "]"}]}], "]"}]}], " ", ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"FindRoot", "::", "\<\"jsing\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Encountered a singular \ Jacobian at the point \\\\\\\"\\\", \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({nax1, nay1}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\" = \\\\\\\"\\\", \\\"MT\ \\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({1.`, 0.5000000000000001`}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\". Try perturbing the \ initial point(s).\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/FindRoot/jsing\\\", ButtonNote -> \ \\\"FindRoot::jsing\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.4825059997368*^9, 3.482506391455186*^9, 3.482506562091242*^9, 3.482619922485175*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"StableGameLyapunov", "[", "Replicator", "]"}], "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{"-", " ", RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Product]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox[ RowBox[{"x", "[", RowBox[{"[", "i", "]"}], "]"}], RowBox[{"NEQ", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1", ",", "i"}], "\[RightDoubleBracket]"}]]}], ")"}]}], RowBox[{"(", RowBox[{ UnderoverscriptBox["\[Product]", RowBox[{"j", "=", "1"}], "2"], SuperscriptBox[ RowBox[{"y", "[", RowBox[{"[", "j", "]"}], "]"}], RowBox[{"NEQ", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2", ",", "j"}], "\[RightDoubleBracket]"}]]}], ")"}]}]}], " ", ";"}]], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"StableGameLyapunov", "[", RowBox[{"Logit", "[", "\[Eta]", "]"}], "]"}], "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", " ", RowBox[{ RowBox[{"\[Eta]", " ", RowBox[{"Log", "[", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}], "]"}]}], "-", RowBox[{"(", RowBox[{ RowBox[{"x", ".", RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}]}], "-", RowBox[{"\[Eta]", " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], RowBox[{"Log", "[", RowBox[{"Max", "[", RowBox[{ RowBox[{ "x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], ",", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "7"}], ")"}]}]}], "]"}], "]"}]}]}]}]}], ")"}], " ", "+", " ", RowBox[{"\[Eta]", " ", RowBox[{"Log", "[", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[Eta]"]]}], "]"}]}], "-", RowBox[{"(", RowBox[{ RowBox[{"y", ".", RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}]}], "-", RowBox[{"\[Eta]", " ", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], RowBox[{"Log", "[", RowBox[{"Max", "[", RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], ",", RowBox[{"10", "^", RowBox[{"(", RowBox[{"-", "7"}], ")"}]}]}], "]"}], "]"}]}]}]}]}], ")"}]}]}], " ", ";"}]], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"StableGameLyapunov", "[", "projection", "]"}], "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", " ", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"x", "[", RowBox[{"[", "i", "]"}], "]"}], "-", RowBox[{"NEQ", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1", ",", "i"}], "\[RightDoubleBracket]"}]}], ")"}], "^", "2"}]}], " ", "+", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"y", "[", RowBox[{"[", "i", "]"}], "]"}], "-", RowBox[{"NEQ", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2", ",", "i"}], "\[RightDoubleBracket]"}]}], ")"}], "^", "2"}]}]}]}], ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4750047121983585`*^9}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"StableGameLyapunov", "[", "BNN", "]"}], "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox[ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "1", "]"}], "[", RowBox[{"x", ",", "y", ",", "F1"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "2"]}], " ", "+", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], SuperscriptBox[ RowBox[{ RowBox[{ RowBox[{"Fhatplus", "[", "2", "]"}], "[", RowBox[{"x", ",", "y", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "2"]}]}]}], " ", ";"}]], "Input", InitializationCell->True], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"StableGameLyapunov", "[", "Smith", "]"}], "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"x", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], SuperscriptBox[ RowBox[{"(", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ")"}], "2"]}]}]}], " ", "+", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "2"], SuperscriptBox[ RowBox[{"(", RowBox[{"Max", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{ RowBox[{"F2", "[", RowBox[{"x", ",", "y"}], "]"}], "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], ",", "0"}], "]"}], ")"}], "2"]}]}]}]}]}], " ", ";"}]], "Input", InitializationCell->True, CellChangeTimes->{3.4815705507526093`*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Other contour functions", "Subsubsection", CellTags->{"contourfunctions", "othercontour"}], Cell["Define your own contour function here.", "Text", FontFamily->"Palatino", CellTags->{"contourfunctions", "othercontour"}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Specification of solution trajectories", "Subsection", CellChangeTimes->{{3.4818065979508896`*^9, 3.4818065990524735`*^9}, { 3.481905004338482*^9, 3.481905007642541*^9}}], Cell[CellGroupData[{ Cell["\<\ Instructions for \"automated\" specification of solution trajectories\ \>", "SmallText"], Cell[TextData[{ "This section specifies the solution trajectories to be included in the \ phase diagram using built-in specifications. These are of three types:\n(i) \ initial conditions drawn from a grid, with the grid including points on the \ boundary ; \n(ii) initial conditions drawn from a grid, with the grid \ excluding points on the boundary ;\n(iii) randomly chosen initial conditions. \ \nTo use one of these options, press the appropriate palette button.\n", StyleBox["endtime", FontWeight->"Bold"], " determines the time interval [0, endtime] of each solution. \nFor the \ grid options, ", StyleBox["gridpoints1d", FontWeight->"Bold"], " specifies the number of initial conditions on each boundary of the grid. \ \nFor the random option, ", StyleBox["randompoints", FontWeight->"Bold"], " specifies the number of random initial conditions.\n", StyleBox["numberofarrows", FontWeight->"Bold"], " specifies how many arrows to draw on each solution. \n", StyleBox["arrowheadlength", FontWeight->"Bold"], " is self-explanatory; it can be set to zero if arrowheads are not desired. \ \nIf numberofarrows = 1 is specified, the arrow appears at the end of each \ solution trajectory. If numberofarrows = n, arrows are drawn at times \ {endtime/n, 2 endtime/n, ... , endtime}. For more on how arrows are drawn, \ see \"Adjusting positions of arrow heads and 'tails'\" below." }], "Text", CellChangeTimes->{{3.481573227361384*^9, 3.48157322817255*^9}}, TextAlignment->Left, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"] }, Closed]], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"endtime", "=", "1"}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"gridpoints1d", "=", "9"}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"randompoints", "=", "60"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"numberofarrows", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"arrowheadlength", "=", ".025"}], " ", ";"}], " "}]}], "Input", CellChangeTimes->{{3.482506354822294*^9, 3.4825063596453533`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "textsl", ",", "valuesl", ",", "names", " ", ",", "texts", ",", "values", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "rowt", ",", "rowv", ",", "name", ",", "text", ",", "value", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", RowBox[{"{", " ", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"textsl", " ", "=", " ", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "\[IndentingNewLine]", RowBox[{ RowBox[{"trajectoryspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", FractionBox[ RowBox[{" ", "i"}], RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]]}], ",", RowBox[{"1", "-", FractionBox[ RowBox[{" ", "j"}], RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]]}]}], "}"}], ",", "endtime", ",", RowBox[{"{", "}"}], ",", RowBox[{"Table", "[", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"numberofarrows", "-", "i", "+", "1"}], ")"}], " ", "endtime"}], "numberofarrows"], ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{"arrowheadlength", ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], ",", "1"}], "}"}]}], "]"}], " ", ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"trajectoryspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]}]], "-", FractionBox[ RowBox[{" ", "i"}], RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]]}], ",", RowBox[{"1", "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]}]], "-", FractionBox[ RowBox[{" ", "j"}], RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]]}]}], "}"}], ",", "endtime", ",", RowBox[{"{", "}"}], ",", RowBox[{"Table", "[", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"numberofarrows", "-", "i", "+", "1"}], ")"}], " ", "endtime"}], "numberofarrows"], ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{"arrowheadlength", ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], "-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], "-", "1"}], ",", "1"}], "}"}]}], "]"}], " ", ",", "1"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"trajectoryspecs", "=", RowBox[{"(", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"vekt", "[", RowBox[{"i", ",", "i"}], "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"Random", "[", "]"}], ",", RowBox[{"Random", "[", "]"}]}], "}"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "randompoints", ",", "1"}], "}"}]}], "]"}], " ", ";", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{ RowBox[{"vekt", "[", RowBox[{"i", ",", "i"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", RowBox[{"1", "-", RowBox[{ RowBox[{"vekt", "[", RowBox[{"i", ",", "i"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}]}], "}"}], ",", "endtime", ",", RowBox[{"{", "}"}], ",", RowBox[{"Table", "[", RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"numberofarrows", "-", "i", "+", "1"}], ")"}], " ", "endtime"}], "numberofarrows"], ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}], " ", ",", RowBox[{"Table", "[", RowBox[{"arrowheadlength", ",", RowBox[{"{", RowBox[{"i", ",", "numberofarrows"}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "randompoints", ",", "1"}], "}"}]}], "]"}]}], " ", ")"}]}], " ", ";"}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"valuesl", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"Join", "[", RowBox[{"rowt", ",", RowBox[{"{", RowBox[{"textsl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"Join", "[", RowBox[{"rowv", ",", RowBox[{"{", RowBox[{"valuesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"Join", "[", RowBox[{"texts", ",", RowBox[{"{", "rowt", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"Join", "[", RowBox[{"values", ",", RowBox[{"{", "rowv", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{ RowBox[{"Column", "[", RowBox[{ RowBox[{"{", "name", "}"}], ",", RowBox[{"Alignment", "\[Rule]", RowBox[{"{", "Center", "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "text", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"400", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{ "ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], " ", "/.", RowBox[{"text", "->", RowBox[{ RowBox[{"texts", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"value", "->", RowBox[{ RowBox[{"values", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", " ", "[", " ", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "3", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, {3.481736647042942*^9, 3.481736703093539*^9}, 3.4817375426908207`*^9, {3.4818119966889615`*^9, 3.481812002957976*^9}, {3.481812105737727*^9, 3.481812272981318*^9}, { 3.4818124484235916`*^9, 3.481812457366451*^9}, {3.481812498485577*^9, 3.481812523040886*^9}, {3.4818125683860893`*^9, 3.4818125706493435`*^9}, { 3.481812612139003*^9, 3.481812639708646*^9}, {3.4818128485990157`*^9, 3.481812864662113*^9}, {3.4818129721767116`*^9, 3.4818130553963757`*^9}, { 3.4818132379588876`*^9, 3.4818133245333757`*^9}, {3.481813355407771*^9, 3.4818133663935676`*^9}, 3.4818134196132183`*^9, {3.4818134879827776`*^9, 3.481813489202236*^9}, {3.4818136452104654`*^9, 3.481813661273563*^9}, { 3.4818137634451456`*^9, 3.481813778596933*^9}, {3.4818140028480997`*^9, 3.481814031477353*^9}, {3.481814092975784*^9, 3.4818141259632177`*^9}, { 3.4818141856590557`*^9, 3.4818141929395247`*^9}, {3.4818142536968894`*^9, 3.481814383273211*^9}, {3.4818144211176286`*^9, 3.4818145387768145`*^9}, { 3.4818146624446397`*^9, 3.4818146646778507`*^9}, {3.48181469749504*^9, 3.4818147106439466`*^9}, {3.4818472323981695`*^9, 3.4818473124933405`*^9}, {3.481847364648336*^9, 3.4818474569710894`*^9}, { 3.4820992459524097`*^9, 3.482099319067544*^9}, {3.482099439260373*^9, 3.4820994431159167`*^9}, {3.4821015492343664`*^9, 3.482101567650848*^9}}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Grid initial conditions (boundary included)\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "trajectoryspecs", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], "trajectoryspecs=Flatten[Table[{{1 - i/(gridpoints1d-1), 1 - \ j/(gridpoints1d-1)}, endtime, {}, \n Table[((numberofarrows - i + \ 1)*endtime)/numberofarrows, {i, numberofarrows}], \n \ Table[arrowheadlength, {i, numberofarrows}]}, {i, 0, (gridpoints1d-1), 1}, \n \ {j, 0, (gridpoints1d-1), 1}], 1];", AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Grid initial conditions (boundary excluded)\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "trajectoryspecs", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], "trajectoryspecs=Flatten[Table[{{1 - 1/(2*(gridpoints1d-1)) - \ i/(gridpoints1d-1), 1 - 1/(2*(gridpoints1d-1)) - \n \ j/(gridpoints1d-1)}, endtime, {}, Table[((numberofarrows - i + 1)*endtime)/\n \ numberofarrows, {i, numberofarrows}], Table[arrowheadlength, \n \ {i, numberofarrows}]}, {i, 0, (gridpoints1d-1) - 1, 1}, \n {j, 0, \ (gridpoints1d-1) - 1, 1}], 1];", AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Random initial conditions\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "trajectoryspecs", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], "trajectoryspecs=(Table[vekt[i, i] = {Random[], Random[]}, {i, 1, \ randompoints, 1}]; \n Table[{{1 - vekt[i, i][[1]], 1 - vekt[i, i][[2]]}, \ endtime, {}, \n Table[((numberofarrows - i + 1)*endtime)/numberofarrows, \ {i, numberofarrows}], \n Table[arrowheadlength, {i, numberofarrows}]}, \ {i, 1, randompoints, 1}]);", AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]]], "Output", CellChangeTimes->{3.482099342170765*^9, 3.4821001072108383`*^9, 3.4821025467387075`*^9}, CellTags->"buttoncell"] }, {2}]], Cell[CellGroupData[{ Cell["\<\ Instructions for \"manual\" specification of solution trajectories\ \>", "SmallText"], Cell[TextData[{ "The user can also specify which solution trajectores to graph directly. To \ do this, ", StyleBox["trajectoryspecs", FontWeight->"Bold"], " must be defined as a table of the following form: {{initial condition 1, \ T1, {color1", StyleBox[", ", FontSlant->"Italic"], StyleBox["thikness1", FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontSlant->"Italic"], StyleBox[" dashing1", FontVariations->{"CompatibilityType"->0}], "}, {Arrow positions 1}, {Head lengths 1}}, {initial condition 2, T2, \ {color2", StyleBox[", ", FontSlant->"Italic"], StyleBox["thickness2", FontVariations->{"CompatibilityType"->0}], StyleBox[",", FontSlant->"Italic"], StyleBox[" dashing2", FontVariations->{"CompatibilityType"->0}], "}, {Arrow positions 2}, {Head lengths 2}}, ... }\nEach initial condition is \ entered as a list {x2, y2} containing the weight placed on each population's \ second strategy. Ti determines time interval [0, Ti] of the ith solution. \ Arrow positions i and Head lengths i should be vectors of the same length, \ where this length is the number of arrowheads to be drawn on the solution \ trajectory. Arrow positions are stated as points in the time interval [0, \ Ti]. For no arrows, set Arrow positions i and Head lengths i to {0}.\n\n\ {color", StyleBox["i, ", FontSlant->"Italic"], StyleBox["thickness", FontVariations->{"CompatibilityType"->0}], StyleBox["i,", FontSlant->"Italic"], StyleBox[" dashing", FontVariations->{"CompatibilityType"->0}], StyleBox["i", FontSlant->"Italic"], "} specifies the appearance of solutions trajectories. You can specify any \ collection of graphics primitives you like (even ones beyond the three \ mentioned here), and you canplace them in any order. To use the default \ appearance, write {}. \ncolor", StyleBox["i", FontSlant->"Italic"], " can be Hue[?], GrayLevel[?] or any other color command;\nthickness", StyleBox["i", FontSlant->"Italic"], " can be Thickness[?] or AbsoluteThickness[?];\ndashing", StyleBox["i", FontSlant->"Italic"], " is specified as Dashing[{???}]. " }], "Text", CellChangeTimes->{{3.4820994262917247`*^9, 3.482099433532136*^9}}] }, Closed]], Cell[BoxData[ RowBox[{ RowBox[{"trajectoryspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", " ", "-", " ", RowBox[{"i", "/", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]}]}], ",", " ", RowBox[{"1", " ", "-", " ", RowBox[{"j", "/", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}]}]}]}], "}"}], ",", " ", "endtime", ",", " ", RowBox[{"{", "}"}], ",", " ", "\n", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ "numberofarrows", " ", "-", " ", "i", " ", "+", " ", "1"}], ")"}], "*", "endtime"}], ")"}], "/", "numberofarrows"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "numberofarrows"}], "}"}]}], "]"}], ",", " ", "\n", " ", RowBox[{"Table", "[", RowBox[{"arrowheadlength", ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "numberofarrows"}], "}"}]}], "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "0", ",", " ", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ", RowBox[{"{", RowBox[{"j", ",", " ", "0", ",", " ", RowBox[{"(", RowBox[{"gridpoints1d", "-", "1"}], ")"}], ",", " ", "1"}], "}"}]}], "]"}], ",", " ", "1"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{ 3.4820994445379615`*^9, {3.482101569904088*^9, 3.4821015743805246`*^9}, { 3.4821024762373314`*^9, 3.482102498669587*^9}}, ImageRegion->{{0, 1}, {0, 1}}, CellTags->{"degisken", "trajectoryspecs"}] }, Closed]], Cell[CellGroupData[{ Cell["Additional options", "Subsection", CellChangeTimes->{{3.4818065979508896`*^9, 3.4818065990524735`*^9}, { 3.481904841955846*^9, 3.481904846233698*^9}}], Cell[CellGroupData[{ Cell["Tuning rest point search", "SmallText"], Cell[TextData[{ StyleBox["RestSearchInit", FontWeight->"Bold"], " contains the initial conditions used in the FindRoot command when the \ program searches for rest points. If you suspect that the program has missed \ some rest points, add initial conditions in the regions where the missing \ rest points should be. Each initial condition is written as {y2, x1}; x2 and \ y1 are computed as 1 - x1 and 1 -y2.\n", StyleBox["RestTolerance", FontWeight->"Bold"], " is a parameter in a filtering procedure used to eliminate false rest \ points. If the speed of the dynamic at a prospective rest point is above \ (RestTolerance) * (the maximum speed of the dynamic), the prospective rest \ point is thrown out." }], "Text"], Cell[BoxData[{ RowBox[{ RowBox[{"RestSearchInit", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0.001", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.001", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.101", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.099", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.201", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.199", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.301", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.299", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.401", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.399", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.501", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.499", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.601", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.599", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.701", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.699", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.801", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.799", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.101"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.201"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.301"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.401"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.501"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.601"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.701"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.801"}], "}"}], ",", RowBox[{"{", RowBox[{"0.901", ",", "0.901"}], "}"}], ",", RowBox[{"{", RowBox[{"0.899", ",", "0.999"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.001"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.099"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.199"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.299"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.399"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.499"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.599"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.699"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.799"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.899"}], "}"}], ",", RowBox[{"{", RowBox[{"0.999", ",", "0.999"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RestSearchInitGen", "[", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", "j", ",", "Init", ",", "RestSearchInit"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"RestSearchInit", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "0"}], ",", RowBox[{"i", "<", "10"}], ",", RowBox[{"i", "++"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "0"}], ",", RowBox[{"j", "<", "10"}], ",", RowBox[{"j", "++"}], ",", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"i", "+", "j"}], "<", "10"}], ","}]}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Init", "=", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"i", ",", "j"}], "}"}], "/", "10"}], "+", RowBox[{"{", RowBox[{ RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{"0", ",", ".01"}], "}"}], "]"}], ",", RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{"0", ",", ".01"}], "}"}], "]"}]}], "}"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"RestSearchInit", "=", RowBox[{"Join", "[", RowBox[{"RestSearchInit", ",", RowBox[{"{", "Init", "}"}]}], "]"}]}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"]", ";"}], "*)"}], "\[IndentingNewLine]", "]"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", "RestSearchInit"}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"RestSearchInit", "=", RowBox[{"Join", "[", RowBox[{ RowBox[{"RestSearchInitGen", "[", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{".999", ",", ".01"}], "}"}], ",", RowBox[{"{", RowBox[{".999", ",", ".999"}], "}"}]}], "}"}]}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.4815718551682673`*^9, 3.4815718565502543`*^9}, { 3.4815719523179617`*^9, 3.4815719580161552`*^9}, {3.481571999515829*^9, 3.481572011683325*^9}, {3.481572136412677*^9, 3.48157221689841*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"RestTolerance", "=", ".01"}], " ", ";"}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Tuning stability tests", "SmallText"], Cell[TextData[{ "The first four parameters determine how rest points are checked for \ stability. The parameter ", StyleBox["numtest", FontWeight->"Bold"], " specifies how many trajectories will be checked. These initial conditions \ are random points at distance ", StyleBox["eps", FontWeight->"Bold"], " from the rest point. Solutions from these points over the time interval \ [0, ", StyleBox["bigT", FontWeight->"Bold"], "] are computed. If any of these solutions winds up more than ", StyleBox["delta", FontWeight->"Bold"], " away from the rest point, the rest point is considered unstable; otherwise \ it is considered stable." }], "Text", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Palatino"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"numtest", "=", "5"}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"eps", "=", ".01"}], " ", ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"delta", "=", ".01"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"bigT", "=", "1"}], " ", ";"}], " "}]}], "Input", ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Adjusting positions of arrow heads and \"tails\"", "SmallText"], Cell[TextData[{ "To draw an arrow, the program must know where to put the tail of the arrow \ and where to put the head. Even if one does not want the base of the arrow \ to appear in the picture, its position of the tail must be specified so that \ the arrow points in the right direction. \nThe parameter ", StyleBox["relarrowbase", FontWeight->"Bold"], " below determines the positions of arrows' tails relative to their heads \ when arrows are drawn on solution trajectories. In particular, if an arrow \ is supposed to appear at a solution trajectory's position at time t, the \ program draws the head at this point, placing the tail at the solution \ trajectory's position at time (t \[Dash] endtime/relarrowbase). \nA value of \ .008 for relarrowbase works well in most cases: the arrow base is not \ visible, and the arrow points in the right direction. If arrow bases are \ visible, a smaller value of relarrowbase should be specified. If arrows \ point in the wrong directions, a larger value of relarrowbase should be \ chosen.\nThe parameter ", StyleBox["arrowheadcenter", FontWeight->"Bold"], " specifies the location of the center of the arrowheads' bases as a \ fraction of the arrowheads' lengths." }], "Text"], Cell[BoxData[{ RowBox[{ RowBox[{"relarrowbase", "=", ".005"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"arrowheadcenter", "=", ".8"}], " ", ";"}]}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Adding extra graphic elements", "SmallText", CellTags->"extragraphicselements"], Cell[TextData[{ "This section allows the user to add dots, lines, arrows, text, and color \ solution trajectories to a phase diagram/contour plot.\n\nEnter the data for \ dots as follows: ", StyleBox["customdots", FontWeight->"Bold"], " = {{center1, radius1, color1, open1}, {center2, radius2, color2, open2}, \ ...}. color1 should be a ", StyleBox["Mathematica", FontSlant->"Italic"], "-defined color function (Hue[.], GrayLevel[.], etc). Set open1 = 0 for \ solid dot and = 1 for a dot with a white center. centers should be entered \ like {{x1,x2},{y1,y2}}.\n \nEnter the data for lines as follows: ", StyleBox["customlines", FontWeight->"Bold"], " = {{startingpoint1, endpoint1, thickness1, dashing1, color1, \ arrowheadlength1}, {startingpoint2, endpoint2, thickness2, dashing2, color2, \ arrowheadlength2},...}. If you want an arrow at the end of the line enter \ the value for arrowheadlength specifying the size of arrow head; if you do \ not want an arrow simply set it to 0. Thickness and Dashing are usual ", StyleBox["Mathematica ", FontSlant->"Italic"], "commands. starting points should be entered like {{x1,x2},{y1,y2}}. \ endpoints should be entered like {{x1,x2},{y1,y2}}. Line start at \ startingpoint and ends at the endpoints as names suggest.\n\nEnter data for \ text as follows: ", StyleBox["customtext ", FontWeight->"Bold"], "= {{\"label1\", position1, \"fontfamily1\",\"fontslant1\", fontsize1}, \ {\"label2\", position2, \"fontfamily2\",\"fontslant2\", fontsize2}, ...}. \ Remember that you are restricted to positions in PlotRange \[Rule] {{-.08, \ 1.1}, {-.08, 1.1}}. positions should be entered in rectangular coordinates \ {x,y}. For example: customtext = {{\"Hello World\", {0, 0}, \"Sans\", \"Plain\ \", 12}};\n\nEnter data for extra solution trajectories as follows: ", StyleBox["customcycles ", FontWeight->"Bold"], "= {{initial condition on simplex 1, endtime1 for NDSolve, beginningtime1 to \ be used in in the plot, {color1, thickness1}, {arrow position1}, {head \ lengths1}}, {initial condition on simplex 2, endtime2 for NDSolve, \ beginningtime2 to be used in in the plot, {color2, thickness2}, {arrow \ position2}, {head lengths2}},...}. \nThe program computes a solution to the \ dynamic from time 0 through endtime?, and then plots the solution trajectory \ from the beginingtime? through endtime. color? should be a ", StyleBox["Mathematica", FontSlant->"Italic"], "-defined color function (Hue[.], GrayLevel[.], etc). (both color and \ thickness can be ignored, just write {} if you do not want to bother with \ these. arrowpositon? must be a number strictly greater than beginingtime? \ and less than endtime (it must be strictly bigger than begining time). Each \ trajectory can have multiple arrows, but even if there is only one arrow, be \ sure to put brackets around the arrow positions and head lengths. Initial \ conditions should be entered like {x2,y2}.\n\nWrite customdots = {}, \ customlines = {}, customtext = {}, and ", "customcycles", " = {} if you do not want to add anything. (This is the default setting.)" }], "Text", CellChangeTimes->{{3.4744621444838734`*^9, 3.474462165544157*^9}, { 3.482099475001766*^9, 3.48209948370428*^9}, 3.4820995528136544`*^9, { 3.4820995942231984`*^9, 3.4820996544698286`*^9}, {3.482099693405816*^9, 3.4820997075561633`*^9}}, CellTags->"extragraphicselements"], Cell["\<\ Example: This example generates one line, one dot, and one piece of text, \ one special solution trajectory (customcycles). customdots={{{{1/2,1/2},{1/2,1/2}}, .01, GrayLevel[0], 1}} ; [draws a \ black dot with white center at the center of the simplex] customlines={{{{1/2, 1/2},{1,0}},{{1/2, 1/2},{0,1}}, Thickness[.004], \ Dashing[{}], GrayLevel[0], 0}} ; [draws a horizantal line through at y=1/2] customtext={{\"trial\", {1/2,1/2}, \"Palatino-Roman\", \"Plain\", 12}} ; customcycles={{{8,.9}, 50, 45, {Hue[.83], Thickness[.005]}, {47}, {.03}}} ; \ \>", "Text", CellChangeTimes->{ 3.482099553835123*^9, 3.4820996171161165`*^9, 3.482099655301024*^9, { 3.482099709048309*^9, 3.4820997098494606`*^9}}, CellTags->"extragraphicselements"], Cell[BoxData[{ RowBox[{ RowBox[{"customdots", "=", RowBox[{"{", "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"customlines", "=", RowBox[{"{", "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"customtext", "=", " ", RowBox[{"{", "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"customcycles", "=", RowBox[{"{", "}"}]}], " ", ";"}]}], "Input", CellChangeTimes->{ 3.48209955480652*^9, {3.482099618417989*^9, 3.4820996316770544`*^9}, 3.4820996720451007`*^9}, CellTags->"extragraphicselements"], Cell[BoxData[{ RowBox[{ RowBox[{"uddots", "=", RowBox[{"Graphics", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customdots", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"udwdots", "=", RowBox[{"Graphics", "[", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "\[Equal]", "1"}], ",", RowBox[{"{", RowBox[{ RowBox[{"GrayLevel", "[", "1", "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{".6", " ", RowBox[{"customdots", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customdots", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "Null"}], "]"}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"extralines", "=", RowBox[{"Graphics", "[", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customlines", "[", RowBox[{"[", RowBox[{"i", ",", "4"}], "]"}], "]"}], ",", RowBox[{"customlines", "[", RowBox[{"[", RowBox[{"i", ",", "5"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "6"}], "\[RightDoubleBracket]"}], ",", RowBox[{"4", "/", "5"}]}], "}"}], "}"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customlines", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customlines", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "Null"}], "]"}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"extratext", "=", RowBox[{"Graphics", "[", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"customtext", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"FontFamily", "\[Rule]", RowBox[{"customtext", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}]}], ",", RowBox[{"FontSlant", "\[Rule]", RowBox[{"customtext", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}]}], ",", RowBox[{"FontSize", "\[Rule]", RowBox[{"customtext", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}]}]}], "]"}], ",", RowBox[{"customtext", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customtext", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "Null"}], "]"}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.474460445160366*^9, 3.4744604495366592`*^9}, { 3.4744604850777645`*^9, 3.4744605016415825`*^9}, {3.4744605449738913`*^9, 3.474460550541898*^9}, {3.474460596187533*^9, 3.4744606236970897`*^9}, { 3.4744610145991793`*^9, 3.474461061506629*^9}, {3.474461194497861*^9, 3.474461217480909*^9}, {3.4744612853484974`*^9, 3.4744612882626877`*^9}, { 3.4744735008523407`*^9, 3.4744735512047434`*^9}, {3.474911590287387*^9, 3.4749115949540977`*^9}, {3.4749143568354883`*^9, 3.474914359589448*^9}, { 3.482099556038291*^9, 3.4820995905679426`*^9}, {3.4820996324882207`*^9, 3.482099635893117*^9}}, CellTags->"extragraphicselements"], Cell[CellGroupData[{ Cell[TextData[{ "These are extra, less used parameters that are used for displaying accesory \ elements in the contour function. If you do not include contour functions in \ your output, these parameters are not used.\n", StyleBox["colorbar", FontWeight->"Bold"], " = 1 to create a color scale (alternatively, a black and white scale) along \ with your contour plot.\n", StyleBox["showcontourformula", FontWeight->"Bold"], " = 1 displays the formula for the contour function in the output notebook." }], "Text", CellChangeTimes->{{3.480779243193115*^9, 3.4807792961292334`*^9}, 3.4807794713011184`*^9, {3.480779514703528*^9, 3.4807795412717314`*^9}, { 3.4807797587995887`*^9, 3.4807799035777693`*^9}, {3.4807799399500704`*^9, 3.4807799407712507`*^9}, {3.480780151674515*^9, 3.4807801526859694`*^9}, { 3.481756068394542*^9, 3.48175606959627*^9}, {3.481806079305114*^9, 3.481806116598739*^9}, {3.4818067166716013`*^9, 3.481806733405664*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"colorbar", "=", "0"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"showcontourformula", "=", "1"}], " ", ";"}]}], "Input", CellChangeTimes->{{3.480779208673478*^9, 3.4807792403690543`*^9}, { 3.480779912300312*^9, 3.480779956343643*^9}, {3.480780155029339*^9, 3.4807802069740314`*^9}, {3.4808105872656336`*^9, 3.480810604312072*^9}, { 3.481299367902998*^9, 3.481299371371703*^9}, {3.4813361046496577`*^9, 3.4813361051496515`*^9}, {3.4817562146147966`*^9, 3.48175621514556*^9}, { 3.4818061298678193`*^9, 3.481806133673291*^9}}] }, Closed]] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Specifications for other graphics", "Section", CellChangeTimes->{{3.4816700653812637`*^9, 3.4816700693269377`*^9}, 3.4818952670660195`*^9}], Cell[CellGroupData[{ Cell["Vector field diagram", "Subsection"], Cell[TextData[{ StyleBox["vectorfielddiagram", FontWeight->"Bold"], " = 1 draws a vector field diagram on the simplex. The vector fields should \ take values in the tangent space of the simplex (i.e., values whose \ components sum to zero). \n", StyleBox["drawoncontour", FontWeight->"Bold"], " = 1 draws the vector field on top of a contour plot." }], "Text", CellChangeTimes->{3.482506367613474*^9, 3.482506493077298*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"vectorfielddiagram", "=", "0"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"drawoncontour", "=", "1"}], " ", ";"}]}], "Input", CellChangeTimes->{3.474836287426262*^9, 3.48250649640436*^9}], Cell[CellGroupData[{ Cell["Instructions for specification of vector fields", "SmallText"], Cell[TextData[{ "Either one or two vector fields is drawn, according to whether ", StyleBox["drawvectorfield1", FontWeight->"Bold"], ", ", StyleBox["drawvectorfield2", FontWeight->"Bold"], ", or both are set to 1.\n", StyleBox["vectorfield?", FontWeight->"Bold"], " specifies the vector field to be drawn. (Here and below, \"?\" equals 1 \ or 2.) Common specifications for this are ", "dyn", " (the dynamic specified in the \"Choice of dynamic\" section) and PhiF (the \ projection of the payoff vector field onto the tangent space of the simplex - \ see \"Payoff-related definitions\" in the \"Choice of game\"section).\n", StyleBox["scale?", FontWeight->"Bold"], " rescales the vectors, as is often needed to prevent the vector field \ arrows from being too long. The program calibrates the output so that \ setting scale1 = scale2 makes the longest vector in each vector field have \ the same length.\n", StyleBox["vf?thickness", FontWeight->"Bold"], " is the thickness of the \"shafts\" of the arrows.\n", StyleBox["arrowheadlengtsvf?", FontWeight->"Bold"], " is self-explanatory; set it to zero if you do not want arrowheads.\n", StyleBox["colorvf?", FontWeight->"Bold"], " determines the color of the vector field. It should be set to Hue[t] or \ GrayLevel[t] using the charts below." }], "Text", CellChangeTimes->{3.4744074876822147`*^9, 3.481570492448773*^9, 3.4820980949673743`*^9}], Cell[BoxData[Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .13736 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.47619 0.00327054 0.47619 [ [ 0 0 0 0 ] [ 1 .13736 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .13736 L 0 .13736 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00327054 0.477324 0.134092 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0192308 0.961538 0.0480769 0.961538 [ [ 0 0 0 0 ] [ 1 .28846 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .28846 L 0 .28846 L closepath clip newpath 1 0 0 r .01923 .04808 m .01923 .24038 L .02019 .24038 L .02019 .04808 L F 1 .006 0 r .02019 .04808 m .02019 .24038 L .02115 .24038 L .02115 .04808 L F 1 .012 0 r .02115 .04808 m .02115 .24038 L .02212 .24038 L .02212 .04808 L F 1 .018 0 r .02212 .04808 m .02212 .24038 L .02308 .24038 L .02308 .04808 L F 1 .024 0 r .02308 .04808 m .02308 .24038 L .02404 .24038 L .02404 .04808 L F 1 .03 0 r .02404 .04808 m .02404 .24038 L .025 .24038 L .025 .04808 L F 1 .036 0 r .025 .04808 m .025 .24038 L .02596 .24038 L .02596 .04808 L F 1 .042 0 r .02596 .04808 m .02596 .24038 L .02692 .24038 L .02692 .04808 L F 1 .048 0 r .02692 .04808 m .02692 .24038 L .02788 .24038 L .02788 .04808 L F 1 .054 0 r .02788 .04808 m .02788 .24038 L .02885 .24038 L .02885 .04808 L F 1 .06 0 r .02885 .04808 m .02885 .24038 L .02981 .24038 L .02981 .04808 L F 1 .066 0 r .02981 .04808 m .02981 .24038 L .03077 .24038 L .03077 .04808 L F 1 .072 0 r .03077 .04808 m .03077 .24038 L .03173 .24038 L .03173 .04808 L F 1 .078 0 r .03173 .04808 m .03173 .24038 L .03269 .24038 L .03269 .04808 L F 1 .084 0 r .03269 .04808 m .03269 .24038 L .03365 .24038 L .03365 .04808 L F 1 .09 0 r .03365 .04808 m .03365 .24038 L .03462 .24038 L .03462 .04808 L F 1 .096 0 r .03462 .04808 m .03462 .24038 L .03558 .24038 L .03558 .04808 L F 1 .102 0 r .03558 .04808 m .03558 .24038 L .03654 .24038 L .03654 .04808 L F 1 .108 0 r .03654 .04808 m .03654 .24038 L .0375 .24038 L .0375 .04808 L F 1 .114 0 r .0375 .04808 m .0375 .24038 L .03846 .24038 L .03846 .04808 L F 1 .12 0 r .03846 .04808 m .03846 .24038 L .03942 .24038 L .03942 .04808 L F 1 .126 0 r .03942 .04808 m .03942 .24038 L .04038 .24038 L .04038 .04808 L F 1 .132 0 r .04038 .04808 m .04038 .24038 L .04135 .24038 L .04135 .04808 L F 1 .138 0 r .04135 .04808 m .04135 .24038 L .04231 .24038 L .04231 .04808 L F 1 .144 0 r .04231 .04808 m .04231 .24038 L .04327 .24038 L .04327 .04808 L F 1 .15 0 r .04327 .04808 m .04327 .24038 L .04423 .24038 L .04423 .04808 L F 1 .156 0 r .04423 .04808 m .04423 .24038 L .04519 .24038 L .04519 .04808 L F 1 .162 0 r .04519 .04808 m .04519 .24038 L .04615 .24038 L .04615 .04808 L F 1 .168 0 r .04615 .04808 m .04615 .24038 L .04712 .24038 L .04712 .04808 L F 1 .174 0 r .04712 .04808 m .04712 .24038 L .04808 .24038 L .04808 .04808 L F 1 .18 0 r .04808 .04808 m .04808 .24038 L .04904 .24038 L .04904 .04808 L F 1 .186 0 r .04904 .04808 m .04904 .24038 L .05 .24038 L .05 .04808 L F 1 .192 0 r .05 .04808 m .05 .24038 L .05096 .24038 L .05096 .04808 L F 1 .198 0 r .05096 .04808 m .05096 .24038 L .05192 .24038 L .05192 .04808 L F 1 .204 0 r .05192 .04808 m .05192 .24038 L .05288 .24038 L .05288 .04808 L F 1 .21 0 r .05288 .04808 m .05288 .24038 L .05385 .24038 L .05385 .04808 L F 1 .216 0 r .05385 .04808 m .05385 .24038 L .05481 .24038 L .05481 .04808 L F 1 .222 0 r .05481 .04808 m .05481 .24038 L .05577 .24038 L .05577 .04808 L F 1 .228 0 r .05577 .04808 m .05577 .24038 L .05673 .24038 L .05673 .04808 L F 1 .234 0 r .05673 .04808 m .05673 .24038 L .05769 .24038 L .05769 .04808 L F 1 .24 0 r .05769 .04808 m .05769 .24038 L .05865 .24038 L .05865 .04808 L F 1 .246 0 r .05865 .04808 m .05865 .24038 L .05962 .24038 L .05962 .04808 L F 1 .252 0 r .05962 .04808 m .05962 .24038 L .06058 .24038 L .06058 .04808 L F 1 .258 0 r .06058 .04808 m .06058 .24038 L .06154 .24038 L .06154 .04808 L F 1 .264 0 r .06154 .04808 m .06154 .24038 L .0625 .24038 L .0625 .04808 L F 1 .27 0 r .0625 .04808 m .0625 .24038 L .06346 .24038 L .06346 .04808 L F 1 .276 0 r .06346 .04808 m .06346 .24038 L .06442 .24038 L .06442 .04808 L F 1 .282 0 r .06442 .04808 m .06442 .24038 L .06538 .24038 L .06538 .04808 L F 1 .288 0 r .06538 .04808 m .06538 .24038 L .06635 .24038 L .06635 .04808 L F 1 .294 0 r .06635 .04808 m .06635 .24038 L .06731 .24038 L .06731 .04808 L F 1 .3 0 r .06731 .04808 m .06731 .24038 L .06827 .24038 L .06827 .04808 L F 1 .306 0 r .06827 .04808 m .06827 .24038 L .06923 .24038 L .06923 .04808 L F 1 .312 0 r .06923 .04808 m .06923 .24038 L .07019 .24038 L .07019 .04808 L F 1 .318 0 r .07019 .04808 m .07019 .24038 L .07115 .24038 L .07115 .04808 L F 1 .324 0 r .07115 .04808 m .07115 .24038 L .07212 .24038 L .07212 .04808 L F 1 .33 0 r .07212 .04808 m .07212 .24038 L .07308 .24038 L .07308 .04808 L F 1 .336 0 r .07308 .04808 m .07308 .24038 L .07404 .24038 L .07404 .04808 L F 1 .342 0 r .07404 .04808 m .07404 .24038 L .075 .24038 L .075 .04808 L F 1 .348 0 r .075 .04808 m .075 .24038 L .07596 .24038 L .07596 .04808 L F 1 .354 0 r .07596 .04808 m .07596 .24038 L .07692 .24038 L .07692 .04808 L F 1 .36 0 r .07692 .04808 m .07692 .24038 L .07788 .24038 L .07788 .04808 L F 1 .366 0 r .07788 .04808 m .07788 .24038 L .07885 .24038 L .07885 .04808 L F 1 .372 0 r .07885 .04808 m .07885 .24038 L .07981 .24038 L .07981 .04808 L F 1 .378 0 r .07981 .04808 m .07981 .24038 L .08077 .24038 L .08077 .04808 L F 1 .384 0 r .08077 .04808 m .08077 .24038 L .08173 .24038 L .08173 .04808 L F 1 .39 0 r .08173 .04808 m .08173 .24038 L .08269 .24038 L .08269 .04808 L F 1 .396 0 r .08269 .04808 m .08269 .24038 L .08365 .24038 L .08365 .04808 L F 1 .402 0 r .08365 .04808 m .08365 .24038 L .08462 .24038 L .08462 .04808 L F 1 .408 0 r .08462 .04808 m .08462 .24038 L .08558 .24038 L .08558 .04808 L F 1 .414 0 r .08558 .04808 m .08558 .24038 L .08654 .24038 L .08654 .04808 L F 1 .42 0 r .08654 .04808 m .08654 .24038 L .0875 .24038 L .0875 .04808 L F 1 .426 0 r .0875 .04808 m .0875 .24038 L .08846 .24038 L .08846 .04808 L F 1 .432 0 r .08846 .04808 m .08846 .24038 L .08942 .24038 L .08942 .04808 L F 1 .438 0 r .08942 .04808 m .08942 .24038 L .09038 .24038 L .09038 .04808 L F 1 .444 0 r .09038 .04808 m .09038 .24038 L .09135 .24038 L .09135 .04808 L F 1 .45 0 r .09135 .04808 m .09135 .24038 L .09231 .24038 L .09231 .04808 L F 1 .456 0 r .09231 .04808 m .09231 .24038 L .09327 .24038 L .09327 .04808 L F 1 .462 0 r .09327 .04808 m .09327 .24038 L .09423 .24038 L .09423 .04808 L F 1 .468 0 r .09423 .04808 m .09423 .24038 L .09519 .24038 L .09519 .04808 L F 1 .474 0 r .09519 .04808 m .09519 .24038 L .09615 .24038 L .09615 .04808 L F 1 .48 0 r .09615 .04808 m .09615 .24038 L .09712 .24038 L .09712 .04808 L F 1 .486 0 r .09712 .04808 m .09712 .24038 L .09808 .24038 L .09808 .04808 L F 1 .492 0 r .09808 .04808 m .09808 .24038 L .09904 .24038 L .09904 .04808 L F 1 .498 0 r .09904 .04808 m .09904 .24038 L .1 .24038 L .1 .04808 L F 1 .504 0 r .1 .04808 m .1 .24038 L .10096 .24038 L .10096 .04808 L F 1 .51 0 r .10096 .04808 m .10096 .24038 L .10192 .24038 L .10192 .04808 L F 1 .516 0 r .10192 .04808 m .10192 .24038 L .10288 .24038 L .10288 .04808 L F 1 .522 0 r .10288 .04808 m .10288 .24038 L .10385 .24038 L .10385 .04808 L F 1 .528 0 r .10385 .04808 m .10385 .24038 L .10481 .24038 L .10481 .04808 L F 1 .534 0 r .10481 .04808 m .10481 .24038 L .10577 .24038 L .10577 .04808 L F 1 .54 0 r .10577 .04808 m .10577 .24038 L .10673 .24038 L .10673 .04808 L F 1 .546 0 r .10673 .04808 m .10673 .24038 L .10769 .24038 L .10769 .04808 L F 1 .552 0 r .10769 .04808 m .10769 .24038 L .10865 .24038 L .10865 .04808 L F 1 .558 0 r .10865 .04808 m .10865 .24038 L .10962 .24038 L .10962 .04808 L F 1 .564 0 r .10962 .04808 m .10962 .24038 L .11058 .24038 L .11058 .04808 L F 1 .57 0 r .11058 .04808 m .11058 .24038 L .11154 .24038 L .11154 .04808 L F 1 .576 0 r .11154 .04808 m .11154 .24038 L .1125 .24038 L .1125 .04808 L F 1 .582 0 r .1125 .04808 m .1125 .24038 L .11346 .24038 L .11346 .04808 L F 1 .588 0 r .11346 .04808 m .11346 .24038 L .11442 .24038 L .11442 .04808 L F 1 .594 0 r .11442 .04808 m .11442 .24038 L .11538 .24038 L .11538 .04808 L F 1 .6 0 r .11538 .04808 m .11538 .24038 L .11635 .24038 L .11635 .04808 L F 1 .606 0 r .11635 .04808 m .11635 .24038 L .11731 .24038 L .11731 .04808 L F 1 .612 0 r .11731 .04808 m .11731 .24038 L .11827 .24038 L .11827 .04808 L F 1 .618 0 r .11827 .04808 m .11827 .24038 L .11923 .24038 L .11923 .04808 L F 1 .624 0 r .11923 .04808 m .11923 .24038 L .12019 .24038 L .12019 .04808 L F 1 .63 0 r .12019 .04808 m .12019 .24038 L .12115 .24038 L .12115 .04808 L F 1 .636 0 r .12115 .04808 m .12115 .24038 L .12212 .24038 L .12212 .04808 L F 1 .642 0 r .12212 .04808 m .12212 .24038 L .12308 .24038 L .12308 .04808 L F 1 .648 0 r .12308 .04808 m .12308 .24038 L .12404 .24038 L .12404 .04808 L F 1 .654 0 r .12404 .04808 m .12404 .24038 L .125 .24038 L .125 .04808 L F 1 .66 0 r .125 .04808 m .125 .24038 L .12596 .24038 L .12596 .04808 L F 1 .666 0 r .12596 .04808 m .12596 .24038 L .12692 .24038 L .12692 .04808 L F 1 .672 0 r .12692 .04808 m .12692 .24038 L .12788 .24038 L .12788 .04808 L F 1 .678 0 r .12788 .04808 m .12788 .24038 L .12885 .24038 L .12885 .04808 L F 1 .684 0 r .12885 .04808 m .12885 .24038 L .12981 .24038 L .12981 .04808 L F 1 .69 0 r .12981 .04808 m .12981 .24038 L .13077 .24038 L .13077 .04808 L F 1 .696 0 r .13077 .04808 m .13077 .24038 L .13173 .24038 L .13173 .04808 L F 1 .702 0 r .13173 .04808 m .13173 .24038 L .13269 .24038 L .13269 .04808 L F 1 .708 0 r .13269 .04808 m .13269 .24038 L .13365 .24038 L .13365 .04808 L F 1 .714 0 r .13365 .04808 m .13365 .24038 L .13462 .24038 L .13462 .04808 L F 1 .72 0 r .13462 .04808 m .13462 .24038 L .13558 .24038 L .13558 .04808 L F 1 .726 0 r .13558 .04808 m .13558 .24038 L .13654 .24038 L .13654 .04808 L F 1 .732 0 r .13654 .04808 m .13654 .24038 L .1375 .24038 L .1375 .04808 L F 1 .738 0 r .1375 .04808 m .1375 .24038 L .13846 .24038 L .13846 .04808 L F 1 .744 0 r .13846 .04808 m .13846 .24038 L .13942 .24038 L .13942 .04808 L F 1 .75 0 r .13942 .04808 m .13942 .24038 L .14038 .24038 L .14038 .04808 L F 1 .756 0 r .14038 .04808 m .14038 .24038 L .14135 .24038 L .14135 .04808 L F 1 .762 0 r .14135 .04808 m .14135 .24038 L .14231 .24038 L .14231 .04808 L F 1 .768 0 r .14231 .04808 m .14231 .24038 L .14327 .24038 L .14327 .04808 L F 1 .774 0 r .14327 .04808 m .14327 .24038 L .14423 .24038 L .14423 .04808 L F 1 .78 0 r .14423 .04808 m .14423 .24038 L .14519 .24038 L .14519 .04808 L F 1 .786 0 r .14519 .04808 m .14519 .24038 L .14615 .24038 L .14615 .04808 L F 1 .792 0 r .14615 .04808 m .14615 .24038 L .14712 .24038 L .14712 .04808 L F 1 .798 0 r .14712 .04808 m .14712 .24038 L .14808 .24038 L .14808 .04808 L F 1 .804 0 r .14808 .04808 m .14808 .24038 L .14904 .24038 L .14904 .04808 L F 1 .81 0 r .14904 .04808 m .14904 .24038 L .15 .24038 L .15 .04808 L F 1 .816 0 r .15 .04808 m .15 .24038 L .15096 .24038 L .15096 .04808 L F 1 .822 0 r .15096 .04808 m .15096 .24038 L .15192 .24038 L .15192 .04808 L F 1 .828 0 r .15192 .04808 m .15192 .24038 L .15288 .24038 L .15288 .04808 L F 1 .834 0 r .15288 .04808 m .15288 .24038 L .15385 .24038 L .15385 .04808 L F 1 .84 0 r .15385 .04808 m .15385 .24038 L .15481 .24038 L .15481 .04808 L F 1 .846 0 r .15481 .04808 m .15481 .24038 L .15577 .24038 L .15577 .04808 L F 1 .852 0 r .15577 .04808 m .15577 .24038 L .15673 .24038 L .15673 .04808 L F 1 .858 0 r .15673 .04808 m .15673 .24038 L .15769 .24038 L .15769 .04808 L F 1 .864 0 r .15769 .04808 m .15769 .24038 L .15865 .24038 L .15865 .04808 L F 1 .87 0 r .15865 .04808 m .15865 .24038 L .15962 .24038 L .15962 .04808 L F 1 .876 0 r .15962 .04808 m .15962 .24038 L .16058 .24038 L .16058 .04808 L F 1 .882 0 r .16058 .04808 m .16058 .24038 L .16154 .24038 L .16154 .04808 L F 1 .888 0 r .16154 .04808 m .16154 .24038 L .1625 .24038 L .1625 .04808 L F 1 .894 0 r .1625 .04808 m .1625 .24038 L .16346 .24038 L .16346 .04808 L F 1 .9 0 r .16346 .04808 m .16346 .24038 L .16442 .24038 L .16442 .04808 L F 1 .906 0 r .16442 .04808 m .16442 .24038 L .16538 .24038 L .16538 .04808 L F 1 .912 0 r .16538 .04808 m .16538 .24038 L .16635 .24038 L .16635 .04808 L F 1 .918 0 r .16635 .04808 m .16635 .24038 L .16731 .24038 L .16731 .04808 L F 1 .924 0 r .16731 .04808 m .16731 .24038 L .16827 .24038 L .16827 .04808 L F 1 .93 0 r .16827 .04808 m .16827 .24038 L .16923 .24038 L .16923 .04808 L F 1 .936 0 r .16923 .04808 m .16923 .24038 L .17019 .24038 L .17019 .04808 L F 1 .942 0 r .17019 .04808 m .17019 .24038 L .17115 .24038 L .17115 .04808 L F 1 .948 0 r .17115 .04808 m .17115 .24038 L .17212 .24038 L .17212 .04808 L F 1 .954 0 r .17212 .04808 m .17212 .24038 L .17308 .24038 L .17308 .04808 L F 1 .96 0 r .17308 .04808 m .17308 .24038 L .17404 .24038 L .17404 .04808 L F 1 .966 0 r .17404 .04808 m .17404 .24038 L .175 .24038 L .175 .04808 L F 1 .972 0 r .175 .04808 m .175 .24038 L .17596 .24038 L .17596 .04808 L F 1 .978 0 r .17596 .04808 m .17596 .24038 L .17692 .24038 L .17692 .04808 L F 1 .984 0 r .17692 .04808 m .17692 .24038 L .17788 .24038 L .17788 .04808 L F 1 .99 0 r .17788 .04808 m .17788 .24038 L .17885 .24038 L .17885 .04808 L F 1 .996 0 r .17885 .04808 m .17885 .24038 L .17981 .24038 L .17981 .04808 L F .998 1 0 r .17981 .04808 m .17981 .24038 L .18077 .24038 L .18077 .04808 L F .992 1 0 r .18077 .04808 m .18077 .24038 L .18173 .24038 L .18173 .04808 L F .986 1 0 r .18173 .04808 m .18173 .24038 L .18269 .24038 L .18269 .04808 L F .98 1 0 r .18269 .04808 m .18269 .24038 L .18365 .24038 L .18365 .04808 L F .974 1 0 r .18365 .04808 m .18365 .24038 L .18462 .24038 L .18462 .04808 L F .968 1 0 r .18462 .04808 m .18462 .24038 L .18558 .24038 L .18558 .04808 L F .962 1 0 r .18558 .04808 m .18558 .24038 L .18654 .24038 L .18654 .04808 L F .956 1 0 r .18654 .04808 m .18654 .24038 L .1875 .24038 L .1875 .04808 L F .95 1 0 r .1875 .04808 m .1875 .24038 L .18846 .24038 L .18846 .04808 L F .944 1 0 r .18846 .04808 m .18846 .24038 L .18942 .24038 L .18942 .04808 L F .938 1 0 r .18942 .04808 m .18942 .24038 L .19038 .24038 L .19038 .04808 L F .932 1 0 r .19038 .04808 m .19038 .24038 L .19135 .24038 L .19135 .04808 L F .926 1 0 r .19135 .04808 m .19135 .24038 L .19231 .24038 L .19231 .04808 L F .92 1 0 r .19231 .04808 m .19231 .24038 L .19327 .24038 L .19327 .04808 L F .914 1 0 r .19327 .04808 m .19327 .24038 L .19423 .24038 L .19423 .04808 L F .908 1 0 r .19423 .04808 m .19423 .24038 L .19519 .24038 L .19519 .04808 L F .902 1 0 r .19519 .04808 m .19519 .24038 L .19615 .24038 L .19615 .04808 L F .896 1 0 r .19615 .04808 m .19615 .24038 L .19712 .24038 L .19712 .04808 L F .89 1 0 r .19712 .04808 m .19712 .24038 L .19808 .24038 L .19808 .04808 L F .884 1 0 r .19808 .04808 m .19808 .24038 L .19904 .24038 L .19904 .04808 L F .878 1 0 r .19904 .04808 m .19904 .24038 L .2 .24038 L .2 .04808 L F .872 1 0 r .2 .04808 m .2 .24038 L .20096 .24038 L .20096 .04808 L F .866 1 0 r .20096 .04808 m .20096 .24038 L .20192 .24038 L .20192 .04808 L F .86 1 0 r .20192 .04808 m .20192 .24038 L .20288 .24038 L .20288 .04808 L F .854 1 0 r .20288 .04808 m .20288 .24038 L .20385 .24038 L .20385 .04808 L F .848 1 0 r .20385 .04808 m .20385 .24038 L .20481 .24038 L .20481 .04808 L F .842 1 0 r .20481 .04808 m .20481 .24038 L .20577 .24038 L .20577 .04808 L F .836 1 0 r .20577 .04808 m .20577 .24038 L .20673 .24038 L .20673 .04808 L F .83 1 0 r .20673 .04808 m .20673 .24038 L .20769 .24038 L .20769 .04808 L F .824 1 0 r .20769 .04808 m .20769 .24038 L .20865 .24038 L .20865 .04808 L F .818 1 0 r .20865 .04808 m .20865 .24038 L .20962 .24038 L .20962 .04808 L F .812 1 0 r .20962 .04808 m .20962 .24038 L .21058 .24038 L .21058 .04808 L F .806 1 0 r .21058 .04808 m .21058 .24038 L .21154 .24038 L .21154 .04808 L F .8 1 0 r .21154 .04808 m .21154 .24038 L .2125 .24038 L .2125 .04808 L F .794 1 0 r .2125 .04808 m .2125 .24038 L .21346 .24038 L .21346 .04808 L F .788 1 0 r .21346 .04808 m .21346 .24038 L .21442 .24038 L .21442 .04808 L F .782 1 0 r .21442 .04808 m .21442 .24038 L .21538 .24038 L .21538 .04808 L F .776 1 0 r .21538 .04808 m .21538 .24038 L .21635 .24038 L .21635 .04808 L F .77 1 0 r .21635 .04808 m .21635 .24038 L .21731 .24038 L .21731 .04808 L F .764 1 0 r .21731 .04808 m .21731 .24038 L .21827 .24038 L .21827 .04808 L F .758 1 0 r .21827 .04808 m .21827 .24038 L .21923 .24038 L .21923 .04808 L F .752 1 0 r .21923 .04808 m .21923 .24038 L .22019 .24038 L .22019 .04808 L F .746 1 0 r .22019 .04808 m .22019 .24038 L .22115 .24038 L .22115 .04808 L F .74 1 0 r .22115 .04808 m .22115 .24038 L .22212 .24038 L .22212 .04808 L F .734 1 0 r .22212 .04808 m .22212 .24038 L .22308 .24038 L .22308 .04808 L F .728 1 0 r .22308 .04808 m .22308 .24038 L .22404 .24038 L .22404 .04808 L F .722 1 0 r .22404 .04808 m .22404 .24038 L .225 .24038 L .225 .04808 L F .716 1 0 r .225 .04808 m .225 .24038 L .22596 .24038 L .22596 .04808 L F .71 1 0 r .22596 .04808 m .22596 .24038 L .22692 .24038 L .22692 .04808 L F .704 1 0 r .22692 .04808 m .22692 .24038 L .22788 .24038 L .22788 .04808 L F .698 1 0 r .22788 .04808 m .22788 .24038 L .22885 .24038 L .22885 .04808 L F .692 1 0 r .22885 .04808 m .22885 .24038 L .22981 .24038 L .22981 .04808 L F .686 1 0 r .22981 .04808 m .22981 .24038 L .23077 .24038 L .23077 .04808 L F .68 1 0 r .23077 .04808 m .23077 .24038 L .23173 .24038 L .23173 .04808 L F .674 1 0 r .23173 .04808 m .23173 .24038 L .23269 .24038 L .23269 .04808 L F .668 1 0 r .23269 .04808 m .23269 .24038 L .23365 .24038 L .23365 .04808 L F .662 1 0 r .23365 .04808 m .23365 .24038 L .23462 .24038 L .23462 .04808 L F .656 1 0 r .23462 .04808 m .23462 .24038 L .23558 .24038 L .23558 .04808 L F .65 1 0 r .23558 .04808 m .23558 .24038 L .23654 .24038 L .23654 .04808 L F .644 1 0 r .23654 .04808 m .23654 .24038 L .2375 .24038 L .2375 .04808 L F .638 1 0 r .2375 .04808 m .2375 .24038 L .23846 .24038 L .23846 .04808 L F .632 1 0 r .23846 .04808 m .23846 .24038 L .23942 .24038 L .23942 .04808 L F .626 1 0 r .23942 .04808 m .23942 .24038 L .24038 .24038 L .24038 .04808 L F .62 1 0 r .24038 .04808 m .24038 .24038 L .24135 .24038 L .24135 .04808 L F .614 1 0 r .24135 .04808 m .24135 .24038 L .24231 .24038 L .24231 .04808 L F .608 1 0 r .24231 .04808 m .24231 .24038 L .24327 .24038 L .24327 .04808 L F .602 1 0 r .24327 .04808 m .24327 .24038 L .24423 .24038 L .24423 .04808 L F .596 1 0 r .24423 .04808 m .24423 .24038 L .24519 .24038 L .24519 .04808 L F .59 1 0 r .24519 .04808 m .24519 .24038 L .24615 .24038 L .24615 .04808 L F .584 1 0 r .24615 .04808 m .24615 .24038 L .24712 .24038 L .24712 .04808 L F .578 1 0 r .24712 .04808 m .24712 .24038 L .24808 .24038 L .24808 .04808 L F .572 1 0 r .24808 .04808 m .24808 .24038 L .24904 .24038 L .24904 .04808 L F .566 1 0 r .24904 .04808 m .24904 .24038 L .25 .24038 L .25 .04808 L F .56 1 0 r .25 .04808 m .25 .24038 L .25096 .24038 L .25096 .04808 L F .554 1 0 r .25096 .04808 m .25096 .24038 L .25192 .24038 L .25192 .04808 L F .548 1 0 r .25192 .04808 m .25192 .24038 L .25288 .24038 L .25288 .04808 L F .542 1 0 r .25288 .04808 m .25288 .24038 L .25385 .24038 L .25385 .04808 L F .536 1 0 r .25385 .04808 m .25385 .24038 L .25481 .24038 L .25481 .04808 L F .53 1 0 r .25481 .04808 m .25481 .24038 L .25577 .24038 L .25577 .04808 L F .524 1 0 r .25577 .04808 m .25577 .24038 L .25673 .24038 L .25673 .04808 L F .518 1 0 r .25673 .04808 m .25673 .24038 L .25769 .24038 L .25769 .04808 L F .512 1 0 r .25769 .04808 m .25769 .24038 L .25865 .24038 L .25865 .04808 L F .506 1 0 r .25865 .04808 m .25865 .24038 L .25962 .24038 L .25962 .04808 L F .5 1 0 r .25962 .04808 m .25962 .24038 L .26058 .24038 L .26058 .04808 L F .494 1 0 r .26058 .04808 m .26058 .24038 L .26154 .24038 L .26154 .04808 L F .488 1 0 r .26154 .04808 m .26154 .24038 L .2625 .24038 L .2625 .04808 L F .482 1 0 r .2625 .04808 m .2625 .24038 L .26346 .24038 L .26346 .04808 L F .476 1 0 r .26346 .04808 m .26346 .24038 L .26442 .24038 L .26442 .04808 L F .47 1 0 r .26442 .04808 m .26442 .24038 L .26538 .24038 L .26538 .04808 L F .464 1 0 r .26538 .04808 m .26538 .24038 L .26635 .24038 L .26635 .04808 L F .458 1 0 r .26635 .04808 m .26635 .24038 L .26731 .24038 L .26731 .04808 L F .452 1 0 r .26731 .04808 m .26731 .24038 L .26827 .24038 L .26827 .04808 L F .446 1 0 r .26827 .04808 m .26827 .24038 L .26923 .24038 L .26923 .04808 L F .44 1 0 r .26923 .04808 m .26923 .24038 L .27019 .24038 L .27019 .04808 L F .434 1 0 r .27019 .04808 m .27019 .24038 L .27115 .24038 L .27115 .04808 L F .428 1 0 r .27115 .04808 m .27115 .24038 L .27212 .24038 L .27212 .04808 L F .422 1 0 r .27212 .04808 m .27212 .24038 L .27308 .24038 L .27308 .04808 L F .416 1 0 r .27308 .04808 m .27308 .24038 L .27404 .24038 L .27404 .04808 L F .41 1 0 r .27404 .04808 m .27404 .24038 L .275 .24038 L .275 .04808 L F .404 1 0 r .275 .04808 m .275 .24038 L .27596 .24038 L .27596 .04808 L F .398 1 0 r .27596 .04808 m .27596 .24038 L .27692 .24038 L .27692 .04808 L F .392 1 0 r .27692 .04808 m .27692 .24038 L .27788 .24038 L .27788 .04808 L F .386 1 0 r .27788 .04808 m .27788 .24038 L .27885 .24038 L .27885 .04808 L F .38 1 0 r .27885 .04808 m .27885 .24038 L .27981 .24038 L .27981 .04808 L F .374 1 0 r .27981 .04808 m .27981 .24038 L .28077 .24038 L .28077 .04808 L F .368 1 0 r .28077 .04808 m .28077 .24038 L .28173 .24038 L .28173 .04808 L F .362 1 0 r .28173 .04808 m .28173 .24038 L .28269 .24038 L .28269 .04808 L F .356 1 0 r .28269 .04808 m .28269 .24038 L .28365 .24038 L .28365 .04808 L F .35 1 0 r .28365 .04808 m .28365 .24038 L .28462 .24038 L .28462 .04808 L F .344 1 0 r .28462 .04808 m .28462 .24038 L .28558 .24038 L .28558 .04808 L F .338 1 0 r .28558 .04808 m .28558 .24038 L .28654 .24038 L .28654 .04808 L F .332 1 0 r .28654 .04808 m .28654 .24038 L .2875 .24038 L .2875 .04808 L F .326 1 0 r .2875 .04808 m .2875 .24038 L .28846 .24038 L .28846 .04808 L F .32 1 0 r .28846 .04808 m .28846 .24038 L .28942 .24038 L .28942 .04808 L F .314 1 0 r .28942 .04808 m .28942 .24038 L .29038 .24038 L .29038 .04808 L F .308 1 0 r .29038 .04808 m .29038 .24038 L .29135 .24038 L .29135 .04808 L F .302 1 0 r .29135 .04808 m .29135 .24038 L .29231 .24038 L .29231 .04808 L F .296 1 0 r .29231 .04808 m .29231 .24038 L .29327 .24038 L .29327 .04808 L F .29 1 0 r .29327 .04808 m .29327 .24038 L .29423 .24038 L .29423 .04808 L F .284 1 0 r .29423 .04808 m .29423 .24038 L .29519 .24038 L .29519 .04808 L F .278 1 0 r .29519 .04808 m .29519 .24038 L .29615 .24038 L .29615 .04808 L F .272 1 0 r .29615 .04808 m .29615 .24038 L .29712 .24038 L .29712 .04808 L F .266 1 0 r .29712 .04808 m .29712 .24038 L .29808 .24038 L .29808 .04808 L F .26 1 0 r .29808 .04808 m .29808 .24038 L .29904 .24038 L .29904 .04808 L F .254 1 0 r .29904 .04808 m .29904 .24038 L .3 .24038 L .3 .04808 L F .248 1 0 r .3 .04808 m .3 .24038 L .30096 .24038 L .30096 .04808 L F .242 1 0 r .30096 .04808 m .30096 .24038 L .30192 .24038 L .30192 .04808 L F .236 1 0 r .30192 .04808 m .30192 .24038 L .30288 .24038 L .30288 .04808 L F .23 1 0 r .30288 .04808 m .30288 .24038 L .30385 .24038 L .30385 .04808 L F .224 1 0 r .30385 .04808 m .30385 .24038 L .30481 .24038 L .30481 .04808 L F .218 1 0 r .30481 .04808 m .30481 .24038 L .30577 .24038 L .30577 .04808 L F .212 1 0 r .30577 .04808 m .30577 .24038 L .30673 .24038 L .30673 .04808 L F .206 1 0 r .30673 .04808 m .30673 .24038 L .30769 .24038 L .30769 .04808 L F .2 1 0 r .30769 .04808 m .30769 .24038 L .30865 .24038 L .30865 .04808 L F .194 1 0 r .30865 .04808 m .30865 .24038 L .30962 .24038 L .30962 .04808 L F .188 1 0 r .30962 .04808 m .30962 .24038 L .31058 .24038 L .31058 .04808 L F .182 1 0 r .31058 .04808 m .31058 .24038 L .31154 .24038 L .31154 .04808 L F .176 1 0 r .31154 .04808 m .31154 .24038 L .3125 .24038 L .3125 .04808 L F .17 1 0 r .3125 .04808 m .3125 .24038 L .31346 .24038 L .31346 .04808 L F .164 1 0 r .31346 .04808 m .31346 .24038 L .31442 .24038 L .31442 .04808 L F .158 1 0 r .31442 .04808 m .31442 .24038 L .31538 .24038 L .31538 .04808 L F .152 1 0 r .31538 .04808 m .31538 .24038 L .31635 .24038 L .31635 .04808 L F .146 1 0 r .31635 .04808 m .31635 .24038 L .31731 .24038 L .31731 .04808 L F .14 1 0 r .31731 .04808 m .31731 .24038 L .31827 .24038 L .31827 .04808 L F .134 1 0 r .31827 .04808 m .31827 .24038 L .31923 .24038 L .31923 .04808 L F .128 1 0 r .31923 .04808 m .31923 .24038 L .32019 .24038 L .32019 .04808 L F .122 1 0 r .32019 .04808 m .32019 .24038 L .32115 .24038 L .32115 .04808 L F .116 1 0 r .32115 .04808 m .32115 .24038 L .32212 .24038 L .32212 .04808 L F .11 1 0 r .32212 .04808 m .32212 .24038 L .32308 .24038 L .32308 .04808 L F .104 1 0 r .32308 .04808 m .32308 .24038 L .32404 .24038 L .32404 .04808 L F .098 1 0 r .32404 .04808 m .32404 .24038 L .325 .24038 L .325 .04808 L F .092 1 0 r .325 .04808 m .325 .24038 L .32596 .24038 L .32596 .04808 L F .086 1 0 r .32596 .04808 m .32596 .24038 L .32692 .24038 L .32692 .04808 L F .08 1 0 r .32692 .04808 m .32692 .24038 L .32788 .24038 L .32788 .04808 L F .074 1 0 r .32788 .04808 m .32788 .24038 L .32885 .24038 L .32885 .04808 L F .068 1 0 r .32885 .04808 m .32885 .24038 L .32981 .24038 L .32981 .04808 L F .062 1 0 r .32981 .04808 m .32981 .24038 L .33077 .24038 L .33077 .04808 L F .056 1 0 r .33077 .04808 m .33077 .24038 L .33173 .24038 L .33173 .04808 L F .05 1 0 r .33173 .04808 m .33173 .24038 L .33269 .24038 L .33269 .04808 L F .044 1 0 r .33269 .04808 m .33269 .24038 L .33365 .24038 L .33365 .04808 L F .038 1 0 r .33365 .04808 m .33365 .24038 L .33462 .24038 L .33462 .04808 L F .032 1 0 r .33462 .04808 m .33462 .24038 L .33558 .24038 L .33558 .04808 L F .026 1 0 r .33558 .04808 m .33558 .24038 L .33654 .24038 L .33654 .04808 L F .02 1 0 r .33654 .04808 m .33654 .24038 L .3375 .24038 L .3375 .04808 L F .014 1 0 r .3375 .04808 m .3375 .24038 L .33846 .24038 L .33846 .04808 L F .008 1 0 r .33846 .04808 m .33846 .24038 L .33942 .24038 L .33942 .04808 L F .002 1 0 r .33942 .04808 m .33942 .24038 L .34038 .24038 L .34038 .04808 L F 0 1 .004 r .34038 .04808 m .34038 .24038 L .34135 .24038 L .34135 .04808 L F 0 1 .01 r .34135 .04808 m .34135 .24038 L .34231 .24038 L .34231 .04808 L F 0 1 .016 r .34231 .04808 m .34231 .24038 L .34327 .24038 L .34327 .04808 L F 0 1 .022 r .34327 .04808 m .34327 .24038 L .34423 .24038 L .34423 .04808 L F 0 1 .028 r .34423 .04808 m .34423 .24038 L .34519 .24038 L .34519 .04808 L F 0 1 .034 r .34519 .04808 m .34519 .24038 L .34615 .24038 L .34615 .04808 L F 0 1 .04 r .34615 .04808 m .34615 .24038 L .34712 .24038 L .34712 .04808 L F 0 1 .046 r .34712 .04808 m .34712 .24038 L .34808 .24038 L .34808 .04808 L F 0 1 .052 r .34808 .04808 m .34808 .24038 L .34904 .24038 L .34904 .04808 L F 0 1 .058 r .34904 .04808 m .34904 .24038 L .35 .24038 L .35 .04808 L F 0 1 .064 r .35 .04808 m .35 .24038 L .35096 .24038 L .35096 .04808 L F 0 1 .07 r .35096 .04808 m .35096 .24038 L .35192 .24038 L .35192 .04808 L F 0 1 .076 r .35192 .04808 m .35192 .24038 L .35288 .24038 L .35288 .04808 L F 0 1 .082 r .35288 .04808 m .35288 .24038 L .35385 .24038 L .35385 .04808 L F 0 1 .088 r .35385 .04808 m .35385 .24038 L .35481 .24038 L .35481 .04808 L F 0 1 .094 r .35481 .04808 m .35481 .24038 L .35577 .24038 L .35577 .04808 L F 0 1 .1 r .35577 .04808 m .35577 .24038 L .35673 .24038 L .35673 .04808 L F 0 1 .106 r .35673 .04808 m .35673 .24038 L .35769 .24038 L .35769 .04808 L F 0 1 .112 r .35769 .04808 m .35769 .24038 L .35865 .24038 L .35865 .04808 L F 0 1 .118 r .35865 .04808 m .35865 .24038 L .35962 .24038 L .35962 .04808 L F 0 1 .124 r .35962 .04808 m .35962 .24038 L .36058 .24038 L .36058 .04808 L F 0 1 .13 r .36058 .04808 m .36058 .24038 L .36154 .24038 L .36154 .04808 L F 0 1 .136 r .36154 .04808 m .36154 .24038 L .3625 .24038 L .3625 .04808 L F 0 1 .142 r .3625 .04808 m .3625 .24038 L .36346 .24038 L .36346 .04808 L F 0 1 .148 r .36346 .04808 m .36346 .24038 L .36442 .24038 L .36442 .04808 L F 0 1 .154 r .36442 .04808 m .36442 .24038 L .36538 .24038 L .36538 .04808 L F 0 1 .16 r .36538 .04808 m .36538 .24038 L .36635 .24038 L .36635 .04808 L F 0 1 .166 r .36635 .04808 m .36635 .24038 L .36731 .24038 L .36731 .04808 L F 0 1 .172 r .36731 .04808 m .36731 .24038 L .36827 .24038 L .36827 .04808 L F 0 1 .178 r .36827 .04808 m .36827 .24038 L .36923 .24038 L .36923 .04808 L F 0 1 .184 r .36923 .04808 m .36923 .24038 L .37019 .24038 L .37019 .04808 L F 0 1 .19 r .37019 .04808 m .37019 .24038 L .37115 .24038 L .37115 .04808 L F 0 1 .196 r .37115 .04808 m .37115 .24038 L .37212 .24038 L .37212 .04808 L F 0 1 .202 r .37212 .04808 m .37212 .24038 L .37308 .24038 L .37308 .04808 L F 0 1 .208 r .37308 .04808 m .37308 .24038 L .37404 .24038 L .37404 .04808 L F 0 1 .214 r .37404 .04808 m .37404 .24038 L .375 .24038 L .375 .04808 L F 0 1 .22 r .375 .04808 m .375 .24038 L .37596 .24038 L .37596 .04808 L F 0 1 .226 r .37596 .04808 m .37596 .24038 L .37692 .24038 L .37692 .04808 L F 0 1 .232 r .37692 .04808 m .37692 .24038 L .37788 .24038 L .37788 .04808 L F 0 1 .238 r .37788 .04808 m .37788 .24038 L .37885 .24038 L .37885 .04808 L F 0 1 .244 r .37885 .04808 m .37885 .24038 L .37981 .24038 L .37981 .04808 L F 0 1 .25 r .37981 .04808 m .37981 .24038 L .38077 .24038 L .38077 .04808 L F 0 1 .256 r .38077 .04808 m .38077 .24038 L .38173 .24038 L .38173 .04808 L F 0 1 .262 r .38173 .04808 m .38173 .24038 L .38269 .24038 L .38269 .04808 L F 0 1 .268 r .38269 .04808 m .38269 .24038 L .38365 .24038 L .38365 .04808 L F 0 1 .274 r .38365 .04808 m .38365 .24038 L .38462 .24038 L .38462 .04808 L F 0 1 .28 r .38462 .04808 m .38462 .24038 L .38558 .24038 L .38558 .04808 L F 0 1 .286 r .38558 .04808 m .38558 .24038 L .38654 .24038 L .38654 .04808 L F 0 1 .292 r .38654 .04808 m .38654 .24038 L .3875 .24038 L .3875 .04808 L F 0 1 .298 r .3875 .04808 m .3875 .24038 L .38846 .24038 L .38846 .04808 L F 0 1 .304 r .38846 .04808 m .38846 .24038 L .38942 .24038 L .38942 .04808 L F 0 1 .31 r .38942 .04808 m .38942 .24038 L .39038 .24038 L .39038 .04808 L F 0 1 .316 r .39038 .04808 m .39038 .24038 L .39135 .24038 L .39135 .04808 L F 0 1 .322 r .39135 .04808 m .39135 .24038 L .39231 .24038 L .39231 .04808 L F 0 1 .328 r .39231 .04808 m .39231 .24038 L .39327 .24038 L .39327 .04808 L F 0 1 .334 r .39327 .04808 m .39327 .24038 L .39423 .24038 L .39423 .04808 L F 0 1 .34 r .39423 .04808 m .39423 .24038 L .39519 .24038 L .39519 .04808 L F 0 1 .346 r .39519 .04808 m .39519 .24038 L .39615 .24038 L .39615 .04808 L F 0 1 .352 r .39615 .04808 m .39615 .24038 L .39712 .24038 L .39712 .04808 L F 0 1 .358 r .39712 .04808 m .39712 .24038 L .39808 .24038 L .39808 .04808 L F 0 1 .364 r .39808 .04808 m .39808 .24038 L .39904 .24038 L .39904 .04808 L F 0 1 .37 r .39904 .04808 m .39904 .24038 L .4 .24038 L .4 .04808 L F 0 1 .376 r .4 .04808 m .4 .24038 L .40096 .24038 L .40096 .04808 L F 0 1 .382 r .40096 .04808 m .40096 .24038 L .40192 .24038 L .40192 .04808 L F 0 1 .388 r .40192 .04808 m .40192 .24038 L .40288 .24038 L .40288 .04808 L F 0 1 .394 r .40288 .04808 m .40288 .24038 L .40385 .24038 L .40385 .04808 L F 0 1 .4 r .40385 .04808 m .40385 .24038 L .40481 .24038 L .40481 .04808 L F 0 1 .406 r .40481 .04808 m .40481 .24038 L .40577 .24038 L .40577 .04808 L F 0 1 .412 r .40577 .04808 m .40577 .24038 L .40673 .24038 L .40673 .04808 L F 0 1 .418 r .40673 .04808 m .40673 .24038 L .40769 .24038 L .40769 .04808 L F 0 1 .424 r .40769 .04808 m .40769 .24038 L .40865 .24038 L .40865 .04808 L F 0 1 .43 r .40865 .04808 m .40865 .24038 L .40962 .24038 L .40962 .04808 L F 0 1 .436 r .40962 .04808 m .40962 .24038 L .41058 .24038 L .41058 .04808 L F 0 1 .442 r .41058 .04808 m .41058 .24038 L .41154 .24038 L .41154 .04808 L F 0 1 .448 r .41154 .04808 m .41154 .24038 L .4125 .24038 L .4125 .04808 L F 0 1 .454 r .4125 .04808 m .4125 .24038 L .41346 .24038 L .41346 .04808 L F 0 1 .46 r .41346 .04808 m .41346 .24038 L .41442 .24038 L .41442 .04808 L F 0 1 .466 r .41442 .04808 m .41442 .24038 L .41538 .24038 L .41538 .04808 L F 0 1 .472 r .41538 .04808 m .41538 .24038 L .41635 .24038 L .41635 .04808 L F 0 1 .478 r .41635 .04808 m .41635 .24038 L .41731 .24038 L .41731 .04808 L F 0 1 .484 r .41731 .04808 m .41731 .24038 L .41827 .24038 L .41827 .04808 L F 0 1 .49 r .41827 .04808 m .41827 .24038 L .41923 .24038 L .41923 .04808 L F 0 1 .496 r .41923 .04808 m .41923 .24038 L .42019 .24038 L .42019 .04808 L F 0 1 .502 r .42019 .04808 m .42019 .24038 L .42115 .24038 L .42115 .04808 L F 0 1 .508 r .42115 .04808 m .42115 .24038 L .42212 .24038 L .42212 .04808 L F 0 1 .514 r .42212 .04808 m .42212 .24038 L .42308 .24038 L .42308 .04808 L F 0 1 .52 r .42308 .04808 m .42308 .24038 L .42404 .24038 L .42404 .04808 L F 0 1 .526 r .42404 .04808 m .42404 .24038 L .425 .24038 L .425 .04808 L F 0 1 .532 r .425 .04808 m .425 .24038 L .42596 .24038 L .42596 .04808 L F 0 1 .538 r .42596 .04808 m .42596 .24038 L .42692 .24038 L .42692 .04808 L F 0 1 .544 r .42692 .04808 m .42692 .24038 L .42788 .24038 L .42788 .04808 L F 0 1 .55 r .42788 .04808 m .42788 .24038 L .42885 .24038 L .42885 .04808 L F 0 1 .556 r .42885 .04808 m .42885 .24038 L .42981 .24038 L .42981 .04808 L F 0 1 .562 r .42981 .04808 m .42981 .24038 L .43077 .24038 L .43077 .04808 L F 0 1 .568 r .43077 .04808 m .43077 .24038 L .43173 .24038 L .43173 .04808 L F 0 1 .574 r .43173 .04808 m .43173 .24038 L .43269 .24038 L .43269 .04808 L F 0 1 .58 r .43269 .04808 m .43269 .24038 L .43365 .24038 L .43365 .04808 L F 0 1 .586 r .43365 .04808 m .43365 .24038 L .43462 .24038 L .43462 .04808 L F 0 1 .592 r .43462 .04808 m .43462 .24038 L .43558 .24038 L .43558 .04808 L F 0 1 .598 r .43558 .04808 m .43558 .24038 L .43654 .24038 L .43654 .04808 L F 0 1 .604 r .43654 .04808 m .43654 .24038 L .4375 .24038 L .4375 .04808 L F 0 1 .61 r .4375 .04808 m .4375 .24038 L .43846 .24038 L .43846 .04808 L F 0 1 .616 r .43846 .04808 m .43846 .24038 L .43942 .24038 L .43942 .04808 L F 0 1 .622 r .43942 .04808 m .43942 .24038 L .44038 .24038 L .44038 .04808 L F 0 1 .628 r .44038 .04808 m .44038 .24038 L .44135 .24038 L .44135 .04808 L F 0 1 .634 r .44135 .04808 m .44135 .24038 L .44231 .24038 L .44231 .04808 L F 0 1 .64 r .44231 .04808 m .44231 .24038 L .44327 .24038 L .44327 .04808 L F 0 1 .646 r .44327 .04808 m .44327 .24038 L .44423 .24038 L .44423 .04808 L F 0 1 .652 r .44423 .04808 m .44423 .24038 L .44519 .24038 L .44519 .04808 L F 0 1 .658 r .44519 .04808 m .44519 .24038 L .44615 .24038 L .44615 .04808 L F 0 1 .664 r .44615 .04808 m .44615 .24038 L .44712 .24038 L .44712 .04808 L F 0 1 .67 r .44712 .04808 m .44712 .24038 L .44808 .24038 L .44808 .04808 L F 0 1 .676 r .44808 .04808 m .44808 .24038 L .44904 .24038 L .44904 .04808 L F 0 1 .682 r .44904 .04808 m .44904 .24038 L .45 .24038 L .45 .04808 L F 0 1 .688 r .45 .04808 m .45 .24038 L .45096 .24038 L .45096 .04808 L F 0 1 .694 r .45096 .04808 m .45096 .24038 L .45192 .24038 L .45192 .04808 L F 0 1 .7 r .45192 .04808 m .45192 .24038 L .45288 .24038 L .45288 .04808 L F 0 1 .706 r .45288 .04808 m .45288 .24038 L .45385 .24038 L .45385 .04808 L F 0 1 .712 r .45385 .04808 m .45385 .24038 L .45481 .24038 L .45481 .04808 L F 0 1 .718 r .45481 .04808 m .45481 .24038 L .45577 .24038 L .45577 .04808 L F 0 1 .724 r .45577 .04808 m .45577 .24038 L .45673 .24038 L .45673 .04808 L F 0 1 .73 r .45673 .04808 m .45673 .24038 L .45769 .24038 L .45769 .04808 L F 0 1 .736 r .45769 .04808 m .45769 .24038 L .45865 .24038 L .45865 .04808 L F 0 1 .742 r .45865 .04808 m .45865 .24038 L .45962 .24038 L .45962 .04808 L F 0 1 .748 r .45962 .04808 m .45962 .24038 L .46058 .24038 L .46058 .04808 L F 0 1 .754 r .46058 .04808 m .46058 .24038 L .46154 .24038 L .46154 .04808 L F 0 1 .76 r .46154 .04808 m .46154 .24038 L .4625 .24038 L .4625 .04808 L F 0 1 .766 r .4625 .04808 m .4625 .24038 L .46346 .24038 L .46346 .04808 L F 0 1 .772 r .46346 .04808 m .46346 .24038 L .46442 .24038 L .46442 .04808 L F 0 1 .778 r .46442 .04808 m .46442 .24038 L .46538 .24038 L .46538 .04808 L F 0 1 .784 r .46538 .04808 m .46538 .24038 L .46635 .24038 L .46635 .04808 L F 0 1 .79 r .46635 .04808 m .46635 .24038 L .46731 .24038 L .46731 .04808 L F 0 1 .796 r .46731 .04808 m .46731 .24038 L .46827 .24038 L .46827 .04808 L F 0 1 .802 r .46827 .04808 m .46827 .24038 L .46923 .24038 L .46923 .04808 L F 0 1 .808 r .46923 .04808 m .46923 .24038 L .47019 .24038 L .47019 .04808 L F 0 1 .814 r .47019 .04808 m .47019 .24038 L .47115 .24038 L .47115 .04808 L F 0 1 .82 r .47115 .04808 m .47115 .24038 L .47212 .24038 L .47212 .04808 L F 0 1 .826 r .47212 .04808 m .47212 .24038 L .47308 .24038 L .47308 .04808 L F 0 1 .832 r .47308 .04808 m .47308 .24038 L .47404 .24038 L .47404 .04808 L F 0 1 .838 r .47404 .04808 m .47404 .24038 L .475 .24038 L .475 .04808 L F 0 1 .844 r .475 .04808 m .475 .24038 L .47596 .24038 L .47596 .04808 L F 0 1 .85 r .47596 .04808 m .47596 .24038 L .47692 .24038 L .47692 .04808 L F 0 1 .856 r .47692 .04808 m .47692 .24038 L .47788 .24038 L .47788 .04808 L F 0 1 .862 r .47788 .04808 m .47788 .24038 L .47885 .24038 L .47885 .04808 L F 0 1 .868 r .47885 .04808 m .47885 .24038 L .47981 .24038 L .47981 .04808 L F 0 1 .874 r .47981 .04808 m .47981 .24038 L .48077 .24038 L .48077 .04808 L F 0 1 .88 r .48077 .04808 m .48077 .24038 L .48173 .24038 L .48173 .04808 L F 0 1 .886 r .48173 .04808 m .48173 .24038 L .48269 .24038 L .48269 .04808 L F 0 1 .892 r .48269 .04808 m .48269 .24038 L .48365 .24038 L .48365 .04808 L F 0 1 .898 r .48365 .04808 m .48365 .24038 L .48462 .24038 L .48462 .04808 L F 0 1 .904 r .48462 .04808 m .48462 .24038 L .48558 .24038 L .48558 .04808 L F 0 1 .91 r .48558 .04808 m .48558 .24038 L .48654 .24038 L .48654 .04808 L F 0 1 .916 r .48654 .04808 m .48654 .24038 L .4875 .24038 L .4875 .04808 L F 0 1 .922 r .4875 .04808 m .4875 .24038 L .48846 .24038 L .48846 .04808 L F 0 1 .928 r .48846 .04808 m .48846 .24038 L .48942 .24038 L .48942 .04808 L F 0 1 .934 r .48942 .04808 m .48942 .24038 L .49038 .24038 L .49038 .04808 L F 0 1 .94 r .49038 .04808 m .49038 .24038 L .49135 .24038 L .49135 .04808 L F 0 1 .946 r .49135 .04808 m .49135 .24038 L .49231 .24038 L .49231 .04808 L F 0 1 .952 r .49231 .04808 m .49231 .24038 L .49327 .24038 L .49327 .04808 L F 0 1 .958 r .49327 .04808 m .49327 .24038 L .49423 .24038 L .49423 .04808 L F 0 1 .964 r .49423 .04808 m .49423 .24038 L .49519 .24038 L .49519 .04808 L F 0 1 .97 r .49519 .04808 m .49519 .24038 L .49615 .24038 L .49615 .04808 L F 0 1 .976 r .49615 .04808 m .49615 .24038 L .49712 .24038 L .49712 .04808 L F 0 1 .982 r .49712 .04808 m .49712 .24038 L .49808 .24038 L .49808 .04808 L F 0 1 .988 r .49808 .04808 m .49808 .24038 L .49904 .24038 L .49904 .04808 L F 0 1 .994 r .49904 .04808 m .49904 .24038 L .5 .24038 L .5 .04808 L F 0 1 1 r .5 .04808 m .5 .24038 L .50096 .24038 L .50096 .04808 L F 0 .994 1 r .50096 .04808 m .50096 .24038 L .50192 .24038 L .50192 .04808 L F 0 .988 1 r .50192 .04808 m .50192 .24038 L .50288 .24038 L .50288 .04808 L F 0 .982 1 r .50288 .04808 m .50288 .24038 L .50385 .24038 L .50385 .04808 L F 0 .976 1 r .50385 .04808 m .50385 .24038 L .50481 .24038 L .50481 .04808 L F 0 .97 1 r .50481 .04808 m .50481 .24038 L .50577 .24038 L .50577 .04808 L F 0 .964 1 r .50577 .04808 m .50577 .24038 L .50673 .24038 L .50673 .04808 L F 0 .958 1 r .50673 .04808 m .50673 .24038 L .50769 .24038 L .50769 .04808 L F 0 .952 1 r .50769 .04808 m .50769 .24038 L .50865 .24038 L .50865 .04808 L F 0 .946 1 r .50865 .04808 m .50865 .24038 L .50962 .24038 L .50962 .04808 L F 0 .94 1 r .50962 .04808 m .50962 .24038 L .51058 .24038 L .51058 .04808 L F 0 .934 1 r .51058 .04808 m .51058 .24038 L .51154 .24038 L .51154 .04808 L F 0 .928 1 r .51154 .04808 m .51154 .24038 L .5125 .24038 L .5125 .04808 L F 0 .922 1 r .5125 .04808 m .5125 .24038 L .51346 .24038 L .51346 .04808 L F 0 .916 1 r .51346 .04808 m .51346 .24038 L .51442 .24038 L .51442 .04808 L F 0 .91 1 r .51442 .04808 m .51442 .24038 L .51538 .24038 L .51538 .04808 L F 0 .904 1 r .51538 .04808 m .51538 .24038 L .51635 .24038 L .51635 .04808 L F 0 .898 1 r .51635 .04808 m .51635 .24038 L .51731 .24038 L .51731 .04808 L F 0 .892 1 r .51731 .04808 m .51731 .24038 L .51827 .24038 L .51827 .04808 L F 0 .886 1 r .51827 .04808 m .51827 .24038 L .51923 .24038 L .51923 .04808 L F 0 .88 1 r .51923 .04808 m .51923 .24038 L .52019 .24038 L .52019 .04808 L F 0 .874 1 r .52019 .04808 m .52019 .24038 L .52115 .24038 L .52115 .04808 L F 0 .868 1 r .52115 .04808 m .52115 .24038 L .52212 .24038 L .52212 .04808 L F 0 .862 1 r .52212 .04808 m .52212 .24038 L .52308 .24038 L .52308 .04808 L F 0 .856 1 r .52308 .04808 m .52308 .24038 L .52404 .24038 L .52404 .04808 L F 0 .85 1 r .52404 .04808 m .52404 .24038 L .525 .24038 L .525 .04808 L F 0 .844 1 r .525 .04808 m .525 .24038 L .52596 .24038 L .52596 .04808 L F 0 .838 1 r .52596 .04808 m .52596 .24038 L .52692 .24038 L .52692 .04808 L F 0 .832 1 r .52692 .04808 m .52692 .24038 L .52788 .24038 L .52788 .04808 L F 0 .826 1 r .52788 .04808 m .52788 .24038 L .52885 .24038 L .52885 .04808 L F 0 .82 1 r .52885 .04808 m .52885 .24038 L .52981 .24038 L .52981 .04808 L F 0 .814 1 r .52981 .04808 m .52981 .24038 L .53077 .24038 L .53077 .04808 L F 0 .808 1 r .53077 .04808 m .53077 .24038 L .53173 .24038 L .53173 .04808 L F 0 .802 1 r .53173 .04808 m .53173 .24038 L .53269 .24038 L .53269 .04808 L F 0 .796 1 r .53269 .04808 m .53269 .24038 L .53365 .24038 L .53365 .04808 L F 0 .79 1 r .53365 .04808 m .53365 .24038 L .53462 .24038 L .53462 .04808 L F 0 .784 1 r .53462 .04808 m .53462 .24038 L .53558 .24038 L .53558 .04808 L F 0 .778 1 r .53558 .04808 m .53558 .24038 L .53654 .24038 L .53654 .04808 L F 0 .772 1 r .53654 .04808 m .53654 .24038 L .5375 .24038 L .5375 .04808 L F 0 .766 1 r .5375 .04808 m .5375 .24038 L .53846 .24038 L .53846 .04808 L F 0 .76 1 r .53846 .04808 m .53846 .24038 L .53942 .24038 L .53942 .04808 L F 0 .754 1 r .53942 .04808 m .53942 .24038 L .54038 .24038 L .54038 .04808 L F 0 .748 1 r .54038 .04808 m .54038 .24038 L .54135 .24038 L .54135 .04808 L F 0 .742 1 r .54135 .04808 m .54135 .24038 L .54231 .24038 L .54231 .04808 L F 0 .736 1 r .54231 .04808 m .54231 .24038 L .54327 .24038 L .54327 .04808 L F 0 .73 1 r .54327 .04808 m .54327 .24038 L .54423 .24038 L .54423 .04808 L F 0 .724 1 r .54423 .04808 m .54423 .24038 L .54519 .24038 L .54519 .04808 L F 0 .718 1 r .54519 .04808 m .54519 .24038 L .54615 .24038 L .54615 .04808 L F 0 .712 1 r .54615 .04808 m .54615 .24038 L .54712 .24038 L .54712 .04808 L F 0 .706 1 r .54712 .04808 m .54712 .24038 L .54808 .24038 L .54808 .04808 L F 0 .7 1 r .54808 .04808 m .54808 .24038 L .54904 .24038 L .54904 .04808 L F 0 .694 1 r .54904 .04808 m .54904 .24038 L .55 .24038 L .55 .04808 L F 0 .688 1 r .55 .04808 m .55 .24038 L .55096 .24038 L .55096 .04808 L F 0 .682 1 r .55096 .04808 m .55096 .24038 L .55192 .24038 L .55192 .04808 L F 0 .676 1 r .55192 .04808 m .55192 .24038 L .55288 .24038 L .55288 .04808 L F 0 .67 1 r .55288 .04808 m .55288 .24038 L .55385 .24038 L .55385 .04808 L F 0 .664 1 r .55385 .04808 m .55385 .24038 L .55481 .24038 L .55481 .04808 L F 0 .658 1 r .55481 .04808 m .55481 .24038 L .55577 .24038 L .55577 .04808 L F 0 .652 1 r .55577 .04808 m .55577 .24038 L .55673 .24038 L .55673 .04808 L F 0 .646 1 r .55673 .04808 m .55673 .24038 L .55769 .24038 L .55769 .04808 L F 0 .64 1 r .55769 .04808 m .55769 .24038 L .55865 .24038 L .55865 .04808 L F 0 .634 1 r .55865 .04808 m .55865 .24038 L .55962 .24038 L .55962 .04808 L F 0 .628 1 r .55962 .04808 m .55962 .24038 L .56058 .24038 L .56058 .04808 L F 0 .622 1 r .56058 .04808 m .56058 .24038 L .56154 .24038 L .56154 .04808 L F 0 .616 1 r .56154 .04808 m .56154 .24038 L .5625 .24038 L .5625 .04808 L F 0 .61 1 r .5625 .04808 m .5625 .24038 L .56346 .24038 L .56346 .04808 L F 0 .604 1 r .56346 .04808 m .56346 .24038 L .56442 .24038 L .56442 .04808 L F 0 .598 1 r .56442 .04808 m .56442 .24038 L .56538 .24038 L .56538 .04808 L F 0 .592 1 r .56538 .04808 m .56538 .24038 L .56635 .24038 L .56635 .04808 L F 0 .586 1 r .56635 .04808 m .56635 .24038 L .56731 .24038 L .56731 .04808 L F 0 .58 1 r .56731 .04808 m .56731 .24038 L .56827 .24038 L .56827 .04808 L F 0 .574 1 r .56827 .04808 m .56827 .24038 L .56923 .24038 L .56923 .04808 L F 0 .568 1 r .56923 .04808 m .56923 .24038 L .57019 .24038 L .57019 .04808 L F 0 .562 1 r .57019 .04808 m .57019 .24038 L .57115 .24038 L .57115 .04808 L F 0 .556 1 r .57115 .04808 m .57115 .24038 L .57212 .24038 L .57212 .04808 L F 0 .55 1 r .57212 .04808 m .57212 .24038 L .57308 .24038 L .57308 .04808 L F 0 .544 1 r .57308 .04808 m .57308 .24038 L .57404 .24038 L .57404 .04808 L F 0 .538 1 r .57404 .04808 m .57404 .24038 L .575 .24038 L .575 .04808 L F 0 .532 1 r .575 .04808 m .575 .24038 L .57596 .24038 L .57596 .04808 L F 0 .526 1 r .57596 .04808 m .57596 .24038 L .57692 .24038 L .57692 .04808 L F 0 .52 1 r .57692 .04808 m .57692 .24038 L .57788 .24038 L .57788 .04808 L F 0 .514 1 r .57788 .04808 m .57788 .24038 L .57885 .24038 L .57885 .04808 L F 0 .508 1 r .57885 .04808 m .57885 .24038 L .57981 .24038 L .57981 .04808 L F 0 .502 1 r .57981 .04808 m .57981 .24038 L .58077 .24038 L .58077 .04808 L F 0 .496 1 r .58077 .04808 m .58077 .24038 L .58173 .24038 L .58173 .04808 L F 0 .49 1 r .58173 .04808 m .58173 .24038 L .58269 .24038 L .58269 .04808 L F 0 .484 1 r .58269 .04808 m .58269 .24038 L .58365 .24038 L .58365 .04808 L F 0 .478 1 r .58365 .04808 m .58365 .24038 L .58462 .24038 L .58462 .04808 L F 0 .472 1 r .58462 .04808 m .58462 .24038 L .58558 .24038 L .58558 .04808 L F 0 .466 1 r .58558 .04808 m .58558 .24038 L .58654 .24038 L .58654 .04808 L F 0 .46 1 r .58654 .04808 m .58654 .24038 L .5875 .24038 L .5875 .04808 L F 0 .454 1 r .5875 .04808 m .5875 .24038 L .58846 .24038 L .58846 .04808 L F 0 .448 1 r .58846 .04808 m .58846 .24038 L .58942 .24038 L .58942 .04808 L F 0 .442 1 r .58942 .04808 m .58942 .24038 L .59038 .24038 L .59038 .04808 L F 0 .436 1 r .59038 .04808 m .59038 .24038 L .59135 .24038 L .59135 .04808 L F 0 .43 1 r .59135 .04808 m .59135 .24038 L .59231 .24038 L .59231 .04808 L F 0 .424 1 r .59231 .04808 m .59231 .24038 L .59327 .24038 L .59327 .04808 L F 0 .418 1 r .59327 .04808 m .59327 .24038 L .59423 .24038 L .59423 .04808 L F 0 .412 1 r .59423 .04808 m .59423 .24038 L .59519 .24038 L .59519 .04808 L F 0 .406 1 r .59519 .04808 m .59519 .24038 L .59615 .24038 L .59615 .04808 L F 0 .4 1 r .59615 .04808 m .59615 .24038 L .59712 .24038 L .59712 .04808 L F 0 .394 1 r .59712 .04808 m .59712 .24038 L .59808 .24038 L .59808 .04808 L F 0 .388 1 r .59808 .04808 m .59808 .24038 L .59904 .24038 L .59904 .04808 L F 0 .382 1 r .59904 .04808 m .59904 .24038 L .6 .24038 L .6 .04808 L F 0 .376 1 r .6 .04808 m .6 .24038 L .60096 .24038 L .60096 .04808 L F 0 .37 1 r .60096 .04808 m .60096 .24038 L .60192 .24038 L .60192 .04808 L F 0 .364 1 r .60192 .04808 m .60192 .24038 L .60288 .24038 L .60288 .04808 L F 0 .358 1 r .60288 .04808 m .60288 .24038 L .60385 .24038 L .60385 .04808 L F 0 .352 1 r .60385 .04808 m .60385 .24038 L .60481 .24038 L .60481 .04808 L F 0 .346 1 r .60481 .04808 m .60481 .24038 L .60577 .24038 L .60577 .04808 L F 0 .34 1 r .60577 .04808 m .60577 .24038 L .60673 .24038 L .60673 .04808 L F 0 .334 1 r .60673 .04808 m .60673 .24038 L .60769 .24038 L .60769 .04808 L F 0 .328 1 r .60769 .04808 m .60769 .24038 L .60865 .24038 L .60865 .04808 L F 0 .322 1 r .60865 .04808 m .60865 .24038 L .60962 .24038 L .60962 .04808 L F 0 .316 1 r .60962 .04808 m .60962 .24038 L .61058 .24038 L .61058 .04808 L F 0 .31 1 r .61058 .04808 m .61058 .24038 L .61154 .24038 L .61154 .04808 L F 0 .304 1 r .61154 .04808 m .61154 .24038 L .6125 .24038 L .6125 .04808 L F 0 .298 1 r .6125 .04808 m .6125 .24038 L .61346 .24038 L .61346 .04808 L F 0 .292 1 r .61346 .04808 m .61346 .24038 L .61442 .24038 L .61442 .04808 L F 0 .286 1 r .61442 .04808 m .61442 .24038 L .61538 .24038 L .61538 .04808 L F 0 .28 1 r .61538 .04808 m .61538 .24038 L .61635 .24038 L .61635 .04808 L F 0 .274 1 r .61635 .04808 m .61635 .24038 L .61731 .24038 L .61731 .04808 L F 0 .268 1 r .61731 .04808 m .61731 .24038 L .61827 .24038 L .61827 .04808 L F 0 .262 1 r .61827 .04808 m .61827 .24038 L .61923 .24038 L .61923 .04808 L F 0 .256 1 r .61923 .04808 m .61923 .24038 L .62019 .24038 L .62019 .04808 L F 0 .25 1 r .62019 .04808 m .62019 .24038 L .62115 .24038 L .62115 .04808 L F 0 .244 1 r .62115 .04808 m .62115 .24038 L .62212 .24038 L .62212 .04808 L F 0 .238 1 r .62212 .04808 m .62212 .24038 L .62308 .24038 L .62308 .04808 L F 0 .232 1 r .62308 .04808 m .62308 .24038 L .62404 .24038 L .62404 .04808 L F 0 .226 1 r .62404 .04808 m .62404 .24038 L .625 .24038 L .625 .04808 L F 0 .22 1 r .625 .04808 m .625 .24038 L .62596 .24038 L .62596 .04808 L F 0 .214 1 r .62596 .04808 m .62596 .24038 L .62692 .24038 L .62692 .04808 L F 0 .208 1 r .62692 .04808 m .62692 .24038 L .62788 .24038 L .62788 .04808 L F 0 .202 1 r .62788 .04808 m .62788 .24038 L .62885 .24038 L .62885 .04808 L F 0 .196 1 r .62885 .04808 m .62885 .24038 L .62981 .24038 L .62981 .04808 L F 0 .19 1 r .62981 .04808 m .62981 .24038 L .63077 .24038 L .63077 .04808 L F 0 .184 1 r .63077 .04808 m .63077 .24038 L .63173 .24038 L .63173 .04808 L F 0 .178 1 r .63173 .04808 m .63173 .24038 L .63269 .24038 L .63269 .04808 L F 0 .172 1 r .63269 .04808 m .63269 .24038 L .63365 .24038 L .63365 .04808 L F 0 .166 1 r .63365 .04808 m .63365 .24038 L .63462 .24038 L .63462 .04808 L F 0 .16 1 r .63462 .04808 m .63462 .24038 L .63558 .24038 L .63558 .04808 L F 0 .154 1 r .63558 .04808 m .63558 .24038 L .63654 .24038 L .63654 .04808 L F 0 .148 1 r .63654 .04808 m .63654 .24038 L .6375 .24038 L .6375 .04808 L F 0 .142 1 r .6375 .04808 m .6375 .24038 L .63846 .24038 L .63846 .04808 L F 0 .136 1 r .63846 .04808 m .63846 .24038 L .63942 .24038 L .63942 .04808 L F 0 .13 1 r .63942 .04808 m .63942 .24038 L .64038 .24038 L .64038 .04808 L F 0 .124 1 r .64038 .04808 m .64038 .24038 L .64135 .24038 L .64135 .04808 L F 0 .118 1 r .64135 .04808 m .64135 .24038 L .64231 .24038 L .64231 .04808 L F 0 .112 1 r .64231 .04808 m .64231 .24038 L .64327 .24038 L .64327 .04808 L F 0 .106 1 r .64327 .04808 m .64327 .24038 L .64423 .24038 L .64423 .04808 L F 0 .1 1 r .64423 .04808 m .64423 .24038 L .64519 .24038 L .64519 .04808 L F 0 .094 1 r .64519 .04808 m .64519 .24038 L .64615 .24038 L .64615 .04808 L F 0 .088 1 r .64615 .04808 m .64615 .24038 L .64712 .24038 L .64712 .04808 L F 0 .082 1 r .64712 .04808 m .64712 .24038 L .64808 .24038 L .64808 .04808 L F 0 .076 1 r .64808 .04808 m .64808 .24038 L .64904 .24038 L .64904 .04808 L F 0 .07 1 r .64904 .04808 m .64904 .24038 L .65 .24038 L .65 .04808 L F 0 .064 1 r .65 .04808 m .65 .24038 L .65096 .24038 L .65096 .04808 L F 0 .058 1 r .65096 .04808 m .65096 .24038 L .65192 .24038 L .65192 .04808 L F 0 .052 1 r .65192 .04808 m .65192 .24038 L .65288 .24038 L .65288 .04808 L F 0 .046 1 r .65288 .04808 m .65288 .24038 L .65385 .24038 L .65385 .04808 L F 0 .04 1 r .65385 .04808 m .65385 .24038 L .65481 .24038 L .65481 .04808 L F 0 .034 1 r .65481 .04808 m .65481 .24038 L .65577 .24038 L .65577 .04808 L F 0 .028 1 r .65577 .04808 m .65577 .24038 L .65673 .24038 L .65673 .04808 L F 0 .022 1 r .65673 .04808 m .65673 .24038 L .65769 .24038 L .65769 .04808 L F 0 .016 1 r .65769 .04808 m .65769 .24038 L .65865 .24038 L .65865 .04808 L F 0 .01 1 r .65865 .04808 m .65865 .24038 L .65962 .24038 L .65962 .04808 L F 0 .004 1 r .65962 .04808 m .65962 .24038 L .66058 .24038 L .66058 .04808 L F .002 0 1 r .66058 .04808 m .66058 .24038 L .66154 .24038 L .66154 .04808 L F .008 0 1 r .66154 .04808 m .66154 .24038 L .6625 .24038 L .6625 .04808 L F .014 0 1 r .6625 .04808 m .6625 .24038 L .66346 .24038 L .66346 .04808 L F .02 0 1 r .66346 .04808 m .66346 .24038 L .66442 .24038 L .66442 .04808 L F .026 0 1 r .66442 .04808 m .66442 .24038 L .66538 .24038 L .66538 .04808 L F .032 0 1 r .66538 .04808 m .66538 .24038 L .66635 .24038 L .66635 .04808 L F .038 0 1 r .66635 .04808 m .66635 .24038 L .66731 .24038 L .66731 .04808 L F .044 0 1 r .66731 .04808 m .66731 .24038 L .66827 .24038 L .66827 .04808 L F .05 0 1 r .66827 .04808 m .66827 .24038 L .66923 .24038 L .66923 .04808 L F .056 0 1 r .66923 .04808 m .66923 .24038 L .67019 .24038 L .67019 .04808 L F .062 0 1 r .67019 .04808 m .67019 .24038 L .67115 .24038 L .67115 .04808 L F .068 0 1 r .67115 .04808 m .67115 .24038 L .67212 .24038 L .67212 .04808 L F .074 0 1 r .67212 .04808 m .67212 .24038 L .67308 .24038 L .67308 .04808 L F .08 0 1 r .67308 .04808 m .67308 .24038 L .67404 .24038 L .67404 .04808 L F .086 0 1 r .67404 .04808 m .67404 .24038 L .675 .24038 L .675 .04808 L F .092 0 1 r .675 .04808 m .675 .24038 L .67596 .24038 L .67596 .04808 L F .098 0 1 r .67596 .04808 m .67596 .24038 L .67692 .24038 L .67692 .04808 L F .104 0 1 r .67692 .04808 m .67692 .24038 L .67788 .24038 L .67788 .04808 L F .11 0 1 r .67788 .04808 m .67788 .24038 L .67885 .24038 L .67885 .04808 L F .116 0 1 r .67885 .04808 m .67885 .24038 L .67981 .24038 L .67981 .04808 L F .122 0 1 r .67981 .04808 m .67981 .24038 L .68077 .24038 L .68077 .04808 L F .128 0 1 r .68077 .04808 m .68077 .24038 L .68173 .24038 L .68173 .04808 L F .134 0 1 r .68173 .04808 m .68173 .24038 L .68269 .24038 L .68269 .04808 L F .14 0 1 r .68269 .04808 m .68269 .24038 L .68365 .24038 L .68365 .04808 L F .146 0 1 r .68365 .04808 m .68365 .24038 L .68462 .24038 L .68462 .04808 L F .152 0 1 r .68462 .04808 m .68462 .24038 L .68558 .24038 L .68558 .04808 L F .158 0 1 r .68558 .04808 m .68558 .24038 L .68654 .24038 L .68654 .04808 L F .164 0 1 r .68654 .04808 m .68654 .24038 L .6875 .24038 L .6875 .04808 L F .17 0 1 r .6875 .04808 m .6875 .24038 L .68846 .24038 L .68846 .04808 L F .176 0 1 r .68846 .04808 m .68846 .24038 L .68942 .24038 L .68942 .04808 L F .182 0 1 r .68942 .04808 m .68942 .24038 L .69038 .24038 L .69038 .04808 L F .188 0 1 r .69038 .04808 m .69038 .24038 L .69135 .24038 L .69135 .04808 L F .194 0 1 r .69135 .04808 m .69135 .24038 L .69231 .24038 L .69231 .04808 L F .2 0 1 r .69231 .04808 m .69231 .24038 L .69327 .24038 L .69327 .04808 L F .206 0 1 r .69327 .04808 m .69327 .24038 L .69423 .24038 L .69423 .04808 L F .212 0 1 r .69423 .04808 m .69423 .24038 L .69519 .24038 L .69519 .04808 L F .218 0 1 r .69519 .04808 m .69519 .24038 L .69615 .24038 L .69615 .04808 L F .224 0 1 r .69615 .04808 m .69615 .24038 L .69712 .24038 L .69712 .04808 L F .23 0 1 r .69712 .04808 m .69712 .24038 L .69808 .24038 L .69808 .04808 L F .236 0 1 r .69808 .04808 m .69808 .24038 L .69904 .24038 L .69904 .04808 L F .242 0 1 r .69904 .04808 m .69904 .24038 L .7 .24038 L .7 .04808 L F .248 0 1 r .7 .04808 m .7 .24038 L .70096 .24038 L .70096 .04808 L F .254 0 1 r .70096 .04808 m .70096 .24038 L .70192 .24038 L .70192 .04808 L F .26 0 1 r .70192 .04808 m .70192 .24038 L .70288 .24038 L .70288 .04808 L F .266 0 1 r .70288 .04808 m .70288 .24038 L .70385 .24038 L .70385 .04808 L F .272 0 1 r .70385 .04808 m .70385 .24038 L .70481 .24038 L .70481 .04808 L F .278 0 1 r .70481 .04808 m .70481 .24038 L .70577 .24038 L .70577 .04808 L F .284 0 1 r .70577 .04808 m .70577 .24038 L .70673 .24038 L .70673 .04808 L F .29 0 1 r .70673 .04808 m .70673 .24038 L .70769 .24038 L .70769 .04808 L F .296 0 1 r .70769 .04808 m .70769 .24038 L .70865 .24038 L .70865 .04808 L F .302 0 1 r .70865 .04808 m .70865 .24038 L .70962 .24038 L .70962 .04808 L F .308 0 1 r .70962 .04808 m .70962 .24038 L .71058 .24038 L .71058 .04808 L F .314 0 1 r .71058 .04808 m .71058 .24038 L .71154 .24038 L .71154 .04808 L F .32 0 1 r .71154 .04808 m .71154 .24038 L .7125 .24038 L .7125 .04808 L F .326 0 1 r .7125 .04808 m .7125 .24038 L .71346 .24038 L .71346 .04808 L F .332 0 1 r .71346 .04808 m .71346 .24038 L .71442 .24038 L .71442 .04808 L F .338 0 1 r .71442 .04808 m .71442 .24038 L .71538 .24038 L .71538 .04808 L F .344 0 1 r .71538 .04808 m .71538 .24038 L .71635 .24038 L .71635 .04808 L F .35 0 1 r .71635 .04808 m .71635 .24038 L .71731 .24038 L .71731 .04808 L F .356 0 1 r .71731 .04808 m .71731 .24038 L .71827 .24038 L .71827 .04808 L F .362 0 1 r .71827 .04808 m .71827 .24038 L .71923 .24038 L .71923 .04808 L F .368 0 1 r .71923 .04808 m .71923 .24038 L .72019 .24038 L .72019 .04808 L F .374 0 1 r .72019 .04808 m .72019 .24038 L .72115 .24038 L .72115 .04808 L F .38 0 1 r .72115 .04808 m .72115 .24038 L .72212 .24038 L .72212 .04808 L F .386 0 1 r .72212 .04808 m .72212 .24038 L .72308 .24038 L .72308 .04808 L F .392 0 1 r .72308 .04808 m .72308 .24038 L .72404 .24038 L .72404 .04808 L F .398 0 1 r .72404 .04808 m .72404 .24038 L .725 .24038 L .725 .04808 L F .404 0 1 r .725 .04808 m .725 .24038 L .72596 .24038 L .72596 .04808 L F .41 0 1 r .72596 .04808 m .72596 .24038 L .72692 .24038 L .72692 .04808 L F .416 0 1 r .72692 .04808 m .72692 .24038 L .72788 .24038 L .72788 .04808 L F .422 0 1 r .72788 .04808 m .72788 .24038 L .72885 .24038 L .72885 .04808 L F .428 0 1 r .72885 .04808 m .72885 .24038 L .72981 .24038 L .72981 .04808 L F .434 0 1 r .72981 .04808 m .72981 .24038 L .73077 .24038 L .73077 .04808 L F .44 0 1 r .73077 .04808 m .73077 .24038 L .73173 .24038 L .73173 .04808 L F .446 0 1 r .73173 .04808 m .73173 .24038 L .73269 .24038 L .73269 .04808 L F .452 0 1 r .73269 .04808 m .73269 .24038 L .73365 .24038 L .73365 .04808 L F .458 0 1 r .73365 .04808 m .73365 .24038 L .73462 .24038 L .73462 .04808 L F .464 0 1 r .73462 .04808 m .73462 .24038 L .73558 .24038 L .73558 .04808 L F .47 0 1 r .73558 .04808 m .73558 .24038 L .73654 .24038 L .73654 .04808 L F .476 0 1 r .73654 .04808 m .73654 .24038 L .7375 .24038 L .7375 .04808 L F .482 0 1 r .7375 .04808 m .7375 .24038 L .73846 .24038 L .73846 .04808 L F .488 0 1 r .73846 .04808 m .73846 .24038 L .73942 .24038 L .73942 .04808 L F .494 0 1 r .73942 .04808 m .73942 .24038 L .74038 .24038 L .74038 .04808 L F .5 0 1 r .74038 .04808 m .74038 .24038 L .74135 .24038 L .74135 .04808 L F .506 0 1 r .74135 .04808 m .74135 .24038 L .74231 .24038 L .74231 .04808 L F .512 0 1 r .74231 .04808 m .74231 .24038 L .74327 .24038 L .74327 .04808 L F .518 0 1 r .74327 .04808 m .74327 .24038 L .74423 .24038 L .74423 .04808 L F .524 0 1 r .74423 .04808 m .74423 .24038 L .74519 .24038 L .74519 .04808 L F .53 0 1 r .74519 .04808 m .74519 .24038 L .74615 .24038 L .74615 .04808 L F .536 0 1 r .74615 .04808 m .74615 .24038 L .74712 .24038 L .74712 .04808 L F .542 0 1 r .74712 .04808 m .74712 .24038 L .74808 .24038 L .74808 .04808 L F .548 0 1 r .74808 .04808 m .74808 .24038 L .74904 .24038 L .74904 .04808 L F .554 0 1 r .74904 .04808 m .74904 .24038 L .75 .24038 L .75 .04808 L F .56 0 1 r .75 .04808 m .75 .24038 L .75096 .24038 L .75096 .04808 L F .566 0 1 r .75096 .04808 m .75096 .24038 L .75192 .24038 L .75192 .04808 L F .572 0 1 r .75192 .04808 m .75192 .24038 L .75288 .24038 L .75288 .04808 L F .578 0 1 r .75288 .04808 m .75288 .24038 L .75385 .24038 L .75385 .04808 L F .584 0 1 r .75385 .04808 m .75385 .24038 L .75481 .24038 L .75481 .04808 L F .59 0 1 r .75481 .04808 m .75481 .24038 L .75577 .24038 L .75577 .04808 L F .596 0 1 r .75577 .04808 m .75577 .24038 L .75673 .24038 L .75673 .04808 L F .602 0 1 r .75673 .04808 m .75673 .24038 L .75769 .24038 L .75769 .04808 L F .608 0 1 r .75769 .04808 m .75769 .24038 L .75865 .24038 L .75865 .04808 L F .614 0 1 r .75865 .04808 m .75865 .24038 L .75962 .24038 L .75962 .04808 L F .62 0 1 r .75962 .04808 m .75962 .24038 L .76058 .24038 L .76058 .04808 L F .626 0 1 r .76058 .04808 m .76058 .24038 L .76154 .24038 L .76154 .04808 L F .632 0 1 r .76154 .04808 m .76154 .24038 L .7625 .24038 L .7625 .04808 L F .638 0 1 r .7625 .04808 m .7625 .24038 L .76346 .24038 L .76346 .04808 L F .644 0 1 r .76346 .04808 m .76346 .24038 L .76442 .24038 L .76442 .04808 L F .65 0 1 r .76442 .04808 m .76442 .24038 L .76538 .24038 L .76538 .04808 L F .656 0 1 r .76538 .04808 m .76538 .24038 L .76635 .24038 L .76635 .04808 L F .662 0 1 r .76635 .04808 m .76635 .24038 L .76731 .24038 L .76731 .04808 L F .668 0 1 r .76731 .04808 m .76731 .24038 L .76827 .24038 L .76827 .04808 L F .674 0 1 r .76827 .04808 m .76827 .24038 L .76923 .24038 L .76923 .04808 L F .68 0 1 r .76923 .04808 m .76923 .24038 L .77019 .24038 L .77019 .04808 L F .686 0 1 r .77019 .04808 m .77019 .24038 L .77115 .24038 L .77115 .04808 L F .692 0 1 r .77115 .04808 m .77115 .24038 L .77212 .24038 L .77212 .04808 L F .698 0 1 r .77212 .04808 m .77212 .24038 L .77308 .24038 L .77308 .04808 L F .704 0 1 r .77308 .04808 m .77308 .24038 L .77404 .24038 L .77404 .04808 L F .71 0 1 r .77404 .04808 m .77404 .24038 L .775 .24038 L .775 .04808 L F .716 0 1 r .775 .04808 m .775 .24038 L .77596 .24038 L .77596 .04808 L F .722 0 1 r .77596 .04808 m .77596 .24038 L .77692 .24038 L .77692 .04808 L F .728 0 1 r .77692 .04808 m .77692 .24038 L .77788 .24038 L .77788 .04808 L F .734 0 1 r .77788 .04808 m .77788 .24038 L .77885 .24038 L .77885 .04808 L F .74 0 1 r .77885 .04808 m .77885 .24038 L .77981 .24038 L .77981 .04808 L F .746 0 1 r .77981 .04808 m .77981 .24038 L .78077 .24038 L .78077 .04808 L F .752 0 1 r .78077 .04808 m .78077 .24038 L .78173 .24038 L .78173 .04808 L F .758 0 1 r .78173 .04808 m .78173 .24038 L .78269 .24038 L .78269 .04808 L F .764 0 1 r .78269 .04808 m .78269 .24038 L .78365 .24038 L .78365 .04808 L F .77 0 1 r .78365 .04808 m .78365 .24038 L .78462 .24038 L .78462 .04808 L F .776 0 1 r .78462 .04808 m .78462 .24038 L .78558 .24038 L .78558 .04808 L F .782 0 1 r .78558 .04808 m .78558 .24038 L .78654 .24038 L .78654 .04808 L F .788 0 1 r .78654 .04808 m .78654 .24038 L .7875 .24038 L .7875 .04808 L F .794 0 1 r .7875 .04808 m .7875 .24038 L .78846 .24038 L .78846 .04808 L F .8 0 1 r .78846 .04808 m .78846 .24038 L .78942 .24038 L .78942 .04808 L F .806 0 1 r .78942 .04808 m .78942 .24038 L .79038 .24038 L .79038 .04808 L F .812 0 1 r .79038 .04808 m .79038 .24038 L .79135 .24038 L .79135 .04808 L F .818 0 1 r .79135 .04808 m .79135 .24038 L .79231 .24038 L .79231 .04808 L F .824 0 1 r .79231 .04808 m .79231 .24038 L .79327 .24038 L .79327 .04808 L F .83 0 1 r .79327 .04808 m .79327 .24038 L .79423 .24038 L .79423 .04808 L F .836 0 1 r .79423 .04808 m .79423 .24038 L .79519 .24038 L .79519 .04808 L F .842 0 1 r .79519 .04808 m .79519 .24038 L .79615 .24038 L .79615 .04808 L F .848 0 1 r .79615 .04808 m .79615 .24038 L .79712 .24038 L .79712 .04808 L F .854 0 1 r .79712 .04808 m .79712 .24038 L .79808 .24038 L .79808 .04808 L F .86 0 1 r .79808 .04808 m .79808 .24038 L .79904 .24038 L .79904 .04808 L F .866 0 1 r .79904 .04808 m .79904 .24038 L .8 .24038 L .8 .04808 L F .872 0 1 r .8 .04808 m .8 .24038 L .80096 .24038 L .80096 .04808 L F .878 0 1 r .80096 .04808 m .80096 .24038 L .80192 .24038 L .80192 .04808 L F .884 0 1 r .80192 .04808 m .80192 .24038 L .80288 .24038 L .80288 .04808 L F .89 0 1 r .80288 .04808 m .80288 .24038 L .80385 .24038 L .80385 .04808 L F .896 0 1 r .80385 .04808 m .80385 .24038 L .80481 .24038 L .80481 .04808 L F .902 0 1 r .80481 .04808 m .80481 .24038 L .80577 .24038 L .80577 .04808 L F .908 0 1 r .80577 .04808 m .80577 .24038 L .80673 .24038 L .80673 .04808 L F .914 0 1 r .80673 .04808 m .80673 .24038 L .80769 .24038 L .80769 .04808 L F .92 0 1 r .80769 .04808 m .80769 .24038 L .80865 .24038 L .80865 .04808 L F .926 0 1 r .80865 .04808 m .80865 .24038 L .80962 .24038 L .80962 .04808 L F .932 0 1 r .80962 .04808 m .80962 .24038 L .81058 .24038 L .81058 .04808 L F .938 0 1 r .81058 .04808 m .81058 .24038 L .81154 .24038 L .81154 .04808 L F .944 0 1 r .81154 .04808 m .81154 .24038 L .8125 .24038 L .8125 .04808 L F .95 0 1 r .8125 .04808 m .8125 .24038 L .81346 .24038 L .81346 .04808 L F .956 0 1 r .81346 .04808 m .81346 .24038 L .81442 .24038 L .81442 .04808 L F .962 0 1 r .81442 .04808 m .81442 .24038 L .81538 .24038 L .81538 .04808 L F .968 0 1 r .81538 .04808 m .81538 .24038 L .81635 .24038 L .81635 .04808 L F .974 0 1 r .81635 .04808 m .81635 .24038 L .81731 .24038 L .81731 .04808 L F .98 0 1 r .81731 .04808 m .81731 .24038 L .81827 .24038 L .81827 .04808 L F .986 0 1 r .81827 .04808 m .81827 .24038 L .81923 .24038 L .81923 .04808 L F .992 0 1 r .81923 .04808 m .81923 .24038 L .82019 .24038 L .82019 .04808 L F .998 0 1 r .82019 .04808 m .82019 .24038 L .82115 .24038 L .82115 .04808 L F 1 0 .996 r .82115 .04808 m .82115 .24038 L .82212 .24038 L .82212 .04808 L F 1 0 .99 r .82212 .04808 m .82212 .24038 L .82308 .24038 L .82308 .04808 L F 1 0 .984 r .82308 .04808 m .82308 .24038 L .82404 .24038 L .82404 .04808 L F 1 0 .978 r .82404 .04808 m .82404 .24038 L .825 .24038 L .825 .04808 L F 1 0 .972 r .825 .04808 m .825 .24038 L .82596 .24038 L .82596 .04808 L F 1 0 .966 r .82596 .04808 m .82596 .24038 L .82692 .24038 L .82692 .04808 L F 1 0 .96 r .82692 .04808 m .82692 .24038 L .82788 .24038 L .82788 .04808 L F 1 0 .954 r .82788 .04808 m .82788 .24038 L .82885 .24038 L .82885 .04808 L F 1 0 .948 r .82885 .04808 m .82885 .24038 L .82981 .24038 L .82981 .04808 L F 1 0 .942 r .82981 .04808 m .82981 .24038 L .83077 .24038 L .83077 .04808 L F 1 0 .936 r .83077 .04808 m .83077 .24038 L .83173 .24038 L .83173 .04808 L F 1 0 .93 r .83173 .04808 m .83173 .24038 L .83269 .24038 L .83269 .04808 L F 1 0 .924 r .83269 .04808 m .83269 .24038 L .83365 .24038 L .83365 .04808 L F 1 0 .918 r .83365 .04808 m .83365 .24038 L .83462 .24038 L .83462 .04808 L F 1 0 .912 r .83462 .04808 m .83462 .24038 L .83558 .24038 L .83558 .04808 L F 1 0 .906 r .83558 .04808 m .83558 .24038 L .83654 .24038 L .83654 .04808 L F 1 0 .9 r .83654 .04808 m .83654 .24038 L .8375 .24038 L .8375 .04808 L F 1 0 .894 r .8375 .04808 m .8375 .24038 L .83846 .24038 L .83846 .04808 L F 1 0 .888 r .83846 .04808 m .83846 .24038 L .83942 .24038 L .83942 .04808 L F 1 0 .882 r .83942 .04808 m .83942 .24038 L .84038 .24038 L .84038 .04808 L F 1 0 .876 r .84038 .04808 m .84038 .24038 L .84135 .24038 L .84135 .04808 L F 1 0 .87 r .84135 .04808 m .84135 .24038 L .84231 .24038 L .84231 .04808 L F 1 0 .864 r .84231 .04808 m .84231 .24038 L .84327 .24038 L .84327 .04808 L F 1 0 .858 r .84327 .04808 m .84327 .24038 L .84423 .24038 L .84423 .04808 L F 1 0 .852 r .84423 .04808 m .84423 .24038 L .84519 .24038 L .84519 .04808 L F 1 0 .846 r .84519 .04808 m .84519 .24038 L .84615 .24038 L .84615 .04808 L F 1 0 .84 r .84615 .04808 m .84615 .24038 L .84712 .24038 L .84712 .04808 L F 1 0 .834 r .84712 .04808 m .84712 .24038 L .84808 .24038 L .84808 .04808 L F 1 0 .828 r .84808 .04808 m .84808 .24038 L .84904 .24038 L .84904 .04808 L F 1 0 .822 r .84904 .04808 m .84904 .24038 L .85 .24038 L .85 .04808 L F 1 0 .816 r .85 .04808 m .85 .24038 L .85096 .24038 L .85096 .04808 L F 1 0 .81 r .85096 .04808 m .85096 .24038 L .85192 .24038 L .85192 .04808 L F 1 0 .804 r .85192 .04808 m .85192 .24038 L .85288 .24038 L .85288 .04808 L F 1 0 .798 r .85288 .04808 m .85288 .24038 L .85385 .24038 L .85385 .04808 L F 1 0 .792 r .85385 .04808 m .85385 .24038 L .85481 .24038 L .85481 .04808 L F 1 0 .786 r .85481 .04808 m .85481 .24038 L .85577 .24038 L .85577 .04808 L F 1 0 .78 r .85577 .04808 m .85577 .24038 L .85673 .24038 L .85673 .04808 L F 1 0 .774 r .85673 .04808 m .85673 .24038 L .85769 .24038 L .85769 .04808 L F 1 0 .768 r .85769 .04808 m .85769 .24038 L .85865 .24038 L .85865 .04808 L F 1 0 .762 r .85865 .04808 m .85865 .24038 L .85962 .24038 L .85962 .04808 L F 1 0 .756 r .85962 .04808 m .85962 .24038 L .86058 .24038 L .86058 .04808 L F 1 0 .75 r .86058 .04808 m .86058 .24038 L .86154 .24038 L .86154 .04808 L F 1 0 .744 r .86154 .04808 m .86154 .24038 L .8625 .24038 L .8625 .04808 L F 1 0 .738 r .8625 .04808 m .8625 .24038 L .86346 .24038 L .86346 .04808 L F 1 0 .732 r .86346 .04808 m .86346 .24038 L .86442 .24038 L .86442 .04808 L F 1 0 .726 r .86442 .04808 m .86442 .24038 L .86538 .24038 L .86538 .04808 L F 1 0 .72 r .86538 .04808 m .86538 .24038 L .86635 .24038 L .86635 .04808 L F 1 0 .714 r .86635 .04808 m .86635 .24038 L .86731 .24038 L .86731 .04808 L F 1 0 .708 r .86731 .04808 m .86731 .24038 L .86827 .24038 L .86827 .04808 L F 1 0 .702 r .86827 .04808 m .86827 .24038 L .86923 .24038 L .86923 .04808 L F 1 0 .696 r .86923 .04808 m .86923 .24038 L .87019 .24038 L .87019 .04808 L F 1 0 .69 r .87019 .04808 m .87019 .24038 L .87115 .24038 L .87115 .04808 L F 1 0 .684 r .87115 .04808 m .87115 .24038 L .87212 .24038 L .87212 .04808 L F 1 0 .678 r .87212 .04808 m .87212 .24038 L .87308 .24038 L .87308 .04808 L F 1 0 .672 r .87308 .04808 m .87308 .24038 L .87404 .24038 L .87404 .04808 L F 1 0 .666 r .87404 .04808 m .87404 .24038 L .875 .24038 L .875 .04808 L F 1 0 .66 r .875 .04808 m .875 .24038 L .87596 .24038 L .87596 .04808 L F 1 0 .654 r .87596 .04808 m .87596 .24038 L .87692 .24038 L .87692 .04808 L F 1 0 .648 r .87692 .04808 m .87692 .24038 L .87788 .24038 L .87788 .04808 L F 1 0 .642 r .87788 .04808 m .87788 .24038 L .87885 .24038 L .87885 .04808 L F 1 0 .636 r .87885 .04808 m .87885 .24038 L .87981 .24038 L .87981 .04808 L F 1 0 .63 r .87981 .04808 m .87981 .24038 L .88077 .24038 L .88077 .04808 L F 1 0 .624 r .88077 .04808 m .88077 .24038 L .88173 .24038 L .88173 .04808 L F 1 0 .618 r .88173 .04808 m .88173 .24038 L .88269 .24038 L .88269 .04808 L F 1 0 .612 r .88269 .04808 m .88269 .24038 L .88365 .24038 L .88365 .04808 L F 1 0 .606 r .88365 .04808 m .88365 .24038 L .88462 .24038 L .88462 .04808 L F 1 0 .6 r .88462 .04808 m .88462 .24038 L .88558 .24038 L .88558 .04808 L F 1 0 .594 r .88558 .04808 m .88558 .24038 L .88654 .24038 L .88654 .04808 L F 1 0 .588 r .88654 .04808 m .88654 .24038 L .8875 .24038 L .8875 .04808 L F 1 0 .582 r .8875 .04808 m .8875 .24038 L .88846 .24038 L .88846 .04808 L F 1 0 .576 r .88846 .04808 m .88846 .24038 L .88942 .24038 L .88942 .04808 L F 1 0 .57 r .88942 .04808 m .88942 .24038 L .89038 .24038 L .89038 .04808 L F 1 0 .564 r .89038 .04808 m .89038 .24038 L .89135 .24038 L .89135 .04808 L F 1 0 .558 r .89135 .04808 m .89135 .24038 L .89231 .24038 L .89231 .04808 L F 1 0 .552 r .89231 .04808 m .89231 .24038 L .89327 .24038 L .89327 .04808 L F 1 0 .546 r .89327 .04808 m .89327 .24038 L .89423 .24038 L .89423 .04808 L F 1 0 .54 r .89423 .04808 m .89423 .24038 L .89519 .24038 L .89519 .04808 L F 1 0 .534 r .89519 .04808 m .89519 .24038 L .89615 .24038 L .89615 .04808 L F 1 0 .528 r .89615 .04808 m .89615 .24038 L .89712 .24038 L .89712 .04808 L F 1 0 .522 r .89712 .04808 m .89712 .24038 L .89808 .24038 L .89808 .04808 L F 1 0 .516 r .89808 .04808 m .89808 .24038 L .89904 .24038 L .89904 .04808 L F 1 0 .51 r .89904 .04808 m .89904 .24038 L .9 .24038 L .9 .04808 L F 1 0 .504 r .9 .04808 m .9 .24038 L .90096 .24038 L .90096 .04808 L F 1 0 .498 r .90096 .04808 m .90096 .24038 L .90192 .24038 L .90192 .04808 L F 1 0 .492 r .90192 .04808 m .90192 .24038 L .90288 .24038 L .90288 .04808 L F 1 0 .486 r .90288 .04808 m .90288 .24038 L .90385 .24038 L .90385 .04808 L F 1 0 .48 r .90385 .04808 m .90385 .24038 L .90481 .24038 L .90481 .04808 L F 1 0 .474 r .90481 .04808 m .90481 .24038 L .90577 .24038 L .90577 .04808 L F 1 0 .468 r .90577 .04808 m .90577 .24038 L .90673 .24038 L .90673 .04808 L F 1 0 .462 r .90673 .04808 m .90673 .24038 L .90769 .24038 L .90769 .04808 L F 1 0 .456 r .90769 .04808 m .90769 .24038 L .90865 .24038 L .90865 .04808 L F 1 0 .45 r .90865 .04808 m .90865 .24038 L .90962 .24038 L .90962 .04808 L F 1 0 .444 r .90962 .04808 m .90962 .24038 L .91058 .24038 L .91058 .04808 L F 1 0 .438 r .91058 .04808 m .91058 .24038 L .91154 .24038 L .91154 .04808 L F 1 0 .432 r .91154 .04808 m .91154 .24038 L .9125 .24038 L .9125 .04808 L F 1 0 .426 r .9125 .04808 m .9125 .24038 L .91346 .24038 L .91346 .04808 L F 1 0 .42 r .91346 .04808 m .91346 .24038 L .91442 .24038 L .91442 .04808 L F 1 0 .414 r .91442 .04808 m .91442 .24038 L .91538 .24038 L .91538 .04808 L F 1 0 .408 r .91538 .04808 m .91538 .24038 L .91635 .24038 L .91635 .04808 L F 1 0 .402 r .91635 .04808 m .91635 .24038 L .91731 .24038 L .91731 .04808 L F 1 0 .396 r .91731 .04808 m .91731 .24038 L .91827 .24038 L .91827 .04808 L F 1 0 .39 r .91827 .04808 m .91827 .24038 L .91923 .24038 L .91923 .04808 L F 1 0 .384 r .91923 .04808 m .91923 .24038 L .92019 .24038 L .92019 .04808 L F 1 0 .378 r .92019 .04808 m .92019 .24038 L .92115 .24038 L .92115 .04808 L F 1 0 .372 r .92115 .04808 m .92115 .24038 L .92212 .24038 L .92212 .04808 L F 1 0 .366 r .92212 .04808 m .92212 .24038 L .92308 .24038 L .92308 .04808 L F 1 0 .36 r .92308 .04808 m .92308 .24038 L .92404 .24038 L .92404 .04808 L F 1 0 .354 r .92404 .04808 m .92404 .24038 L .925 .24038 L .925 .04808 L F 1 0 .348 r .925 .04808 m .925 .24038 L .92596 .24038 L .92596 .04808 L F 1 0 .342 r .92596 .04808 m .92596 .24038 L .92692 .24038 L .92692 .04808 L F 1 0 .336 r .92692 .04808 m .92692 .24038 L .92788 .24038 L .92788 .04808 L F 1 0 .33 r .92788 .04808 m .92788 .24038 L .92885 .24038 L .92885 .04808 L F 1 0 .324 r .92885 .04808 m .92885 .24038 L .92981 .24038 L .92981 .04808 L F 1 0 .318 r .92981 .04808 m .92981 .24038 L .93077 .24038 L .93077 .04808 L F 1 0 .312 r .93077 .04808 m .93077 .24038 L .93173 .24038 L .93173 .04808 L F 1 0 .306 r .93173 .04808 m .93173 .24038 L .93269 .24038 L .93269 .04808 L F 1 0 .3 r .93269 .04808 m .93269 .24038 L .93365 .24038 L .93365 .04808 L F 1 0 .294 r .93365 .04808 m .93365 .24038 L .93462 .24038 L .93462 .04808 L F 1 0 .288 r .93462 .04808 m .93462 .24038 L .93558 .24038 L .93558 .04808 L F 1 0 .282 r .93558 .04808 m .93558 .24038 L .93654 .24038 L .93654 .04808 L F 1 0 .276 r .93654 .04808 m .93654 .24038 L .9375 .24038 L .9375 .04808 L F 1 0 .27 r .9375 .04808 m .9375 .24038 L .93846 .24038 L .93846 .04808 L F 1 0 .264 r .93846 .04808 m .93846 .24038 L .93942 .24038 L .93942 .04808 L F 1 0 .258 r .93942 .04808 m .93942 .24038 L .94038 .24038 L .94038 .04808 L F 1 0 .252 r .94038 .04808 m .94038 .24038 L .94135 .24038 L .94135 .04808 L F 1 0 .246 r .94135 .04808 m .94135 .24038 L .94231 .24038 L .94231 .04808 L F 1 0 .24 r .94231 .04808 m .94231 .24038 L .94327 .24038 L .94327 .04808 L F 1 0 .234 r .94327 .04808 m .94327 .24038 L .94423 .24038 L .94423 .04808 L F 1 0 .228 r .94423 .04808 m .94423 .24038 L .94519 .24038 L .94519 .04808 L F 1 0 .222 r .94519 .04808 m .94519 .24038 L .94615 .24038 L .94615 .04808 L F 1 0 .216 r .94615 .04808 m .94615 .24038 L .94712 .24038 L .94712 .04808 L F 1 0 .21 r .94712 .04808 m .94712 .24038 L .94808 .24038 L .94808 .04808 L F 1 0 .204 r .94808 .04808 m .94808 .24038 L .94904 .24038 L .94904 .04808 L F 1 0 .198 r .94904 .04808 m .94904 .24038 L .95 .24038 L .95 .04808 L F 1 0 .192 r .95 .04808 m .95 .24038 L .95096 .24038 L .95096 .04808 L F 1 0 .186 r .95096 .04808 m .95096 .24038 L .95192 .24038 L .95192 .04808 L F 1 0 .18 r .95192 .04808 m .95192 .24038 L .95288 .24038 L .95288 .04808 L F 1 0 .174 r .95288 .04808 m .95288 .24038 L .95385 .24038 L .95385 .04808 L F 1 0 .168 r .95385 .04808 m .95385 .24038 L .95481 .24038 L .95481 .04808 L F 1 0 .162 r .95481 .04808 m .95481 .24038 L .95577 .24038 L .95577 .04808 L F 1 0 .156 r .95577 .04808 m .95577 .24038 L .95673 .24038 L .95673 .04808 L F 1 0 .15 r .95673 .04808 m .95673 .24038 L .95769 .24038 L .95769 .04808 L F 1 0 .144 r .95769 .04808 m .95769 .24038 L .95865 .24038 L .95865 .04808 L F 1 0 .138 r .95865 .04808 m .95865 .24038 L .95962 .24038 L .95962 .04808 L F 1 0 .132 r .95962 .04808 m .95962 .24038 L .96058 .24038 L .96058 .04808 L F 1 0 .126 r .96058 .04808 m .96058 .24038 L .96154 .24038 L .96154 .04808 L F 1 0 .12 r .96154 .04808 m .96154 .24038 L .9625 .24038 L .9625 .04808 L F 1 0 .114 r .9625 .04808 m .9625 .24038 L .96346 .24038 L .96346 .04808 L F 1 0 .108 r .96346 .04808 m .96346 .24038 L .96442 .24038 L .96442 .04808 L F 1 0 .102 r .96442 .04808 m .96442 .24038 L .96538 .24038 L .96538 .04808 L F 1 0 .096 r .96538 .04808 m .96538 .24038 L .96635 .24038 L .96635 .04808 L F 1 0 .09 r .96635 .04808 m .96635 .24038 L .96731 .24038 L .96731 .04808 L F 1 0 .084 r .96731 .04808 m .96731 .24038 L .96827 .24038 L .96827 .04808 L F 1 0 .078 r .96827 .04808 m .96827 .24038 L .96923 .24038 L .96923 .04808 L F 1 0 .072 r .96923 .04808 m .96923 .24038 L .97019 .24038 L .97019 .04808 L F 1 0 .066 r .97019 .04808 m .97019 .24038 L .97115 .24038 L .97115 .04808 L F 1 0 .06 r .97115 .04808 m .97115 .24038 L .97212 .24038 L .97212 .04808 L F 1 0 .054 r .97212 .04808 m .97212 .24038 L .97308 .24038 L .97308 .04808 L F 1 0 .048 r .97308 .04808 m .97308 .24038 L .97404 .24038 L .97404 .04808 L F 1 0 .042 r .97404 .04808 m .97404 .24038 L .975 .24038 L .975 .04808 L F 1 0 .036 r .975 .04808 m .975 .24038 L .97596 .24038 L .97596 .04808 L F 1 0 .03 r .97596 .04808 m .97596 .24038 L .97692 .24038 L .97692 .04808 L F 1 0 .024 r .97692 .04808 m .97692 .24038 L .97788 .24038 L .97788 .04808 L F 1 0 .018 r .97788 .04808 m .97788 .24038 L .97885 .24038 L .97885 .04808 L F 1 0 .012 r .97885 .04808 m .97885 .24038 L .97981 .24038 L .97981 .04808 L F 1 0 .006 r .97981 .04808 m .97981 .24038 L .98077 .24038 L .98077 .04808 L F 1 0 0 r .98077 .04808 m .98077 .24038 L .98173 .24038 L .98173 .04808 L F 0 g .5 Mabswid [ ] 0 setdash .01923 .04808 m .01923 .0625 L s .11538 .04808 m .11538 .0625 L s .21154 .04808 m .21154 .0625 L s .30769 .04808 m .30769 .0625 L s .40385 .04808 m .40385 .0625 L s .5 .04808 m .5 .0625 L s .59615 .04808 m .59615 .0625 L s .69231 .04808 m .69231 .0625 L s .78846 .04808 m .78846 .0625 L s .88462 .04808 m .88462 .0625 L s .98077 .04808 m .98077 .0625 L s .5 .04808 m .5 .08173 L s .01923 .04808 m .01923 .08173 L s .98077 .04808 m .98077 .08173 L s gsave .01923 .01923 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .98077 .01923 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.522676 0.00327054 0.97619 0.134092 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0192308 0.961538 0.0480769 0.961538 [ [ 0 0 0 0 ] [ 1 .28846 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .28846 L 0 .28846 L closepath clip newpath 0 g .01923 .04808 m .01923 .24038 L .02019 .24038 L .02019 .04808 L F .001 g .02019 .04808 m .02019 .24038 L .02115 .24038 L .02115 .04808 L F .002 g .02115 .04808 m .02115 .24038 L .02212 .24038 L .02212 .04808 L F .003 g .02212 .04808 m .02212 .24038 L .02308 .24038 L .02308 .04808 L F .004 g .02308 .04808 m .02308 .24038 L .02404 .24038 L .02404 .04808 L F .005 g .02404 .04808 m .02404 .24038 L .025 .24038 L .025 .04808 L F .006 g .025 .04808 m .025 .24038 L .02596 .24038 L .02596 .04808 L F .007 g .02596 .04808 m .02596 .24038 L .02692 .24038 L .02692 .04808 L F .008 g .02692 .04808 m .02692 .24038 L .02788 .24038 L .02788 .04808 L F .009 g .02788 .04808 m .02788 .24038 L .02885 .24038 L .02885 .04808 L F .01 g .02885 .04808 m .02885 .24038 L .02981 .24038 L .02981 .04808 L F .011 g .02981 .04808 m .02981 .24038 L .03077 .24038 L .03077 .04808 L F .012 g .03077 .04808 m .03077 .24038 L .03173 .24038 L .03173 .04808 L F .013 g .03173 .04808 m .03173 .24038 L .03269 .24038 L .03269 .04808 L F .014 g .03269 .04808 m .03269 .24038 L .03365 .24038 L .03365 .04808 L F .015 g .03365 .04808 m .03365 .24038 L .03462 .24038 L .03462 .04808 L F .016 g .03462 .04808 m .03462 .24038 L .03558 .24038 L .03558 .04808 L F .017 g .03558 .04808 m .03558 .24038 L .03654 .24038 L .03654 .04808 L F .018 g .03654 .04808 m .03654 .24038 L .0375 .24038 L .0375 .04808 L F .019 g .0375 .04808 m .0375 .24038 L .03846 .24038 L .03846 .04808 L F .02 g .03846 .04808 m .03846 .24038 L .03942 .24038 L .03942 .04808 L F .021 g .03942 .04808 m .03942 .24038 L .04038 .24038 L .04038 .04808 L F .022 g .04038 .04808 m .04038 .24038 L .04135 .24038 L .04135 .04808 L F .023 g .04135 .04808 m .04135 .24038 L .04231 .24038 L .04231 .04808 L F .024 g .04231 .04808 m .04231 .24038 L .04327 .24038 L .04327 .04808 L F .025 g .04327 .04808 m .04327 .24038 L .04423 .24038 L .04423 .04808 L F .026 g .04423 .04808 m .04423 .24038 L .04519 .24038 L .04519 .04808 L F .027 g .04519 .04808 m .04519 .24038 L .04615 .24038 L .04615 .04808 L F .028 g .04615 .04808 m .04615 .24038 L .04712 .24038 L .04712 .04808 L F .029 g .04712 .04808 m .04712 .24038 L .04808 .24038 L .04808 .04808 L F .03 g .04808 .04808 m .04808 .24038 L .04904 .24038 L .04904 .04808 L F .031 g .04904 .04808 m .04904 .24038 L .05 .24038 L .05 .04808 L F .032 g .05 .04808 m .05 .24038 L .05096 .24038 L .05096 .04808 L F .033 g .05096 .04808 m .05096 .24038 L .05192 .24038 L .05192 .04808 L F .034 g .05192 .04808 m .05192 .24038 L .05288 .24038 L .05288 .04808 L F .035 g .05288 .04808 m .05288 .24038 L .05385 .24038 L .05385 .04808 L F .036 g .05385 .04808 m .05385 .24038 L .05481 .24038 L .05481 .04808 L F .037 g .05481 .04808 m .05481 .24038 L .05577 .24038 L .05577 .04808 L F .038 g .05577 .04808 m .05577 .24038 L .05673 .24038 L .05673 .04808 L F .039 g .05673 .04808 m .05673 .24038 L .05769 .24038 L .05769 .04808 L F .04 g .05769 .04808 m .05769 .24038 L .05865 .24038 L .05865 .04808 L F .041 g .05865 .04808 m .05865 .24038 L .05962 .24038 L .05962 .04808 L F .042 g .05962 .04808 m .05962 .24038 L .06058 .24038 L .06058 .04808 L F .043 g .06058 .04808 m .06058 .24038 L .06154 .24038 L .06154 .04808 L F .044 g .06154 .04808 m .06154 .24038 L .0625 .24038 L .0625 .04808 L F .045 g .0625 .04808 m .0625 .24038 L .06346 .24038 L .06346 .04808 L F .046 g .06346 .04808 m .06346 .24038 L .06442 .24038 L .06442 .04808 L F .047 g .06442 .04808 m .06442 .24038 L .06538 .24038 L .06538 .04808 L F .048 g .06538 .04808 m .06538 .24038 L .06635 .24038 L .06635 .04808 L F .049 g .06635 .04808 m .06635 .24038 L .06731 .24038 L .06731 .04808 L F .05 g .06731 .04808 m .06731 .24038 L .06827 .24038 L .06827 .04808 L F .051 g .06827 .04808 m .06827 .24038 L .06923 .24038 L .06923 .04808 L F .052 g .06923 .04808 m .06923 .24038 L .07019 .24038 L .07019 .04808 L F .053 g .07019 .04808 m .07019 .24038 L .07115 .24038 L .07115 .04808 L F .054 g .07115 .04808 m .07115 .24038 L .07212 .24038 L .07212 .04808 L F .055 g .07212 .04808 m .07212 .24038 L .07308 .24038 L .07308 .04808 L F .056 g .07308 .04808 m .07308 .24038 L .07404 .24038 L .07404 .04808 L F .057 g .07404 .04808 m .07404 .24038 L .075 .24038 L .075 .04808 L F .058 g .075 .04808 m .075 .24038 L .07596 .24038 L .07596 .04808 L F .059 g .07596 .04808 m .07596 .24038 L .07692 .24038 L .07692 .04808 L F .06 g .07692 .04808 m .07692 .24038 L .07788 .24038 L .07788 .04808 L F .061 g .07788 .04808 m .07788 .24038 L .07885 .24038 L .07885 .04808 L F .062 g .07885 .04808 m .07885 .24038 L .07981 .24038 L .07981 .04808 L F .063 g .07981 .04808 m .07981 .24038 L .08077 .24038 L .08077 .04808 L F .064 g .08077 .04808 m .08077 .24038 L .08173 .24038 L .08173 .04808 L F .065 g .08173 .04808 m .08173 .24038 L .08269 .24038 L .08269 .04808 L F .066 g .08269 .04808 m .08269 .24038 L .08365 .24038 L .08365 .04808 L F .067 g .08365 .04808 m .08365 .24038 L .08462 .24038 L .08462 .04808 L F .068 g .08462 .04808 m .08462 .24038 L .08558 .24038 L .08558 .04808 L F .069 g .08558 .04808 m .08558 .24038 L .08654 .24038 L .08654 .04808 L F .07 g .08654 .04808 m .08654 .24038 L .0875 .24038 L .0875 .04808 L F .071 g .0875 .04808 m .0875 .24038 L .08846 .24038 L .08846 .04808 L F .072 g .08846 .04808 m .08846 .24038 L .08942 .24038 L .08942 .04808 L F .073 g .08942 .04808 m .08942 .24038 L .09038 .24038 L .09038 .04808 L F .074 g .09038 .04808 m .09038 .24038 L .09135 .24038 L .09135 .04808 L F .075 g .09135 .04808 m .09135 .24038 L .09231 .24038 L .09231 .04808 L F .076 g .09231 .04808 m .09231 .24038 L .09327 .24038 L .09327 .04808 L F .077 g .09327 .04808 m .09327 .24038 L .09423 .24038 L .09423 .04808 L F .078 g .09423 .04808 m .09423 .24038 L .09519 .24038 L .09519 .04808 L F .079 g .09519 .04808 m .09519 .24038 L .09615 .24038 L .09615 .04808 L F .08 g .09615 .04808 m .09615 .24038 L .09712 .24038 L .09712 .04808 L F .081 g .09712 .04808 m .09712 .24038 L .09808 .24038 L .09808 .04808 L F .082 g .09808 .04808 m .09808 .24038 L .09904 .24038 L .09904 .04808 L F .083 g .09904 .04808 m .09904 .24038 L .1 .24038 L .1 .04808 L F .084 g .1 .04808 m .1 .24038 L .10096 .24038 L .10096 .04808 L F .085 g .10096 .04808 m .10096 .24038 L .10192 .24038 L .10192 .04808 L F .086 g .10192 .04808 m .10192 .24038 L .10288 .24038 L .10288 .04808 L F .087 g .10288 .04808 m .10288 .24038 L .10385 .24038 L .10385 .04808 L F .088 g .10385 .04808 m .10385 .24038 L .10481 .24038 L .10481 .04808 L F .089 g .10481 .04808 m .10481 .24038 L .10577 .24038 L .10577 .04808 L F .09 g .10577 .04808 m .10577 .24038 L .10673 .24038 L .10673 .04808 L F .091 g .10673 .04808 m .10673 .24038 L .10769 .24038 L .10769 .04808 L F .092 g .10769 .04808 m .10769 .24038 L .10865 .24038 L .10865 .04808 L F .093 g .10865 .04808 m .10865 .24038 L .10962 .24038 L .10962 .04808 L F .094 g .10962 .04808 m .10962 .24038 L .11058 .24038 L .11058 .04808 L F .095 g .11058 .04808 m .11058 .24038 L .11154 .24038 L .11154 .04808 L F .096 g .11154 .04808 m .11154 .24038 L .1125 .24038 L .1125 .04808 L F .097 g .1125 .04808 m .1125 .24038 L .11346 .24038 L .11346 .04808 L F .098 g .11346 .04808 m .11346 .24038 L .11442 .24038 L .11442 .04808 L F .099 g .11442 .04808 m .11442 .24038 L .11538 .24038 L .11538 .04808 L F .1 g .11538 .04808 m .11538 .24038 L .11635 .24038 L .11635 .04808 L F .101 g .11635 .04808 m .11635 .24038 L .11731 .24038 L .11731 .04808 L F .102 g .11731 .04808 m .11731 .24038 L .11827 .24038 L .11827 .04808 L F .103 g .11827 .04808 m .11827 .24038 L .11923 .24038 L .11923 .04808 L F .104 g .11923 .04808 m .11923 .24038 L .12019 .24038 L .12019 .04808 L F .105 g .12019 .04808 m .12019 .24038 L .12115 .24038 L .12115 .04808 L F .106 g .12115 .04808 m .12115 .24038 L .12212 .24038 L .12212 .04808 L F .107 g .12212 .04808 m .12212 .24038 L .12308 .24038 L .12308 .04808 L F .108 g .12308 .04808 m .12308 .24038 L .12404 .24038 L .12404 .04808 L F .109 g .12404 .04808 m .12404 .24038 L .125 .24038 L .125 .04808 L F .11 g .125 .04808 m .125 .24038 L .12596 .24038 L .12596 .04808 L F .111 g .12596 .04808 m .12596 .24038 L .12692 .24038 L .12692 .04808 L F .112 g .12692 .04808 m .12692 .24038 L .12788 .24038 L .12788 .04808 L F .113 g .12788 .04808 m .12788 .24038 L .12885 .24038 L .12885 .04808 L F .114 g .12885 .04808 m .12885 .24038 L .12981 .24038 L .12981 .04808 L F .115 g .12981 .04808 m .12981 .24038 L .13077 .24038 L .13077 .04808 L F .116 g .13077 .04808 m .13077 .24038 L .13173 .24038 L .13173 .04808 L F .117 g .13173 .04808 m .13173 .24038 L .13269 .24038 L .13269 .04808 L F .118 g .13269 .04808 m .13269 .24038 L .13365 .24038 L .13365 .04808 L F .119 g .13365 .04808 m .13365 .24038 L .13462 .24038 L .13462 .04808 L F .12 g .13462 .04808 m .13462 .24038 L .13558 .24038 L .13558 .04808 L F .121 g .13558 .04808 m .13558 .24038 L .13654 .24038 L .13654 .04808 L F .122 g .13654 .04808 m .13654 .24038 L .1375 .24038 L .1375 .04808 L F .123 g .1375 .04808 m .1375 .24038 L .13846 .24038 L .13846 .04808 L F .124 g .13846 .04808 m .13846 .24038 L .13942 .24038 L .13942 .04808 L F .125 g .13942 .04808 m .13942 .24038 L .14038 .24038 L .14038 .04808 L F .126 g .14038 .04808 m .14038 .24038 L .14135 .24038 L .14135 .04808 L F .127 g .14135 .04808 m .14135 .24038 L .14231 .24038 L .14231 .04808 L F .128 g .14231 .04808 m .14231 .24038 L .14327 .24038 L .14327 .04808 L F .129 g .14327 .04808 m .14327 .24038 L .14423 .24038 L .14423 .04808 L F .13 g .14423 .04808 m .14423 .24038 L .14519 .24038 L .14519 .04808 L F .131 g .14519 .04808 m .14519 .24038 L .14615 .24038 L .14615 .04808 L F .132 g .14615 .04808 m .14615 .24038 L .14712 .24038 L .14712 .04808 L F .133 g .14712 .04808 m .14712 .24038 L .14808 .24038 L .14808 .04808 L F .134 g .14808 .04808 m .14808 .24038 L .14904 .24038 L .14904 .04808 L F .135 g .14904 .04808 m .14904 .24038 L .15 .24038 L .15 .04808 L F .136 g .15 .04808 m .15 .24038 L .15096 .24038 L .15096 .04808 L F .137 g .15096 .04808 m .15096 .24038 L .15192 .24038 L .15192 .04808 L F .138 g .15192 .04808 m .15192 .24038 L .15288 .24038 L .15288 .04808 L F .139 g .15288 .04808 m .15288 .24038 L .15385 .24038 L .15385 .04808 L F .14 g .15385 .04808 m .15385 .24038 L .15481 .24038 L .15481 .04808 L F .141 g .15481 .04808 m .15481 .24038 L .15577 .24038 L .15577 .04808 L F .142 g .15577 .04808 m .15577 .24038 L .15673 .24038 L .15673 .04808 L F .143 g .15673 .04808 m .15673 .24038 L .15769 .24038 L .15769 .04808 L F .144 g .15769 .04808 m .15769 .24038 L .15865 .24038 L .15865 .04808 L F .145 g .15865 .04808 m .15865 .24038 L .15962 .24038 L .15962 .04808 L F .146 g .15962 .04808 m .15962 .24038 L .16058 .24038 L .16058 .04808 L F .147 g .16058 .04808 m .16058 .24038 L .16154 .24038 L .16154 .04808 L F .148 g .16154 .04808 m .16154 .24038 L .1625 .24038 L .1625 .04808 L F .149 g .1625 .04808 m .1625 .24038 L .16346 .24038 L .16346 .04808 L F .15 g .16346 .04808 m .16346 .24038 L .16442 .24038 L .16442 .04808 L F .151 g .16442 .04808 m .16442 .24038 L .16538 .24038 L .16538 .04808 L F .152 g .16538 .04808 m .16538 .24038 L .16635 .24038 L .16635 .04808 L F .153 g .16635 .04808 m .16635 .24038 L .16731 .24038 L .16731 .04808 L F .154 g .16731 .04808 m .16731 .24038 L .16827 .24038 L .16827 .04808 L F .155 g .16827 .04808 m .16827 .24038 L .16923 .24038 L .16923 .04808 L F .156 g .16923 .04808 m .16923 .24038 L .17019 .24038 L .17019 .04808 L F .157 g .17019 .04808 m .17019 .24038 L .17115 .24038 L .17115 .04808 L F .158 g .17115 .04808 m .17115 .24038 L .17212 .24038 L .17212 .04808 L F .159 g .17212 .04808 m .17212 .24038 L .17308 .24038 L .17308 .04808 L F .16 g .17308 .04808 m .17308 .24038 L .17404 .24038 L .17404 .04808 L F .161 g .17404 .04808 m .17404 .24038 L .175 .24038 L .175 .04808 L F .162 g .175 .04808 m .175 .24038 L .17596 .24038 L .17596 .04808 L F .163 g .17596 .04808 m .17596 .24038 L .17692 .24038 L .17692 .04808 L F .164 g .17692 .04808 m .17692 .24038 L .17788 .24038 L .17788 .04808 L F .165 g .17788 .04808 m .17788 .24038 L .17885 .24038 L .17885 .04808 L F .166 g .17885 .04808 m .17885 .24038 L .17981 .24038 L .17981 .04808 L F .167 g .17981 .04808 m .17981 .24038 L .18077 .24038 L .18077 .04808 L F .168 g .18077 .04808 m .18077 .24038 L .18173 .24038 L .18173 .04808 L F .169 g .18173 .04808 m .18173 .24038 L .18269 .24038 L .18269 .04808 L F .17 g .18269 .04808 m .18269 .24038 L .18365 .24038 L .18365 .04808 L F .171 g .18365 .04808 m .18365 .24038 L .18462 .24038 L .18462 .04808 L F .172 g .18462 .04808 m .18462 .24038 L .18558 .24038 L .18558 .04808 L F .173 g .18558 .04808 m .18558 .24038 L .18654 .24038 L .18654 .04808 L F .174 g .18654 .04808 m .18654 .24038 L .1875 .24038 L .1875 .04808 L F .175 g .1875 .04808 m .1875 .24038 L .18846 .24038 L .18846 .04808 L F .176 g .18846 .04808 m .18846 .24038 L .18942 .24038 L .18942 .04808 L F .177 g .18942 .04808 m .18942 .24038 L .19038 .24038 L .19038 .04808 L F .178 g .19038 .04808 m .19038 .24038 L .19135 .24038 L .19135 .04808 L F .179 g .19135 .04808 m .19135 .24038 L .19231 .24038 L .19231 .04808 L F .18 g .19231 .04808 m .19231 .24038 L .19327 .24038 L .19327 .04808 L F .181 g .19327 .04808 m .19327 .24038 L .19423 .24038 L .19423 .04808 L F .182 g .19423 .04808 m .19423 .24038 L .19519 .24038 L .19519 .04808 L F .183 g .19519 .04808 m .19519 .24038 L .19615 .24038 L .19615 .04808 L F .184 g .19615 .04808 m .19615 .24038 L .19712 .24038 L .19712 .04808 L F .185 g .19712 .04808 m .19712 .24038 L .19808 .24038 L .19808 .04808 L F .186 g .19808 .04808 m .19808 .24038 L .19904 .24038 L .19904 .04808 L F .187 g .19904 .04808 m .19904 .24038 L .2 .24038 L .2 .04808 L F .188 g .2 .04808 m .2 .24038 L .20096 .24038 L .20096 .04808 L F .189 g .20096 .04808 m .20096 .24038 L .20192 .24038 L .20192 .04808 L F .19 g .20192 .04808 m .20192 .24038 L .20288 .24038 L .20288 .04808 L F .191 g .20288 .04808 m .20288 .24038 L .20385 .24038 L .20385 .04808 L F .192 g .20385 .04808 m .20385 .24038 L .20481 .24038 L .20481 .04808 L F .193 g .20481 .04808 m .20481 .24038 L .20577 .24038 L .20577 .04808 L F .194 g .20577 .04808 m .20577 .24038 L .20673 .24038 L .20673 .04808 L F .195 g .20673 .04808 m .20673 .24038 L .20769 .24038 L .20769 .04808 L F .196 g .20769 .04808 m .20769 .24038 L .20865 .24038 L .20865 .04808 L F .197 g .20865 .04808 m .20865 .24038 L .20962 .24038 L .20962 .04808 L F .198 g .20962 .04808 m .20962 .24038 L .21058 .24038 L .21058 .04808 L F .199 g .21058 .04808 m .21058 .24038 L .21154 .24038 L .21154 .04808 L F .2 g .21154 .04808 m .21154 .24038 L .2125 .24038 L .2125 .04808 L F .201 g .2125 .04808 m .2125 .24038 L .21346 .24038 L .21346 .04808 L F .202 g .21346 .04808 m .21346 .24038 L .21442 .24038 L .21442 .04808 L F .203 g .21442 .04808 m .21442 .24038 L .21538 .24038 L .21538 .04808 L F .204 g .21538 .04808 m .21538 .24038 L .21635 .24038 L .21635 .04808 L F .205 g .21635 .04808 m .21635 .24038 L .21731 .24038 L .21731 .04808 L F .206 g .21731 .04808 m .21731 .24038 L .21827 .24038 L .21827 .04808 L F .207 g .21827 .04808 m .21827 .24038 L .21923 .24038 L .21923 .04808 L F .208 g .21923 .04808 m .21923 .24038 L .22019 .24038 L .22019 .04808 L F .209 g .22019 .04808 m .22019 .24038 L .22115 .24038 L .22115 .04808 L F .21 g .22115 .04808 m .22115 .24038 L .22212 .24038 L .22212 .04808 L F .211 g .22212 .04808 m .22212 .24038 L .22308 .24038 L .22308 .04808 L F .212 g .22308 .04808 m .22308 .24038 L .22404 .24038 L .22404 .04808 L F .213 g .22404 .04808 m .22404 .24038 L .225 .24038 L .225 .04808 L F .214 g .225 .04808 m .225 .24038 L .22596 .24038 L .22596 .04808 L F .215 g .22596 .04808 m .22596 .24038 L .22692 .24038 L .22692 .04808 L F .216 g .22692 .04808 m .22692 .24038 L .22788 .24038 L .22788 .04808 L F .217 g .22788 .04808 m .22788 .24038 L .22885 .24038 L .22885 .04808 L F .218 g .22885 .04808 m .22885 .24038 L .22981 .24038 L .22981 .04808 L F .219 g .22981 .04808 m .22981 .24038 L .23077 .24038 L .23077 .04808 L F .22 g .23077 .04808 m .23077 .24038 L .23173 .24038 L .23173 .04808 L F .221 g .23173 .04808 m .23173 .24038 L .23269 .24038 L .23269 .04808 L F .222 g .23269 .04808 m .23269 .24038 L .23365 .24038 L .23365 .04808 L F .223 g .23365 .04808 m .23365 .24038 L .23462 .24038 L .23462 .04808 L F .224 g .23462 .04808 m .23462 .24038 L .23558 .24038 L .23558 .04808 L F .225 g .23558 .04808 m .23558 .24038 L .23654 .24038 L .23654 .04808 L F .226 g .23654 .04808 m .23654 .24038 L .2375 .24038 L .2375 .04808 L F .227 g .2375 .04808 m .2375 .24038 L .23846 .24038 L .23846 .04808 L F .228 g .23846 .04808 m .23846 .24038 L .23942 .24038 L .23942 .04808 L F .229 g .23942 .04808 m .23942 .24038 L .24038 .24038 L .24038 .04808 L F .23 g .24038 .04808 m .24038 .24038 L .24135 .24038 L .24135 .04808 L F .231 g .24135 .04808 m .24135 .24038 L .24231 .24038 L .24231 .04808 L F .232 g .24231 .04808 m .24231 .24038 L .24327 .24038 L .24327 .04808 L F .233 g .24327 .04808 m .24327 .24038 L .24423 .24038 L .24423 .04808 L F .234 g .24423 .04808 m .24423 .24038 L .24519 .24038 L .24519 .04808 L F .235 g .24519 .04808 m .24519 .24038 L .24615 .24038 L .24615 .04808 L F .236 g .24615 .04808 m .24615 .24038 L .24712 .24038 L .24712 .04808 L F .237 g .24712 .04808 m .24712 .24038 L .24808 .24038 L .24808 .04808 L F .238 g .24808 .04808 m .24808 .24038 L .24904 .24038 L .24904 .04808 L F .239 g .24904 .04808 m .24904 .24038 L .25 .24038 L .25 .04808 L F .24 g .25 .04808 m .25 .24038 L .25096 .24038 L .25096 .04808 L F .241 g .25096 .04808 m .25096 .24038 L .25192 .24038 L .25192 .04808 L F .242 g .25192 .04808 m .25192 .24038 L .25288 .24038 L .25288 .04808 L F .243 g .25288 .04808 m .25288 .24038 L .25385 .24038 L .25385 .04808 L F .244 g .25385 .04808 m .25385 .24038 L .25481 .24038 L .25481 .04808 L F .245 g .25481 .04808 m .25481 .24038 L .25577 .24038 L .25577 .04808 L F .246 g .25577 .04808 m .25577 .24038 L .25673 .24038 L .25673 .04808 L F .247 g .25673 .04808 m .25673 .24038 L .25769 .24038 L .25769 .04808 L F .248 g .25769 .04808 m .25769 .24038 L .25865 .24038 L .25865 .04808 L F .249 g .25865 .04808 m .25865 .24038 L .25962 .24038 L .25962 .04808 L F .25 g .25962 .04808 m .25962 .24038 L .26058 .24038 L .26058 .04808 L F .251 g .26058 .04808 m .26058 .24038 L .26154 .24038 L .26154 .04808 L F .252 g .26154 .04808 m .26154 .24038 L .2625 .24038 L .2625 .04808 L F .253 g .2625 .04808 m .2625 .24038 L .26346 .24038 L .26346 .04808 L F .254 g .26346 .04808 m .26346 .24038 L .26442 .24038 L .26442 .04808 L F .255 g .26442 .04808 m .26442 .24038 L .26538 .24038 L .26538 .04808 L F .256 g .26538 .04808 m .26538 .24038 L .26635 .24038 L .26635 .04808 L F .257 g .26635 .04808 m .26635 .24038 L .26731 .24038 L .26731 .04808 L F .258 g .26731 .04808 m .26731 .24038 L .26827 .24038 L .26827 .04808 L F .259 g .26827 .04808 m .26827 .24038 L .26923 .24038 L .26923 .04808 L F .26 g .26923 .04808 m .26923 .24038 L .27019 .24038 L .27019 .04808 L F .261 g .27019 .04808 m .27019 .24038 L .27115 .24038 L .27115 .04808 L F .262 g .27115 .04808 m .27115 .24038 L .27212 .24038 L .27212 .04808 L F .263 g .27212 .04808 m .27212 .24038 L .27308 .24038 L .27308 .04808 L F .264 g .27308 .04808 m .27308 .24038 L .27404 .24038 L .27404 .04808 L F .265 g .27404 .04808 m .27404 .24038 L .275 .24038 L .275 .04808 L F .266 g .275 .04808 m .275 .24038 L .27596 .24038 L .27596 .04808 L F .267 g .27596 .04808 m .27596 .24038 L .27692 .24038 L .27692 .04808 L F .268 g .27692 .04808 m .27692 .24038 L .27788 .24038 L .27788 .04808 L F .269 g .27788 .04808 m .27788 .24038 L .27885 .24038 L .27885 .04808 L F .27 g .27885 .04808 m .27885 .24038 L .27981 .24038 L .27981 .04808 L F .271 g .27981 .04808 m .27981 .24038 L .28077 .24038 L .28077 .04808 L F .272 g .28077 .04808 m .28077 .24038 L .28173 .24038 L .28173 .04808 L F .273 g .28173 .04808 m .28173 .24038 L .28269 .24038 L .28269 .04808 L F .274 g .28269 .04808 m .28269 .24038 L .28365 .24038 L .28365 .04808 L F .275 g .28365 .04808 m .28365 .24038 L .28462 .24038 L .28462 .04808 L F .276 g .28462 .04808 m .28462 .24038 L .28558 .24038 L .28558 .04808 L F .277 g .28558 .04808 m .28558 .24038 L .28654 .24038 L .28654 .04808 L F .278 g .28654 .04808 m .28654 .24038 L .2875 .24038 L .2875 .04808 L F .279 g .2875 .04808 m .2875 .24038 L .28846 .24038 L .28846 .04808 L F .28 g .28846 .04808 m .28846 .24038 L .28942 .24038 L .28942 .04808 L F .281 g .28942 .04808 m .28942 .24038 L .29038 .24038 L .29038 .04808 L F .282 g .29038 .04808 m .29038 .24038 L .29135 .24038 L .29135 .04808 L F .283 g .29135 .04808 m .29135 .24038 L .29231 .24038 L .29231 .04808 L F .284 g .29231 .04808 m .29231 .24038 L .29327 .24038 L .29327 .04808 L F .285 g .29327 .04808 m .29327 .24038 L .29423 .24038 L .29423 .04808 L F .286 g .29423 .04808 m .29423 .24038 L .29519 .24038 L .29519 .04808 L F .287 g .29519 .04808 m .29519 .24038 L .29615 .24038 L .29615 .04808 L F .288 g .29615 .04808 m .29615 .24038 L .29712 .24038 L .29712 .04808 L F .289 g .29712 .04808 m .29712 .24038 L .29808 .24038 L .29808 .04808 L F .29 g .29808 .04808 m .29808 .24038 L .29904 .24038 L .29904 .04808 L F .291 g .29904 .04808 m .29904 .24038 L .3 .24038 L .3 .04808 L F .292 g .3 .04808 m .3 .24038 L .30096 .24038 L .30096 .04808 L F .293 g .30096 .04808 m .30096 .24038 L .30192 .24038 L .30192 .04808 L F .294 g .30192 .04808 m .30192 .24038 L .30288 .24038 L .30288 .04808 L F .295 g .30288 .04808 m .30288 .24038 L .30385 .24038 L .30385 .04808 L F .296 g .30385 .04808 m .30385 .24038 L .30481 .24038 L .30481 .04808 L F .297 g .30481 .04808 m .30481 .24038 L .30577 .24038 L .30577 .04808 L F .298 g .30577 .04808 m .30577 .24038 L .30673 .24038 L .30673 .04808 L F .299 g .30673 .04808 m .30673 .24038 L .30769 .24038 L .30769 .04808 L F .3 g .30769 .04808 m .30769 .24038 L .30865 .24038 L .30865 .04808 L F .301 g .30865 .04808 m .30865 .24038 L .30962 .24038 L .30962 .04808 L F .302 g .30962 .04808 m .30962 .24038 L .31058 .24038 L .31058 .04808 L F .303 g .31058 .04808 m .31058 .24038 L .31154 .24038 L .31154 .04808 L F .304 g .31154 .04808 m .31154 .24038 L .3125 .24038 L .3125 .04808 L F .305 g .3125 .04808 m .3125 .24038 L .31346 .24038 L .31346 .04808 L F .306 g .31346 .04808 m .31346 .24038 L .31442 .24038 L .31442 .04808 L F .307 g .31442 .04808 m .31442 .24038 L .31538 .24038 L .31538 .04808 L F .308 g .31538 .04808 m .31538 .24038 L .31635 .24038 L .31635 .04808 L F .309 g .31635 .04808 m .31635 .24038 L .31731 .24038 L .31731 .04808 L F .31 g .31731 .04808 m .31731 .24038 L .31827 .24038 L .31827 .04808 L F .311 g .31827 .04808 m .31827 .24038 L .31923 .24038 L .31923 .04808 L F .312 g .31923 .04808 m .31923 .24038 L .32019 .24038 L .32019 .04808 L F .313 g .32019 .04808 m .32019 .24038 L .32115 .24038 L .32115 .04808 L F .314 g .32115 .04808 m .32115 .24038 L .32212 .24038 L .32212 .04808 L F .315 g .32212 .04808 m .32212 .24038 L .32308 .24038 L .32308 .04808 L F .316 g .32308 .04808 m .32308 .24038 L .32404 .24038 L .32404 .04808 L F .317 g .32404 .04808 m .32404 .24038 L .325 .24038 L .325 .04808 L F .318 g .325 .04808 m .325 .24038 L .32596 .24038 L .32596 .04808 L F .319 g .32596 .04808 m .32596 .24038 L .32692 .24038 L .32692 .04808 L F .32 g .32692 .04808 m .32692 .24038 L .32788 .24038 L .32788 .04808 L F .321 g .32788 .04808 m .32788 .24038 L .32885 .24038 L .32885 .04808 L F .322 g .32885 .04808 m .32885 .24038 L .32981 .24038 L .32981 .04808 L F .323 g .32981 .04808 m .32981 .24038 L .33077 .24038 L .33077 .04808 L F .324 g .33077 .04808 m .33077 .24038 L .33173 .24038 L .33173 .04808 L F .325 g .33173 .04808 m .33173 .24038 L .33269 .24038 L .33269 .04808 L F .326 g .33269 .04808 m .33269 .24038 L .33365 .24038 L .33365 .04808 L F .327 g .33365 .04808 m .33365 .24038 L .33462 .24038 L .33462 .04808 L F .328 g .33462 .04808 m .33462 .24038 L .33558 .24038 L .33558 .04808 L F .329 g .33558 .04808 m .33558 .24038 L .33654 .24038 L .33654 .04808 L F .33 g .33654 .04808 m .33654 .24038 L .3375 .24038 L .3375 .04808 L F .331 g .3375 .04808 m .3375 .24038 L .33846 .24038 L .33846 .04808 L F .332 g .33846 .04808 m .33846 .24038 L .33942 .24038 L .33942 .04808 L F .333 g .33942 .04808 m .33942 .24038 L .34038 .24038 L .34038 .04808 L F .334 g .34038 .04808 m .34038 .24038 L .34135 .24038 L .34135 .04808 L F .335 g .34135 .04808 m .34135 .24038 L .34231 .24038 L .34231 .04808 L F .336 g .34231 .04808 m .34231 .24038 L .34327 .24038 L .34327 .04808 L F .337 g .34327 .04808 m .34327 .24038 L .34423 .24038 L .34423 .04808 L F .338 g .34423 .04808 m .34423 .24038 L .34519 .24038 L .34519 .04808 L F .339 g .34519 .04808 m .34519 .24038 L .34615 .24038 L .34615 .04808 L F .34 g .34615 .04808 m .34615 .24038 L .34712 .24038 L .34712 .04808 L F .341 g .34712 .04808 m .34712 .24038 L .34808 .24038 L .34808 .04808 L F .342 g .34808 .04808 m .34808 .24038 L .34904 .24038 L .34904 .04808 L F .343 g .34904 .04808 m .34904 .24038 L .35 .24038 L .35 .04808 L F .344 g .35 .04808 m .35 .24038 L .35096 .24038 L .35096 .04808 L F .345 g .35096 .04808 m .35096 .24038 L .35192 .24038 L .35192 .04808 L F .346 g .35192 .04808 m .35192 .24038 L .35288 .24038 L .35288 .04808 L F .347 g .35288 .04808 m .35288 .24038 L .35385 .24038 L .35385 .04808 L F .348 g .35385 .04808 m .35385 .24038 L .35481 .24038 L .35481 .04808 L F .349 g .35481 .04808 m .35481 .24038 L .35577 .24038 L .35577 .04808 L F .35 g .35577 .04808 m .35577 .24038 L .35673 .24038 L .35673 .04808 L F .351 g .35673 .04808 m .35673 .24038 L .35769 .24038 L .35769 .04808 L F .352 g .35769 .04808 m .35769 .24038 L .35865 .24038 L .35865 .04808 L F .353 g .35865 .04808 m .35865 .24038 L .35962 .24038 L .35962 .04808 L F .354 g .35962 .04808 m .35962 .24038 L .36058 .24038 L .36058 .04808 L F .355 g .36058 .04808 m .36058 .24038 L .36154 .24038 L .36154 .04808 L F .356 g .36154 .04808 m .36154 .24038 L .3625 .24038 L .3625 .04808 L F .357 g .3625 .04808 m .3625 .24038 L .36346 .24038 L .36346 .04808 L F .358 g .36346 .04808 m .36346 .24038 L .36442 .24038 L .36442 .04808 L F .359 g .36442 .04808 m .36442 .24038 L .36538 .24038 L .36538 .04808 L F .36 g .36538 .04808 m .36538 .24038 L .36635 .24038 L .36635 .04808 L F .361 g .36635 .04808 m .36635 .24038 L .36731 .24038 L .36731 .04808 L F .362 g .36731 .04808 m .36731 .24038 L .36827 .24038 L .36827 .04808 L F .363 g .36827 .04808 m .36827 .24038 L .36923 .24038 L .36923 .04808 L F .364 g .36923 .04808 m .36923 .24038 L .37019 .24038 L .37019 .04808 L F .365 g .37019 .04808 m .37019 .24038 L .37115 .24038 L .37115 .04808 L F .366 g .37115 .04808 m .37115 .24038 L .37212 .24038 L .37212 .04808 L F .367 g .37212 .04808 m .37212 .24038 L .37308 .24038 L .37308 .04808 L F .368 g .37308 .04808 m .37308 .24038 L .37404 .24038 L .37404 .04808 L F .369 g .37404 .04808 m .37404 .24038 L .375 .24038 L .375 .04808 L F .37 g .375 .04808 m .375 .24038 L .37596 .24038 L .37596 .04808 L F .371 g .37596 .04808 m .37596 .24038 L .37692 .24038 L .37692 .04808 L F .372 g .37692 .04808 m .37692 .24038 L .37788 .24038 L .37788 .04808 L F .373 g .37788 .04808 m .37788 .24038 L .37885 .24038 L .37885 .04808 L F .374 g .37885 .04808 m .37885 .24038 L .37981 .24038 L .37981 .04808 L F .375 g .37981 .04808 m .37981 .24038 L .38077 .24038 L .38077 .04808 L F .376 g .38077 .04808 m .38077 .24038 L .38173 .24038 L .38173 .04808 L F .377 g .38173 .04808 m .38173 .24038 L .38269 .24038 L .38269 .04808 L F .378 g .38269 .04808 m .38269 .24038 L .38365 .24038 L .38365 .04808 L F .379 g .38365 .04808 m .38365 .24038 L .38462 .24038 L .38462 .04808 L F .38 g .38462 .04808 m .38462 .24038 L .38558 .24038 L .38558 .04808 L F .381 g .38558 .04808 m .38558 .24038 L .38654 .24038 L .38654 .04808 L F .382 g .38654 .04808 m .38654 .24038 L .3875 .24038 L .3875 .04808 L F .383 g .3875 .04808 m .3875 .24038 L .38846 .24038 L .38846 .04808 L F .384 g .38846 .04808 m .38846 .24038 L .38942 .24038 L .38942 .04808 L F .385 g .38942 .04808 m .38942 .24038 L .39038 .24038 L .39038 .04808 L F .386 g .39038 .04808 m .39038 .24038 L .39135 .24038 L .39135 .04808 L F .387 g .39135 .04808 m .39135 .24038 L .39231 .24038 L .39231 .04808 L F .388 g .39231 .04808 m .39231 .24038 L .39327 .24038 L .39327 .04808 L F .389 g .39327 .04808 m .39327 .24038 L .39423 .24038 L .39423 .04808 L F .39 g .39423 .04808 m .39423 .24038 L .39519 .24038 L .39519 .04808 L F .391 g .39519 .04808 m .39519 .24038 L .39615 .24038 L .39615 .04808 L F .392 g .39615 .04808 m .39615 .24038 L .39712 .24038 L .39712 .04808 L F .393 g .39712 .04808 m .39712 .24038 L .39808 .24038 L .39808 .04808 L F .394 g .39808 .04808 m .39808 .24038 L .39904 .24038 L .39904 .04808 L F .395 g .39904 .04808 m .39904 .24038 L .4 .24038 L .4 .04808 L F .396 g .4 .04808 m .4 .24038 L .40096 .24038 L .40096 .04808 L F .397 g .40096 .04808 m .40096 .24038 L .40192 .24038 L .40192 .04808 L F .398 g .40192 .04808 m .40192 .24038 L .40288 .24038 L .40288 .04808 L F .399 g .40288 .04808 m .40288 .24038 L .40385 .24038 L .40385 .04808 L F .4 g .40385 .04808 m .40385 .24038 L .40481 .24038 L .40481 .04808 L F .401 g .40481 .04808 m .40481 .24038 L .40577 .24038 L .40577 .04808 L F .402 g .40577 .04808 m .40577 .24038 L .40673 .24038 L .40673 .04808 L F .403 g .40673 .04808 m .40673 .24038 L .40769 .24038 L .40769 .04808 L F .404 g .40769 .04808 m .40769 .24038 L .40865 .24038 L .40865 .04808 L F .405 g .40865 .04808 m .40865 .24038 L .40962 .24038 L .40962 .04808 L F .406 g .40962 .04808 m .40962 .24038 L .41058 .24038 L .41058 .04808 L F .407 g .41058 .04808 m .41058 .24038 L .41154 .24038 L .41154 .04808 L F .408 g .41154 .04808 m .41154 .24038 L .4125 .24038 L .4125 .04808 L F .409 g .4125 .04808 m .4125 .24038 L .41346 .24038 L .41346 .04808 L F .41 g .41346 .04808 m .41346 .24038 L .41442 .24038 L .41442 .04808 L F .411 g .41442 .04808 m .41442 .24038 L .41538 .24038 L .41538 .04808 L F .412 g .41538 .04808 m .41538 .24038 L .41635 .24038 L .41635 .04808 L F .413 g .41635 .04808 m .41635 .24038 L .41731 .24038 L .41731 .04808 L F .414 g .41731 .04808 m .41731 .24038 L .41827 .24038 L .41827 .04808 L F .415 g .41827 .04808 m .41827 .24038 L .41923 .24038 L .41923 .04808 L F .416 g .41923 .04808 m .41923 .24038 L .42019 .24038 L .42019 .04808 L F .417 g .42019 .04808 m .42019 .24038 L .42115 .24038 L .42115 .04808 L F .418 g .42115 .04808 m .42115 .24038 L .42212 .24038 L .42212 .04808 L F .419 g .42212 .04808 m .42212 .24038 L .42308 .24038 L .42308 .04808 L F .42 g .42308 .04808 m .42308 .24038 L .42404 .24038 L .42404 .04808 L F .421 g .42404 .04808 m .42404 .24038 L .425 .24038 L .425 .04808 L F .422 g .425 .04808 m .425 .24038 L .42596 .24038 L .42596 .04808 L F .423 g .42596 .04808 m .42596 .24038 L .42692 .24038 L .42692 .04808 L F .424 g .42692 .04808 m .42692 .24038 L .42788 .24038 L .42788 .04808 L F .425 g .42788 .04808 m .42788 .24038 L .42885 .24038 L .42885 .04808 L F .426 g .42885 .04808 m .42885 .24038 L .42981 .24038 L .42981 .04808 L F .427 g .42981 .04808 m .42981 .24038 L .43077 .24038 L .43077 .04808 L F .428 g .43077 .04808 m .43077 .24038 L .43173 .24038 L .43173 .04808 L F .429 g .43173 .04808 m .43173 .24038 L .43269 .24038 L .43269 .04808 L F .43 g .43269 .04808 m .43269 .24038 L .43365 .24038 L .43365 .04808 L F .431 g .43365 .04808 m .43365 .24038 L .43462 .24038 L .43462 .04808 L F .432 g .43462 .04808 m .43462 .24038 L .43558 .24038 L .43558 .04808 L F .433 g .43558 .04808 m .43558 .24038 L .43654 .24038 L .43654 .04808 L F .434 g .43654 .04808 m .43654 .24038 L .4375 .24038 L .4375 .04808 L F .435 g .4375 .04808 m .4375 .24038 L .43846 .24038 L .43846 .04808 L F .436 g .43846 .04808 m .43846 .24038 L .43942 .24038 L .43942 .04808 L F .437 g .43942 .04808 m .43942 .24038 L .44038 .24038 L .44038 .04808 L F .438 g .44038 .04808 m .44038 .24038 L .44135 .24038 L .44135 .04808 L F .439 g .44135 .04808 m .44135 .24038 L .44231 .24038 L .44231 .04808 L F .44 g .44231 .04808 m .44231 .24038 L .44327 .24038 L .44327 .04808 L F .441 g .44327 .04808 m .44327 .24038 L .44423 .24038 L .44423 .04808 L F .442 g .44423 .04808 m .44423 .24038 L .44519 .24038 L .44519 .04808 L F .443 g .44519 .04808 m .44519 .24038 L .44615 .24038 L .44615 .04808 L F .444 g .44615 .04808 m .44615 .24038 L .44712 .24038 L .44712 .04808 L F .445 g .44712 .04808 m .44712 .24038 L .44808 .24038 L .44808 .04808 L F .446 g .44808 .04808 m .44808 .24038 L .44904 .24038 L .44904 .04808 L F .447 g .44904 .04808 m .44904 .24038 L .45 .24038 L .45 .04808 L F .448 g .45 .04808 m .45 .24038 L .45096 .24038 L .45096 .04808 L F .449 g .45096 .04808 m .45096 .24038 L .45192 .24038 L .45192 .04808 L F .45 g .45192 .04808 m .45192 .24038 L .45288 .24038 L .45288 .04808 L F .451 g .45288 .04808 m .45288 .24038 L .45385 .24038 L .45385 .04808 L F .452 g .45385 .04808 m .45385 .24038 L .45481 .24038 L .45481 .04808 L F .453 g .45481 .04808 m .45481 .24038 L .45577 .24038 L .45577 .04808 L F .454 g .45577 .04808 m .45577 .24038 L .45673 .24038 L .45673 .04808 L F .455 g .45673 .04808 m .45673 .24038 L .45769 .24038 L .45769 .04808 L F .456 g .45769 .04808 m .45769 .24038 L .45865 .24038 L .45865 .04808 L F .457 g .45865 .04808 m .45865 .24038 L .45962 .24038 L .45962 .04808 L F .458 g .45962 .04808 m .45962 .24038 L .46058 .24038 L .46058 .04808 L F .459 g .46058 .04808 m .46058 .24038 L .46154 .24038 L .46154 .04808 L F .46 g .46154 .04808 m .46154 .24038 L .4625 .24038 L .4625 .04808 L F .461 g .4625 .04808 m .4625 .24038 L .46346 .24038 L .46346 .04808 L F .462 g .46346 .04808 m .46346 .24038 L .46442 .24038 L .46442 .04808 L F .463 g .46442 .04808 m .46442 .24038 L .46538 .24038 L .46538 .04808 L F .464 g .46538 .04808 m .46538 .24038 L .46635 .24038 L .46635 .04808 L F .465 g .46635 .04808 m .46635 .24038 L .46731 .24038 L .46731 .04808 L F .466 g .46731 .04808 m .46731 .24038 L .46827 .24038 L .46827 .04808 L F .467 g .46827 .04808 m .46827 .24038 L .46923 .24038 L .46923 .04808 L F .468 g .46923 .04808 m .46923 .24038 L .47019 .24038 L .47019 .04808 L F .469 g .47019 .04808 m .47019 .24038 L .47115 .24038 L .47115 .04808 L F .47 g .47115 .04808 m .47115 .24038 L .47212 .24038 L .47212 .04808 L F .471 g .47212 .04808 m .47212 .24038 L .47308 .24038 L .47308 .04808 L F .472 g .47308 .04808 m .47308 .24038 L .47404 .24038 L .47404 .04808 L F .473 g .47404 .04808 m .47404 .24038 L .475 .24038 L .475 .04808 L F .474 g .475 .04808 m .475 .24038 L .47596 .24038 L .47596 .04808 L F .475 g .47596 .04808 m .47596 .24038 L .47692 .24038 L .47692 .04808 L F .476 g .47692 .04808 m .47692 .24038 L .47788 .24038 L .47788 .04808 L F .477 g .47788 .04808 m .47788 .24038 L .47885 .24038 L .47885 .04808 L F .478 g .47885 .04808 m .47885 .24038 L .47981 .24038 L .47981 .04808 L F .479 g .47981 .04808 m .47981 .24038 L .48077 .24038 L .48077 .04808 L F .48 g .48077 .04808 m .48077 .24038 L .48173 .24038 L .48173 .04808 L F .481 g .48173 .04808 m .48173 .24038 L .48269 .24038 L .48269 .04808 L F .482 g .48269 .04808 m .48269 .24038 L .48365 .24038 L .48365 .04808 L F .483 g .48365 .04808 m .48365 .24038 L .48462 .24038 L .48462 .04808 L F .484 g .48462 .04808 m .48462 .24038 L .48558 .24038 L .48558 .04808 L F .485 g .48558 .04808 m .48558 .24038 L .48654 .24038 L .48654 .04808 L F .486 g .48654 .04808 m .48654 .24038 L .4875 .24038 L .4875 .04808 L F .487 g .4875 .04808 m .4875 .24038 L .48846 .24038 L .48846 .04808 L F .488 g .48846 .04808 m .48846 .24038 L .48942 .24038 L .48942 .04808 L F .489 g .48942 .04808 m .48942 .24038 L .49038 .24038 L .49038 .04808 L F .49 g .49038 .04808 m .49038 .24038 L .49135 .24038 L .49135 .04808 L F .491 g .49135 .04808 m .49135 .24038 L .49231 .24038 L .49231 .04808 L F .492 g .49231 .04808 m .49231 .24038 L .49327 .24038 L .49327 .04808 L F .493 g .49327 .04808 m .49327 .24038 L .49423 .24038 L .49423 .04808 L F .494 g .49423 .04808 m .49423 .24038 L .49519 .24038 L .49519 .04808 L F .495 g .49519 .04808 m .49519 .24038 L .49615 .24038 L .49615 .04808 L F .496 g .49615 .04808 m .49615 .24038 L .49712 .24038 L .49712 .04808 L F .497 g .49712 .04808 m .49712 .24038 L .49808 .24038 L .49808 .04808 L F .498 g .49808 .04808 m .49808 .24038 L .49904 .24038 L .49904 .04808 L F .499 g .49904 .04808 m .49904 .24038 L .5 .24038 L .5 .04808 L F .5 g .5 .04808 m .5 .24038 L .50096 .24038 L .50096 .04808 L F .501 g .50096 .04808 m .50096 .24038 L .50192 .24038 L .50192 .04808 L F .502 g .50192 .04808 m .50192 .24038 L .50288 .24038 L .50288 .04808 L F .503 g .50288 .04808 m .50288 .24038 L .50385 .24038 L .50385 .04808 L F .504 g .50385 .04808 m .50385 .24038 L .50481 .24038 L .50481 .04808 L F .505 g .50481 .04808 m .50481 .24038 L .50577 .24038 L .50577 .04808 L F .506 g .50577 .04808 m .50577 .24038 L .50673 .24038 L .50673 .04808 L F .507 g .50673 .04808 m .50673 .24038 L .50769 .24038 L .50769 .04808 L F .508 g .50769 .04808 m .50769 .24038 L .50865 .24038 L .50865 .04808 L F .509 g .50865 .04808 m .50865 .24038 L .50962 .24038 L .50962 .04808 L F .51 g .50962 .04808 m .50962 .24038 L .51058 .24038 L .51058 .04808 L F .511 g .51058 .04808 m .51058 .24038 L .51154 .24038 L .51154 .04808 L F .512 g .51154 .04808 m .51154 .24038 L .5125 .24038 L .5125 .04808 L F .513 g .5125 .04808 m .5125 .24038 L .51346 .24038 L .51346 .04808 L F .514 g .51346 .04808 m .51346 .24038 L .51442 .24038 L .51442 .04808 L F .515 g .51442 .04808 m .51442 .24038 L .51538 .24038 L .51538 .04808 L F .516 g .51538 .04808 m .51538 .24038 L .51635 .24038 L .51635 .04808 L F .517 g .51635 .04808 m .51635 .24038 L .51731 .24038 L .51731 .04808 L F .518 g .51731 .04808 m .51731 .24038 L .51827 .24038 L .51827 .04808 L F .519 g .51827 .04808 m .51827 .24038 L .51923 .24038 L .51923 .04808 L F .52 g .51923 .04808 m .51923 .24038 L .52019 .24038 L .52019 .04808 L F .521 g .52019 .04808 m .52019 .24038 L .52115 .24038 L .52115 .04808 L F .522 g .52115 .04808 m .52115 .24038 L .52212 .24038 L .52212 .04808 L F .523 g .52212 .04808 m .52212 .24038 L .52308 .24038 L .52308 .04808 L F .524 g .52308 .04808 m .52308 .24038 L .52404 .24038 L .52404 .04808 L F .525 g .52404 .04808 m .52404 .24038 L .525 .24038 L .525 .04808 L F .526 g .525 .04808 m .525 .24038 L .52596 .24038 L .52596 .04808 L F .527 g .52596 .04808 m .52596 .24038 L .52692 .24038 L .52692 .04808 L F .528 g .52692 .04808 m .52692 .24038 L .52788 .24038 L .52788 .04808 L F .529 g .52788 .04808 m .52788 .24038 L .52885 .24038 L .52885 .04808 L F .53 g .52885 .04808 m .52885 .24038 L .52981 .24038 L .52981 .04808 L F .531 g .52981 .04808 m .52981 .24038 L .53077 .24038 L .53077 .04808 L F .532 g .53077 .04808 m .53077 .24038 L .53173 .24038 L .53173 .04808 L F .533 g .53173 .04808 m .53173 .24038 L .53269 .24038 L .53269 .04808 L F .534 g .53269 .04808 m .53269 .24038 L .53365 .24038 L .53365 .04808 L F .535 g .53365 .04808 m .53365 .24038 L .53462 .24038 L .53462 .04808 L F .536 g .53462 .04808 m .53462 .24038 L .53558 .24038 L .53558 .04808 L F .537 g .53558 .04808 m .53558 .24038 L .53654 .24038 L .53654 .04808 L F .538 g .53654 .04808 m .53654 .24038 L .5375 .24038 L .5375 .04808 L F .539 g .5375 .04808 m .5375 .24038 L .53846 .24038 L .53846 .04808 L F .54 g .53846 .04808 m .53846 .24038 L .53942 .24038 L .53942 .04808 L F .541 g .53942 .04808 m .53942 .24038 L .54038 .24038 L .54038 .04808 L F .542 g .54038 .04808 m .54038 .24038 L .54135 .24038 L .54135 .04808 L F .543 g .54135 .04808 m .54135 .24038 L .54231 .24038 L .54231 .04808 L F .544 g .54231 .04808 m .54231 .24038 L .54327 .24038 L .54327 .04808 L F .545 g .54327 .04808 m .54327 .24038 L .54423 .24038 L .54423 .04808 L F .546 g .54423 .04808 m .54423 .24038 L .54519 .24038 L .54519 .04808 L F .547 g .54519 .04808 m .54519 .24038 L .54615 .24038 L .54615 .04808 L F .548 g .54615 .04808 m .54615 .24038 L .54712 .24038 L .54712 .04808 L F .549 g .54712 .04808 m .54712 .24038 L .54808 .24038 L .54808 .04808 L F .55 g .54808 .04808 m .54808 .24038 L .54904 .24038 L .54904 .04808 L F .551 g .54904 .04808 m .54904 .24038 L .55 .24038 L .55 .04808 L F .552 g .55 .04808 m .55 .24038 L .55096 .24038 L .55096 .04808 L F .553 g .55096 .04808 m .55096 .24038 L .55192 .24038 L .55192 .04808 L F .554 g .55192 .04808 m .55192 .24038 L .55288 .24038 L .55288 .04808 L F .555 g .55288 .04808 m .55288 .24038 L .55385 .24038 L .55385 .04808 L F .556 g .55385 .04808 m .55385 .24038 L .55481 .24038 L .55481 .04808 L F .557 g .55481 .04808 m .55481 .24038 L .55577 .24038 L .55577 .04808 L F .558 g .55577 .04808 m .55577 .24038 L .55673 .24038 L .55673 .04808 L F .559 g .55673 .04808 m .55673 .24038 L .55769 .24038 L .55769 .04808 L F .56 g .55769 .04808 m .55769 .24038 L .55865 .24038 L .55865 .04808 L F .561 g .55865 .04808 m .55865 .24038 L .55962 .24038 L .55962 .04808 L F .562 g .55962 .04808 m .55962 .24038 L .56058 .24038 L .56058 .04808 L F .563 g .56058 .04808 m .56058 .24038 L .56154 .24038 L .56154 .04808 L F .564 g .56154 .04808 m .56154 .24038 L .5625 .24038 L .5625 .04808 L F .565 g .5625 .04808 m .5625 .24038 L .56346 .24038 L .56346 .04808 L F .566 g .56346 .04808 m .56346 .24038 L .56442 .24038 L .56442 .04808 L F .567 g .56442 .04808 m .56442 .24038 L .56538 .24038 L .56538 .04808 L F .568 g .56538 .04808 m .56538 .24038 L .56635 .24038 L .56635 .04808 L F .569 g .56635 .04808 m .56635 .24038 L .56731 .24038 L .56731 .04808 L F .57 g .56731 .04808 m .56731 .24038 L .56827 .24038 L .56827 .04808 L F .571 g .56827 .04808 m .56827 .24038 L .56923 .24038 L .56923 .04808 L F .572 g .56923 .04808 m .56923 .24038 L .57019 .24038 L .57019 .04808 L F .573 g .57019 .04808 m .57019 .24038 L .57115 .24038 L .57115 .04808 L F .574 g .57115 .04808 m .57115 .24038 L .57212 .24038 L .57212 .04808 L F .575 g .57212 .04808 m .57212 .24038 L .57308 .24038 L .57308 .04808 L F .576 g .57308 .04808 m .57308 .24038 L .57404 .24038 L .57404 .04808 L F .577 g .57404 .04808 m .57404 .24038 L .575 .24038 L .575 .04808 L F .578 g .575 .04808 m .575 .24038 L .57596 .24038 L .57596 .04808 L F .579 g .57596 .04808 m .57596 .24038 L .57692 .24038 L .57692 .04808 L F .58 g .57692 .04808 m .57692 .24038 L .57788 .24038 L .57788 .04808 L F .581 g .57788 .04808 m .57788 .24038 L .57885 .24038 L .57885 .04808 L F .582 g .57885 .04808 m .57885 .24038 L .57981 .24038 L .57981 .04808 L F .583 g .57981 .04808 m .57981 .24038 L .58077 .24038 L .58077 .04808 L F .584 g .58077 .04808 m .58077 .24038 L .58173 .24038 L .58173 .04808 L F .585 g .58173 .04808 m .58173 .24038 L .58269 .24038 L .58269 .04808 L F .586 g .58269 .04808 m .58269 .24038 L .58365 .24038 L .58365 .04808 L F .587 g .58365 .04808 m .58365 .24038 L .58462 .24038 L .58462 .04808 L F .588 g .58462 .04808 m .58462 .24038 L .58558 .24038 L .58558 .04808 L F .589 g .58558 .04808 m .58558 .24038 L .58654 .24038 L .58654 .04808 L F .59 g .58654 .04808 m .58654 .24038 L .5875 .24038 L .5875 .04808 L F .591 g .5875 .04808 m .5875 .24038 L .58846 .24038 L .58846 .04808 L F .592 g .58846 .04808 m .58846 .24038 L .58942 .24038 L .58942 .04808 L F .593 g .58942 .04808 m .58942 .24038 L .59038 .24038 L .59038 .04808 L F .594 g .59038 .04808 m .59038 .24038 L .59135 .24038 L .59135 .04808 L F .595 g .59135 .04808 m .59135 .24038 L .59231 .24038 L .59231 .04808 L F .596 g .59231 .04808 m .59231 .24038 L .59327 .24038 L .59327 .04808 L F .597 g .59327 .04808 m .59327 .24038 L .59423 .24038 L .59423 .04808 L F .598 g .59423 .04808 m .59423 .24038 L .59519 .24038 L .59519 .04808 L F .599 g .59519 .04808 m .59519 .24038 L .59615 .24038 L .59615 .04808 L F .6 g .59615 .04808 m .59615 .24038 L .59712 .24038 L .59712 .04808 L F .601 g .59712 .04808 m .59712 .24038 L .59808 .24038 L .59808 .04808 L F .602 g .59808 .04808 m .59808 .24038 L .59904 .24038 L .59904 .04808 L F .603 g .59904 .04808 m .59904 .24038 L .6 .24038 L .6 .04808 L F .604 g .6 .04808 m .6 .24038 L .60096 .24038 L .60096 .04808 L F .605 g .60096 .04808 m .60096 .24038 L .60192 .24038 L .60192 .04808 L F .606 g .60192 .04808 m .60192 .24038 L .60288 .24038 L .60288 .04808 L F .607 g .60288 .04808 m .60288 .24038 L .60385 .24038 L .60385 .04808 L F .608 g .60385 .04808 m .60385 .24038 L .60481 .24038 L .60481 .04808 L F .609 g .60481 .04808 m .60481 .24038 L .60577 .24038 L .60577 .04808 L F .61 g .60577 .04808 m .60577 .24038 L .60673 .24038 L .60673 .04808 L F .611 g .60673 .04808 m .60673 .24038 L .60769 .24038 L .60769 .04808 L F .612 g .60769 .04808 m .60769 .24038 L .60865 .24038 L .60865 .04808 L F .613 g .60865 .04808 m .60865 .24038 L .60962 .24038 L .60962 .04808 L F .614 g .60962 .04808 m .60962 .24038 L .61058 .24038 L .61058 .04808 L F .615 g .61058 .04808 m .61058 .24038 L .61154 .24038 L .61154 .04808 L F .616 g .61154 .04808 m .61154 .24038 L .6125 .24038 L .6125 .04808 L F .617 g .6125 .04808 m .6125 .24038 L .61346 .24038 L .61346 .04808 L F .618 g .61346 .04808 m .61346 .24038 L .61442 .24038 L .61442 .04808 L F .619 g .61442 .04808 m .61442 .24038 L .61538 .24038 L .61538 .04808 L F .62 g .61538 .04808 m .61538 .24038 L .61635 .24038 L .61635 .04808 L F .621 g .61635 .04808 m .61635 .24038 L .61731 .24038 L .61731 .04808 L F .622 g .61731 .04808 m .61731 .24038 L .61827 .24038 L .61827 .04808 L F .623 g .61827 .04808 m .61827 .24038 L .61923 .24038 L .61923 .04808 L F .624 g .61923 .04808 m .61923 .24038 L .62019 .24038 L .62019 .04808 L F .625 g .62019 .04808 m .62019 .24038 L .62115 .24038 L .62115 .04808 L F .626 g .62115 .04808 m .62115 .24038 L .62212 .24038 L .62212 .04808 L F .627 g .62212 .04808 m .62212 .24038 L .62308 .24038 L .62308 .04808 L F .628 g .62308 .04808 m .62308 .24038 L .62404 .24038 L .62404 .04808 L F .629 g .62404 .04808 m .62404 .24038 L .625 .24038 L .625 .04808 L F .63 g .625 .04808 m .625 .24038 L .62596 .24038 L .62596 .04808 L F .631 g .62596 .04808 m .62596 .24038 L .62692 .24038 L .62692 .04808 L F .632 g .62692 .04808 m .62692 .24038 L .62788 .24038 L .62788 .04808 L F .633 g .62788 .04808 m .62788 .24038 L .62885 .24038 L .62885 .04808 L F .634 g .62885 .04808 m .62885 .24038 L .62981 .24038 L .62981 .04808 L F .635 g .62981 .04808 m .62981 .24038 L .63077 .24038 L .63077 .04808 L F .636 g .63077 .04808 m .63077 .24038 L .63173 .24038 L .63173 .04808 L F .637 g .63173 .04808 m .63173 .24038 L .63269 .24038 L .63269 .04808 L F .638 g .63269 .04808 m .63269 .24038 L .63365 .24038 L .63365 .04808 L F .639 g .63365 .04808 m .63365 .24038 L .63462 .24038 L .63462 .04808 L F .64 g .63462 .04808 m .63462 .24038 L .63558 .24038 L .63558 .04808 L F .641 g .63558 .04808 m .63558 .24038 L .63654 .24038 L .63654 .04808 L F .642 g .63654 .04808 m .63654 .24038 L .6375 .24038 L .6375 .04808 L F .643 g .6375 .04808 m .6375 .24038 L .63846 .24038 L .63846 .04808 L F .644 g .63846 .04808 m .63846 .24038 L .63942 .24038 L .63942 .04808 L F .645 g .63942 .04808 m .63942 .24038 L .64038 .24038 L .64038 .04808 L F .646 g .64038 .04808 m .64038 .24038 L .64135 .24038 L .64135 .04808 L F .647 g .64135 .04808 m .64135 .24038 L .64231 .24038 L .64231 .04808 L F .648 g .64231 .04808 m .64231 .24038 L .64327 .24038 L .64327 .04808 L F .649 g .64327 .04808 m .64327 .24038 L .64423 .24038 L .64423 .04808 L F .65 g .64423 .04808 m .64423 .24038 L .64519 .24038 L .64519 .04808 L F .651 g .64519 .04808 m .64519 .24038 L .64615 .24038 L .64615 .04808 L F .652 g .64615 .04808 m .64615 .24038 L .64712 .24038 L .64712 .04808 L F .653 g .64712 .04808 m .64712 .24038 L .64808 .24038 L .64808 .04808 L F .654 g .64808 .04808 m .64808 .24038 L .64904 .24038 L .64904 .04808 L F .655 g .64904 .04808 m .64904 .24038 L .65 .24038 L .65 .04808 L F .656 g .65 .04808 m .65 .24038 L .65096 .24038 L .65096 .04808 L F .657 g .65096 .04808 m .65096 .24038 L .65192 .24038 L .65192 .04808 L F .658 g .65192 .04808 m .65192 .24038 L .65288 .24038 L .65288 .04808 L F .659 g .65288 .04808 m .65288 .24038 L .65385 .24038 L .65385 .04808 L F .66 g .65385 .04808 m .65385 .24038 L .65481 .24038 L .65481 .04808 L F .661 g .65481 .04808 m .65481 .24038 L .65577 .24038 L .65577 .04808 L F .662 g .65577 .04808 m .65577 .24038 L .65673 .24038 L .65673 .04808 L F .663 g .65673 .04808 m .65673 .24038 L .65769 .24038 L .65769 .04808 L F .664 g .65769 .04808 m .65769 .24038 L .65865 .24038 L .65865 .04808 L F .665 g .65865 .04808 m .65865 .24038 L .65962 .24038 L .65962 .04808 L F .666 g .65962 .04808 m .65962 .24038 L .66058 .24038 L .66058 .04808 L F .667 g .66058 .04808 m .66058 .24038 L .66154 .24038 L .66154 .04808 L F .668 g .66154 .04808 m .66154 .24038 L .6625 .24038 L .6625 .04808 L F .669 g .6625 .04808 m .6625 .24038 L .66346 .24038 L .66346 .04808 L F .67 g .66346 .04808 m .66346 .24038 L .66442 .24038 L .66442 .04808 L F .671 g .66442 .04808 m .66442 .24038 L .66538 .24038 L .66538 .04808 L F .672 g .66538 .04808 m .66538 .24038 L .66635 .24038 L .66635 .04808 L F .673 g .66635 .04808 m .66635 .24038 L .66731 .24038 L .66731 .04808 L F .674 g .66731 .04808 m .66731 .24038 L .66827 .24038 L .66827 .04808 L F .675 g .66827 .04808 m .66827 .24038 L .66923 .24038 L .66923 .04808 L F .676 g .66923 .04808 m .66923 .24038 L .67019 .24038 L .67019 .04808 L F .677 g .67019 .04808 m .67019 .24038 L .67115 .24038 L .67115 .04808 L F .678 g .67115 .04808 m .67115 .24038 L .67212 .24038 L .67212 .04808 L F .679 g .67212 .04808 m .67212 .24038 L .67308 .24038 L .67308 .04808 L F .68 g .67308 .04808 m .67308 .24038 L .67404 .24038 L .67404 .04808 L F .681 g .67404 .04808 m .67404 .24038 L .675 .24038 L .675 .04808 L F .682 g .675 .04808 m .675 .24038 L .67596 .24038 L .67596 .04808 L F .683 g .67596 .04808 m .67596 .24038 L .67692 .24038 L .67692 .04808 L F .684 g .67692 .04808 m .67692 .24038 L .67788 .24038 L .67788 .04808 L F .685 g .67788 .04808 m .67788 .24038 L .67885 .24038 L .67885 .04808 L F .686 g .67885 .04808 m .67885 .24038 L .67981 .24038 L .67981 .04808 L F .687 g .67981 .04808 m .67981 .24038 L .68077 .24038 L .68077 .04808 L F .688 g .68077 .04808 m .68077 .24038 L .68173 .24038 L .68173 .04808 L F .689 g .68173 .04808 m .68173 .24038 L .68269 .24038 L .68269 .04808 L F .69 g .68269 .04808 m .68269 .24038 L .68365 .24038 L .68365 .04808 L F .691 g .68365 .04808 m .68365 .24038 L .68462 .24038 L .68462 .04808 L F .692 g .68462 .04808 m .68462 .24038 L .68558 .24038 L .68558 .04808 L F .693 g .68558 .04808 m .68558 .24038 L .68654 .24038 L .68654 .04808 L F .694 g .68654 .04808 m .68654 .24038 L .6875 .24038 L .6875 .04808 L F .695 g .6875 .04808 m .6875 .24038 L .68846 .24038 L .68846 .04808 L F .696 g .68846 .04808 m .68846 .24038 L .68942 .24038 L .68942 .04808 L F .697 g .68942 .04808 m .68942 .24038 L .69038 .24038 L .69038 .04808 L F .698 g .69038 .04808 m .69038 .24038 L .69135 .24038 L .69135 .04808 L F .699 g .69135 .04808 m .69135 .24038 L .69231 .24038 L .69231 .04808 L F .7 g .69231 .04808 m .69231 .24038 L .69327 .24038 L .69327 .04808 L F .701 g .69327 .04808 m .69327 .24038 L .69423 .24038 L .69423 .04808 L F .702 g .69423 .04808 m .69423 .24038 L .69519 .24038 L .69519 .04808 L F .703 g .69519 .04808 m .69519 .24038 L .69615 .24038 L .69615 .04808 L F .704 g .69615 .04808 m .69615 .24038 L .69712 .24038 L .69712 .04808 L F .705 g .69712 .04808 m .69712 .24038 L .69808 .24038 L .69808 .04808 L F .706 g .69808 .04808 m .69808 .24038 L .69904 .24038 L .69904 .04808 L F .707 g .69904 .04808 m .69904 .24038 L .7 .24038 L .7 .04808 L F .708 g .7 .04808 m .7 .24038 L .70096 .24038 L .70096 .04808 L F .709 g .70096 .04808 m .70096 .24038 L .70192 .24038 L .70192 .04808 L F .71 g .70192 .04808 m .70192 .24038 L .70288 .24038 L .70288 .04808 L F .711 g .70288 .04808 m .70288 .24038 L .70385 .24038 L .70385 .04808 L F .712 g .70385 .04808 m .70385 .24038 L .70481 .24038 L .70481 .04808 L F .713 g .70481 .04808 m .70481 .24038 L .70577 .24038 L .70577 .04808 L F .714 g .70577 .04808 m .70577 .24038 L .70673 .24038 L .70673 .04808 L F .715 g .70673 .04808 m .70673 .24038 L .70769 .24038 L .70769 .04808 L F .716 g .70769 .04808 m .70769 .24038 L .70865 .24038 L .70865 .04808 L F .717 g .70865 .04808 m .70865 .24038 L .70962 .24038 L .70962 .04808 L F .718 g .70962 .04808 m .70962 .24038 L .71058 .24038 L .71058 .04808 L F .719 g .71058 .04808 m .71058 .24038 L .71154 .24038 L .71154 .04808 L F .72 g .71154 .04808 m .71154 .24038 L .7125 .24038 L .7125 .04808 L F .721 g .7125 .04808 m .7125 .24038 L .71346 .24038 L .71346 .04808 L F .722 g .71346 .04808 m .71346 .24038 L .71442 .24038 L .71442 .04808 L F .723 g .71442 .04808 m .71442 .24038 L .71538 .24038 L .71538 .04808 L F .724 g .71538 .04808 m .71538 .24038 L .71635 .24038 L .71635 .04808 L F .725 g .71635 .04808 m .71635 .24038 L .71731 .24038 L .71731 .04808 L F .726 g .71731 .04808 m .71731 .24038 L .71827 .24038 L .71827 .04808 L F .727 g .71827 .04808 m .71827 .24038 L .71923 .24038 L .71923 .04808 L F .728 g .71923 .04808 m .71923 .24038 L .72019 .24038 L .72019 .04808 L F .729 g .72019 .04808 m .72019 .24038 L .72115 .24038 L .72115 .04808 L F .73 g .72115 .04808 m .72115 .24038 L .72212 .24038 L .72212 .04808 L F .731 g .72212 .04808 m .72212 .24038 L .72308 .24038 L .72308 .04808 L F .732 g .72308 .04808 m .72308 .24038 L .72404 .24038 L .72404 .04808 L F .733 g .72404 .04808 m .72404 .24038 L .725 .24038 L .725 .04808 L F .734 g .725 .04808 m .725 .24038 L .72596 .24038 L .72596 .04808 L F .735 g .72596 .04808 m .72596 .24038 L .72692 .24038 L .72692 .04808 L F .736 g .72692 .04808 m .72692 .24038 L .72788 .24038 L .72788 .04808 L F .737 g .72788 .04808 m .72788 .24038 L .72885 .24038 L .72885 .04808 L F .738 g .72885 .04808 m .72885 .24038 L .72981 .24038 L .72981 .04808 L F .739 g .72981 .04808 m .72981 .24038 L .73077 .24038 L .73077 .04808 L F .74 g .73077 .04808 m .73077 .24038 L .73173 .24038 L .73173 .04808 L F .741 g .73173 .04808 m .73173 .24038 L .73269 .24038 L .73269 .04808 L F .742 g .73269 .04808 m .73269 .24038 L .73365 .24038 L .73365 .04808 L F .743 g .73365 .04808 m .73365 .24038 L .73462 .24038 L .73462 .04808 L F .744 g .73462 .04808 m .73462 .24038 L .73558 .24038 L .73558 .04808 L F .745 g .73558 .04808 m .73558 .24038 L .73654 .24038 L .73654 .04808 L F .746 g .73654 .04808 m .73654 .24038 L .7375 .24038 L .7375 .04808 L F .747 g .7375 .04808 m .7375 .24038 L .73846 .24038 L .73846 .04808 L F .748 g .73846 .04808 m .73846 .24038 L .73942 .24038 L .73942 .04808 L F .749 g .73942 .04808 m .73942 .24038 L .74038 .24038 L .74038 .04808 L F .75 g .74038 .04808 m .74038 .24038 L .74135 .24038 L .74135 .04808 L F .751 g .74135 .04808 m .74135 .24038 L .74231 .24038 L .74231 .04808 L F .752 g .74231 .04808 m .74231 .24038 L .74327 .24038 L .74327 .04808 L F .753 g .74327 .04808 m .74327 .24038 L .74423 .24038 L .74423 .04808 L F .754 g .74423 .04808 m .74423 .24038 L .74519 .24038 L .74519 .04808 L F .755 g .74519 .04808 m .74519 .24038 L .74615 .24038 L .74615 .04808 L F .756 g .74615 .04808 m .74615 .24038 L .74712 .24038 L .74712 .04808 L F .757 g .74712 .04808 m .74712 .24038 L .74808 .24038 L .74808 .04808 L F .758 g .74808 .04808 m .74808 .24038 L .74904 .24038 L .74904 .04808 L F .759 g .74904 .04808 m .74904 .24038 L .75 .24038 L .75 .04808 L F .76 g .75 .04808 m .75 .24038 L .75096 .24038 L .75096 .04808 L F .761 g .75096 .04808 m .75096 .24038 L .75192 .24038 L .75192 .04808 L F .762 g .75192 .04808 m .75192 .24038 L .75288 .24038 L .75288 .04808 L F .763 g .75288 .04808 m .75288 .24038 L .75385 .24038 L .75385 .04808 L F .764 g .75385 .04808 m .75385 .24038 L .75481 .24038 L .75481 .04808 L F .765 g .75481 .04808 m .75481 .24038 L .75577 .24038 L .75577 .04808 L F .766 g .75577 .04808 m .75577 .24038 L .75673 .24038 L .75673 .04808 L F .767 g .75673 .04808 m .75673 .24038 L .75769 .24038 L .75769 .04808 L F .768 g .75769 .04808 m .75769 .24038 L .75865 .24038 L .75865 .04808 L F .769 g .75865 .04808 m .75865 .24038 L .75962 .24038 L .75962 .04808 L F .77 g .75962 .04808 m .75962 .24038 L .76058 .24038 L .76058 .04808 L F .771 g .76058 .04808 m .76058 .24038 L .76154 .24038 L .76154 .04808 L F .772 g .76154 .04808 m .76154 .24038 L .7625 .24038 L .7625 .04808 L F .773 g .7625 .04808 m .7625 .24038 L .76346 .24038 L .76346 .04808 L F .774 g .76346 .04808 m .76346 .24038 L .76442 .24038 L .76442 .04808 L F .775 g .76442 .04808 m .76442 .24038 L .76538 .24038 L .76538 .04808 L F .776 g .76538 .04808 m .76538 .24038 L .76635 .24038 L .76635 .04808 L F .777 g .76635 .04808 m .76635 .24038 L .76731 .24038 L .76731 .04808 L F .778 g .76731 .04808 m .76731 .24038 L .76827 .24038 L .76827 .04808 L F .779 g .76827 .04808 m .76827 .24038 L .76923 .24038 L .76923 .04808 L F .78 g .76923 .04808 m .76923 .24038 L .77019 .24038 L .77019 .04808 L F .781 g .77019 .04808 m .77019 .24038 L .77115 .24038 L .77115 .04808 L F .782 g .77115 .04808 m .77115 .24038 L .77212 .24038 L .77212 .04808 L F .783 g .77212 .04808 m .77212 .24038 L .77308 .24038 L .77308 .04808 L F .784 g .77308 .04808 m .77308 .24038 L .77404 .24038 L .77404 .04808 L F .785 g .77404 .04808 m .77404 .24038 L .775 .24038 L .775 .04808 L F .786 g .775 .04808 m .775 .24038 L .77596 .24038 L .77596 .04808 L F .787 g .77596 .04808 m .77596 .24038 L .77692 .24038 L .77692 .04808 L F .788 g .77692 .04808 m .77692 .24038 L .77788 .24038 L .77788 .04808 L F .789 g .77788 .04808 m .77788 .24038 L .77885 .24038 L .77885 .04808 L F .79 g .77885 .04808 m .77885 .24038 L .77981 .24038 L .77981 .04808 L F .791 g .77981 .04808 m .77981 .24038 L .78077 .24038 L .78077 .04808 L F .792 g .78077 .04808 m .78077 .24038 L .78173 .24038 L .78173 .04808 L F .793 g .78173 .04808 m .78173 .24038 L .78269 .24038 L .78269 .04808 L F .794 g .78269 .04808 m .78269 .24038 L .78365 .24038 L .78365 .04808 L F .795 g .78365 .04808 m .78365 .24038 L .78462 .24038 L .78462 .04808 L F .796 g .78462 .04808 m .78462 .24038 L .78558 .24038 L .78558 .04808 L F .797 g .78558 .04808 m .78558 .24038 L .78654 .24038 L .78654 .04808 L F .798 g .78654 .04808 m .78654 .24038 L .7875 .24038 L .7875 .04808 L F .799 g .7875 .04808 m .7875 .24038 L .78846 .24038 L .78846 .04808 L F .8 g .78846 .04808 m .78846 .24038 L .78942 .24038 L .78942 .04808 L F .801 g .78942 .04808 m .78942 .24038 L .79038 .24038 L .79038 .04808 L F .802 g .79038 .04808 m .79038 .24038 L .79135 .24038 L .79135 .04808 L F .803 g .79135 .04808 m .79135 .24038 L .79231 .24038 L .79231 .04808 L F .804 g .79231 .04808 m .79231 .24038 L .79327 .24038 L .79327 .04808 L F .805 g .79327 .04808 m .79327 .24038 L .79423 .24038 L .79423 .04808 L F .806 g .79423 .04808 m .79423 .24038 L .79519 .24038 L .79519 .04808 L F .807 g .79519 .04808 m .79519 .24038 L .79615 .24038 L .79615 .04808 L F .808 g .79615 .04808 m .79615 .24038 L .79712 .24038 L .79712 .04808 L F .809 g .79712 .04808 m .79712 .24038 L .79808 .24038 L .79808 .04808 L F .81 g .79808 .04808 m .79808 .24038 L .79904 .24038 L .79904 .04808 L F .811 g .79904 .04808 m .79904 .24038 L .8 .24038 L .8 .04808 L F .812 g .8 .04808 m .8 .24038 L .80096 .24038 L .80096 .04808 L F .813 g .80096 .04808 m .80096 .24038 L .80192 .24038 L .80192 .04808 L F .814 g .80192 .04808 m .80192 .24038 L .80288 .24038 L .80288 .04808 L F .815 g .80288 .04808 m .80288 .24038 L .80385 .24038 L .80385 .04808 L F .816 g .80385 .04808 m .80385 .24038 L .80481 .24038 L .80481 .04808 L F .817 g .80481 .04808 m .80481 .24038 L .80577 .24038 L .80577 .04808 L F .818 g .80577 .04808 m .80577 .24038 L .80673 .24038 L .80673 .04808 L F .819 g .80673 .04808 m .80673 .24038 L .80769 .24038 L .80769 .04808 L F .82 g .80769 .04808 m .80769 .24038 L .80865 .24038 L .80865 .04808 L F .821 g .80865 .04808 m .80865 .24038 L .80962 .24038 L .80962 .04808 L F .822 g .80962 .04808 m .80962 .24038 L .81058 .24038 L .81058 .04808 L F .823 g .81058 .04808 m .81058 .24038 L .81154 .24038 L .81154 .04808 L F .824 g .81154 .04808 m .81154 .24038 L .8125 .24038 L .8125 .04808 L F .825 g .8125 .04808 m .8125 .24038 L .81346 .24038 L .81346 .04808 L F .826 g .81346 .04808 m .81346 .24038 L .81442 .24038 L .81442 .04808 L F .827 g .81442 .04808 m .81442 .24038 L .81538 .24038 L .81538 .04808 L F .828 g .81538 .04808 m .81538 .24038 L .81635 .24038 L .81635 .04808 L F .829 g .81635 .04808 m .81635 .24038 L .81731 .24038 L .81731 .04808 L F .83 g .81731 .04808 m .81731 .24038 L .81827 .24038 L .81827 .04808 L F .831 g .81827 .04808 m .81827 .24038 L .81923 .24038 L .81923 .04808 L F .832 g .81923 .04808 m .81923 .24038 L .82019 .24038 L .82019 .04808 L F .833 g .82019 .04808 m .82019 .24038 L .82115 .24038 L .82115 .04808 L F .834 g .82115 .04808 m .82115 .24038 L .82212 .24038 L .82212 .04808 L F .835 g .82212 .04808 m .82212 .24038 L .82308 .24038 L .82308 .04808 L F .836 g .82308 .04808 m .82308 .24038 L .82404 .24038 L .82404 .04808 L F .837 g .82404 .04808 m .82404 .24038 L .825 .24038 L .825 .04808 L F .838 g .825 .04808 m .825 .24038 L .82596 .24038 L .82596 .04808 L F .839 g .82596 .04808 m .82596 .24038 L .82692 .24038 L .82692 .04808 L F .84 g .82692 .04808 m .82692 .24038 L .82788 .24038 L .82788 .04808 L F .841 g .82788 .04808 m .82788 .24038 L .82885 .24038 L .82885 .04808 L F .842 g .82885 .04808 m .82885 .24038 L .82981 .24038 L .82981 .04808 L F .843 g .82981 .04808 m .82981 .24038 L .83077 .24038 L .83077 .04808 L F .844 g .83077 .04808 m .83077 .24038 L .83173 .24038 L .83173 .04808 L F .845 g .83173 .04808 m .83173 .24038 L .83269 .24038 L .83269 .04808 L F .846 g .83269 .04808 m .83269 .24038 L .83365 .24038 L .83365 .04808 L F .847 g .83365 .04808 m .83365 .24038 L .83462 .24038 L .83462 .04808 L F .848 g .83462 .04808 m .83462 .24038 L .83558 .24038 L .83558 .04808 L F .849 g .83558 .04808 m .83558 .24038 L .83654 .24038 L .83654 .04808 L F .85 g .83654 .04808 m .83654 .24038 L .8375 .24038 L .8375 .04808 L F .851 g .8375 .04808 m .8375 .24038 L .83846 .24038 L .83846 .04808 L F .852 g .83846 .04808 m .83846 .24038 L .83942 .24038 L .83942 .04808 L F .853 g .83942 .04808 m .83942 .24038 L .84038 .24038 L .84038 .04808 L F .854 g .84038 .04808 m .84038 .24038 L .84135 .24038 L .84135 .04808 L F .855 g .84135 .04808 m .84135 .24038 L .84231 .24038 L .84231 .04808 L F .856 g .84231 .04808 m .84231 .24038 L .84327 .24038 L .84327 .04808 L F .857 g .84327 .04808 m .84327 .24038 L .84423 .24038 L .84423 .04808 L F .858 g .84423 .04808 m .84423 .24038 L .84519 .24038 L .84519 .04808 L F .859 g .84519 .04808 m .84519 .24038 L .84615 .24038 L .84615 .04808 L F .86 g .84615 .04808 m .84615 .24038 L .84712 .24038 L .84712 .04808 L F .861 g .84712 .04808 m .84712 .24038 L .84808 .24038 L .84808 .04808 L F .862 g .84808 .04808 m .84808 .24038 L .84904 .24038 L .84904 .04808 L F .863 g .84904 .04808 m .84904 .24038 L .85 .24038 L .85 .04808 L F .864 g .85 .04808 m .85 .24038 L .85096 .24038 L .85096 .04808 L F .865 g .85096 .04808 m .85096 .24038 L .85192 .24038 L .85192 .04808 L F .866 g .85192 .04808 m .85192 .24038 L .85288 .24038 L .85288 .04808 L F .867 g .85288 .04808 m .85288 .24038 L .85385 .24038 L .85385 .04808 L F .868 g .85385 .04808 m .85385 .24038 L .85481 .24038 L .85481 .04808 L F .869 g .85481 .04808 m .85481 .24038 L .85577 .24038 L .85577 .04808 L F .87 g .85577 .04808 m .85577 .24038 L .85673 .24038 L .85673 .04808 L F .871 g .85673 .04808 m .85673 .24038 L .85769 .24038 L .85769 .04808 L F .872 g .85769 .04808 m .85769 .24038 L .85865 .24038 L .85865 .04808 L F .873 g .85865 .04808 m .85865 .24038 L .85962 .24038 L .85962 .04808 L F .874 g .85962 .04808 m .85962 .24038 L .86058 .24038 L .86058 .04808 L F .875 g .86058 .04808 m .86058 .24038 L .86154 .24038 L .86154 .04808 L F .876 g .86154 .04808 m .86154 .24038 L .8625 .24038 L .8625 .04808 L F .877 g .8625 .04808 m .8625 .24038 L .86346 .24038 L .86346 .04808 L F .878 g .86346 .04808 m .86346 .24038 L .86442 .24038 L .86442 .04808 L F .879 g .86442 .04808 m .86442 .24038 L .86538 .24038 L .86538 .04808 L F .88 g .86538 .04808 m .86538 .24038 L .86635 .24038 L .86635 .04808 L F .881 g .86635 .04808 m .86635 .24038 L .86731 .24038 L .86731 .04808 L F .882 g .86731 .04808 m .86731 .24038 L .86827 .24038 L .86827 .04808 L F .883 g .86827 .04808 m .86827 .24038 L .86923 .24038 L .86923 .04808 L F .884 g .86923 .04808 m .86923 .24038 L .87019 .24038 L .87019 .04808 L F .885 g .87019 .04808 m .87019 .24038 L .87115 .24038 L .87115 .04808 L F .886 g .87115 .04808 m .87115 .24038 L .87212 .24038 L .87212 .04808 L F .887 g .87212 .04808 m .87212 .24038 L .87308 .24038 L .87308 .04808 L F .888 g .87308 .04808 m .87308 .24038 L .87404 .24038 L .87404 .04808 L F .889 g .87404 .04808 m .87404 .24038 L .875 .24038 L .875 .04808 L F .89 g .875 .04808 m .875 .24038 L .87596 .24038 L .87596 .04808 L F .891 g .87596 .04808 m .87596 .24038 L .87692 .24038 L .87692 .04808 L F .892 g .87692 .04808 m .87692 .24038 L .87788 .24038 L .87788 .04808 L F .893 g .87788 .04808 m .87788 .24038 L .87885 .24038 L .87885 .04808 L F .894 g .87885 .04808 m .87885 .24038 L .87981 .24038 L .87981 .04808 L F .895 g .87981 .04808 m .87981 .24038 L .88077 .24038 L .88077 .04808 L F .896 g .88077 .04808 m .88077 .24038 L .88173 .24038 L .88173 .04808 L F .897 g .88173 .04808 m .88173 .24038 L .88269 .24038 L .88269 .04808 L F .898 g .88269 .04808 m .88269 .24038 L .88365 .24038 L .88365 .04808 L F .899 g .88365 .04808 m .88365 .24038 L .88462 .24038 L .88462 .04808 L F .9 g .88462 .04808 m .88462 .24038 L .88558 .24038 L .88558 .04808 L F .901 g .88558 .04808 m .88558 .24038 L .88654 .24038 L .88654 .04808 L F .902 g .88654 .04808 m .88654 .24038 L .8875 .24038 L .8875 .04808 L F .903 g .8875 .04808 m .8875 .24038 L .88846 .24038 L .88846 .04808 L F .904 g .88846 .04808 m .88846 .24038 L .88942 .24038 L .88942 .04808 L F .905 g .88942 .04808 m .88942 .24038 L .89038 .24038 L .89038 .04808 L F .906 g .89038 .04808 m .89038 .24038 L .89135 .24038 L .89135 .04808 L F .907 g .89135 .04808 m .89135 .24038 L .89231 .24038 L .89231 .04808 L F .908 g .89231 .04808 m .89231 .24038 L .89327 .24038 L .89327 .04808 L F .909 g .89327 .04808 m .89327 .24038 L .89423 .24038 L .89423 .04808 L F .91 g .89423 .04808 m .89423 .24038 L .89519 .24038 L .89519 .04808 L F .911 g .89519 .04808 m .89519 .24038 L .89615 .24038 L .89615 .04808 L F .912 g .89615 .04808 m .89615 .24038 L .89712 .24038 L .89712 .04808 L F .913 g .89712 .04808 m .89712 .24038 L .89808 .24038 L .89808 .04808 L F .914 g .89808 .04808 m .89808 .24038 L .89904 .24038 L .89904 .04808 L F .915 g .89904 .04808 m .89904 .24038 L .9 .24038 L .9 .04808 L F .916 g .9 .04808 m .9 .24038 L .90096 .24038 L .90096 .04808 L F .917 g .90096 .04808 m .90096 .24038 L .90192 .24038 L .90192 .04808 L F .918 g .90192 .04808 m .90192 .24038 L .90288 .24038 L .90288 .04808 L F .919 g .90288 .04808 m .90288 .24038 L .90385 .24038 L .90385 .04808 L F .92 g .90385 .04808 m .90385 .24038 L .90481 .24038 L .90481 .04808 L F .921 g .90481 .04808 m .90481 .24038 L .90577 .24038 L .90577 .04808 L F .922 g .90577 .04808 m .90577 .24038 L .90673 .24038 L .90673 .04808 L F .923 g .90673 .04808 m .90673 .24038 L .90769 .24038 L .90769 .04808 L F .924 g .90769 .04808 m .90769 .24038 L .90865 .24038 L .90865 .04808 L F .925 g .90865 .04808 m .90865 .24038 L .90962 .24038 L .90962 .04808 L F .926 g .90962 .04808 m .90962 .24038 L .91058 .24038 L .91058 .04808 L F .927 g .91058 .04808 m .91058 .24038 L .91154 .24038 L .91154 .04808 L F .928 g .91154 .04808 m .91154 .24038 L .9125 .24038 L .9125 .04808 L F .929 g .9125 .04808 m .9125 .24038 L .91346 .24038 L .91346 .04808 L F .93 g .91346 .04808 m .91346 .24038 L .91442 .24038 L .91442 .04808 L F .931 g .91442 .04808 m .91442 .24038 L .91538 .24038 L .91538 .04808 L F .932 g .91538 .04808 m .91538 .24038 L .91635 .24038 L .91635 .04808 L F .933 g .91635 .04808 m .91635 .24038 L .91731 .24038 L .91731 .04808 L F .934 g .91731 .04808 m .91731 .24038 L .91827 .24038 L .91827 .04808 L F .935 g .91827 .04808 m .91827 .24038 L .91923 .24038 L .91923 .04808 L F .936 g .91923 .04808 m .91923 .24038 L .92019 .24038 L .92019 .04808 L F .937 g .92019 .04808 m .92019 .24038 L .92115 .24038 L .92115 .04808 L F .938 g .92115 .04808 m .92115 .24038 L .92212 .24038 L .92212 .04808 L F .939 g .92212 .04808 m .92212 .24038 L .92308 .24038 L .92308 .04808 L F .94 g .92308 .04808 m .92308 .24038 L .92404 .24038 L .92404 .04808 L F .941 g .92404 .04808 m .92404 .24038 L .925 .24038 L .925 .04808 L F .942 g .925 .04808 m .925 .24038 L .92596 .24038 L .92596 .04808 L F .943 g .92596 .04808 m .92596 .24038 L .92692 .24038 L .92692 .04808 L F .944 g .92692 .04808 m .92692 .24038 L .92788 .24038 L .92788 .04808 L F .945 g .92788 .04808 m .92788 .24038 L .92885 .24038 L .92885 .04808 L F .946 g .92885 .04808 m .92885 .24038 L .92981 .24038 L .92981 .04808 L F .947 g .92981 .04808 m .92981 .24038 L .93077 .24038 L .93077 .04808 L F .948 g .93077 .04808 m .93077 .24038 L .93173 .24038 L .93173 .04808 L F .949 g .93173 .04808 m .93173 .24038 L .93269 .24038 L .93269 .04808 L F .95 g .93269 .04808 m .93269 .24038 L .93365 .24038 L .93365 .04808 L F .951 g .93365 .04808 m .93365 .24038 L .93462 .24038 L .93462 .04808 L F .952 g .93462 .04808 m .93462 .24038 L .93558 .24038 L .93558 .04808 L F .953 g .93558 .04808 m .93558 .24038 L .93654 .24038 L .93654 .04808 L F .954 g .93654 .04808 m .93654 .24038 L .9375 .24038 L .9375 .04808 L F .955 g .9375 .04808 m .9375 .24038 L .93846 .24038 L .93846 .04808 L F .956 g .93846 .04808 m .93846 .24038 L .93942 .24038 L .93942 .04808 L F .957 g .93942 .04808 m .93942 .24038 L .94038 .24038 L .94038 .04808 L F .958 g .94038 .04808 m .94038 .24038 L .94135 .24038 L .94135 .04808 L F .959 g .94135 .04808 m .94135 .24038 L .94231 .24038 L .94231 .04808 L F .96 g .94231 .04808 m .94231 .24038 L .94327 .24038 L .94327 .04808 L F .961 g .94327 .04808 m .94327 .24038 L .94423 .24038 L .94423 .04808 L F .962 g .94423 .04808 m .94423 .24038 L .94519 .24038 L .94519 .04808 L F .963 g .94519 .04808 m .94519 .24038 L .94615 .24038 L .94615 .04808 L F .964 g .94615 .04808 m .94615 .24038 L .94712 .24038 L .94712 .04808 L F .965 g .94712 .04808 m .94712 .24038 L .94808 .24038 L .94808 .04808 L F .966 g .94808 .04808 m .94808 .24038 L .94904 .24038 L .94904 .04808 L F .967 g .94904 .04808 m .94904 .24038 L .95 .24038 L .95 .04808 L F .968 g .95 .04808 m .95 .24038 L .95096 .24038 L .95096 .04808 L F .969 g .95096 .04808 m .95096 .24038 L .95192 .24038 L .95192 .04808 L F .97 g .95192 .04808 m .95192 .24038 L .95288 .24038 L .95288 .04808 L F .971 g .95288 .04808 m .95288 .24038 L .95385 .24038 L .95385 .04808 L F .972 g .95385 .04808 m .95385 .24038 L .95481 .24038 L .95481 .04808 L F .973 g .95481 .04808 m .95481 .24038 L .95577 .24038 L .95577 .04808 L F .974 g .95577 .04808 m .95577 .24038 L .95673 .24038 L .95673 .04808 L F .975 g .95673 .04808 m .95673 .24038 L .95769 .24038 L .95769 .04808 L F .976 g .95769 .04808 m .95769 .24038 L .95865 .24038 L .95865 .04808 L F .977 g .95865 .04808 m .95865 .24038 L .95962 .24038 L .95962 .04808 L F .978 g .95962 .04808 m .95962 .24038 L .96058 .24038 L .96058 .04808 L F .979 g .96058 .04808 m .96058 .24038 L .96154 .24038 L .96154 .04808 L F .98 g .96154 .04808 m .96154 .24038 L .9625 .24038 L .9625 .04808 L F .981 g .9625 .04808 m .9625 .24038 L .96346 .24038 L .96346 .04808 L F .982 g .96346 .04808 m .96346 .24038 L .96442 .24038 L .96442 .04808 L F .983 g .96442 .04808 m .96442 .24038 L .96538 .24038 L .96538 .04808 L F .984 g .96538 .04808 m .96538 .24038 L .96635 .24038 L .96635 .04808 L F .985 g .96635 .04808 m .96635 .24038 L .96731 .24038 L .96731 .04808 L F .986 g .96731 .04808 m .96731 .24038 L .96827 .24038 L .96827 .04808 L F .987 g .96827 .04808 m .96827 .24038 L .96923 .24038 L .96923 .04808 L F .988 g .96923 .04808 m .96923 .24038 L .97019 .24038 L .97019 .04808 L F .989 g .97019 .04808 m .97019 .24038 L .97115 .24038 L .97115 .04808 L F .99 g .97115 .04808 m .97115 .24038 L .97212 .24038 L .97212 .04808 L F .991 g .97212 .04808 m .97212 .24038 L .97308 .24038 L .97308 .04808 L F .992 g .97308 .04808 m .97308 .24038 L .97404 .24038 L .97404 .04808 L F .993 g .97404 .04808 m .97404 .24038 L .975 .24038 L .975 .04808 L F .994 g .975 .04808 m .975 .24038 L .97596 .24038 L .97596 .04808 L F .995 g .97596 .04808 m .97596 .24038 L .97692 .24038 L .97692 .04808 L F .996 g .97692 .04808 m .97692 .24038 L .97788 .24038 L .97788 .04808 L F .997 g .97788 .04808 m .97788 .24038 L .97885 .24038 L .97885 .04808 L F .998 g .97885 .04808 m .97885 .24038 L .97981 .24038 L .97981 .04808 L F .999 g .97981 .04808 m .97981 .24038 L .98077 .24038 L .98077 .04808 L F 1 g .98077 .04808 m .98077 .24038 L .98173 .24038 L .98173 .04808 L F .2 0 1 r .5 Mabswid [ ] 0 setdash .01923 .04808 m .01923 .0625 L s .11538 .04808 m .11538 .0625 L s .21154 .04808 m .21154 .0625 L s .30769 .04808 m .30769 .0625 L s .40385 .04808 m .40385 .0625 L s .5 .04808 m .5 .0625 L s .59615 .04808 m .59615 .0625 L s .69231 .04808 m .69231 .0625 L s .78846 .04808 m .78846 .0625 L s .88462 .04808 m .88462 .0625 L s .98077 .04808 m .98077 .0625 L s .5 .04808 m .5 .08173 L s .01923 .04808 m .01923 .08173 L s .98077 .04808 m .98077 .08173 L s 0 g gsave .01923 .01923 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore gsave .98077 .01923 -66 -10.2813 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 20.5625 translate 1 -1 scale 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 69.000 12.813 moveto %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", GeneratedCell->False, CellAutoOverwrite->False, ImageSize->{503, 68.875}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["CompressedBitmap", "\<\ eJzt2GVwFcsWBeAVnIcTCBIkOFxcgzsJFtw9aIKGBHd3h4u7uxfu7h6Cu7sn QbJun7kk71SqHu/H+cF99VZXzXTPqdl7qmd6fzN1vLy7+bTp5N3Nt5W3m6e/ t5+Pb6sAN48u/uanqE6AUzCA8slhxjQja7O1ELP9PfzPI2ezj2ICrpg+uuld Ix07W2cltu2jhee1XSDQ1kX99y8p/+sZ/w+Zwu9m4M8+daTjpL98DrhuyxcN jAsmBlOC6cAsYG7QHSwBVgCrgrXARmAL0Af0A3uA/cHh4FhwKmwZFoErwY3g NnAfeAQ8A14Gb4D3wefgWzAYDMNX4iPxknhM3CaCiPO2ueEQsYvYTKwllhLz iBnERGIkMZjoTQQQHYnWRDOiHlGNqEiUIYpY4dmJTDRzhwuRgIhFa02a5cR4 YBLQFUwP/gHmAQuDJUEP0AusDTYGW1lz6Ar2AgeAI8AJ4DRwLrgYXAVuAreD +8Hj4FnwCngLfAC+AD+AIbbwUOID8YJ4RNyiWcw4Rxwn9hM7iU3EGmIJMZeY TkwgRhCDiF5EV6KDNYfGRF3Ci/AkShGFiXzEH0R6IhWRhIhHxLTNKhYYH3QB U4EZwOxW+RUBy4CeYDWwHtgEbA12BP3B3uBAcCQ4EfwTnAcuBdeAm8Fd4AHw hJXhKngbfAi+BD+CoWapIIwIJt4Tz4n7xE3iMnGWOEbsI3YQG4mVxGLLgKnE eGI40Z/oSfgRvkRLohFRh6hKVCBKEu5EbiIbkc62ys0yRFwihu0OpLGtyGv5 QScnpyhRokSNGjVatGgxYsSIGTNmrFixYseOHSdOnLhx48aLFy9+/PgJEiRI mDBhokSJnJ2dkyRJkjRpUhcXl+TJk6dIkcJkcHV1TZUqVerUqdOmTevm5pYu Xbr06dNnyJAhU6ZMmTNnzpIlS9asWbNly5Y9e/YcOXLkzJkzV65cuXPnzpMn T758+Ux4gQIFChYsWKhQocKFCxcpUqRo0aLFihUrXrx4iRIlSpUqVbp06TJl ypQtW7ZcuXIVKlTw8PDw9PSsWLFipUqVqlSpUrVqVZOhWrVq1atXr1GjRq1a tWrXrl2nTp26devWr1+/QYMGDRs2bNSoUePGjZs0adKsWbPmzZu3aNHC29u7 ZcuWrVu3btOmjQlv166dj4+Pr69vhw4dOnbs2KlTp86dO3fp0qVr167+/v4B AQHdunXr3r17z549e/Xq1bt37z59+vTt27dfv34DBgwYOHCgyTB48OAhQ4YM GzZs+PDhI0aMGDly5KhRo0aPHj127Nhx48aNHz9+woQJEydOnDx58pQpU6ZO nTpt2rTp06fPmDFj5syZJnz27Nlz5syZN2/e/PnzFyxYsHDhwkWLFi1ZsmTp 0qXLli1bvnz5ihUrVq5cuXr16jVr1qxdu3bdunXr16/fuHHjpk2bNm/ebDJs 3bp127Zt27dv37Fjx86dO3ft2rV79+69e/fu27dv//79Bw4cOHjw4OHDh48c OXL06NFjx44dP378xIkTp06dOn36tAk/e/bsuXPnLly4cPHixUuXLl2+fPnK lStXr14NCgq6du3a9evXb9y4cevWrdu3b9+5c+fu3bv37t178ODBw4cPHz16 9PjxY5Ph6dOnz58/f/HixcuXL1+9evX69eu3b9++e/fu/fv3Hz58+Pjx46dP n758+RIcHBwSEhIaGvr169fv37//+PEjLCzMhCeNpGQMCxNnCxNTdtnAvHaY mLKrY5VdS9DXwqRneNmNt2Fiy2AwWW2V3Q4Lk2MWJoHgzfCye2/DxFwvNLzm HlqYXLUwMe2AVXMRmMwh/rRqzmAy0MLEn2hv1VwTq+YiMHG3wk3NZQjHJL6p ORsm5gUe086TjGAOMB9oPClleVIdrAs2tXlim4PxpA84CBxleTLd8mSJ5ckW cCd40PLkHGg8uQM+Al/99MS0EOId8Yx4YIfJUWIvsd3CZJXBhJhNTCPGWZgM sDDpYmFimsGktoWJh4VJISIPkdXCxNXCJA4R3bz5GBtMACYDU4OZwJyWcUXB smBFsAbYAGwGtgE7gQFgX1My4GhwEjgDnA8uB9eaZQzuBg+BJ60MQeBd8DH4 GvwEfrU9rh/EZ+It8ZS4R9wgLhFniCPEHmIbsYFYQSyylJxMjCWGEf2IHkRn wodoQTQkahFViHJECaIgkYvIQrgRyWk+GPCvv78HIitpiIwePfovlDREJk6c OELJZMmSRVIyTZo09kpmzJjx10rmzZs3QklDpLu7u72ShsiSJUtGKGmILF++ vL2SlStXtlfSEFmzZs0IJevVqxdJyaZNm9or2apVq0hKtm/f3l5JPz8/eyV7 9Ohhr6Qhsn///hFKGiKHDh1qr6QhcsyYMRFKGiInTZr0CyXnzp1rr+TixYsj Kblq1Sp7JTds2PALJQ2Re/bsiVDSEHno0CF7JQ2RJ0+ejFDSEHn+/Hl7JQMD A+2VvHnzpr2S9+/fj6Tks2fP7JV88+ZNJCU/f/4coaQh8tu3b1JSSkpJKSkl paSUlJJSUkr+85T8+fedA0oeo0NK5qXDSrLDb1bSm44oaZ6pg0qeBx1Rkpj1 D1IyZcqUDimZP7+DSnp5eTmiZNu2bX+vkrNmzXJQyS1btjii5JkzZxxU8smT J1JSSkpJKSklpaSUlJJSUkpKSSkpJaWklJSSUlJKSkkp+T+sJKWk40qGUUo6 qCTDlQwyAynpoJKDBg2Sko4oCRcZKSNlpIyUkTJSRspIGSkjZaSMlJEyUkbK SBkpI2WkjJSRMlJGykgZKSNlpIyUkTJSRspIGSkjZaSMlJEyUkbKSBkpI2Wk jJSRMlJGykgZKSNlpIyUkTJSRspIGSkjZaSMlJEyUkbKSBkpI2WkjJSRMlJG ykgZKSNlpIyUkTJSRspIGSkjZaSMlJEyUkbKSBkpI2WkjJSRMlJGykgZKSNl pIyUkTJSRspIGSkjZaSMlJEyUkbKSBkpI2WkjJSRMlJGykgZKSNlpIyUkTJS RspIGSkjZaSMlJEyUkbKSBkpI2WkjJSRMlJGykgZKSNlpIyUkTJSRspIGSkj ZaSMlJEyUkbKSBkpI2WkjJSRMlJGykgZKSNlpIyUkb/BSLNjyG8YwekvWZ6g lA==\ \>"], ImageRangeCache->{{{37.875, 439.25}, {456.688, 402.625}} -> {0, 2, 0, 0}, {{ 51.125, 229.625}, {455.375, 403.875}} -> {0, 2, 0, 0}, {{247.438, 425.938}, {455.375, 403.875}} -> {-1, 2, 0, 0}}]], "Text"], Cell[TextData[{ "The base points for the vectors in the diagram can be chosen from a grid \n\ (i) with the grid including points on the boundary (i.e., the dots in the \ diagram below);\n(ii) with the grid excluding points on the boundary \ (i.e.,the \"x\"s in the diagram below).\nOption (i) is the default setting.\n\ To switch options, press the appropriate palette button.\n", StyleBox["gridpoints1dvf", FontWeight->"Bold"], " specifies the number of initial conditions on each boundary of the grid.\n", StyleBox["drawrestpoints", FontWeight->"Bold"], " = 1 causes the rest points of the dynamic to be drawn on the diagram.\n", StyleBox["arrowsfromrestpoints ", FontWeight->"Bold"], "= 1 causes vector field arrows to be drawn from the rest points (in \ addition to all other arrows)." }], "Text", CellChangeTimes->{{3.4815732457478223`*^9, 3.481573246589032*^9}}] }, Closed]], Cell[BoxData[{ RowBox[{ RowBox[{"drawvectorfield1", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield1", "=", "PhiF"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vf1thickness", "=", ".001"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"scale1", "=", ".06"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"arrowheadlengthvf1", "=", ".01"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"colorvf1", "=", " ", RowBox[{"Hue", "[", ".64", "]"}]}], " ", ";"}]}], "Input"], Cell[BoxData[{ RowBox[{ RowBox[{"drawvectorfield2", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield2", "=", "dyn"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vf2thickness", "=", ".001"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"scale2", "=", ".06"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"arrowheadlengthvf2", "=", ".01"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"colorvf2", "=", " ", RowBox[{"Hue", "[", ".84", "]"}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"gridpoints1dvf", "=", " ", "25"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"drawrestpoints", "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"arrowsfromrestpoints", "=", " ", "1"}], " ", ";"}]}], "Input", CellChangeTimes->{3.4744074895348787`*^9, 3.4815704924888306`*^9, 3.482098094977389*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"MatrixButtons", "[", "rowsize_", "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "namesl", ",", "textsl", ",", "valuesl", ",", "names", " ", ",", "texts", ",", "values", ",", "buttons", ",", "row", ",", "butrow", ",", "rown", ",", "rowt", ",", "rowv", ",", "name", ",", "text", ",", "value", ",", "but", ",", "button"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"namesl", " ", "=", RowBox[{"{", " ", RowBox[{ "\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"textsl", " ", "=", " ", RowBox[{"{", " ", RowBox[{ "\"\\"", ",", "\"\\""}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", "\n", RowBox[{ RowBox[{"vectorfieldspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ FractionBox["i", RowBox[{"gridpoints1dvf", "-", "1"}]], ",", RowBox[{"1", "-", FractionBox[ RowBox[{" ", "i"}], RowBox[{"gridpoints1dvf", "-", "1"}]]}]}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["j", RowBox[{"gridpoints1dvf", "-", "1"}]], ",", RowBox[{"1", "-", FractionBox["j", RowBox[{"gridpoints1dvf", "-", "1"}]]}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", RowBox[{"gridpoints1dvf", "-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", RowBox[{"gridpoints1dvf", "-", "1"}], ",", "1"}], "}"}]}], "]"}], " ", ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"vectorfieldspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ FractionBox["i", RowBox[{"gridpoints1dvf", "-", "1"}]], "+", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]]}], ",", RowBox[{"1", "-", FractionBox[ RowBox[{" ", "i"}], RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]], "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ FractionBox["j", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]], "+", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]]}], ",", RowBox[{"1", "-", FractionBox["j", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]], "-", FractionBox["1", RowBox[{"2", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]]}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}], "-", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", RowBox[{ RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}], "-", "1"}], ",", "1"}], "}"}]}], "]"}], " ", ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", RowBox[{"valuesl", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"names", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"rown", "=", RowBox[{"Join", "[", RowBox[{"rown", ",", RowBox[{"{", RowBox[{"namesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"Join", "[", RowBox[{"rowt", ",", RowBox[{"{", RowBox[{"textsl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"Join", "[", RowBox[{"rowv", ",", RowBox[{"{", RowBox[{"valuesl", "[", RowBox[{"[", "row", "]"}], "]"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"Or", "[", RowBox[{ RowBox[{"IntegerQ", "[", RowBox[{"row", "/", "rowsize"}], "]"}], ",", RowBox[{"row", "==", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"namesl", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"names", "=", RowBox[{"Join", "[", RowBox[{"names", ",", RowBox[{"{", "rown", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"texts", "=", RowBox[{"Join", "[", RowBox[{"texts", ",", RowBox[{"{", "rowt", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"values", "=", RowBox[{"Join", "[", RowBox[{"values", ",", RowBox[{"{", "rowv", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rown", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowt", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"rowv", "=", RowBox[{"{", "}"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{"row", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"names", ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"butrow", "=", RowBox[{"{", "}"}]}], ";", "\[IndentingNewLine]", RowBox[{"but", "=", "1"}], ";", "\[IndentingNewLine]", RowBox[{"While", "[", " ", RowBox[{ RowBox[{"but", "<=", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], ",", "1"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"button", ":=", "\[IndentingNewLine]", RowBox[{"Button", "[", RowBox[{ RowBox[{"Column", "[", RowBox[{ RowBox[{"{", "name", "}"}], ",", RowBox[{"Alignment", "\[Rule]", RowBox[{"{", "Center", "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", "Next", ",", "CellTags", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"SelectionMove", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "All", ",", "CellContents", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"NotebookWrite", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "text", ",", RowBox[{"AutoScroll", "->", "False"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"400", ",", "30"}], "}"}]}]}], "*)"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"button", "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Style", "[", RowBox[{"button", ",", RowBox[{ "ControlsRendering", "\[Rule]", "\"\\""}]}], "]"}], " ", "/.", RowBox[{"text", "->", RowBox[{ RowBox[{"texts", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"name", "->", RowBox[{ RowBox[{"names", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}], "/.", RowBox[{"value", "->", RowBox[{ RowBox[{"values", "[", RowBox[{"[", "row", "]"}], "]"}], "[", RowBox[{"[", "but", "]"}], "]"}]}]}]}], ";", "\[IndentingNewLine]", RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", "button", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"butrow", "=", RowBox[{"Join", "[", RowBox[{"butrow", ",", RowBox[{"{", RowBox[{ RowBox[{"Row", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], ",", "button"}], "}"}]}], "]"}]}], ";"}], "*)"}], "\[IndentingNewLine]", RowBox[{"but", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"buttons", "=", RowBox[{"Join", "[", RowBox[{"buttons", ",", RowBox[{"{", "butrow", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"row", "++"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"TableForm", " ", "[", " ", RowBox[{"buttons", ",", RowBox[{"TableAlignments", "->", RowBox[{"{", RowBox[{"Left", ",", "Top"}], "}"}]}], ",", RowBox[{"TableSpacing", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Column", "[", "buttons", "]"}], "*)"}], "\[IndentingNewLine]", "]"}]}], ";"}], "\n", RowBox[{"MatrixButtons", "[", "3", "]"}]}], "Input", Evaluatable->False, CellOpen->False, CellChangeTimes->{{3.4813040162966223`*^9, 3.4813041889350376`*^9}, { 3.481304234246958*^9, 3.481304348854866*^9}, {3.4813044130259194`*^9, 3.4813044667127323`*^9}, {3.481304497212342*^9, 3.481304516258973*^9}, { 3.481304591711132*^9, 3.481304623616974*^9}, {3.481304658444653*^9, 3.481304715787669*^9}, {3.481304754318426*^9, 3.481304856879613*^9}, { 3.481304924394374*^9, 3.481304929097439*^9}, {3.4813049637844944`*^9, 3.481305049955267*^9}, {3.481305109251383*^9, 3.4813052103282137`*^9}, { 3.4813052726867905`*^9, 3.4813054179505563`*^9}, {3.4813054936370873`*^9, 3.481305606760639*^9}, {3.481305668931719*^9, 3.4813057399464345`*^9}, { 3.4813058200547843`*^9, 3.4813059389126377`*^9}, {3.481305992286955*^9, 3.4813059950056696`*^9}, {3.4813060594423447`*^9, 3.4813061026605415`*^9}, {3.4813061575348396`*^9, 3.4813061668159704`*^9}, 3.4813062421118817`*^9, 3.4813062726896152`*^9, {3.481306358922887*^9, 3.481306400750476*^9}, {3.481306526514491*^9, 3.4813065369518576`*^9}, { 3.4813065678420877`*^9, 3.481306572404529*^9}, 3.481306608185321*^9, { 3.4813066523878803`*^9, 3.481306668168928*^9}, {3.481306704777835*^9, 3.4813067154651976`*^9}, 3.481306939040461*^9, {3.4813069856961136`*^9, 3.4813069858836117`*^9}, 3.481307054163987*^9, {3.481307101772753*^9, 3.4813071138350983`*^9}, {3.481307407643838*^9, 3.4813077466394987`*^9}, { 3.4813077909826813`*^9, 3.48130781959169*^9}, {3.4813078599192986`*^9, 3.481307957918044*^9}, {3.481308040010743*^9, 3.481308046416911*^9}, 3.4813080794633636`*^9, 3.4813081524936786`*^9, {3.481308210524186*^9, 3.481308338163177*^9}, 3.4813083718189964`*^9, {3.4813085571447487`*^9, 3.481308586503748*^9}, {3.4813086184408393`*^9, 3.481308738251806*^9}, { 3.481308930858715*^9, 3.4813091517777624`*^9}, {3.4813091950740833`*^9, 3.481309202620862*^9}, {3.4813099727203794`*^9, 3.4813100351414557`*^9}, { 3.4813100751096935`*^9, 3.4813101295777464`*^9}, {3.481310159749235*^9, 3.4813101717647066`*^9}, {3.4813102025768123`*^9, 3.481310210326713*^9}, { 3.4813102772946057`*^9, 3.4813103037630167`*^9}, {3.4813103642778673`*^9, 3.4813104031523695`*^9}, {3.4813110125508194`*^9, 3.48131103905048*^9}, { 3.4813110842686515`*^9, 3.4813111395023193`*^9}, {3.4813117891346292`*^9, 3.481311813509317*^9}, {3.4813118455401573`*^9, 3.481311848555743*^9}, { 3.481311983491516*^9, 3.481311996303852*^9}, {3.481312245331915*^9, 3.481312262878565*^9}, {3.4813124766258287`*^9, 3.4813124780789356`*^9}, { 3.481312562234108*^9, 3.4813125631559715`*^9}, {3.481313376067441*^9, 3.4813133832704735`*^9}, {3.4813140008563185`*^9, 3.4813141425888796`*^9}, {3.481314173932228*^9, 3.4813141780571756`*^9}, { 3.481314220525382*^9, 3.4813142451031923`*^9}, {3.4813143191022453`*^9, 3.481314320055358*^9}, {3.481314353383056*^9, 3.481314360445466*^9}, { 3.4813144028980474`*^9, 3.481314405194893*^9}, {3.4813144915531626`*^9, 3.4813145915675077`*^9}, {3.4813146929724593`*^9, 3.481314706347288*^9}, { 3.4813148354706354`*^9, 3.4813148468611145`*^9}, {3.4813157963547544`*^9, 3.4813158533558493`*^9}, {3.481315901981783*^9, 3.481315960669737*^9}, { 3.481316084544737*^9, 3.481316093107237*^9}, {3.481316151857237*^9, 3.481316184232237*^9}, {3.481316289559544*^9, 3.481316322527872*^9}, { 3.4813163535431004`*^9, 3.481316372355359*^9}, {3.481316418932888*^9, 3.481316420276621*^9}, {3.4813164900569777`*^9, 3.481316570165327*^9}, { 3.48131666333601*^9, 3.481316718241557*^9}, 3.4813167995217667`*^9, { 3.4813168815207167`*^9, 3.4813168975517616`*^9}, {3.4813169714570656`*^9, 3.481316996425496*^9}, {3.4813170544403787`*^9, 3.481317077674456*^9}, { 3.481317108767808*^9, 3.4813171147208567`*^9}, {3.481317148236053*^9, 3.481317162079626*^9}, {3.4813172156883144`*^9, 3.4813172161570587`*^9}, { 3.4813172564065437`*^9, 3.4813172577815256`*^9}, {3.481317415967001*^9, 3.4813174182013474`*^9}, {3.481318095723925*^9, 3.481318181488452*^9}, 3.481318284596507*^9, {3.481318343611377*^9, 3.4813184077043066`*^9}, { 3.481318575702156*^9, 3.481318581561456*^9}, {3.4813186265921297`*^9, 3.4813186395294642`*^9}, {3.481319531174301*^9, 3.4813195706269207`*^9}, { 3.4813301870935183`*^9, 3.481330195575715*^9}, {3.481330234031011*^9, 3.481330240229925*^9}, {3.4813303413653507`*^9, 3.481330348635805*^9}, 3.481381740593504*^9, {3.48138186256188*^9, 3.4813818701868315`*^9}, 3.4814015869376*^9, {3.481405450326758*^9, 3.4814055598442364`*^9}, { 3.4814056617908287`*^9, 3.481405789714774*^9}, {3.4814058901191483`*^9, 3.4814059033681993`*^9}, {3.481405941803467*^9, 3.481405984975545*^9}, { 3.481406077548659*^9, 3.481406079601611*^9}, 3.481406131906822*^9, { 3.4814061894595785`*^9, 3.4814061927543163`*^9}, {3.481406239131003*^9, 3.481406257597556*^9}, {3.481406398980856*^9, 3.481406411659086*^9}, { 3.4814064803979273`*^9, 3.481406480728403*^9}, {3.481406518092129*^9, 3.4814066497113886`*^9}, {3.4814066834098444`*^9, 3.48140673647615*^9}, { 3.481408508784604*^9, 3.4814085588966618`*^9}, {3.481408601387761*^9, 3.481408603090209*^9}, {3.4814086420261965`*^9, 3.4814087494506655`*^9}, { 3.4814087986514125`*^9, 3.481408857345811*^9}, {3.4814089003977165`*^9, 3.4814089629676876`*^9}, 3.4814131600728283`*^9, 3.4814132208702507`*^9, { 3.4814132796547785`*^9, 3.481413291952462*^9}, {3.481413334613806*^9, 3.481413495364955*^9}, {3.4814135595772877`*^9, 3.4814136320014286`*^9}, { 3.4814137487793465`*^9, 3.481413779022835*^9}, {3.481414435946512*^9, 3.481414512348054*^9}, {3.4814148679674177`*^9, 3.48141493700995*^9}, { 3.481415020183816*^9, 3.4814150755877504`*^9}, {3.481415141352315*^9, 3.481415154190776*^9}, {3.4814151844943504`*^9, 3.4814152094502354`*^9}, { 3.481415278549595*^9, 3.4814152928501587`*^9}, {3.481415420553787*^9, 3.4814154999078927`*^9}, {3.481415562497893*^9, 3.481415584309256*^9}, { 3.481415703060011*^9, 3.481415703450573*^9}, 3.4814158990017614`*^9, { 3.4814171364611406`*^9, 3.4814171462952814`*^9}, {3.481424072987533*^9, 3.4814241197147236`*^9}, {3.4814832782005634`*^9, 3.4814832867829046`*^9}, 3.4816703314238143`*^9, {3.481670369408434*^9, 3.4816704575852256`*^9}, { 3.4816706146811185`*^9, 3.4816707845954432`*^9}, {3.4816708405859537`*^9, 3.481670920480837*^9}, {3.4816709715042048`*^9, 3.4816709719949102`*^9}, { 3.4816711094525647`*^9, 3.4816711098431263`*^9}, {3.4816711965377874`*^9, 3.481671238237749*^9}, {3.4816713148579235`*^9, 3.481671340214384*^9}, { 3.4816713745737906`*^9, 3.4816716260353746`*^9}, {3.481671755331293*^9, 3.481671785134147*^9}, {3.4816718832952957`*^9, 3.4816719397865267`*^9}, 3.4816719758984528`*^9, {3.481673176244466*^9, 3.4816732875745506`*^9}, 3.4816733183988733`*^9, {3.481673362101715*^9, 3.4816733707441425`*^9}, 3.481673653340496*^9, {3.4816745940231314`*^9, 3.4816746022149105`*^9}, { 3.4817346006152563`*^9, 3.481734607925768*^9}, {3.481736647042942*^9, 3.481736703093539*^9}, 3.4817375426908207`*^9, {3.4818119966889615`*^9, 3.481812002957976*^9}, {3.481812105737727*^9, 3.481812272981318*^9}, { 3.4818124484235916`*^9, 3.481812457366451*^9}, {3.481812498485577*^9, 3.481812523040886*^9}, {3.4818125683860893`*^9, 3.4818125706493435`*^9}, { 3.481812612139003*^9, 3.481812639708646*^9}, {3.4818128485990157`*^9, 3.481812864662113*^9}, {3.4818129721767116`*^9, 3.4818130553963757`*^9}, { 3.4818132379588876`*^9, 3.4818133245333757`*^9}, {3.481813355407771*^9, 3.4818133663935676`*^9}, 3.4818134196132183`*^9, {3.4818134879827776`*^9, 3.481813489202236*^9}, {3.4818136452104654`*^9, 3.481813661273563*^9}, { 3.4818137634451456`*^9, 3.481813778596933*^9}, {3.4818140028480997`*^9, 3.481814031477353*^9}, {3.481814092975784*^9, 3.4818141259632177`*^9}, { 3.4818141856590557`*^9, 3.4818141929395247`*^9}, {3.4818142536968894`*^9, 3.481814383273211*^9}, {3.4818144211176286`*^9, 3.4818145387768145`*^9}, { 3.4818146624446397`*^9, 3.4818146646778507`*^9}, {3.48181469749504*^9, 3.4818147106439466`*^9}, {3.4818472323981695`*^9, 3.4818473124933405`*^9}, {3.481847364648336*^9, 3.4818474569710894`*^9}, { 3.4818475630135713`*^9, 3.48184763238332*^9}, {3.481847664829976*^9, 3.4818476670431585`*^9}, {3.4820998349293165`*^9, 3.4820998684675426`*^9}, {3.4820999000729885`*^9, 3.4820999301262035`*^9}, {3.4821000243016205`*^9, 3.4821000262344*^9}, { 3.482100245629875*^9, 3.482100322710712*^9}, {3.4821003801533103`*^9, 3.4821004105670433`*^9}, {3.4821006368824687`*^9, 3.4821006416593375`*^9}}, CellTags->"buttoncell"], Cell[BoxData[ TagBox[GridBox[{ { StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Grid initial conditions (boundary included)\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "vectorfieldspecs", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], "vectorfieldspecs=Flatten[Table[{{i/(gridpoints1dvf-1), 1 - \ i/(gridpoints1dvf-1)}, \n {j/(gridpoints1dvf-1), 1 - \ j/(gridpoints1dvf-1)}}, {i, 0, (gridpoints1dvf-1), 1}, \n {j, 0, \ (gridpoints1dvf-1), 1}], 1];", AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False], StyleBox[ ButtonBox[ TagBox[GridBox[{ {"\<\"Grid initial conditions (boundary excluded)\"\>"} }, GridBoxAlignment->{"Columns" -> {{Center}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Column"], Appearance->Automatic, ButtonFunction:>(NotebookFind[ SelectedNotebook[], "vectorfieldspecs", Next, CellTags, AutoScroll -> False]; SelectionMove[ SelectedNotebook[], All, CellContents, AutoScroll -> False]; NotebookWrite[ SelectedNotebook[], "vectorfieldspecs=Flatten[Table[{{i/(gridpoints1dvf-1) + \ 1/(2*(gridpoints1dvf-1)), \n 1 - i/(gridpoints1dvf-1) - \ 1/(2*(gridpoints1dvf-1))}, \n {j/(gridpoints1dvf-1) + \ 1/(2*(gridpoints1dvf-1)), 1 - j/(gridpoints1dvf-1) - \n \ 1/(2*(gridpoints1dvf-1))}}, {i, 0, (gridpoints1dvf-1) - 1, 1}, \n {j, \ 0, gridpoints1dvf - 1, 1}], 1];", AutoScroll -> False]; Null), Evaluator->Automatic, Method->"Preemptive"], ControlsRendering->"Generic", StripOnInput->False]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], Function[BoxForm`e$, TableForm[ BoxForm`e$, TableAlignments -> {Left, Top}, TableSpacing -> {1, 1}]]]], "Output", CellChangeTimes->{3.4821031113105216`*^9}, CellTags->"buttoncell"] }, Closed]], Cell[BoxData[ RowBox[{ RowBox[{"vectorfieldspecs", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"i", "/", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}], ",", " ", RowBox[{"1", " ", "-", " ", RowBox[{"i", "/", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]}]}], "}"}], ",", " ", "\n", " ", RowBox[{"{", RowBox[{ RowBox[{"j", "/", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}], ",", " ", RowBox[{"1", " ", "-", " ", RowBox[{"j", "/", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}]}]}]}], "}"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "0", ",", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ", RowBox[{"{", RowBox[{"j", ",", " ", "0", ",", " ", RowBox[{"(", RowBox[{"gridpoints1dvf", "-", "1"}], ")"}], ",", " ", "1"}], "}"}]}], "]"}], ",", " ", "1"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.48157142642176*^9, 3.481571426491861*^9}, 3.4821000278967905`*^9, {3.482100330281598*^9, 3.482100352032875*^9}}, CellTags->"vectorfieldspecs"] }, Open ]], Cell[CellGroupData[{ Cell["3D graph of the contour function", "Subsection"], Cell[TextData[{ StyleBox["graphcontour3d", FontWeight->"Bold"], " = 1 creates a 3d plot of the contour function. \n", StyleBox["shiftpercentage", FontWeight->"Bold"], " specifies the distance above the simplex that the lowest point on the \ contour function will appear, as a percentage of the distance from the \ minimum value of the function to the maximum value of the function.\n", StyleBox["grayline", FontWeight->"Bold"], " = 1 draws a gray line on the edges of the 3d plot.\n", StyleBox["heightratio", FontWeight->"Bold"], " specifies the ratios of the three coordinates in the graphical output. \ The default setting is {1, 1, 1.25}.\n \n", StyleBox["vpoint", FontWeight->"Bold"], " determines the value for the ", StyleBox["Mathematica", FontSlant->"Italic"], " command ViewPoint and hence the point from which the 3d plot is observed. \ In ", StyleBox["Mathematica", FontSlant->"Italic"], ", ViewPoint ", StyleBox["->", "MR"], " {", StyleBox["x", "TI"], StyleBox[",", "MR"], " ", StyleBox["y", "TI"], StyleBox[",", "MR"], " ", StyleBox["z", "TI"], Cell[BoxData[ FormBox["}", TraditionalForm]], "InlineFormula"], " gives the position of the view point relative to the center of the three\ \[Hyphen]dimensional box that contains the object being plotted. The view \ point is given in a special scaled coordinate system in which the longest \ side of the bounding box has length 1. (When heightratio is at its default \ setting of {1, 1, 1.25}, the longest side corresponds to the z coordinate. \ The center of the bounding box is taken to have coordinates ", StyleBox["{0,", "MR"], " ", StyleBox["0,", "MR"], " ", StyleBox["0}", "MR"], ". Choosing ", StyleBox["ViewPoint", "MR"], " further away from the object reduces the distortion associated with \ perspective." }], "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"graphcontour3d", "=", "0"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"grayline", "=", "1"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"shiftpercentage", "=", ".2"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"heightratio", "=", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1.25"}], "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vpoint", "=", RowBox[{"{", RowBox[{ RowBox[{"-", "2.730"}], ",", " ", RowBox[{"-", "1.673"}], ",", " ", "1.096"}], "}"}]}], " ", ";"}]}], "Input", CellChangeTimes->{{3.474836128758108*^9, 3.4748361292988863`*^9}, 3.482506377695066*^9}] }, Closed]] }, Closed]] }, Open ]], Cell[BoxData["\[IndentingNewLine]"], "Input", Evaluatable->False, CellChangeTimes->{3.481906257486692*^9}], Cell[CellGroupData[{ Cell["Program Core", "Subtitle", CellDingbat->None], Cell[CellGroupData[{ Cell["Solving the differential equation", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"time1", "=", RowBox[{"AbsoluteTime", "[", "]"}]}], " ", ";"}]], "Input", CellChangeTimes->{3.4807858604080477`*^9}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"x", "[", "t", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"x1", "[", "t", "]"}], ",", RowBox[{"1", "-", RowBox[{"x1", "[", "t", "]"}]}]}], "}"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"y", "[", "t", "]"}], "=", RowBox[{"{", RowBox[{ RowBox[{"y1", "[", "t", "]"}], ",", RowBox[{"1", "-", RowBox[{"y1", "[", "t", "]"}]}]}], "}"}]}], " ", ";"}]}], "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"G", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"dyn", "[", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["y1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"dyn", "[", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"x1", "[", "0", "]"}], "\[Equal]", RowBox[{"1", "-", RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}]}], ",", RowBox[{ RowBox[{"y1", "[", "0", "]"}], "\[Equal]", RowBox[{"1", "-", RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x1", ",", "y1"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "trajectoryspecs", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";"}]], "Input", CellChangeTimes->{{3.4744074923088675`*^9, 3.4744074933804083`*^9}, { 3.481570492498845*^9, 3.481570492508859*^9}, {3.482098095007432*^9, 3.4820980950174465`*^9}, {3.4821023717470818`*^9, 3.4821023766941953`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"GCycle", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Equal]", "0"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"dyn", "[", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["y1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"dyn", "[", RowBox[{ RowBox[{"x", "[", "t", "]"}], ",", RowBox[{"y", "[", "t", "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"x1", "[", "0", "]"}], "\[Equal]", RowBox[{"1", "-", RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}]}], ",", RowBox[{ RowBox[{"y1", "[", "0", "]"}], "\[Equal]", RowBox[{"1", "-", RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x1", ",", "y1"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], "]"}]}], " ", ";"}]], "Input", CellChangeTimes->{{3.47440749468228*^9, 3.4744074955535326`*^9}, { 3.481570492508859*^9, 3.4815704925188737`*^9}, {3.4820980950474896`*^9, 3.4820980950575037`*^9}, {3.4820996729263678`*^9, 3.482099676651725*^9}}, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Plotting the solutions", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"vectorfielddiagram", "\[Equal]", "0"}], ",", " ", RowBox[{ RowBox[{"drawvectorfield1", "=", "0"}], " ", ";", " ", RowBox[{"drawvectorfield2", "=", "0"}]}]}], " ", "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"phasediagram", "\[Equal]", "0"}], ",", RowBox[{"includecontourplot", "=", "0"}]}], "]"}], " ", ";"}]}], "Input"], Cell[CellGroupData[{ Cell["Rest points and stability test", "Subsection"], Cell[BoxData[ RowBox[{ RowBox[{"TolLevel", "=", RowBox[{"Times", "[", RowBox[{"RestTolerance", ",", " ", RowBox[{"Max", "[", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Chop", "[", RowBox[{ RowBox[{"Speed", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"1", "-", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"1", "-", "j"}]}], "}"}]}], "]"}], ",", SuperscriptBox["10", RowBox[{"-", "5"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "1", ",", ".05"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "1", ",", ".05"}], "}"}]}], "]"}], "]"}], "]"}]}], "]"}]}], " ", ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", " ", "1"}], ",", RowBox[{ RowBox[{"RePos", "=", RowBox[{"RestPoints", "[", RowBox[{ "dyn", ",", "F1", ",", "F2", ",", "RestSearchInit", ",", "TolLevel"}], "]"}]}], " ", ";", RowBox[{"TestStability", "[", RowBox[{ "dyn", ",", "F1", ",", "F2", ",", "bigT", ",", " ", "numtest", ",", " ", "eps", ",", " ", "delta", ",", "RestSearchInit", ",", "TolLevel"}], "]"}]}]}], "]"}], " ", ";"}]], "Input", CellChangeTimes->{{3.474407497486312*^9, 3.474407498237392*^9}, { 3.4815704925188737`*^9, 3.4815704925188737`*^9}, {3.4820980950875473`*^9, 3.4820980950875473`*^9}}] }, Closed]], Cell["Drawing vector fields on the simplex", "Subsection"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"customvectorfield", "[", RowBox[{ "points_", ",", "vectors_", ",", "color_", ",", "magninorm_", ",", "magnihead_", ",", "gridpoints_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"rescaler", ",", "maxnorm"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"maxnorm", "=", RowBox[{"Max", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Norm", "[", RowBox[{"vectors", "[", RowBox[{"[", "i", "]"}], "]"}], " ", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectors", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"rescaler", "=", RowBox[{"1", "/", RowBox[{"(", RowBox[{"gridpoints", "-", "1"}], ")"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"rescaler", "=", RowBox[{"magninorm", " ", RowBox[{"rescaler", "/", "maxnorm"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Norm", "[", RowBox[{"vectors", "[", RowBox[{"[", "i", "]"}], "]"}], "]"}], ">", RowBox[{".01", "*", "maxnorm"}]}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"color", ",", RowBox[{"Arrowheads", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"magnihead", " ", "/", RowBox[{"(", RowBox[{"2", "gridpoints"}], ")"}]}], ",", ".99"}], "}"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"points", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{ RowBox[{"points", "[", RowBox[{"[", "i", "]"}], "]"}], "+", RowBox[{ RowBox[{"vectors", "[", RowBox[{"[", "i", "]"}], "]"}], "rescaler"}]}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{"color", ",", "\[IndentingNewLine]", RowBox[{"Disk", "[", RowBox[{ RowBox[{"points", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"Scaled", "[", "0.005", "]"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectors", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.4750285855187626`*^9, 3.4750286151013002`*^9}, { 3.4750286726941147`*^9, 3.4750288166010427`*^9}, {3.4750288716101418`*^9, 3.4750289343103*^9}, {3.475028976811414*^9, 3.4750289888086653`*^9}, { 3.4750290529909544`*^9, 3.475029124503785*^9}, {3.4750292732877254`*^9, 3.4750293337146153`*^9}, {3.4750293654802923`*^9, 3.4750295536659575`*^9}, {3.4750296048896136`*^9, 3.475029621353287*^9}, { 3.4750298234538937`*^9, 3.475029912041276*^9}, 3.475030337653276*^9, { 3.4750303698195286`*^9, 3.4750303857524395`*^9}, {3.475030433861617*^9, 3.4750304373866854`*^9}, {3.4750308542260714`*^9, 3.4750308658828325`*^9}, {3.4750309075126934`*^9, 3.4750309810684614`*^9}, {3.475031070757428*^9, 3.475031072479905*^9}, { 3.475031317652446*^9, 3.4750313941123896`*^9}, 3.475031446167241*^9, { 3.475031594009828*^9, 3.475031606227396*^9}, {3.4750316461447945`*^9, 3.475031679282444*^9}, {3.475031814426772*^9, 3.4750318298088903`*^9}, { 3.475031893640676*^9, 3.475032024198409*^9}, {3.4750320562545033`*^9, 3.475032081410676*^9}, {3.4750323309494953`*^9, 3.4750323384903383`*^9}, { 3.4750323774062967`*^9, 3.475032434197959*^9}, {3.475032492361594*^9, 3.475032525769633*^9}, 3.4750325591376133`*^9, {3.475032599305372*^9, 3.4750326035014057`*^9}, 3.4750326544947305`*^9, {3.4750327445294805`*^9, 3.475032809642691*^9}, 3.4750328423397074`*^9, {3.4750330135158463`*^9, 3.475033022749123*^9}, 3.4750330538538494`*^9, {3.475033263004594*^9, 3.4750332960120564`*^9}, {3.4750336325989866`*^9, 3.475033633011221*^9}, { 3.4750340043945336`*^9, 3.475034046114524*^9}, {3.4750340970077047`*^9, 3.475034131457241*^9}, {3.4750342246312184`*^9, 3.4750342688648233`*^9}, { 3.475034307941012*^9, 3.4750343084016743`*^9}, {3.475034542534034*^9, 3.475034543386965*^9}, {3.47503538353778*^9, 3.4750353913389974`*^9}, { 3.475035565339197*^9, 3.4750355973051624`*^9}, {3.475035629251098*^9, 3.47503567220286*^9}, {3.475035729615415*^9, 3.475035729975933*^9}, 3.4750358147678585`*^9, {3.475035864799801*^9, 3.475035906880309*^9}, { 3.4750359526861753`*^9, 3.4750359666262197`*^9}, {3.4750360017967925`*^9, 3.4750360290760183`*^9}, {3.475036094580209*^9, 3.4750361496894517`*^9}, { 3.475036180724077*^9, 3.475036181815647*^9}, {3.4750362158245497`*^9, 3.4750362439149413`*^9}, 3.4750363311904373`*^9, {3.475036362054818*^9, 3.4750364519641013`*^9}, {3.475036605324623*^9, 3.4750366103919096`*^9}, { 3.47503671386069*^9, 3.4750367197191143`*^9}, {3.4750367956082373`*^9, 3.4750368415943623`*^9}, {3.4750369036135416`*^9, 3.4750369537356133`*^9}, {3.4750370158849797`*^9, 3.475037124881709*^9}, { 3.4750371719293604`*^9, 3.475037183185546*^9}, {3.4750372188968964`*^9, 3.4750372719231443`*^9}, {3.475037308065114*^9, 3.475037357426092*^9}, { 3.4750374659321156`*^9, 3.4750374690966663`*^9}, {3.4750375113874774`*^9, 3.4750375311659174`*^9}, 3.4750375918531814`*^9, {3.4750376875407734`*^9, 3.475037690254676*^9}, {3.475037725735695*^9, 3.475037729761484*^9}, { 3.4750378045490227`*^9, 3.475037821573503*^9}, 3.4750379430911245`*^9, { 3.475038102300056*^9, 3.475038151150299*^9}, 3.480863936695631*^9, { 3.480863979336256*^9, 3.480863986476881*^9}}], Cell[BoxData[ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"vectorfielddiagram", "\[Equal]", "1"}], " ", "&&", " ", RowBox[{"(", RowBox[{ RowBox[{"drawvectorfield1", "\[Equal]", "1"}], " ", "||", " ", RowBox[{"drawvectorfield2", "\[Equal]", "1"}]}], ")"}]}], ",", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"drawvectorfield1", "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorf1", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}], ";"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], " ", "&&", " ", RowBox[{"arrowsfromrestpoints", "\[Equal]", "1"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorf1", "=", RowBox[{"customvectorfield", " ", "[", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "colorvf1", ",", "1.5", ",", ".8", ",", "gridpoints1dvf"}], "]"}]}], ";"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorf1", "=", RowBox[{"customvectorfield", " ", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield1", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "colorvf1", ",", "1.5", ",", ".8", ",", "gridpoints1dvf"}], "]"}]}], ";"}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}], " ", ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"drawvectorfield2", "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"vectorf2", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], " ", "&&", " ", RowBox[{"arrowsfromrestpoints", "\[Equal]", "1"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorf2", "=", RowBox[{"customvectorfield", " ", "[", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"testrest", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "colorvf2", ",", "1.5", ",", ".8", ",", "gridpoints1dvf"}], "]"}]}], ";"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorf2", "=", RowBox[{"customvectorfield", " ", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2", ",", "2"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1", ",", "1"}], "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], " ", "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "4", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"vectorfield2", "[", RowBox[{ RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"vectorfieldspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}], ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "vectorfieldspecs", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "colorvf2", ",", "1.5", ",", ".8", ",", "gridpoints1dvf"}], "]"}]}], ";"}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}]}]}], " ", "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.474409954579438*^9, 3.474409965885696*^9}, 3.474410059590437*^9, {3.474411264432915*^9, 3.4744112661553917`*^9}, { 3.4744116091886497`*^9, 3.474411659190549*^9}, {3.4744123256688976`*^9, 3.474412328432872*^9}, {3.474412365966843*^9, 3.474412367268715*^9}, { 3.474413032935898*^9, 3.4744130631293135`*^9}, {3.4744134674306707`*^9, 3.4744134677010593`*^9}, {3.4744135541954317`*^9, 3.4744136513551407`*^9}, {3.474413735275813*^9, 3.47441374325729*^9}, { 3.4744138135583773`*^9, 3.474414013936507*^9}, 3.474414044710758*^9, { 3.4748346690119486`*^9, 3.474834677499152*^9}, 3.4748349834947605`*^9, { 3.4748350407883787`*^9, 3.474835104676106*^9}, {3.474835159185567*^9, 3.4748351841832514`*^9}, {3.474835221063692*^9, 3.47483524289749*^9}, { 3.474835285613969*^9, 3.474835288696415*^9}, {3.4750384882350035`*^9, 3.475038572616338*^9}, {3.4750386241604548`*^9, 3.4750386281962576`*^9}, { 3.475038751563651*^9, 3.4750389399044724`*^9}, {3.475038973953432*^9, 3.475039023755043*^9}, {3.475039098853029*^9, 3.47503931464332*^9}, { 3.475039346378954*^9, 3.4750394584501038`*^9}, {3.475039492028387*^9, 3.4750395462663774`*^9}, {3.4820999929966063`*^9, 3.482100020375976*^9}, { 3.4821003576309247`*^9, 3.482100366193237*^9}}], Cell[CellGroupData[{ Cell["Drawing Solutions to Diff Eqs if there is no contour plot", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"e", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", "t", "]"}]}], ",", RowBox[{"x1", "[", "t", "]"}]}], "}"}], "/.", "\[InvisibleSpace]", RowBox[{ "G", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], " ", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"trajectoryspecs", "[", RowBox[{"[", RowBox[{"i", ",", "2"}], "]"}], "]"}]}], "}"}], ",", " ", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", RowBox[{"PlotPoints", "\[Rule]", " ", "ppoints"}], ",", " ", RowBox[{"Axes", "\[Rule]", RowBox[{"{", RowBox[{"False", ",", "False"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.08"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.08"}], "}"}]}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "trajectoryspecs", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";"}]], "Input", CellChangeTimes->{{3.4821023413333488`*^9, 3.482102343616632*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"ecycle", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Equal]", "0"}], ",", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"ParametricPlot", "[", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", "t", "]"}]}], ",", RowBox[{"x1", "[", "t", "]"}]}], "}"}], "/.", RowBox[{ "GCycle", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], ",", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"DisplayFunction", "\[Rule]", "Identity"}], ",", RowBox[{"Axes", "\[Rule]", RowBox[{"{", RowBox[{"False", ",", "False"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.08"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.08"}], "}"}]}], "}"}]}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.4820996777032366`*^9, 3.482099680286952*^9}}, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Specifying color scale/gray scale", "Subsection"], Cell["\<\ The approximate minimum and maximum values of the contour function are \ computed here. These values are then used to assign colors/gray levels \ optimally.\ \>", "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], " ", "||", RowBox[{"drawoncontour", "\[Equal]", "1"}], "||", RowBox[{"graphcontour3d", " ", "\[Equal]", " ", "1"}]}], " ", ",", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"ContourFunction", " ", "===", " ", "Speed"}], ",", RowBox[{"MinAttained", "=", "0"}], ",", RowBox[{ RowBox[{"nrmlzdmin", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Chop", "[", RowBox[{ RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"1", "-", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"1", "-", "j"}]}], "}"}]}], "]"}], ",", SuperscriptBox["10", RowBox[{"-", "5"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "1", ",", ".025"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "1", ",", ".025"}], "}"}]}], "]"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"MinAttained", "=", RowBox[{"Min", "[", "nrmlzdmin", "]"}]}]}]}], "]"}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], " ", "||", " ", RowBox[{"drawoncontour", "\[Equal]", "1"}], "||", RowBox[{"graphcontour3d", " ", "\[Equal]", " ", "1"}]}], ",", RowBox[{ RowBox[{"nrmlzd", "=", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Chop", "[", RowBox[{ RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"1", "-", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{"1", "-", "j"}]}], "}"}]}], "]"}], ",", SuperscriptBox["10", RowBox[{"-", "5"}]]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "1", ",", ".025"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "1", ",", ".025"}], "}"}]}], "]"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"MaxAttained", "=", RowBox[{"Max", "[", "nrmlzd", "]"}]}]}]}], " ", "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"distancefrommin", "=", RowBox[{"shiftpercentage", " ", RowBox[{"(", RowBox[{"MaxAttained", "-", "MinAttained"}], ")"}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"btwf", "[", "\[CapitalPsi]_", "]"}], "=", RowBox[{"1", "-", RowBox[{"Max", "[", RowBox[{"0", ",", RowBox[{"Min", "[", RowBox[{ FractionBox[ RowBox[{"\[CapitalPsi]", "-", "MinAttained"}], RowBox[{"MaxAttained", "-", "MinAttained"}]], ",", "1"}], "]"}]}], "]"}]}]}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], " ", "||", RowBox[{"drawoncontour", "\[Equal]", "1"}], "||", " ", RowBox[{"graphcontour3d", " ", "\[Equal]", " ", "1"}]}], ")"}], " ", "&&", " ", RowBox[{"color", "\[Equal]", "0"}]}], ",", RowBox[{ RowBox[{"ConColFun", "[", "\[CapitalPsi]_", "]"}], "=", RowBox[{"GrayLevel", "[", RowBox[{ FractionBox[".95", "1.45"], RowBox[{"(", RowBox[{"1", "-", RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}], "+", ".45"}], ")"}]}], " ", "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], " ", "||", RowBox[{"drawoncontour", "\[Equal]", "1"}], "||", " ", RowBox[{"graphcontour3d", " ", "\[Equal]", " ", "1"}]}], ")"}], "&&", " ", RowBox[{"color", "==", "1"}]}], ",", RowBox[{ RowBox[{"ConColFun", "[", "\[CapitalPsi]_", "]"}], "=", RowBox[{"Hue", "[", " ", RowBox[{"Which", "[", RowBox[{ RowBox[{ RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}], "\[LessEqual]", FractionBox["1", "2"]}], ",", RowBox[{ FractionBox["2", "5"], RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}]}], ",", RowBox[{ FractionBox["1", "2"], "<", RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}], "\[LessEqual]", FractionBox["2", "3"]}], ",", " ", RowBox[{ RowBox[{ FractionBox["6", "5"], RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}]}], "-", FractionBox["2", "5"]}], ",", RowBox[{ FractionBox["2", "3"], "<", RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}]}], ",", RowBox[{ RowBox[{ FractionBox["3", "4"], RowBox[{"btwf", "[", "\[CapitalPsi]", "]"}]}], "-", FractionBox["1", "10"]}]}], "]"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], " ", "||", " ", RowBox[{"drawoncontour", "\[Equal]", "1"}]}], ")"}], "&&", " ", RowBox[{"colorbar", "\[Equal]", "1"}]}], ",", RowBox[{"simplexcolorbar", "=", RowBox[{"If", "[", RowBox[{ RowBox[{"color", "\[Equal]", "1"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Graphics", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Hue", "[", RowBox[{"Which", "[", RowBox[{ RowBox[{ RowBox[{"1", "-", "#1"}], " ", "\[LessEqual]", FractionBox["1", "2"]}], ",", RowBox[{ FractionBox["2", "5"], RowBox[{"(", RowBox[{"1", "-", "#1"}], ")"}]}], ",", RowBox[{ FractionBox["1", "2"], "<", RowBox[{"(", RowBox[{"1", "-", "#1"}], ")"}], "\[LessEqual]", FractionBox["2", "3"]}], ",", " ", RowBox[{ RowBox[{ FractionBox["6", "5"], RowBox[{"(", RowBox[{"1", "-", "#1"}], ")"}]}], "-", FractionBox["2", "5"]}], ",", RowBox[{ FractionBox["2", "3"], "<", RowBox[{"(", RowBox[{"1", "-", "#1"}], ")"}]}], ",", RowBox[{ RowBox[{ FractionBox["3", "4"], RowBox[{"(", RowBox[{"1", "-", "#1"}], ")"}]}], "-", FractionBox["1", "10"]}]}], "]"}], "]"}], ",", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"1.03", ",", FractionBox[ RowBox[{"#1", "+", "1.5"}], "3"]}], "}"}], ",", RowBox[{"{", RowBox[{"1.08", ",", FractionBox[ RowBox[{"#1", " ", "+", "1.51"}], "3"]}], "}"}]}], "]"}]}], "}"}], "&"}], ")"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", "1", ",", ".01"}], "]"}]}], "]"}], ",", " ", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"PaddedForm", "[", " ", RowBox[{"MinAttained", ",", " ", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"1.08", ",", ".48"}], "}"}]}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"PaddedForm", "[", RowBox[{"MaxAttained", ",", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"1.08", ",", ".85"}], "}"}]}], "]"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"Graphics", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GrayLevel", "[", RowBox[{ FractionBox[".95", "1.45"], RowBox[{"(", RowBox[{ RowBox[{"(", "#1", ")"}], "+", ".45"}], ")"}]}], "]"}], ",", RowBox[{"Rectangle", "[", RowBox[{ RowBox[{"{", RowBox[{"1.03", ",", FractionBox[ RowBox[{"#1", "+", "1.5"}], "3"]}], "}"}], ",", RowBox[{"{", RowBox[{"1.08", ",", FractionBox[ RowBox[{"#1", " ", "+", "1.51"}], "3"]}], "}"}]}], "]"}]}], "}"}], "&"}], ")"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", "1", ",", ".01"}], "]"}]}], "]"}], ",", " ", RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"PaddedForm", "[", RowBox[{"MinAttained", ",", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"1.08", ",", ".48"}], "}"}]}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"PaddedForm", "[", " ", RowBox[{"MaxAttained", ",", RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"1.08", ",", ".85"}], "}"}]}], "]"}]}], "}"}], "]"}]}], "}"}]}], "]"}]}], " ", ",", RowBox[{"simplexcolorbar", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], " ", "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], ",", RowBox[{"simplexcolorbarph", "=", "simplexcolorbar"}], ",", RowBox[{"simplexcolorbarph", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"drawoncontour", "\[Equal]", "1"}], ",", RowBox[{"simplexcolorbarvf", "=", "simplexcolorbar"}], ",", RowBox[{"simplexcolorbarvf", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.4820990006196384`*^9, 3.4820990022720146`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Drawing Solutions to Diff Eqs if there is a contour plot", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"includecontourplot", "==", "1"}], " ", "||", " ", RowBox[{"drawoncontour", "\[Equal]", "1"}]}], ",", "\[IndentingNewLine]", " ", RowBox[{ RowBox[{ RowBox[{"g", "[", "y_", "]"}], ":=", RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ",", RowBox[{"1", "-", RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"con", "=", RowBox[{"ContourPlot", "[", RowBox[{ RowBox[{"g", "[", RowBox[{"{", RowBox[{"y1", ",", "y2"}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"y1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"y2", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", " ", RowBox[{"PlotPoints", "\[Rule]", "plotprecision"}], ",", RowBox[{"Contours", "\[Rule]", "numberofcontours"}], ",", RowBox[{"Frame", "\[Rule]", "None"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}], ",", " ", RowBox[{"ContourStyle", " ", "\[Rule]", " ", "None"}], ",", RowBox[{"ColorFunctionScaling", " ", "\[Rule]", " ", "False"}], " ", ",", " ", RowBox[{"ColorFunction", "\[Rule]", " ", RowBox[{"(", RowBox[{ RowBox[{"ConColFun", "[", "#", "]"}], "&"}], ")"}]}]}], "]"}]}]}], " ", ",", RowBox[{"con", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"includecontourplot", "==", "1"}], " ", ",", RowBox[{"conph", "=", "con"}], ",", RowBox[{"conph", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"drawoncontour", "\[Equal]", "1"}], ",", RowBox[{"convf", "=", "con"}], ",", RowBox[{"convf", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.47446330120716*^9, 3.4744633052429633`*^9}, 3.4820990030431232`*^9}, ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["Drawing 3D Plot of contour function", "Subsection"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"graphcontour3d", "==", "1"}], ",", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"frestricted3d", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "[", RowBox[{"[", "1", "]"}], "]"}], "\[GreaterEqual]", "0"}], "&&", RowBox[{ RowBox[{"x", "[", RowBox[{"[", "2", "]"}], "]"}], "\[GreaterEqual]", "0"}], "&&", RowBox[{ RowBox[{"y", "[", RowBox[{"[", "1", "]"}], "]"}], "\[GreaterEqual]", "0"}], "&&", RowBox[{ RowBox[{"y", "[", RowBox[{"[", "2", "]"}], "]"}], "\[GreaterEqual]", "0"}], "&&", RowBox[{ RowBox[{ RowBox[{"x", "[", RowBox[{"[", "1", "]"}], "]"}], "+", RowBox[{"x", "[", RowBox[{"[", "2", "]"}], "]"}]}], "\[Equal]", "1"}], "&&", RowBox[{ RowBox[{ RowBox[{"y", "[", RowBox[{"[", "1", "]"}], "]"}], "+", RowBox[{"y", "[", RowBox[{"[", "2", "]"}], "]"}]}], "\[Equal]", "1"}]}], ",", RowBox[{"ContourFunction", "[", RowBox[{"x", ",", "y"}], "]"}], ",", RowBox[{"-", " ", "Infty"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\n", RowBox[{ RowBox[{"g3d", "[", "y_", "]"}], ":=", RowBox[{"frestricted3d", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ",", RowBox[{"1", "-", RowBox[{ "y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ "y", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"confunplt", "=", " ", RowBox[{"Plot3D", "[", " ", RowBox[{ RowBox[{"g3d", "[", RowBox[{"{", RowBox[{"y1", ",", "y2"}], "}"}], "]"}], " ", ",", " ", RowBox[{"{", RowBox[{"y1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"y2", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", "\[IndentingNewLine]", RowBox[{"PlotPoints", " ", "\[Rule]", " ", "plotprecision"}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin"}], ",", RowBox[{"MaxAttained", "+", ".05"}]}], "}"}]}], ",", " ", RowBox[{"ViewPoint", "\[Rule]", "vpoint"}], ",", " ", RowBox[{"ColorFunctionScaling", "\[Rule]", " ", "False"}], " ", ",", " ", RowBox[{"ColorFunction", "\[Rule]", " ", RowBox[{"(", RowBox[{ RowBox[{"ConColFun", "[", "#", "]"}], "&"}], ")"}]}], ",", " ", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Mesh", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"BoxRatios", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1.25"}], "}"}]}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"edgeline1", "=", " ", RowBox[{"ParametricPlot3D", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"y1", ",", "0", ",", "0", ",", RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "y1"}], ",", "y1"}], "}"}]}], "]"}], ",", RowBox[{"GrayLevel", "[", ".3", "]"}]}], "}"}], " ", ",", " ", RowBox[{"{", RowBox[{"y1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", "\[IndentingNewLine]", RowBox[{"PlotPoints", " ", "\[Rule]", "200"}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin"}], ",", RowBox[{"MaxAttained", "+", ".05"}]}], "}"}]}], ",", " ", RowBox[{"PlotRegion", "->", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin", "-", ".1"}], ",", RowBox[{"MaxAttained", "+", ".15"}]}], "}"}]}], ",", " ", "\[IndentingNewLine]", RowBox[{"ViewPoint", "\[Rule]", "vpoint"}], ",", " ", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"BoxRatios", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1.25"}], "}"}]}]}], "]"}]}], " ", ";", RowBox[{"edgeline2", "=", " ", RowBox[{"ParametricPlot3D", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"y1", ",", "1", ",", "1", ",", RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"1", "-", "y1"}], ",", "y1"}], "}"}]}], "]"}], ",", RowBox[{"GrayLevel", "[", ".3", "]"}]}], "}"}], " ", ",", " ", RowBox[{"{", RowBox[{"y1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", "\[IndentingNewLine]", RowBox[{"PlotPoints", " ", "\[Rule]", " ", "200"}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin"}], ",", RowBox[{"MaxAttained", "+", ".05"}]}], "}"}]}], ",", " ", RowBox[{"ViewPoint", "\[Rule]", "vpoint"}], ",", " ", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"BoxRatios", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1.25"}], "}"}]}]}], "]"}]}], " ", ";", " ", RowBox[{"edgeline3", "=", " ", RowBox[{"ParametricPlot3D", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "y2", ",", RowBox[{"g3d", "[", RowBox[{"{", RowBox[{"0", ",", "y2"}], "}"}], "]"}], ",", RowBox[{"GrayLevel", "[", ".3", "]"}]}], "}"}], " ", ",", " ", RowBox[{"{", RowBox[{"y2", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", "\[IndentingNewLine]", RowBox[{"PlotPoints", " ", "\[Rule]", " ", "200"}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin"}], ",", RowBox[{"MaxAttained", "+", ".05"}]}], "}"}]}], ",", " ", RowBox[{"ViewPoint", "\[Rule]", "vpoint"}], ",", " ", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"BoxRatios", " ", "\[Rule]", " ", "heightratio"}]}], "]"}]}], ";", " ", "\[IndentingNewLine]", RowBox[{"edgeline4", "=", " ", RowBox[{"ParametricPlot3D", "[", " ", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "y2", ",", RowBox[{"g3d", "[", RowBox[{"{", RowBox[{"1", ",", "y2"}], "}"}], "]"}], ",", RowBox[{"GrayLevel", "[", ".3", "]"}]}], "}"}], " ", ",", " ", RowBox[{"{", RowBox[{"y2", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "Identity"}], ",", "\[IndentingNewLine]", RowBox[{"PlotPoints", " ", "\[Rule]", " ", "200"}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin"}], ",", RowBox[{"MaxAttained", "+", ".05"}]}], "}"}]}], ",", " ", RowBox[{"ViewPoint", "\[Rule]", "vpoint"}], ",", " ", "\[IndentingNewLine]", RowBox[{"Axes", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}], ",", " ", RowBox[{"BoxRatios", " ", "\[Rule]", " ", "heightratio"}]}], "]"}]}], ";"}]}], " ", "]"}], ";"}]], "Input", CellChangeTimes->{{3.4744634288707314`*^9, 3.474463429421523*^9}, { 3.4748370502831964`*^9, 3.474837050513528*^9}, {3.4748402487175226`*^9, 3.474840249428545*^9}, {3.4748402829667706`*^9, 3.4748403262389927`*^9}, { 3.474840366576996*^9, 3.474840400115222*^9}, {3.4748406270315113`*^9, 3.474840678405383*^9}, {3.4748407320625386`*^9, 3.4748407487966013`*^9}, { 3.474840831996236*^9, 3.474840839476993*^9}, {3.47484086965038*^9, 3.4748408806762342`*^9}, {3.474840934984326*^9, 3.4748410701987543`*^9}, { 3.4748412389614234`*^9, 3.4748412660003033`*^9}, {3.474841311575838*^9, 3.474841391420649*^9}, {3.4748414349432316`*^9, 3.4748414659678426`*^9}, { 3.474858180098568*^9, 3.47485820727765*^9}, {3.4748616280774126`*^9, 3.474861662456848*^9}, {3.4820990037541456`*^9, 3.4820990054365644`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Drawing Triangle and Dots", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ The cells belongs to this group is for drawing white area around the simplex.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"Tri", "=", RowBox[{"Graphics", "[", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], "]"}], "]"}]}], ";"}]], "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell["\<\ This part draws the dots for the rest points. TestStability[dyn,F,bigT, \ numtest, eps, delta,RestSearchInit,TolLevel] must be called in order to \ determine stability of points. Hence you may need to modify this part if \ StabilityCheck do not work for your choice of dynamic.\ \>", "Text", CellChangeTimes->{3.4744074994992065`*^9, 3.481570492548917*^9, 3.4820980951175904`*^9}, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", " ", "1"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"DOTS", "=", RowBox[{"Graphics", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"testrest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"testrest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", "0.01"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"WDots", "=", RowBox[{"Graphics", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"GrayLevel", "[", "1", "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"unstbl", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2", ",", "2"}], "\[RightDoubleBracket]"}], ",", RowBox[{"unstbl", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", "0.006"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "unstbl", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], "]"}]}]}], ",", RowBox[{ RowBox[{"DOTS", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}], " ", ";", " ", RowBox[{"WDots", "=", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}]}]}]}], " ", "]"}], " ", ";"}]], "Input", ImageRegion->{{0, 1}, {0, 1}}] }, Closed]], Cell[CellGroupData[{ Cell["\<\ These cells draw the triangle, lines, and dots for the 3D plot of contour \ function\ \>", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"graphcontour3d", "\[Equal]", "1"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"graphf", "[", RowBox[{"x_", ",", "y_"}], "]"}], " ", ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ",", RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", RowBox[{"ContourFunction", "[", RowBox[{"x", ",", "y"}], "]"}]}], "}"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"graphmin", "[", RowBox[{"x_", ",", "y_"}], "]"}], " ", ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"y", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ",", RowBox[{"x", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Tri3d", "=", RowBox[{"Graphics3D", "[", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"1", ",", "0", ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], " ", "}"}], " ", "]"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], ",", RowBox[{ RowBox[{"SeveralLines", "=", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{ RowBox[{"Dashing", "[", RowBox[{"{", RowBox[{".01", ",", " ", ".01"}], "}"}], "]"}], ",", " ", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"graphmin", "[", RowBox[{ RowBox[{"RePos", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"RePos", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"graphf", "[", RowBox[{ RowBox[{"RePos", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"RePos", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}]}], "}"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{ RowBox[{"Dimensions", "[", "RePos", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "1"}], "}"}]}], "]"}], "]"}]}], "}"}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"SeveralPoints", "=", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{ RowBox[{"PointSize", " ", "[", ".02", "]"}], ",", " ", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Point", "[", RowBox[{"graphmin", "[", RowBox[{ RowBox[{"stblpnts", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"stblpnts", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "stblpnts", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], "]"}], ",", RowBox[{"GrayLevel", "[", ".5", "]"}], ",", RowBox[{"Flatten", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"Point", "[", RowBox[{"graphmin", "[", RowBox[{ RowBox[{"unstbl", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"unstbl", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "unstbl", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], "]"}]}], "}"}], "]"}]}]}]}], "]"}]}]}], "]"}], " ", ";"}]], "Input", CellChangeTimes->{3.482099006337861*^9}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Arrows", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"ar", "=", RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[NotEqual]", " ", "0"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Join", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Select", "[", RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "3"}], "\[RightDoubleBracket]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"Hue", "[", "__", "]"}]}], "]"}], " ", "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"GrayLevel", "[", "__", "]"}]}], "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"RGBColor", "[", "__", "]"}]}], "\[IndentingNewLine]", "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"CMYKColor", "[", "__", "]"}]}], "]"}]}], ")"}], "&"}]}], "]"}], ",", RowBox[{"{", RowBox[{"GrayLevel", "[", "0", "]"}], "}"}]}], "\[IndentingNewLine]", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{"GrayLevel", "[", "0", "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], ",", "arrowheadcenter"}], "}"}], "}"}], "]"}], ",", RowBox[{"Arrow", "[", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", RowBox[{ RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{"relarrowbase", " ", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}]}], "]"}]}], ",", RowBox[{"x1", "[", RowBox[{ RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{"relarrowbase", " ", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}], "/.", "\[InvisibleSpace]", RowBox[{ "G", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "]"}]}], ",", RowBox[{"x1", "[", RowBox[{ RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "]"}]}], "}"}], "/.", "\[InvisibleSpace]", RowBox[{ "G", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "trajectoryspecs", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}]}], " ", ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4744154143502035`*^9, 3.4744157690802803`*^9}, { 3.4744158293970113`*^9, 3.4744158834847856`*^9}, {3.474415925485179*^9, 3.474415946755765*^9}, {3.4749115513013277`*^9, 3.4749115559179664`*^9}, { 3.474912076536579*^9, 3.47491207970113*^9}, {3.4749121604171934`*^9, 3.4749121612884464`*^9}, {3.47491235200268*^9, 3.474912366423416*^9}, 3.4749124139717875`*^9, {3.4749124547103662`*^9, 3.474912454930683*^9}, { 3.4749125209556227`*^9, 3.4749125462219534`*^9}, {3.474913089783557*^9, 3.474913110923955*^9}, {3.4749135822817345`*^9, 3.4749135826522675`*^9}, { 3.482102344618072*^9, 3.4821023536210175`*^9}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[BoxData[ RowBox[{ RowBox[{"arcycle", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", RowBox[{"{", "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "\[NotEqual]", " ", "0"}], " ", ",", RowBox[{ RowBox[{"Join", "[", RowBox[{ RowBox[{"Select", "[", RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "4"}], "\[RightDoubleBracket]"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"Hue", "[", "__", "]"}]}], "]"}], " ", "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"GrayLevel", "[", "__", "]"}]}], "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"RGBColor", "[", "__", "]"}]}], "]"}], "||", RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{"CMYKColor", "[", "__", "]"}]}], "]"}]}], ")"}], "&"}]}], "\[IndentingNewLine]", "]"}], ",", RowBox[{"{", RowBox[{"GrayLevel", "[", "0", "]"}], "}"}]}], "\[IndentingNewLine]", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", "\[IndentingNewLine]", RowBox[{"GrayLevel", "[", "0", "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "6"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], ",", "arrowheadcenter"}], "}"}], "}"}], "]"}], ",", RowBox[{"Arrow", "[", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", RowBox[{ RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{"relarrowbase", " ", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}]}], "]"}]}], ",", RowBox[{"x1", "[", RowBox[{ RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "-", RowBox[{"relarrowbase", " ", RowBox[{"trajectoryspecs", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}]}], "]"}]}], "}"}], "/.", RowBox[{ "GCycle", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"Flatten", "[", "\[IndentingNewLine]", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "-", RowBox[{"y1", "[", RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "]"}]}], ",", RowBox[{"x1", "[", RowBox[{ RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "5"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}], "]"}]}], "}"}], "/.", RowBox[{ "GCycle", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"customcycles", "\[LeftDoubleBracket]", RowBox[{"i", ",", "6"}], "\[RightDoubleBracket]"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "customcycles", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.4744150826432323`*^9, 3.474415114098462*^9}, { 3.474415289500678*^9, 3.4744153065552015`*^9}, {3.4744159816259055`*^9, 3.4744160280126066`*^9}, {3.474416064304792*^9, 3.474416113265194*^9}, { 3.4749116169757633`*^9, 3.474911624276261*^9}, {3.4749135455088577`*^9, 3.47491354822276*^9}, {3.4820996815287375`*^9, 3.482099687176859*^9}, { 3.4821023551231775`*^9, 3.482102356054517*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Generating the output notebook", "Section"], Cell[BoxData[ RowBox[{ RowBox[{"OutputToOneNotebook", "=", "0"}], ";"}]], "Input", CellChangeTimes->{{3.4819270007532053`*^9, 3.4819270530183587`*^9}, 3.481927590451149*^9, 3.4819278444263477`*^9, 3.4819282299507046`*^9, 3.4819286333107076`*^9, 3.4821029124245377`*^9, 3.4825065437120028`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "Redirecting"}]}]}]}]}], " ", "output", " ", "to", " ", "a", " ", "new", " ", RowBox[{ RowBox[{ RowBox[{"notebook", "--"}], "--"}], "--"}]}], "-"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"tmpstring", "=", RowBox[{"StringTake", "[", RowBox[{ RowBox[{"CurrentValue", "[", RowBox[{"$nb", ",", "\"\\""}], "]"}], ",", "13"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Which", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Not", "[", RowBox[{"tmpstring", "==", "\"\\""}], "]"}], " ", "&&", " ", RowBox[{"OutputToOneNotebook", "==", "1"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"$nb", "=", RowBox[{"CreateWindow", "[", RowBox[{ RowBox[{"WindowSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"650", ",", "550"}], "}"}]}], ",", " ", RowBox[{"WindowTitle", "->", "\"\\""}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"NotebookCounter", " ", "=", "1"}], ";"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Not", "[", RowBox[{"tmpstring", "==", "\"\\""}], "]"}], " ", "&&", " ", RowBox[{"OutputToOneNotebook", "==", "0"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"$nb", "=", RowBox[{"CreateWindow", "[", RowBox[{ RowBox[{"WindowSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"650", ",", "550"}], "}"}]}], ",", RowBox[{"WindowTitle", "->", RowBox[{"ToString", "[", RowBox[{"Row", "[", RowBox[{"{", "\"\\"", "}"}], "]"}], "]"}]}]}], "]"}]}], ";", RowBox[{"NotebookCounter", "=", "1"}], ";"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmpstring", "==", "\"\\""}], " ", "&&", " ", RowBox[{"OutputToOneNotebook", "==", "0"}]}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"NotebookCounter", "=", RowBox[{"NotebookCounter", " ", "+", "1"}]}], ";", "\[IndentingNewLine]", RowBox[{"$nb", "=", RowBox[{"CreateWindow", "[", RowBox[{ RowBox[{"WindowSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"650", ",", "550"}], "}"}]}], ",", RowBox[{"WindowTitle", "->", RowBox[{"ToString", "[", RowBox[{"Row", "[", RowBox[{"{", RowBox[{"\"\\"", ",", "NotebookCounter"}], "}"}], "]"}], "]"}]}]}], "]"}]}], ";"}]}], "\[IndentingNewLine]", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"$DisplayFunction", "=", RowBox[{ RowBox[{"NotebookWrite", "[", RowBox[{"$nb", ",", " ", RowBox[{"Cell", "[", RowBox[{ RowBox[{"GraphicsData", "[", RowBox[{"\"\\"", ",", " ", RowBox[{"ExportString", "[", RowBox[{"#", ",", "\"\\""}], "]"}]}], "]"}], ",", "\"\\""}], "]"}]}], "]"}], "&"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"$Post", "=", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"#", "=!=", " ", "Null"}], ",", RowBox[{"NotebookWrite", "[", RowBox[{"$nb", ",", RowBox[{"Cell", "[", RowBox[{ RowBox[{"BoxData", "[", RowBox[{"MakeBoxes", "[", RowBox[{"#", ",", "StandardForm"}], "]"}], "]"}], ",", "\"\\""}], "]"}]}], "]"}]}], "]"}], "&"}]}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Unprotect", "[", "Print", "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", "x_", "]"}], " ", ":=", " ", RowBox[{"NotebookWrite", "[", RowBox[{"$nb", ",", RowBox[{"Cell", "[", RowBox[{"BoxData", "[", RowBox[{"MakeBoxes", "[", RowBox[{"x", ",", "StandardForm"}], "]"}], "]"}], "]"}]}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", "x__", "]"}], " ", ":=", RowBox[{"Map", "[", RowBox[{"Print", ",", RowBox[{"{", "x", "}"}]}], "]"}]}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Protect", "[", "Print", "]"}], " ", ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "Redirecting"}]}]}]}]}]}]}]}], " ", "code", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"ends", "--"}], "--"}], "--"}], "--"}], "--"}]}], "-", RowBox[{"--", RowBox[{"--", "-"}]}]}], "*)"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{ 3.4744628258336067`*^9, 3.474464139362368*^9, {3.4744670890838594`*^9, 3.474467110013955*^9}, {3.4744688011456833`*^9, 3.474468802697915*^9}, { 3.4821017907115936`*^9, 3.4821017988833437`*^9}, 3.4821028906932898`*^9}, CellTags->"printingcell"], Cell[BoxData[ RowBox[{ RowBox[{"NotebookWrite", "[", RowBox[{"$nb", ",", RowBox[{"Cell", "[", RowBox[{ RowBox[{ "BoxData", "[", "\"\<\[LightBulb]\[LightBulb]\[LightBulb] DYNAMO \[LightBulb]\ \[LightBulb]\[LightBulb]\>\"", "]"}], ",", "\"\\"", ",", " ", RowBox[{"FontColor", "\[Rule]", " ", RowBox[{"Hue", "[", ".19", "]"}]}], ",", RowBox[{"Background", "\[Rule]", " ", RowBox[{"Hue", "[", ".72", "]"}]}], ",", RowBox[{"TextAlignment", "\[Rule]", " ", "Center"}], ",", RowBox[{"CellFrame", "\[Rule]", " ", "True"}]}], "]"}]}], "]"}], " ", ";"}]], "Input", CellChangeTimes->{{3.474475842869723*^9, 3.4744758471659*^9}}], Cell[CellGroupData[{ Cell["Text output - the game", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"Style", "[", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"GridBox", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "\"\<\>\"", "}"}], ",", RowBox[{"{", "\"\\"", "}"}]}], "}"}], "]"}], "]"}], ",", "\"\\""}], "]"}], "]"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{"x", ",", "y"}], "]"}], " ", "\[Equal]", " ", RowBox[{"A", ".", "y"}]}], ",", RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Normal form game: \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"DisplayForm", "[", RowBox[{"GridBox", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "\"\<\>\"", "}"}], ",", RowBox[{"{", RowBox[{"strategy", "[", "1", "]"}], "}"}], ",", RowBox[{"{", RowBox[{"strategy", "[", "2", "]"}], "}"}]}], "}"}], "]"}], "]"}], " ", ",", "\[IndentingNewLine]", RowBox[{"DisplayForm", "[", RowBox[{"GridBox", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"strategy", "[", "3", "]"}], ",", RowBox[{"strategy", "[", "4", "]"}]}], "}"}], "}"}], ",", "U"}], "]"}], "]"}], "]"}]}], "}"}], "\[IndentingNewLine]", "]"}], "]"}]}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Payoff vector field: F\>\"", "}"}], "]"}], "]"}], ",", RowBox[{"MatrixForm", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], ",", " ", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< = \>\"", "}"}], "]"}], "]"}], ",", RowBox[{"MatrixForm", "[", RowBox[{"Flatten", "[", RowBox[{"F", "[", RowBox[{ RowBox[{"{", RowBox[{"x1", ",", "x2"}], "}"}], ",", RowBox[{"{", RowBox[{"y1", ",", "y2"}], "}"}]}], "]"}], "]"}], "]"}]}], "}"}], "]"}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"findnashequilibria", "\[Equal]", "1"}], ",", " ", RowBox[{ RowBox[{"If", "[", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"NashEq", "[", RowBox[{"F1", ",", "F2"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "1"}], ",", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Nash equilibrium:\>\"", "}"}], "]"}], "]"}], "]"}], ",", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Nash equilibria:\>\"", "}"}], "]"}], "]"}], "]"}]}], "]"}], " ", ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"NashEq", "[", RowBox[{"F1", ",", "F2"}], "]"}], "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{ RowBox[{"Dimensions", "[", RowBox[{"NashEq", "[", RowBox[{"F1", ",", "F2"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "]"}], ";"}]}], "Input", CellChangeTimes->{{3.4744652297202253`*^9, 3.4744652305013485`*^9}, 3.4744652739137726`*^9, {3.47446538996064*^9, 3.4744654114415283`*^9}, { 3.4744657681945133`*^9, 3.4744658496516433`*^9}, {3.474465912091427*^9, 3.4744659346037984`*^9}, {3.4744761436922846`*^9, 3.4744762944891195`*^9}, {3.474476361195038*^9, 3.474476407892185*^9}, { 3.474476518981924*^9, 3.474476528335374*^9}, {3.4744770460698395`*^9, 3.474477081831262*^9}, {3.474477217456281*^9, 3.4744772567227435`*^9}, { 3.474477311120964*^9, 3.4744773117518716`*^9}, 3.4744792889549503`*^9, { 3.474479577770246*^9, 3.474479630065443*^9}, {3.474479705734249*^9, 3.4744797091491594`*^9}, {3.474479746492857*^9, 3.474479838815611*^9}, { 3.4744799072840633`*^9, 3.474479933932382*^9}, {3.474479972587966*^9, 3.474480022910326*^9}, {3.474480076717697*^9, 3.474480078730592*^9}, { 3.4744801120985727`*^9, 3.4744802178806796`*^9}, {3.4744802661000156`*^9, 3.4744805247218957`*^9}, {3.4744805637780557`*^9, 3.474480644454062*^9}, { 3.4744806825187964`*^9, 3.474480733251747*^9}, {3.474480765978806*^9, 3.4744807751119385`*^9}, {3.475025134728011*^9, 3.47502515327468*^9}, { 3.475025418295761*^9, 3.475025457662368*^9}, {3.4750255107286735`*^9, 3.4750255123109484`*^9}, {3.4820970812204885`*^9, 3.4820970905935726`*^9}, {3.482097140910684*^9, 3.482097148034717*^9}, { 3.482097374697899*^9, 3.482097375038741*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"FindRoot", "::", "\<\"jsing\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Encountered a singular \ Jacobian at the point \\\\\\\"\\\", \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({nax1, nay1}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\" = \\\\\\\"\\\", \\\"MT\ \\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({1.`, 0.5000000000000001`}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\". Try perturbing the \ initial point(s).\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/FindRoot/jsing\\\", ButtonNote -> \ \\\"FindRoot::jsing\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.4826199555176973`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"FindRoot", "::", "\<\"jsing\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Encountered a singular \ Jacobian at the point \\\\\\\"\\\", \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({nax1, nay1}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\" = \\\\\\\"\\\", \\\"MT\ \\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({1.`, 0.5000000000000001`}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\". Try perturbing the \ initial point(s).\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/FindRoot/jsing\\\", ButtonNote -> \ \\\"FindRoot::jsing\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.482619955714903*^9}], Cell[BoxData[ RowBox[{ RowBox[{"FindRoot", "::", "\<\"jsing\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Encountered a singular \ Jacobian at the point \\\\\\\"\\\", \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({nax1, nay1}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\" = \\\\\\\"\\\", \\\"MT\ \\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\({1.`, 0.5000000000000001`}\\), \ \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\". Try perturbing the \ initial point(s).\\\\\\\"\\\", \\\"MT\\\"]\\) \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/FindRoot/jsing\\\", ButtonNote -> \ \\\"FindRoot::jsing\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.482619955875456*^9}], Cell[BoxData[ RowBox[{ RowBox[{"General", "::", "\<\"stop\"\>"}], RowBox[{ ":", " "}], "\<\"\\!\\(\\*StyleBox[\\\"\\\\\\\"Further output of \\\\\\\"\\\ \", \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\!\\(FindRoot :: \\\"jsing\\\"\ \\), \\\"MT\\\"]\\)\[NoBreak]\\!\\(\\*StyleBox[\\\"\\\\\\\" will be \ suppressed during this calculation.\\\\\\\"\\\", \\\"MT\\\"]\\) \ \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \ ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \ ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.4826199559062643`*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Text output - the dynamic", "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"Style", "[", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"GridBox", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "\"\<\>\"", "}"}], ",", RowBox[{"{", "\"\\"", "}"}]}], "}"}], "]"}], "]"}], ",", "\"\\""}], "]"}], "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Name of dynamic: \>\"", "}"}], "]"}], "]"}], ",", " ", "dyn"}], " ", "}"}], "]"}], "]"}], " ", ";"}], "\n"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Law of motion: \>\"", "}"}], "]"}], "]"}], ",", " ", RowBox[{"Row", "[", RowBox[{"{", " ", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< \!\(\*SubscriptBox[\(V\), \(F\)]\)\>\"", "}"}], "]"}], "]"}], ",", RowBox[{"MatrixForm", "[", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], ",", " ", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< = \>\"", "}"}], "]"}], "]"}], ",", RowBox[{"MatrixForm", "[", RowBox[{"Simplify", "[", RowBox[{"dyn", "[", RowBox[{ RowBox[{"{", RowBox[{"x1", ",", "x2"}], "}"}], ",", RowBox[{"{", RowBox[{"y1", ",", "y2"}], "}"}], ",", "F1", ",", "F2"}], "]"}], "]"}], "]"}]}], " ", "}"}], "]"}]}], " ", "]"}], ";"}], " "}]}], "Input", CellChangeTimes->{{3.4744075007209635`*^9, 3.4744075347599087`*^9}, { 3.4744660145287247`*^9, 3.47446606534179*^9}, {3.474480893792593*^9, 3.4744810714280205`*^9}, {3.4815704925589314`*^9, 3.4815704925589314`*^9}, { 3.482098095157648*^9, 3.4820980951676626`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Text output - stability of rest points", "Text"], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "stblpnts", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "1"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Stable rest point:\>\"", "}"}], "]"}], "]"}], "]"}], ",", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Stable rest points:\>\"", "}"}], "]"}], "]"}], "]"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "stblpnts", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "0"}], ",", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< None\>\"", "}"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"stblpnts", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{ RowBox[{"Dimensions", "[", "stblpnts", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], " ", "]"}], "]"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "unstbl", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "1"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Unstable rest point:\>\"", "}"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Unstable rest points:\>\"", "}"}], "]"}], "]"}], "]"}]}], "]"}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Dimensions", "[", "unstbl", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< None\>\"", "}"}], "]"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"unstbl", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", RowBox[{ RowBox[{"Dimensions", "[", "unstbl", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]}], "\[IndentingNewLine]", "]"}], " ", ";"}]}], "\[IndentingNewLine]", "]"}]}]], "Input", CellChangeTimes->{{3.4744811007802267`*^9, 3.4744811710512714`*^9}, { 3.474481208264782*^9, 3.474481211339203*^9}, 3.4744812504854927`*^9, { 3.47448132363067*^9, 3.474481814296212*^9}, {3.474481853382416*^9, 3.4744820200721035`*^9}, {3.4744820531997385`*^9, 3.474482227570472*^9}, { 3.474921890112877*^9, 3.4749218918653965`*^9}, {3.474921990917827*^9, 3.4749220127191763`*^9}, {3.47492206314168*^9, 3.474922086004555*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Text output - the contour function", "Text"], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], "||", " ", RowBox[{"graphcontour3d", "\[Equal]", "1"}]}], ",", RowBox[{"Print", "[", RowBox[{"Style", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"GridBox", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "\"\<\>\"", "}"}], ",", RowBox[{"{", "\"\\"", "}"}]}], "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", "\"\\""}], "]"}], "]"}]}], " ", "\[IndentingNewLine]", "]"}], ";"}], "\n"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"includecontourplot", "\[Equal]", "1"}], "||", " ", RowBox[{"graphcontour3d", "\[Equal]", "1"}]}], ",", RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Name of Contour Function: \>\"", "}"}], "]"}], "]"}], ",", " ", "\[IndentingNewLine]", "ContourFunction"}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]}], "\[IndentingNewLine]", "]"}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"showcontourformula", "\[Equal]", "1"}], ",", RowBox[{"Print", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Definition of Contour Function: \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< \[Psi]\>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", " ", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< = \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ContourFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"x1", ",", "x2"}], "}"}], ",", RowBox[{"{", RowBox[{"y1", ",", "y2"}], "}"}]}], "]"}]}], " ", "\[IndentingNewLine]", "}"}], "]"}]}], "\[IndentingNewLine]", "]"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Minimum Value = \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"N", "[", "MinAttained", "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\< Maximum Value = \>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"N", "[", "MaxAttained", "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}], " ", ";"}], " "}]}], "Input", CellChangeTimes->{{3.474466109635482*^9, 3.474466160278302*^9}, { 3.47448228501307*^9, 3.4744824248541517`*^9}, {3.474482460485387*^9, 3.4744827969042015`*^9}, {3.4744828588432655`*^9, 3.4744828619277*^9}, { 3.4820990072091136`*^9, 3.4820990081104097`*^9}}] }, Closed]], Cell["Generating the vector field diagram", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"vectorfielddiagram", "\[Equal]", "1"}], ",", " ", "\[IndentingNewLine]", RowBox[{"Show", "[", " ", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"drawrestpoints", "\[Equal]", "1"}], ",", RowBox[{"{", RowBox[{ "convf", ",", "simplexcolorbarvf", ",", " ", "Tri", ",", "vectorf1", ",", "vectorf2", ",", "DOTS", ",", "WDots"}], "}"}], ",", RowBox[{"{", RowBox[{ "convf", ",", "simplexcolorbarvf", ",", " ", "Tri", ",", "vectorf1", ",", "vectorf2"}], "}"}]}], "]"}], ",", RowBox[{"DisplayFunction", "\[Rule]", " ", "$DisplayFunction"}], ",", "\[IndentingNewLine]", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"500", ",", "500"}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.1"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"BaseStyle", "->", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "2", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".025"}], ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "1", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".025"}], ",", "1"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "3", "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "1.025"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "4", "]"}], ",", RowBox[{"{", RowBox[{"1", ",", "1.025"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}]}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}], " "}]], "Input", CellChangeTimes->{ 3.4744168929863777`*^9, {3.474466213675083*^9, 3.4744662162888412`*^9}, { 3.474466418739952*^9, 3.4744664201720114`*^9}, {3.4744664709450192`*^9, 3.474466519645046*^9}, {3.4750405649139895`*^9, 3.4750406155768394`*^9}}], Cell[CellGroupData[{ Cell["Generating the phase diagram on simplex ", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"phasediagram", "\[Equal]", "1"}], ",", " ", RowBox[{"Show", "[", RowBox[{ RowBox[{"{", RowBox[{ "conph", ",", "Tri", ",", "e", ",", "ecycle", ",", "simplexcolorbarph", ",", "extralines", ",", "uddots", ",", "udwdots", ",", "extratext", ",", "ar", ",", "arcycle", ",", "DOTS", ",", "WDots"}], "}"}], ",", RowBox[{"DisplayFunction", " ", "\[Rule]", " ", "$DisplayFunction"}], ",", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"500", ",", "500"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".08"}], ",", "1.1"}], "}"}]}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", " ", "Automatic"}], ",", RowBox[{"BaseStyle", "->", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "}"}]}], ",", RowBox[{"Epilog", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "2", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".025"}], ",", "0"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "1", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".025"}], ",", "1"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "3", "]"}], ",", RowBox[{"{", RowBox[{"0", ",", "1.025"}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"strategy", "[", "4", "]"}], ",", RowBox[{"{", RowBox[{"1", ",", "1.025"}], "}"}]}], "]"}]}], "}"}]}]}], " ", "]"}]}], " ", "]"}], " "}]], "Input", CellChangeTimes->{3.4744164949340067`*^9, 3.4744665518513565`*^9}] }, Closed]], Cell["Generating the 3D plot of the contour function", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"graphcontour3d", "\[Equal]", " ", "1"}], ",", " ", RowBox[{"Show", "[", RowBox[{"confunplt", ",", RowBox[{"Which", "[", RowBox[{ RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], " ", "&&", " ", RowBox[{"grayline", "\[Equal]", "1"}]}], ",", RowBox[{"{", RowBox[{ "Tri3d", ",", "SeveralLines", ",", "SeveralPoints", ",", "edgeline1", ",", "edgeline2", ",", "edgeline3", ",", "edgeline4"}], "}"}], ",", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "1"}], " ", "&&", " ", RowBox[{"grayline", "\[Equal]", "0"}]}], ",", RowBox[{"{", RowBox[{"Tri3d", ",", "SeveralLines", ",", "SeveralPoints"}], "}"}], ",", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "0"}], " ", "&&", " ", RowBox[{"grayline", "\[Equal]", "1"}]}], ",", RowBox[{"{", RowBox[{ "Tri3d", ",", "edgeline1", ",", "edgeline2", ",", "edgeline3", ",", "edgeline4"}], "}"}], ",", RowBox[{ RowBox[{"findrestpoints", "\[Equal]", "0"}], " ", "&&", " ", RowBox[{"grayline", "\[Equal]", "0"}]}], ",", "Tri3d"}], "]"}], ",", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"strategy", "[", "2", "]"}], ",", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".04"}], ",", RowBox[{"-", ".04"}], ",", " ", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"strategy", "[", "1", "]"}], ",", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".04"}], ",", "1.04", ",", " ", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"strategy", "[", "3", "]"}], ",", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "]"}], ",", RowBox[{"{", RowBox[{".04", ",", "1.06", ",", " ", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"strategy", "[", "4", "]"}], ",", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "]"}], ",", RowBox[{"{", RowBox[{"1.04", ",", "1.06", ",", " ", RowBox[{"MinAttained", "-", "distancefrommin"}]}], "}"}]}], "]"}]}], "}"}], " ", "]"}], ",", " ", RowBox[{"ImageSize", "\[Rule]", " ", RowBox[{"{", RowBox[{"500", ",", "500"}], "}"}]}], ",", RowBox[{"PlotRange", "->", RowBox[{"{", RowBox[{ RowBox[{"MinAttained", "-", "distancefrommin", "-", ".1"}], ",", RowBox[{"MaxAttained", "+", ".15"}]}], "}"}]}]}], "]"}]}], "]"}], " "}]], "Input", CellChangeTimes->{{3.474466597827467*^9, 3.474466607261032*^9}, { 3.4748610949307857`*^9, 3.4748611108336525`*^9}, {3.474861791021715*^9, 3.4748618103795505`*^9}, 3.4748618424256306`*^9, {3.474861921329088*^9, 3.474862038948216*^9}, {3.474862070743936*^9, 3.4748620808684945`*^9}, { 3.474862183075461*^9, 3.474862215351872*^9}, {3.474862401289237*^9, 3.474862443399789*^9}, {3.4748626861588593`*^9, 3.4748626945909843`*^9}, 3.474862741288131*^9, {3.474862921216856*^9, 3.4748629308707376`*^9}, { 3.4748629938713284`*^9, 3.4748630022333517`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Print", "[", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\\"", "}"}], "]"}], "]"}], ",", RowBox[{"If", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Quotient", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}], ">", "9"}], ",", RowBox[{"Quotient", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}], ",", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\<0\>\"", "}"}], "]"}], "]"}], ",", RowBox[{"Quotient", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\<:\>\"", "}"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Round", "[", RowBox[{"Mod", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}], "]"}], ">", "9"}], ",", RowBox[{"Round", "[", RowBox[{"Mod", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{"{", RowBox[{ RowBox[{"DisplayForm", "[", RowBox[{"RowBox", "[", RowBox[{"{", "\"\<0\>\"", "}"}], "]"}], "]"}], ",", RowBox[{"Round", "[", RowBox[{"Mod", "[", RowBox[{ RowBox[{ RowBox[{"AbsoluteTime", "[", "]"}], " ", "-", " ", "time1"}], ",", "60"}], "]"}], "]"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}], " ", ";"}]], "Input", CellChangeTimes->CompressedData[" 1:eJxTTMoPSmViYGAQBmIQHZTMa8v2+KXj44zDYDpP5ZrABCC9YuMfIRDtly8g DqK3zlKXBNFWPgdlQfTEw05yIDogp0wNREdpvFIH0W8CRCxB9DvD9dYg+sCx 474gOmPSXH8Q/UeoKwVEX5KfCKafO22vANFn3HdWgehbs8KbQPSMOafB9AXe hNlgOm/eMhD9RfrsRhDNOLtlG4hedijoLIj+dEv+HIjmPfftMoh+tU37EYgW mh3yDKwuJeYFiD63NfMniFYKu/UH7K4t9xknAumez9JMILqOJ4QTRK+KmSMC olv41lYIvQf6o1exEkQDABD1rqM= "]], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "Returning"}]}]}]}]}], " ", "to", " ", "original", " ", "output", " ", RowBox[{ RowBox[{ RowBox[{"production", "--"}], "--"}], "--"}]}], "-"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"$DisplayFunction", "=", RowBox[{ RowBox[{"CellPrint", "[", RowBox[{"Cell", "[", RowBox[{ RowBox[{"GraphicsData", "[", RowBox[{"\"\\"", ",", RowBox[{"ExportString", "[", RowBox[{"#", ",", "\"\\""}], "]"}]}], "]"}], ",", "\"\\""}], "]"}], "]"}], "&"}]}], ";"}], "\n", RowBox[{ RowBox[{"$Post", "=", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"#1", "=!=", "Null"}], ",", RowBox[{"CellPrint", "[", RowBox[{"Cell", "[", RowBox[{ RowBox[{"BoxData", "[", RowBox[{"MakeBoxes", "[", RowBox[{"#1", ",", "StandardForm"}], "]"}], "]"}], ",", "\"\\""}], "]"}], "]"}]}], "]"}], "&"}]}], ";"}], "\n", RowBox[{ RowBox[{"Unprotect", "[", "Print", "]"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"Print", "[", "x_", "]"}], ":=", RowBox[{"CellPrint", "[", RowBox[{"Cell", "[", RowBox[{"BoxData", "[", RowBox[{"MakeBoxes", "[", RowBox[{"x", ",", "StandardForm"}], "]"}], "]"}], "]"}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"Print", "[", "x__", "]"}], ":=", RowBox[{"Print", "/@", RowBox[{"{", "x", "}"}]}]}], ";"}], "\n", RowBox[{ RowBox[{"Protect", "[", "Print", "]"}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", RowBox[{"--", "code"}]}]}]}]}]}]}]}], " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"ends", "--"}], "--"}], "--"}], "--"}], "--"}]}], "-", RowBox[{"--", RowBox[{"--", "-"}]}]}], "*)"}]}]}]], "Input", CellChangeTimes->{{3.474463029536517*^9, 3.4744630427254815`*^9}, { 3.474464168474229*^9, 3.4744641696559277`*^9}, {3.474464379727997*^9, 3.474464386367544*^9}, {3.474467076205341*^9, 3.4744670820537505`*^9}, { 3.474468634325808*^9, 3.4744686348465567`*^9}, {3.474469449648184*^9, 3.47446945054948*^9}, {3.474469481123443*^9, 3.4744694823251715`*^9}}] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Initialization Cells; Procedure Library", "Subtitle", CellChangeTimes->{{3.482619869710248*^9, 3.482619871821666*^9}}], Cell["Preliminary definitions and calculations", "Section", InitializationCell->True], Cell[CellGroupData[{ Cell["Calculation of restricted equilibria and Nash equilibria ", "Section", InitializationCell->True], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Clear", "[", "NashEq", "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"NashEq", "::", "usage"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"NashEq", "::", "notes"}], "=", "\"\\""}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"NashEq", "[", RowBox[{"F1_", ",", "F2_"}], "]"}], ":=", RowBox[{"Module", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ "usex", ",", "yusey", ",", "i", ",", "j", ",", "nnR", ",", "TnnTR", ",", "nnsonuc", ",", "nnfin", ",", "RawRestRep", ",", "RestRep", ",", "grd1", ",", "Nash0", ",", "Nash1"}], "}"}], ",", RowBox[{ RowBox[{"usex", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"i", " ", ".1"}], "-", ".1"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", "11"}], "}"}]}], "]"}]}], " ", ";", " ", RowBox[{"yusey", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"i", " ", ".1"}], "-", ".1"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", "11"}], "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"i", "=", "1"}], " ", ";", " ", RowBox[{"j", "=", "1"}], " ", ";", " ", "\[IndentingNewLine]", RowBox[{"nax", "=", RowBox[{"{", RowBox[{"nax1", ",", " ", RowBox[{"1", "-", "nax1"}]}], "}"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"nay", "=", RowBox[{"{", RowBox[{"nay1", ",", RowBox[{"1", "-", "nay1"}]}], "}"}]}], " ", ";", " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Finds", " ", "rest", " ", "of", " ", "replicator", " ", "by", " ", "\"\\"", " ", "where", " ", "grids", " ", "are", " ", "given", " ", "by", " ", "usex", " ", "and", " ", "yusey"}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nnR", "=", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"0", "\[Equal]", RowBox[{ RowBox[{"Replicator", "[", RowBox[{"nax", ",", "nay", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{"0", "\[Equal]", RowBox[{ RowBox[{"Replicator", "[", RowBox[{"nax", ",", "nay", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"nax1", ",", RowBox[{ "usex", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"nay1", ",", RowBox[{ "yusey", "\[LeftDoubleBracket]", "j", "\[RightDoubleBracket]"}]}], "}"}], ",", " ", RowBox[{"MaxIterations", " ", "\[Rule]", "1000"}]}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", "yusey", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "usex", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "1"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "This", " ", "function", " ", "is", " ", "defined", " ", "to", " ", "eliminate", " ", "double", " ", "countings", " ", "in", " ", "nnR", " ", "caused", " ", "by", " ", "grid", " ", RowBox[{"search", "."}]}], " ", "*)"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"TnnTR", "[", "H_", "]"}], ":=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Abs", "[", RowBox[{ RowBox[{"(", RowBox[{"nax1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1"}], "\[RightDoubleBracket]"}]}], ")"}], "-", " ", RowBox[{"(", RowBox[{"nax1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}]}], ")"}]}], "]"}], ">", ".01"}], " ", "||", " ", RowBox[{ RowBox[{"Abs", "[", RowBox[{ RowBox[{"(", RowBox[{"nay1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2"}], "\[RightDoubleBracket]"}]}], ")"}], "-", " ", RowBox[{"(", RowBox[{"nay1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], " ", ")"}]}], "]"}], ">", ".01"}]}], " ", ")"}], " ", ",", RowBox[{ "H", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "2", ",", RowBox[{ RowBox[{"Dimensions", "[", "H", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Using", " ", "TnnTR", " ", "we", " ", "eliminate", " ", "double", " ", "countings", " ", "by", " ", "following", " ", "two", " ", "lines"}], " ", "*)"}], " ", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"nnsonuc", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"FixedPointList", "[", RowBox[{"TnnTR", ",", "nnR"}], "]"}], ",", RowBox[{"{", "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"nnfin", "=", RowBox[{"Chop", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{ "nnsonuc", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "nnsonuc", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", SuperscriptBox["10", RowBox[{"-", "6"}]]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Following", " ", "two", " ", "lines", " ", "eliminates", " ", "the", " ", "values", " ", "outside", " ", "the", " ", RowBox[{"simplex", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"RawRestRep", "=", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"nax1", ",", RowBox[{"1", "-", "nax1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"nay1", ",", RowBox[{"1", "-", "nay1"}]}], "}"}]}], "}"}], " ", "/.", " ", "nnfin"}], ",", SuperscriptBox["10", RowBox[{"-", "6"}]]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"RestRep", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Min", "[", RowBox[{ "RawRestRep", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "]"}], "<", RowBox[{"-", SuperscriptBox["10", RowBox[{"-", "6"}]]}]}], ",", "outside", ",", RowBox[{ "RawRestRep", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "RawRestRep", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "outside"}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"grd1", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Following", " ", "three", " ", "lines", " ", "eliminate", " ", "the", " ", "rest", " ", "point", " ", "that", " ", "are", " ", "not", " ", "Nash", " ", RowBox[{"Eq", "."}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Nash0", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"F1", "[", RowBox[{ RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}], "]"}], ".", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}]}], "+", ".00001"}], " ", "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F1", "[", RowBox[{ RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}], "]"}], ".", RowBox[{"grd1", "[", RowBox[{"[", "i", "]"}], "]"}]}]}], " ", "&&", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{"F2", "[", RowBox[{ RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}], "]"}], ".", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}], "+", ".00001"}], " ", "\[GreaterEqual]", " ", RowBox[{ RowBox[{"F2", "[", RowBox[{ RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "1"}], "]"}], "]"}], ",", RowBox[{"RestRep", "[", RowBox[{"[", RowBox[{"j", ",", "2"}], "]"}], "]"}]}], "]"}], ".", RowBox[{"grd1", "[", RowBox[{"[", "i", "]"}], "]"}]}]}]}], ")"}], ",", " ", RowBox[{"RestRep", "[", RowBox[{"[", "j", "]"}], "]"}], ",", "sil"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "grd1", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", "RestRep", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"Nash1", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"MatrixQ", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Nash0", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "1"}], "]"}], "]"}], ",", RowBox[{"Nash0", "[", RowBox[{"[", "i", "]"}], "]"}], ",", "sil"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "Nash0", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "sil"}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Nash2", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Nash1", "[", RowBox[{"[", RowBox[{"i", ",", "1"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "Nash1", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}]}], ";", " ", "Nash2"}]}], " ", "]"}]}], " ", ";"}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.480869146617506*^9, 3.480869151461256*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Calculation of rest points (smooth dynamics)", "Section", InitializationCell->True], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Clear", "[", "RestPointsSmooth", "]"}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"RestPointsSmooth", "::", "usage"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RestPointsSmooth", "[", RowBox[{ "dyn_", ",", "F1_", ",", "F2_", ",", " ", "RestSearchInit_", ",", " ", "TolLevel_"}], "]"}], ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "sonuc", ",", "vfield", ",", "TR", ",", "fin", ",", "RAWresult"}], "}"}], ",", " ", RowBox[{ RowBox[{"srex", "=", RowBox[{"{", RowBox[{"srex1", ",", RowBox[{"1", "-", "srex1"}]}], "}"}]}], " ", ";", " ", RowBox[{"srey", "=", RowBox[{"{", RowBox[{"srey1", ",", RowBox[{"1", "-", "srey1"}]}], "}"}]}], " ", ";", " ", "\[IndentingNewLine]", RowBox[{ RowBox[{"vfield", "[", RowBox[{"dyn", ",", "x_", ",", "y_", ",", "k1_", ",", "k2_"}], "]"}], " ", ":=", " ", RowBox[{"dyn", "[", RowBox[{"x", ",", "y", ",", "k1", ",", "k2"}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "Finds", " ", "restpoints", " ", "by", " ", "grid", " ", "search"}], " ", "*)"}], " ", RowBox[{"R", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"FindRoot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"0", "\[Equal]", RowBox[{ RowBox[{"vfield", "[", RowBox[{ "dyn", ",", "srex", ",", "srey", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{"0", "\[Equal]", RowBox[{ RowBox[{"vfield", "[", RowBox[{ "dyn", ",", "srex", ",", "srey", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"srex1", ",", RowBox[{"RestSearchInit", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"srey1", ",", RowBox[{"RestSearchInit", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], "}"}], ",", " ", RowBox[{"MaxIterations", " ", "\[Rule]", "1000"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "RestSearchInit", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Eleminates", " ", "double", " ", "countings"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"TR", "[", "H_", "]"}], ":=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"Abs", "[", RowBox[{ RowBox[{"(", RowBox[{"srex1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"1", ",", "1"}], "\[RightDoubleBracket]"}]}], ")"}], "-", " ", RowBox[{"(", RowBox[{"srex1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}]}], ")"}]}], "]"}], ">", ".01"}], " ", "||", " ", RowBox[{ RowBox[{"Abs", "[", RowBox[{ RowBox[{"(", RowBox[{"srey1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"1", ",", "2"}], "\[RightDoubleBracket]"}]}], ")"}], "-", " ", RowBox[{"(", RowBox[{"srey1", " ", "/.", " ", RowBox[{"H", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}]}], " ", ")"}]}], "]"}], ">", ".01"}]}], " ", ")"}], " ", ",", RowBox[{ "H", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "2", ",", RowBox[{ RowBox[{"Dimensions", "[", "H", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "0"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"sonuc", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"FixedPointList", "[", RowBox[{"TR", ",", "R"}], "]"}], ",", RowBox[{"{", "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"fin", "=", RowBox[{"Chop", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{ "sonuc", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "sonuc", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", SuperscriptBox["10", RowBox[{"-", "6"}]]}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"RAWresult", "=", RowBox[{"Chop", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"srex1", ",", RowBox[{"1", "-", "srex1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"srey1", ",", RowBox[{"1", "-", "srey1"}]}], "}"}]}], "}"}], " ", "/.", " ", "fin"}], ",", SuperscriptBox["10", RowBox[{"-", "6"}]]}], "]"}]}], " ", ";", " ", RowBox[{"midresult", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Min", "[", RowBox[{ "RAWresult", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}], "]"}], "<", RowBox[{"-", SuperscriptBox["10", RowBox[{"-", "6"}]]}]}], ",", "outside", ",", RowBox[{ "RAWresult", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "RAWresult", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "outside"}], "]"}]}], " ", ";", " ", RowBox[{"result", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Max", "[", RowBox[{"Abs", "[", RowBox[{"dyn", "[", RowBox[{ RowBox[{"midresult", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"midresult", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2"}], "\[RightDoubleBracket]"}], ",", "F1", ",", "F2"}], "]"}], "]"}], "]"}], " ", ">", " ", "TolLevel"}], ",", " ", "notrest", ",", RowBox[{ "midresult", "\[LeftDoubleBracket]", "i", "\[RightDoubleBracket]"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "midresult", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ",", "notrest"}], "]"}]}], " ", ";", "\[IndentingNewLine]", " ", "result"}]}], " ", "]"}]}], " ", ";"}], "\[IndentingNewLine]"}], "Input", InitializationCell->True, CellChangeTimes->{{3.474407538805726*^9, 3.4744075467471457`*^9}, { 3.48157049257896*^9, 3.4815704926190176`*^9}, {3.482098095187691*^9, 3.4820980952377634`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Specification of rest points", "Section", InitializationCell->True], Cell[BoxData[{ RowBox[{ RowBox[{"Clear", "[", "RestPoints", "]"}], " ", ";"}], "\n", RowBox[{ RowBox[{ RowBox[{ RowBox[{"RestPoints", "::", "usage"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]"}], "\n", RowBox[{ RowBox[{ RowBox[{"RestPoints", "[", RowBox[{ "dyn_", ",", "F1_", ",", "F2_", ",", "RestSearchInit_", ",", "TolLevel_"}], "]"}], ":=", RowBox[{"Which", "[", RowBox[{ RowBox[{ RowBox[{"RPCharacterization", "[", "dyn", "]"}], "===", " ", "Automatic"}], ",", RowBox[{"RestPointsSmooth", "[", RowBox[{ "dyn", ",", "F1", ",", "F2", ",", " ", "RestSearchInit", ",", "TolLevel"}], "]"}], ",", " ", RowBox[{ RowBox[{"RPCharacterization", "[", "dyn", "]"}], "===", " ", "Nash"}], ",", " ", RowBox[{"NashEq", "[", RowBox[{"F1", ",", "F2"}], "]"}], ",", " ", RowBox[{ RowBox[{"RPCharacterization", "[", "dyn", "]"}], "===", " ", "RestrictedEquilibria"}], ",", " ", RowBox[{"RestPointsSmooth", "[", RowBox[{ "Replicator", ",", "F1", ",", "F2", ",", " ", "RestSearchInit", ",", " ", "TolLevel"}], "]"}]}], "]"}]}], " ", ";"}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.474407547708528*^9, 3.474407552184965*^9}, { 3.481570492629032*^9, 3.4815704926390467`*^9}, {3.482098095267806*^9, 3.482098095287835*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Testing stability of rest points", "Section", InitializationCell->True], Cell[BoxData[{ RowBox[{ RowBox[{"Clear", "[", "TestStability", "]"}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TestStability", "::", "usage"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TestStability", "::", "notes"}], "=", "\"\\""}], " ", ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TestStability", "[", RowBox[{ "dyn_", ",", "F1_", ",", "F2_", ",", "bigT_", ",", " ", "numtest_", ",", " ", "eps_", ",", " ", "delta_", ",", "RestSearchInit_", ",", "TolLevel_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "xtest0", ",", "vfield", ",", "G1", ",", "G3", ",", "dim", ",", "Stability"}], "}"}], ",", " ", RowBox[{ RowBox[{"testrest", "=", RowBox[{"RestPoints", "[", RowBox[{ "dyn", ",", "F1", ",", "F2", ",", "RestSearchInit", ",", "TolLevel"}], "]"}]}], " ", ";", " ", RowBox[{"(*", " ", RowBox[{ "chooses", " ", "initial", " ", "point", " ", "inside", " ", "the", " ", "epsilon", " ", "neighorborhood", " ", "and", " ", "guarantees", " ", "that", " ", "they", " ", "are", " ", "inside", " ", "the", " ", "simplex"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"For", "[", RowBox[{ RowBox[{"j", "=", "1"}], ",", RowBox[{"j", "<", RowBox[{"numtest", "+", "1"}]}], ",", RowBox[{"j", "++"}], ",", RowBox[{"(", RowBox[{ RowBox[{"Label", "[", "AA", "]"}], ";", RowBox[{"\[Theta]", "=", " ", RowBox[{"RandomReal", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"2", " ", "Pi"}]}], "}"}], "]"}]}], ";", RowBox[{ RowBox[{"xtest0", "[", RowBox[{"i", ",", "j"}], "]"}], "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"testrest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "1", ",", "1"}], "\[RightDoubleBracket]"}], ",", RowBox[{"testrest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "2", ",", "1"}], "\[RightDoubleBracket]"}]}], "}"}], "+", " ", RowBox[{"eps", " ", RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], ",", RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "}"}]}]}]}], ";", " ", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Min", "[", RowBox[{"xtest0", "[", RowBox[{"i", ",", "j"}], "]"}], "]"}], "<", "0"}], "||", RowBox[{ RowBox[{"Max", "[", RowBox[{"xtest0", "[", RowBox[{"i", ",", "j"}], "]"}], "]"}], ">", "1"}]}], ",", " ", RowBox[{"Goto", "[", "AA", "]"}]}], "]"}]}], ")"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"xtest", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"xtest0", "[", RowBox[{"i", ",", "j"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "numtest"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Clear", "[", "vfield", "]"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"vfield", "[", RowBox[{"dyn", ",", " ", "x_", ",", "y_", ",", "m1_", ",", "m2_"}], "]"}], " ", ":=", " ", RowBox[{"dyn", "[", RowBox[{"x", ",", "y", ",", "m1", ",", "m2"}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{"-", "Solving"}], " ", "differential", " ", "equations", " ", "to", " ", "find", " ", RowBox[{"sol", ".", " ", "trajectories"}], " ", "for", " ", "each", " ", "initial", " ", RowBox[{"cond", ".", "-"}]}], "*)"}], "\[IndentingNewLine]", RowBox[{"trex", "=", RowBox[{"{", RowBox[{ RowBox[{"trex1", "[", "t", "]"}], ",", RowBox[{"1", "-", RowBox[{"trex1", "[", "t", "]"}]}]}], "}"}]}], ";", " ", RowBox[{"trey", "=", RowBox[{"{", RowBox[{ RowBox[{"trey1", "[", "t", "]"}], ",", RowBox[{"1", "-", RowBox[{"trey1", "[", "t", "]"}]}]}], "}"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"G1", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["trex1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"vfield", "[", RowBox[{ "dyn", ",", "trex", ",", "trey", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{ SuperscriptBox["trey1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", RowBox[{ RowBox[{"vfield", "[", RowBox[{ "dyn", ",", "trex", ",", "trey", ",", "F1", ",", "F2"}], "]"}], "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"trex1", "[", "0", "]"}], "\[Equal]", RowBox[{ RowBox[{"xtest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "j"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], ",", RowBox[{ RowBox[{"trey1", "[", "0", "]"}], "\[Equal]", RowBox[{ RowBox[{"xtest", "\[LeftDoubleBracket]", RowBox[{"i", ",", "j"}], "\[RightDoubleBracket]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"trex1", ",", "trey1"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "bigT"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "testrest", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", "xtest", "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"-", " ", "Checking"}], " ", "Stability", " ", "usuing", " ", "delta", " ", "neighborhood"}], " ", "-"}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"G3", "=", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"trex1", "[", "bigT", "]"}], ",", RowBox[{"1", "-", RowBox[{"trex1", "[", "bigT", "]"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"trey1", "[", "bigT", "]"}], ",", RowBox[{"1", "-", RowBox[{"trey1", "[", "bigT", "]"}]}]}], "}"}]}], "}"}], " ", "/.", " ", "G1"}]}], " ", ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Dimensions", "[", "G3", "]"}], ";", "\[IndentingNewLine]", RowBox[{"Stability", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ StyleBox[ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "2"], ScriptLevel->0], StyleBox[" ", ScriptLevel->0], RowBox[{ RowBox[{ RowBox[{ StyleBox["(", ScriptLevel->0], RowBox[{ StyleBox[ RowBox[{"Flatten", "[", RowBox[{"testrest", "[", RowBox[{"[", "j", "]"}], "]"}], "]"}], ScriptLevel->0], StyleBox["-", ScriptLevel->0], RowBox[{ StyleBox["Flatten", ScriptLevel->0], StyleBox["[", ScriptLevel->0], RowBox[{"G3", "[", RowBox[{"[", RowBox[{"j", ",", "k", ",", "1"}], "]"}], "]"}], "]"}]}], ")"}], "\[LeftDoubleBracket]", RowBox[{ RowBox[{"2", " ", "i"}], "-", "1"}], "\[RightDoubleBracket]"}], "^", "2"}]}], ")"}], "^", RowBox[{"(", RowBox[{"1", "/", "2"}], ")"}]}], " ", "<", " ", "delta"}], ",", "1", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", RowBox[{ RowBox[{"Dimensions", "[", "G3", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", RowBox[{ RowBox[{"Dimensions", "[", "G3", "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"dim", "=", RowBox[{ RowBox[{"Dimensions", "[", "Stability", "]"}], "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ "stores", " ", "stable", " ", "and", " ", "unstable", " ", "restpoints"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"stblpnts", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", StyleBox[" ", ScriptLevel->0], RowBox[{ RowBox[{ RowBox[{ StyleBox[ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "dim"], ScriptLevel->0], StyleBox[" ", ScriptLevel->0], RowBox[{"Stability", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "\[Equal]", "dim"}], StyleBox[",", ScriptLevel->0], RowBox[{"testrest", "[", RowBox[{"[", "i", "]"}], "]"}]}], " ", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "Stability", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "Null"}], "]"}]}], " ", ";", "\[IndentingNewLine]", RowBox[{"unstbl", "=", RowBox[{"DeleteCases", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", StyleBox[" ", ScriptLevel->0], RowBox[{ RowBox[{ RowBox[{ StyleBox[ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], "dim"], ScriptLevel->0], StyleBox[" ", ScriptLevel->0], RowBox[{"Stability", "[", RowBox[{"[", RowBox[{"i", ",", "j"}], "]"}], "]"}]}], "\[NotEqual]", "dim"}], ",", RowBox[{"testrest", "[", RowBox[{"[", "i", "]"}], "]"}]}], " ", "]"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{ RowBox[{"Dimensions", "[", "Stability", "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}]}], "]"}], ",", "Null"}], "]"}]}], " ", ";", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"stblpnts", ",", "unstbl"}], "}"}]}]}], "]"}]}], " ", ";"}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.4744075601864705`*^9, 3.474407568318163*^9}, { 3.4744695570426097`*^9, 3.474469557653488*^9}, 3.474469605083183*^9, { 3.4815704926490607`*^9, 3.48157049273919*^9}, {3.482098095307864*^9, 3.482098095377965*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Maintenance", "Section", CellChangeTimes->{{3.4818469396171713`*^9, 3.481846942020627*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", " ", "All", ",", " ", "CellContents", ",", " ", RowBox[{"AutoScroll", " ", "->", " ", "False"}]}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellOpen", "\[Rule]", "True"}], ",", RowBox[{"Evaluatable", "->", "True"}]}], "]"}], ";"}]}], "Input", Evaluatable->True, CellOpen->True, CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.4818493853439536`*^9, 3.481849414545944*^9}, 3.4818959691255317`*^9}, CellTags->"maintenance"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", "\"\\"", ",", " ", "All", ",", " ", "CellContents", ",", " ", RowBox[{"AutoScroll", " ", "->", " ", "False"}]}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellOpen", "\[Rule]", "False"}], ",", RowBox[{"Evaluatable", "->", "False"}]}], "]"}], ";"}]}], "Input", Evaluatable->True, CellOpen->True, CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.4818494226475935`*^9, 3.48184942971776*^9}, 3.4818959755447617`*^9}, CellTags->"maintenance"], Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", " ", "\"\\"", ",", " ", "All", ",", " ", "CellTags", ",", " ", RowBox[{"AutoScroll", " ", "->", " ", "False"}]}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellOpen", "\[Rule]", "True"}], ",", RowBox[{"Evaluatable", "->", "True"}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.4818493853439536`*^9, 3.481849414545944*^9}, {3.4818960755886183`*^9, 3.481896078693082*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", " ", "\"\\"", ",", " ", "All", ",", " ", "CellContents", ",", " ", RowBox[{"AutoScroll", " ", "->", "False"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellTags", "\[Rule]", "\"\\""}]}], "]"}], ";"}]}], "Input", Evaluatable->True, CellOpen->True, CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.481849177434995*^9, 3.481849189842837*^9}, {3.4818493141315556`*^9, 3.4818493371746893`*^9}}, CellTags->"maintenance"], Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", " ", "\"\\"", ",", " ", "All", ",", " ", "CellTags", ",", " ", RowBox[{"AutoScroll", " ", "->", " ", "False"}]}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellOpen", "\[Rule]", "True"}], ",", RowBox[{"Evaluatable", "->", "True"}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.4818493853439536`*^9, 3.481849414545944*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"NotebookFind", "[", RowBox[{ RowBox[{"SelectedNotebook", "[", "]"}], ",", " ", "\"\\"", ",", " ", "All", ",", " ", "CellTags", ",", " ", RowBox[{"AutoScroll", " ", "->", " ", "False"}]}], "]"}], ";"}], "\n", RowBox[{ RowBox[{"SetOptions", "[", RowBox[{ RowBox[{"NotebookSelection", "[", RowBox[{"SelectedNotebook", "[", "]"}], "]"}], ",", RowBox[{"CellOpen", "\[Rule]", "False"}], ",", RowBox[{"Evaluatable", "->", "False"}]}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.481847785483467*^9, 3.4818477881372833`*^9}, { 3.4818478639262624`*^9, 3.4818478712568035`*^9}, {3.481848153082048*^9, 3.4818481535927825`*^9}, {3.48184819919836*^9, 3.481848199729123*^9}, 3.481848285382286*^9, {3.4818483763130383`*^9, 3.4818484167612*^9}, 3.4818484551564093`*^9, 3.481848541961229*^9, {3.4818487279286366`*^9, 3.481848750410965*^9}, {3.481848821112629*^9, 3.481848822374443*^9}, { 3.4818490590948305`*^9, 3.481849064392448*^9}, 3.4818491129923315`*^9, { 3.4818494226475935`*^9, 3.48184942971776*^9}}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Credits", "Subtitle"], Cell[TextData[{ "Dynamo 2x2\nVersion 0.2.5 (May 9, 2010)\nby William H. Sandholm, Emin \ Dokumaci, and Francisco Franchetti\n\nmail:\t\t\tDepartment of Economics\n\t\t\ \tUniversity of Wisconsin\n\t\t\t1180 Observatory Drive\n\t\t\tMadison WI \ 53706\n\ne-mail:\t\t\twhs@ssc.wisc.edu\n\t\t\tedokumaci@wisc.edu\n\t\t\t\ franchetti@wisc.edu\n\t\nwebsites:\t\t", ButtonBox["http://www.ssc.wisc.edu/~whs/", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://www.ssc.wisc.edu/~whs/"], None}], "\n\t\t\t", ButtonBox["http://www.ssc.wisc.edu/~edokumac/\n\t\t\t\ https://mywebspace.wisc.edu/franchetti/web", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://www.ssc.wisc.edu/~edokumac/"], None}], "\n\t\t\nDynamo website:\t\t", ButtonBox["http://www.ssc.wisc.edu/~whs/dynamo", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://www.ssc.wisc.edu/~whs/dynamo"], None}], "\n \nFinancial support from the National Science Foundation under Grants \ SES-0092145, SES-0617753, and SES-0851580 is gratefully acknowledged." }], "Text", CellChangeTimes->{{3.480864918617506*^9, 3.480864924476881*^9}, { 3.481905709554278*^9, 3.481905778468186*^9}, 3.4819058117058973`*^9, { 3.481905909877186*^9, 3.4819059561979647`*^9}, 3.4819059899391937`*^9, { 3.4825056464385567`*^9, 3.482505647181192*^9}, 3.482619890704235*^9}, FontFamily->"Palatino"] }, Closed]] }, AutoGeneratedPackage->Automatic, ScreenStyleEnvironment->"Working", WindowToolbars->{}, PrintAction->"PrintToNotebook", InitializationCellEvaluation->True, InitializationCellWarning->False, CellGrouping->Manual, WindowSize->{1074, 793}, WindowMargins->{{59, Automatic}, {Automatic, 125}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (February 18, 2009)", StyleDefinitions->Notebook[{ Cell[ CellGroupData[{ Cell["Style Definitions", "Title"], Cell[ "Modify the definitions below to change the default appearance of all \ cells in a given style. Make modifications to any definition using commands \ in the Format menu.", "Text"], Cell[ CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[ StyleData[All, "Working"], PageWidth -> WindowWidth, CellBracketOptions -> { "Color" -> RGBColor[0.269993, 0.308507, 0.6]}, CellLabelMargins -> {{12, Inherited}, {Inherited, Inherited}}, ScriptMinSize -> 9], Cell[ StyleData[All, "Presentation"], PageWidth -> WindowWidth, CellLabelMargins -> {{24, Inherited}, {Inherited, Inherited}}, ScriptMinSize -> 12], Cell[ StyleData[All, "Condensed"], PageWidth -> WindowWidth, CellLabelMargins -> {{8, Inherited}, {Inherited, Inherited}}, ScriptMinSize -> 8], Cell[ StyleData[All, "SlideShow"], PageWidth -> WindowWidth, ScrollingOptions -> {"PagewiseDisplay" -> True}, ShowCellBracket -> False, ScriptMinSize -> 9], Cell[ StyleData[All, "Printout"], PageWidth -> PaperWidth, CellLabelMargins -> {{2, Inherited}, {Inherited, Inherited}}, ScriptMinSize -> 5, PrivateFontOptions -> {"FontType" -> "Outline"}]}, Closed]], Cell[ CellGroupData[{ Cell["Notebook Options", "Section"], Cell[ "The options defined for the style below will be used at the \ Notebook level.", "Text"], Cell[ StyleData["Notebook"], PageHeaders -> {{ Cell[ TextData[{ CounterBox["Page"]}], "PageNumber"], None, Cell[ TextData[{ ValueBox["FileName"]}], "Header"]}, { Cell[ TextData[{ ValueBox["FileName"]}], "Header"], None, Cell[ TextData[{ CounterBox["Page"]}], "PageNumber"]}}, CellFrameLabelMargins -> 6, StyleMenuListing -> None]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Title"], CellMargins -> {{27, Inherited}, {10, 30}}, CellGroupingRules -> {"TitleGrouping", 0}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 11}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Title", CounterAssignments -> {{"Section", 0}, {"Equation", 0}, { "Figure", 0}, {"Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily -> "Helvetica", FontSize -> 36, FontWeight -> "Bold"], Cell[ StyleData["Title", "Presentation"], CellMargins -> {{27, 10}, {10, 30}}, LineSpacing -> {1, 0}, FontSize -> 44], Cell[ StyleData["Title", "Condensed"], CellMargins -> {{8, 10}, {4, 8}}, FontSize -> 20], Cell[ StyleData["Title", "SlideShow"]], Cell[ StyleData["Title", "Printout"], CellMargins -> {{2, 10}, {12, 30}}, FontSize -> 24]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subtitle"], CellMargins -> {{27, Inherited}, {20, 2}}, CellGroupingRules -> {"TitleGrouping", 10}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subtitle", CounterAssignments -> {{"Section", 0}, {"Equation", 0}, { "Figure", 0}, {"Subsubtitle", 0}}, FontFamily -> "Helvetica", FontSize -> 24], Cell[ StyleData["Subtitle", "Presentation"], CellMargins -> {{27, 10}, {20, 2}}, LineSpacing -> {1, 0}, FontSize -> 36], Cell[ StyleData["Subtitle", "Condensed"], CellMargins -> {{8, 10}, {4, 4}}, FontSize -> 14], Cell[ StyleData["Subtitle", "SlideShow"]], Cell[ StyleData["Subtitle", "Printout"], CellMargins -> {{2, 10}, {12, 8}}, FontSize -> 18]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubtitle"], CellMargins -> {{27, Inherited}, {8, 2}}, CellGroupingRules -> {"TitleGrouping", 20}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subsubtitle", CounterAssignments -> {{"Section", 0}, {"Equation", 0}, { "Figure", 0}}, FontFamily -> "Helvetica", FontSize -> 16], Cell[ StyleData["Subsubtitle", "Presentation"], CellMargins -> {{24, 10}, {20, 20}}, LineSpacing -> {1, 0}, FontSize -> 24], Cell[ StyleData["Subsubtitle", "Condensed"], CellMargins -> {{8, 10}, {8, 8}}, FontSize -> 12], Cell[ StyleData["Subsubtitle", "SlideShow"]], Cell[ StyleData["Subsubtitle", "Printout"], CellMargins -> {{2, 10}, {12, 8}}, FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Section"], CellFrame -> {{0, 0}, {0, 1}}, CellMargins -> {{27, Inherited}, {8, 34}}, CellGroupingRules -> {"SectionGrouping", 30}, PageBreakBelow -> False, CellFrameMargins -> 4, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 2}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily -> "Helvetica", FontSize -> 20, FontWeight -> "Bold"], Cell[ StyleData["Section", "Presentation"], CellMargins -> {{40, 10}, {11, 32}}, LineSpacing -> {1, 0}, FontSize -> 24], Cell[ StyleData["Section", "Condensed"], CellMargins -> {{18, Inherited}, {6, 12}}, FontSize -> 12], Cell[ StyleData["Section", "SlideShow"]], Cell[ StyleData["Section", "Printout"], CellMargins -> {{2, 0}, {7, 22}}, FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsection"], CellDingbat -> "\[FilledSmallSquare]", CellMargins -> {{60, Inherited}, {8, 12}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily -> "Verdana", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["Subsection", "Presentation"], CellMargins -> {{36, 10}, {11, 32}}, LineSpacing -> {1, 0}, FontSize -> 22], Cell[ StyleData["Subsection", "Condensed"], CellMargins -> {{16, Inherited}, {6, 12}}, FontSize -> 12], Cell[ StyleData["Subsection", "SlideShow"]], Cell[ StyleData["Subsection", "Printout"], CellMargins -> {{9, 0}, {7, 22}}, FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubsection"], CellDingbat -> "\[FilledSmallSquare]", CellMargins -> {{60, Inherited}, {2, 10}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, DefaultNewInlineCellStyle -> "None", InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "Subsubsection", FontFamily -> "Verdana", FontWeight -> "Plain", FontSlant -> "Plain", FontTracking -> "Plain", FontVariations -> { "CompatibilityType" -> 0, "Masked" -> False, "Outline" -> False, "RotationAngle" -> 0, "Shadow" -> False, "StrikeThrough" -> False, "Underline" -> False}], Cell[ StyleData["Subsubsection", "Presentation"], CellMargins -> {{34, 10}, {11, 26}}, LineSpacing -> {1, 0}, FontSize -> 18], Cell[ StyleData["Subsubsection", "Condensed"], CellMargins -> {{17, Inherited}, {6, 12}}, FontSize -> 10], Cell[ StyleData["Subsubsection", "SlideShow"]], Cell[ StyleData["Subsubsection", "Printout"], CellMargins -> {{9, 0}, {7, 14}}, FontSize -> 11]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Text"], CellMargins -> {{60, 10}, {7, 7}}, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, LineSpacing -> {1, 3}, CounterIncrements -> "Text", FontFamily -> "Palatino"], Cell[ StyleData["Text", "Presentation"], CellMargins -> {{24, 10}, {10, 10}}, LineSpacing -> {1, 5}, FontSize -> 16], Cell[ StyleData["Text", "Condensed"], CellMargins -> {{8, 10}, {6, 6}}, LineSpacing -> {1, 1}, FontSize -> 11], Cell[ StyleData["Text", "SlideShow"]], Cell[ StyleData["Text", "Printout"], CellMargins -> {{2, 2}, {6, 6}}, TextJustification -> 0.5, Hyphenation -> True, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SmallText"], CellMargins -> {{60, 10}, {6, 6}}, DefaultNewInlineCellStyle -> "None", LineSpacing -> {1, 3}, LanguageCategory -> "NaturalLanguage", CounterIncrements -> "SmallText", FontFamily -> "Trebuchet MS", FontSize -> 12, FontSlant -> "Italic"], Cell[ StyleData["SmallText", "Presentation"], CellMargins -> {{24, 10}, {8, 8}}, LineSpacing -> {1, 5}, FontSize -> 12], Cell[ StyleData["SmallText", "Condensed"], CellMargins -> {{8, 10}, {5, 5}}, LineSpacing -> {1, 2}, FontSize -> 9], Cell[ StyleData["SmallText", "SlideShow"]], Cell[ StyleData["SmallText", "Printout"], CellMargins -> {{2, 2}, {5, 5}}, TextJustification -> 0.5, Hyphenation -> True, FontSize -> 7]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell[ "The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. Some attributes for these styles are actually set in FormatType Styles \ (in the last section of this stylesheet). ", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["Input"], CellMargins -> {{66, 10}, {5, 7}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", FontWeight -> "Bold"], Cell[ StyleData["Input", "Presentation"], CellMargins -> {{72, Inherited}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 16], Cell[ StyleData["Input", "Condensed"], CellMargins -> {{40, 10}, {2, 3}}, FontSize -> 11], Cell[ StyleData["Input", "SlideShow"]], Cell[ StyleData["Input", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InputOnly"], CellMargins -> {{66, 10}, {7, 7}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, DefaultFormatType -> DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, ShowStringCharacters -> True, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["InputOnly", "Presentation"], CellMargins -> {{72, Inherited}, {8, 10}}, LineSpacing -> {1, 0}, FontSize -> 16], Cell[ StyleData["InputOnly", "Condensed"], CellMargins -> {{40, 10}, {2, 3}}, FontSize -> 11], Cell[ StyleData["InputOnly", "SlideShow"]], Cell[ StyleData["InputOnly", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Output"], CellMargins -> {{66, 10}, {7, 5}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> None, FormatType -> InputForm, CounterIncrements -> "Output"], Cell[ StyleData["Output", "Presentation"], CellMargins -> {{72, Inherited}, {10, 8}}, LineSpacing -> {1, 0}, FontSize -> 16], Cell[ StyleData["Output", "Condensed"], CellMargins -> {{41, Inherited}, {3, 2}}, FontSize -> 11], Cell[ StyleData["Output", "SlideShow"]], Cell[ StyleData["Output", "Printout"], CellMargins -> {{39, 0}, {6, 4}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Message"], CellMargins -> {{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "OutputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> None, FormatType -> InputForm, CounterIncrements -> "Message", StyleMenuListing -> None, AutoStyleOptions -> {"UnmatchedBracketStyle" -> None}, FontFamily -> "Helvetica", FontSize -> 10, FontColor -> RGBColor[0.6, 0.100008, 0.100008]], Cell[ StyleData["Message", "Presentation"], CellMargins -> {{72, Inherited}, {Inherited, Inherited}}, LineSpacing -> {1, 0}, FontSize -> 16], Cell[ StyleData["Message", "Condensed"], CellMargins -> {{41, Inherited}, {Inherited, Inherited}}, FontSize -> 11], Cell[ StyleData["Message", "SlideShow"]], Cell[ StyleData["Message", "Printout"], CellMargins -> {{39, Inherited}, {Inherited, Inherited}}, FontSize -> 7, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Print"], CellMargins -> {{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> None, FormatType -> InputForm, CounterIncrements -> "Print", StyleMenuListing -> None], Cell[ StyleData["Print", "Presentation"], CellMargins -> {{72, Inherited}, {Inherited, Inherited}}, LineSpacing -> {1, 0}, FontSize -> 16], Cell[ StyleData["Print", "Condensed"], CellMargins -> {{41, Inherited}, {Inherited, Inherited}}, FontSize -> 11], Cell[ StyleData["Print", "SlideShow"]], Cell[ StyleData["Print", "Printout"], CellMargins -> {{39, Inherited}, {Inherited, Inherited}}, FontSize -> 8]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Graphics"], CellMargins -> {{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, DefaultFormatType -> DefaultOutputFormatType, LanguageCategory -> None, FormatType -> InputForm, CounterIncrements -> "Graphics", ImageMargins -> {{43, Inherited}, {Inherited, 0}}, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 10], Cell[ StyleData["Graphics", "Presentation"], ImageMargins -> {{62, Inherited}, {Inherited, 0}}], Cell[ StyleData["Graphics", "Condensed"], ImageMargins -> {{38, Inherited}, {Inherited, 0}}, Magnification -> 0.6], Cell[ StyleData["Graphics", "SlideShow"]], Cell[ StyleData["Graphics", "Printout"], ImageMargins -> {{30, Inherited}, {Inherited, 0}}, Magnification -> 0.8]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["CellLabel"], LanguageCategory -> None, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 9, FontColor -> RGBColor[0.269993, 0.308507, 0.6]], Cell[ StyleData["CellLabel", "Presentation"], FontSize -> 12], Cell[ StyleData["CellLabel", "Condensed"], FontSize -> 9], Cell[ StyleData["CellLabel", "SlideShow"]], Cell[ StyleData["CellLabel", "Printout"], FontFamily -> "Courier", FontSize -> 8, FontSlant -> "Italic", FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["FrameLabel"], LanguageCategory -> None, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 9], Cell[ StyleData["FrameLabel", "Presentation"], FontSize -> 12], Cell[ StyleData["FrameLabel", "Condensed"], FontSize -> 9], Cell[ StyleData["FrameLabel", "SlideShow"]], Cell[ StyleData["FrameLabel", "Printout"], FontFamily -> "Courier", FontSize -> 8, FontSlant -> "Italic", FontColor -> GrayLevel[0]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Inline Formatting", "Section"], Cell[ "These styles are for modifying individual words or letters in a \ cell exclusive of the cell tag.", "Text"], Cell[ StyleData["RM"], StyleMenuListing -> None, FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["BF"], StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["IT"], StyleMenuListing -> None, FontSlant -> "Italic"], Cell[ StyleData["TR"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["TI"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["TB"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["TBI"], StyleMenuListing -> None, FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> {"HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["SR"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["SO"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["SB"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["SBO"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ CellGroupData[{ Cell[ StyleData["SO10"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["SO10", "Printout"], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 7, FontWeight -> "Plain", FontSlant -> "Italic"]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["InlineFormula"], CellMargins -> {{10, 4}, {0, 8}}, CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", ScriptLevel -> 1, SingleLetterItalics -> True], Cell[ StyleData["InlineFormula", "Presentation"], CellMargins -> {{24, 10}, {10, 10}}, LineSpacing -> {1, 5}, FontSize -> 16], Cell[ StyleData["InlineFormula", "Condensed"], CellMargins -> {{8, 10}, {6, 6}}, LineSpacing -> {1, 1}, FontSize -> 11], Cell[ StyleData["InlineFormula", "SlideShow"]], Cell[ StyleData["InlineFormula", "Printout"], CellMargins -> {{2, 0}, {6, 6}}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DisplayFormula"], CellMargins -> {{60, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling -> True, DefaultFormatType -> DefaultInputFormatType, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", ScriptLevel -> 0, SingleLetterItalics -> True, UnderoverscriptBoxOptions -> {LimitsPositioning -> True}], Cell[ StyleData["DisplayFormula", "Presentation"], LineSpacing -> {1, 5}, FontSize -> 16], Cell[ StyleData["DisplayFormula", "Condensed"], LineSpacing -> {1, 1}, FontSize -> 11], Cell[ StyleData["DisplayFormula", "SlideShow"]], Cell[ StyleData["DisplayFormula", "Printout"], FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Program"], CellFrame -> {{0, 0}, {0.5, 0.5}}, CellMargins -> {{60, 4}, {0, 8}}, CellHorizontalScrolling -> True, Hyphenation -> False, LanguageCategory -> "Formula", ScriptLevel -> 1, FontFamily -> "Courier"], Cell[ StyleData["Program", "Presentation"], CellMargins -> {{24, 10}, {10, 10}}, LineSpacing -> {1, 5}, FontSize -> 16], Cell[ StyleData["Program", "Condensed"], CellMargins -> {{8, 10}, {6, 6}}, LineSpacing -> {1, 1}, FontSize -> 11], Cell[ StyleData["Program", "SlideShow"]], Cell[ StyleData["Program", "Printout"], CellMargins -> {{2, 0}, {6, 6}}, FontSize -> 9]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Outline Styles", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["Outline1"], CellMargins -> {{60, 10}, {7, 7}}, CellGroupingRules -> {"SectionGrouping", 50}, ParagraphIndent -> -38, CounterIncrements -> "Outline1", CounterAssignments -> {{"Outline2", 0}, {"Outline3", 0}, { "Outline4", 0}}, FontSize -> 18, FontWeight -> "Bold", CounterBoxOptions -> {CounterFunction :> CapitalRomanNumeral}], Cell[ StyleData["Outline1", "SlideShow"]], Cell[ StyleData["Outline1", "Printout"], CounterBoxOptions -> {CounterFunction :> CapitalRomanNumeral}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Outline2"], CellMargins -> {{90, 10}, {7, 7}}, CellGroupingRules -> {"SectionGrouping", 60}, ParagraphIndent -> -27, CounterIncrements -> "Outline2", CounterAssignments -> {{"Outline3", 0}, {"Outline4", 0}}, FontSize -> 15, FontWeight -> "Bold", CounterBoxOptions -> {CounterFunction :> (Part[ CharacterRange["A", "Z"], #]& )}], Cell[ StyleData["Outline2", "SlideShow"]], Cell[ StyleData["Outline2", "Printout"], CounterBoxOptions -> {CounterFunction :> (Part[ CharacterRange["A", "Z"], #]& )}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Outline3"], CellMargins -> {{120, 10}, {7, 7}}, CellGroupingRules -> {"SectionGrouping", 70}, ParagraphIndent -> -21, CounterIncrements -> "Outline3", CounterAssignments -> {{"Outline4", 0}}, FontSize -> 12, CounterBoxOptions -> {CounterFunction :> Identity}], Cell[ StyleData["Outline3", "SlideShow"]], Cell[ StyleData["Outline3", "Printout"], CounterBoxOptions -> {CounterFunction :> Identity}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Outline4"], CellMargins -> {{150, 10}, {7, 7}}, CellGroupingRules -> {"SectionGrouping", 80}, ParagraphIndent -> -18, CounterIncrements -> "Outline4", FontSize -> 10, CounterBoxOptions -> {CounterFunction :> (Part[ CharacterRange["a", "z"], #]& )}], Cell[ StyleData["Outline4", "SlideShow"]], Cell[ StyleData["Outline4", "Printout"]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell[ "The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["Hyperlink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Hyperlink", "Presentation"], FontSize -> 16], Cell[ StyleData["Hyperlink", "Condensed"], FontSize -> 11], Cell[ StyleData["Hyperlink", "SlideShow"]], Cell[ StyleData["Hyperlink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ "The following styles are for linking automatically to the on-line \ help system.", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["MainBookLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MainBook", #]}]& )}], Cell[ StyleData["MainBookLink", "Presentation"], FontSize -> 16], Cell[ StyleData["MainBookLink", "Condensed"], FontSize -> 11], Cell[ StyleData["MainBookLink", "SlideShow"]], Cell[ StyleData["MainBookLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AddOnsLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["AddOns", #]}]& )}], Cell[ StyleData["AddOnsLink", "Presentation"], FontSize -> 16], Cell[ StyleData["AddOnsLink", "Condensed"], FontSize -> 11], Cell[ StyleData["AddOnsLink", "SlideShow"]], Cell[ StyleData["AddOnsLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLink", "Presentation"], FontSize -> 16], Cell[ StyleData["RefGuideLink", "Condensed"], FontSize -> 11], Cell[ StyleData["RefGuideLink", "SlideShow"]], Cell[ StyleData["RefGuideLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLinkText"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLinkText", "Presentation"], FontSize -> 16], Cell[ StyleData["RefGuideLinkText", "Condensed"], FontSize -> 11], Cell[ StyleData["RefGuideLinkText", "SlideShow"]], Cell[ StyleData["RefGuideLinkText", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GettingStartedLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["GettingStarted", #]}]& )}], Cell[ StyleData["GettingStartedLink", "Presentation"], FontSize -> 16], Cell[ StyleData["GettingStartedLink", "Condensed"], FontSize -> 11], Cell[ StyleData["GettingStartedLink", "SlideShow"]], Cell[ StyleData["GettingStartedLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemosLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["Demos", #]}]& )}], Cell[ StyleData["DemosLink", "SlideShow"]], Cell[ StyleData["DemosLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TourLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["Tour", #]}]& )}], Cell[ StyleData["TourLink", "SlideShow"]], Cell[ StyleData["TourLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OtherInformationLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["OtherInformation", #]}]& )}], Cell[ StyleData["OtherInformationLink", "Presentation"], FontSize -> 16], Cell[ StyleData["OtherInformationLink", "Condensed"], FontSize -> 11], Cell[ StyleData["OtherInformationLink", "SlideShow"]], Cell[ StyleData["OtherInformationLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["MasterIndexLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MasterIndex", #]}]& )}], Cell[ StyleData["MasterIndexLink", "SlideShow"]], Cell[ StyleData["MasterIndexLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[ StyleData["Header"], CellMargins -> {{0, 0}, {4, 1}}, DefaultNewInlineCellStyle -> "None", LanguageCategory -> "NaturalLanguage", StyleMenuListing -> None, FontSize -> 10, FontSlant -> "Italic"], Cell[ StyleData["Footer"], CellMargins -> {{0, 0}, {0, 4}}, DefaultNewInlineCellStyle -> "None", LanguageCategory -> "NaturalLanguage", StyleMenuListing -> None, FontSize -> 9, FontSlant -> "Italic"], Cell[ StyleData["PageNumber"], CellMargins -> {{0, 0}, {4, 1}}, StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell["Palette Styles", "Section"], Cell[ "The cells below define styles that define standard ButtonFunctions, \ for use in palette buttons.", "Text"], Cell[ StyleData["Paste"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, Placeholder]}]& )}], Cell[ StyleData["Evaluate"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[], All]}]& )}], Cell[ StyleData["EvaluateCell"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[], All]}]& )}], Cell[ StyleData["CopyEvaluate"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[], All]}]& )}], Cell[ StyleData["CopyEvaluateCell"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{ FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[], All]}]& )}]}, Closed]], Cell[ CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell[ "The cells below define styles useful for making placeholder objects \ in palette templates.", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["Placeholder"], Placeholder -> True, StyleMenuListing -> None, FontSlant -> "Italic", FontColor -> RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions -> { Editable -> False, Selectable -> False, StripWrapperBoxes -> False}], Cell[ StyleData["Placeholder", "Presentation"]], Cell[ StyleData["Placeholder", "Condensed"]], Cell[ StyleData["Placeholder", "SlideShow"]], Cell[ StyleData["Placeholder", "Printout"]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["PrimaryPlaceholder"], StyleMenuListing -> None, DrawHighlighted -> True, FontSlant -> "Italic", Background -> RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions -> { Editable -> False, Selectable -> False, StripWrapperBoxes -> False}], Cell[ StyleData["PrimaryPlaceholder", "Presentation"]], Cell[ StyleData["PrimaryPlaceholder", "Condensed"]], Cell[ StyleData["PrimaryPlaceholder", "SlideShow"]], Cell[ StyleData["PrimaryPlaceholder", "Printout"]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["FormatType Styles", "Section"], Cell[ "The cells below define styles that are mixed in with the styles of \ most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. This is particularly true of Input and Output.", "Text"], Cell[ StyleData["CellExpression"], PageWidth -> Infinity, CellMargins -> {{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel -> False, ShowSpecialCharacters -> False, AllowInlineCells -> False, Hyphenation -> False, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 12, Background -> GrayLevel[1]], Cell[ StyleData["InputForm"], InputAutoReplacements -> {}, AllowInlineCells -> False, Hyphenation -> False, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["OutputForm"], PageWidth -> Infinity, TextAlignment -> Left, LineSpacing -> {0.6, 1}, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["StandardForm"], InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement" -> True, LineSpacing -> {1.25, 0}, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["TraditionalForm"], InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement" -> True, LineSpacing -> {1.25, 0}, SingleLetterItalics -> True, TraditionalFunctionNotation -> True, DelimiterMatching -> None, StyleMenuListing -> None], Cell[ "The style defined below is mixed in to any cell that is in an \ inline cell within another.", "Text"], Cell[ StyleData["InlineCell"], LanguageCategory -> "Formula", ScriptLevel -> 1, StyleMenuListing -> None], Cell[ StyleData["InlineCellEditing"], StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216]]}, Closed]], Cell[ CellGroupData[{ Cell["Automatic Styles", "Section"], Cell[ "The cells below define styles that are used to affect the display \ of certain types of objects in typeset expressions. For example, \ \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and \ parenthesis characters are displayed (typically by coloring them to make them \ stand out).", "Text"], Cell[ StyleData["UnmatchedBracket"], StyleMenuListing -> None, FontColor -> RGBColor[0.760006, 0.330007, 0.8]], Cell[ StyleData["Completions"], StyleMenuListing -> None, FontFamily -> "Courier"]}, Closed]], Cell[ CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["MathCaption"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{66, 12}, {2, 24}}, PageBreakBelow -> False, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> GrayLevel[0.700008], CellFrameLabelMargins -> 4, LineSpacing -> {1, 1}, ParagraphSpacing -> {0, 8}, StyleMenuListing -> None, FontColor -> GrayLevel[0.2]], Cell[ StyleData["MathCaption", "Presentation"], FontSize -> 18], Cell[ StyleData["MathCaption", "SlideShow"]], Cell[ StyleData["MathCaption", "Printout"], CellMargins -> {{39, 0}, {0, 14}}, Hyphenation -> True, FontSize -> 9, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ObjectName"], ShowCellBracket -> True, CellMargins -> {{66, 4}, {8, 8}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelAutoDelete -> False, CellLabelMargins -> {{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultInputFormatType, ShowSpecialCharacters -> Automatic, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Mathematica", FormatType -> StandardForm, ShowStringCharacters -> True, NumberMarks -> True, StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["ObjectName", "Presentation"], FontSize -> 18], Cell[ StyleData["ObjectName", "SlideShow"]], Cell[ StyleData["ObjectName", "Printout"], ShowCellBracket -> False, CellMargins -> {{39, 0}, {6, 6}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Usage"], ShowCellBracket -> True, CellMargins -> {{66, 4}, {8, 8}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelAutoDelete -> False, CellLabelMargins -> {{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultInputFormatType, ShowSpecialCharacters -> Automatic, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Mathematica", FormatType -> StandardForm, ShowStringCharacters -> True, NumberMarks -> True, StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["Usage", "Presentation"], FontSize -> 18], Cell[ StyleData["Usage", "SlideShow"]], Cell[ StyleData["Usage", "Printout"], ShowCellBracket -> False, CellMargins -> {{39, 0}, {6, 6}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Notes"], ShowCellBracket -> True, CellMargins -> {{66, 4}, {8, 8}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelAutoDelete -> False, CellLabelMargins -> {{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultInputFormatType, ShowSpecialCharacters -> Automatic, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Mathematica", FormatType -> StandardForm, ShowStringCharacters -> True, NumberMarks -> True, StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["Notes", "Presentation"], FontSize -> 18], Cell[ StyleData["Notes", "SlideShow"]], Cell[ StyleData["Notes", "Printout"], ShowCellBracket -> False, CellMargins -> {{39, 0}, {6, 6}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineOutput"], ShowCellBracket -> True, CellMargins -> {{66, 4}, {8, 8}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelAutoDelete -> False, CellLabelMargins -> {{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType -> DefaultInputFormatType, ShowSpecialCharacters -> Automatic, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Mathematica", FormatType -> StandardForm, ShowStringCharacters -> True, NumberMarks -> True, StyleMenuListing -> None, FontWeight -> "Bold"], Cell[ StyleData["InlineOutput", "Presentation"], FontSize -> 18], Cell[ StyleData["InlineOutput", "SlideShow"]], Cell[ StyleData["InlineOutput", "Printout"], ShowCellBracket -> False, CellMargins -> {{39, 0}, {6, 6}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[ CellGroupData[{ Cell[ StyleData["Box"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["Box", "Presentation"], FontSize -> 18], Cell[ StyleData["Box", "SlideShow"]], Cell[ StyleData["Box", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DoubleBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Top}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[1.4]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DoubleBox", "Presentation"], FontSize -> 18], Cell[ StyleData["DoubleBox", "SlideShow"]], Cell[ StyleData["DoubleBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["1ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["1ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["1ColumnBox", "SlideShow"]], Cell[ StyleData["1ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["2ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics -> False, LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.31], { Scaled[0.67]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["2ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["2ColumnBox", "SlideShow"]], Cell[ StyleData["2ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["2ColumnEvenBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> {{ Scaled[0.46]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["2ColumnEvenBox", "Presentation"], FontSize -> 18], Cell[ StyleData["2ColumnEvenBox", "SlideShow"]], Cell[ StyleData["2ColumnEvenBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["2ColumnSmallBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {Right, {Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> {{ Scaled[0.35]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[1.0499999999999998`]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["2ColumnSmallBox", "Presentation"], FontSize -> 18], Cell[ StyleData["2ColumnSmallBox", "SlideShow"]], Cell[ StyleData["2ColumnSmallBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["3ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> {{ Scaled[0.32]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["3ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["3ColumnBox", "SlideShow"]], Cell[ StyleData["3ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["3ColumnSmallBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {Right, Center, {Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> {{ Scaled[0.24]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[1.0499999999999998`]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["3ColumnSmallBox", "Presentation"], FontSize -> 18], Cell[ StyleData["3ColumnSmallBox", "SlideShow"]], Cell[ StyleData["3ColumnSmallBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["4ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics -> False, LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.13], Scaled[0.35], Scaled[0.13], { Scaled[0.35]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["4ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["4ColumnBox", "SlideShow"]], Cell[ StyleData["4ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["5ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> {{ Scaled[0.202]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["5ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["5ColumnBox", "SlideShow"]], Cell[ StyleData["5ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["6ColumnBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { BoxFrame -> 0.5, FrameMargins -> {{True, True}, {True, True}}}, GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.12], Scaled[0.22], Scaled[0.12], Scaled[0.12], Scaled[0.22], { Scaled[0.12]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["6ColumnBox", "Presentation"], FontSize -> 18], Cell[ StyleData["6ColumnBox", "SlideShow"]], Cell[ StyleData["6ColumnBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["FramedBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.5599999999999999]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["FramedBox", "Presentation"], FontSize -> 18], Cell[ StyleData["FramedBox", "SlideShow"]], Cell[ StyleData["FramedBox", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBox"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.4], { Scaled[0.6]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBox", "Presentation"], FontSize -> 18], Cell[ StyleData["DefinitionBox", "SlideShow"]], Cell[ StyleData["DefinitionBox", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBox3Col"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.35], Scaled[0.2], { Scaled[0.45]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBox3Col", "Presentation"], FontSize -> 18], Cell[ StyleData["DefinitionBox3Col", "SlideShow"]], Cell[ StyleData["DefinitionBox3Col", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBox4Col"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.15], Scaled[0.35], Scaled[0.15], { Scaled[0.35]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBox4Col", "Presentation"], FontSize -> 18], Cell[ StyleData["DefinitionBox4Col", "SlideShow"]], Cell[ StyleData["DefinitionBox4Col", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBox5Col"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> {{ Scaled[0.2]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBox5Col", "Presentation"], FontSize -> 18], Cell[ StyleData["DefinitionBox5Col", "SlideShow"]], Cell[ StyleData["DefinitionBox5Col", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBox6Col"], CellFrame -> 0.5, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakWithin -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.13], Scaled[0.24], Scaled[0.13], Scaled[0.13], Scaled[0.24], { Scaled[0.13]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBox6Col", "Presentation"], FontSize -> 18], Cell[ StyleData["DefinitionBox6Col", "SlideShow"]], Cell[ StyleData["DefinitionBox6Col", "Printout"], CellMargins -> {{2, 4}, {0, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TopBox"], CellFrame -> {{0.5, 0.5}, {0, 0.5}}, CellMargins -> {{27, 12}, {0, 8}}, CellHorizontalScrolling -> True, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.31], { Scaled[0.62]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["TopBox", "Presentation"], FontSize -> 18], Cell[ StyleData["TopBox", "SlideShow"]], Cell[ StyleData["TopBox", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["MiddleBox"], CellFrame -> {{0.5, 0.5}, {0, 0}}, CellMargins -> {{27, 12}, {0, -7}}, CellHorizontalScrolling -> True, PageBreakAbove -> False, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.31], { Scaled[0.62]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["MiddleBox", "Presentation"], FontSize -> 18], Cell[ StyleData["MiddleBox", "SlideShow"]], Cell[ StyleData["MiddleBox", "Printout"], CellMargins -> {{2, 0}, {0, 2}}, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["BottomBox"], CellFrame -> {{0.5, 0.5}, {0.5, 0}}, CellMargins -> {{27, 12}, {0, -7}}, CellHorizontalScrolling -> True, PageBreakAbove -> False, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.31], { Scaled[0.62]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["BottomBox", "Presentation"], FontSize -> 18], Cell[ StyleData["BottomBox", "SlideShow"]], Cell[ StyleData["BottomBox", "Printout"], CellMargins -> {{2, 0}, {0, -5}}, FontSize -> 10, Background -> GrayLevel[1], GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{All}}, "ColumnsIndexed" -> {}, "Rows" -> {{2.2}}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TopSpanBox"], CellFrame -> {{0.5, 0.5}, {0, 0.5}}, CellMargins -> {{27, 12}, {-2, 8}}, CellHorizontalScrolling -> True, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.9], { Scaled[0.03]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["TopSpanBox", "Presentation"], FontSize -> 18], Cell[ StyleData["TopSpanBox", "SlideShow"]], Cell[ StyleData["TopSpanBox", "Printout"], CellMargins -> {{2, 0}, {-2, 8}}, FontSize -> 10, Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["MiddleSpanBox"], CellFrame -> {{0.5, 0.5}, {0, 0}}, CellMargins -> {{27, 12}, {0, 0}}, CellHorizontalScrolling -> True, PageBreakAbove -> False, PageBreakBelow -> False, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], AutoIndent -> False, AutoSpacing -> False, LineIndent -> 0, StyleMenuListing -> None, FontWeight -> "Plain", Background -> RGBColor[0.964706, 0.929412, 0.839216], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.9], { Scaled[0.03]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["MiddleSpanBox", "Presentation"], FontSize -> 18], Cell[ StyleData["MiddleSpanBox", "SlideShow"]], Cell[ StyleData["MiddleSpanBox", "Printout"], CellMargins -> {{2, 0}, {-5, 0}}, FontSize -> 10, Background -> GrayLevel[1], GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{All}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.8}}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Picture"], CellMargins -> {{27, Inherited}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, StyleMenuListing -> None], Cell[ StyleData["Picture", "Presentation"], FontSize -> 18], Cell[ StyleData["Picture", "SlideShow"]], Cell[ StyleData["Picture", "Printout"], CellMargins -> {{2, Inherited}, {4, 4}}, Magnification -> 0.65]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OpenCloseItemizedPicture"], CellMargins -> {{88, 4}, {4, 4}}, PrivateCellOptions -> {"DefaultCellGroupOpen" -> False}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, StyleMenuListing -> None], Cell[ StyleData["OpenCloseItemizedPicture", "Presentation"], FontSize -> 18], Cell[ StyleData["OpenCloseItemizedPicture", "SlideShow"]], Cell[ StyleData["OpenCloseItemizedPicture", "Printout"], CellMargins -> {{76, 2}, {0, 0}}, CellElementSpacings -> { "CellMinHeight" -> 1, "ClosedCellHeight" -> 0}, CellOpen -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ItemizedPicture"], CellMargins -> {{88, 4}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, StyleMenuListing -> None], Cell[ StyleData["ItemizedPicture", "Presentation"], FontSize -> 18], Cell[ StyleData["ItemizedPicture", "SlideShow"]], Cell[ StyleData["ItemizedPicture", "Printout"], CellMargins -> {{77, 2}, {4, -4}}, Magnification -> 0.5]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ListGraphic"], CellMargins -> {{88, 4}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, StyleMenuListing -> None], Cell[ StyleData["ListGraphic", "Presentation"], FontSize -> 18], Cell[ StyleData["ListGraphic", "SlideShow"]], Cell[ StyleData["ListGraphic", "Printout"], CellMargins -> {{77, 2}, {4, -4}}, Magnification -> 0.5]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["ListNoteBox"], CellFrame -> 0.5, CellMargins -> {{88, 12}, {8, 8}}, CellHorizontalScrolling -> True, CellFrameColor -> RGBColor[0.74902, 0.694118, 0.552941], LineIndent -> 0, StyleMenuListing -> None, Background -> RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions -> { FrameMargins -> {{15.600000000000001`, 15.600000000000001`}, {11.700000000000001`, 11.700000000000001`}}}, GridBoxOptions -> {GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["ListNoteBox", "Presentation"], FontSize -> 18], Cell[ StyleData["ListNoteBox", "SlideShow"]], Cell[ StyleData["ListNoteBox", "Printout"], CellMargins -> {{77, 4}, {6, 2}}, FontSize -> 10, Background -> GrayLevel[0.900008]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["PictureGroup"], CellMargins -> {{41, 4}, {0, 4}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, StyleMenuListing -> None], Cell[ StyleData["PictureGroup", "Presentation"], FontSize -> 18], Cell[ StyleData["PictureGroup", "SlideShow"]], Cell[ StyleData["PictureGroup", "Printout"], CellMargins -> {{76, 2}, {0, 0}}, CellElementSpacings -> { "CellMinHeight" -> 1, "ClosedCellHeight" -> 0}, CellOpen -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Sound"], ShowCellBracket -> True, CellMargins -> {{27, Inherited}, {0, 8}}, StyleMenuListing -> None], Cell[ StyleData["Sound", "Presentation"], FontSize -> 18], Cell[ StyleData["Sound", "SlideShow"]], Cell[ StyleData["Sound", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 10]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Tables", "Subsection"], Cell[ CellGroupData[{ Cell[ StyleData["2ColumnTable"], CellMargins -> {{35, 4}, {0, 8}}, CellHorizontalScrolling -> True, LineIndent -> 0, StyleMenuListing -> None, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.34], { Scaled[0.64]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["2ColumnTable", "Presentation"], FontSize -> 18], Cell[ StyleData["2ColumnTable", "SlideShow"]], Cell[ StyleData["2ColumnTable", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["2ColumnEvenTable"], CellMargins -> {{35, 4}, {0, 8}}, CellHorizontalScrolling -> True, LineIndent -> 0, StyleMenuListing -> None, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> {{ Scaled[0.49]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["2ColumnEvenTable", "Presentation"], FontSize -> 18], Cell[ StyleData["2ColumnEvenTable", "SlideShow"]], Cell[ StyleData["2ColumnEvenTable", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["3ColumnTable"], CellMargins -> {{35, 4}, {0, 8}}, CellHorizontalScrolling -> True, LineIndent -> 0, StyleMenuListing -> None, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.28], Scaled[0.28], { Scaled[0.43]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["3ColumnTable", "Presentation"], FontSize -> 18], Cell[ StyleData["3ColumnTable", "SlideShow"]], Cell[ StyleData["3ColumnTable", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9]}, Closed]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Slide Show Styles", "Section"], Cell[ CellGroupData[{ Cell[ StyleData["SlideShowNavigationBar"], Editable -> False, CellFrame -> True, CellMargins -> {{0, 0}, {3, 3}}, CellElementSpacings -> {"CellMinHeight" -> 0.8125}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> False, CellFrameColor -> GrayLevel[1], CellFrameLabelMargins -> False, TextAlignment -> Center, CounterIncrements -> "SlideShowNavigationBar", StyleMenuListing -> None, FontSize -> 10, Magnification -> 1, Background -> GrayLevel[0.8], GridBoxOptions -> { BaselinePosition -> Center, GridBoxAlignment -> { "Columns" -> { Center, Center, Center, Center, Center, Center, Right, { Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> { "Columns" -> {3.5, 3.5, 3.5, 3.5, 13, 5, {4}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["SlideShowNavigationBar", "Presentation"]], Cell[ StyleData["SlideShowNavigationBar", "SlideShow"], Deletable -> False, ShowCellBracket -> False, CellMargins -> {{-1, -1}, {-1, -1}}, PageBreakAbove -> True, CellFrameMargins -> {{1, 1}, {0, 0}}], Cell[ StyleData["SlideShowNavigationBar", "Printout"], CellMargins -> {{18, 4}, {4, 4}}, LineSpacing -> {1, 3}, FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideShowSection"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{0, 0}, {10, 0}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CellFrameMargins -> {{12, 4}, {6, 12}}, InputAutoReplacements -> {"TeX" -> StyleBox[ RowBox[{"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX" -> StyleBox[ RowBox[{"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, 0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma" -> "Mathematica", "Mma" -> "Mathematica", "MMA" -> "Mathematica", "gridMathematica" -> FormBox[ RowBox[{"grid", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], "webMathematica" -> FormBox[ RowBox[{"web", AdjustmentBox[ StyleBox["Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 18, FontWeight -> "Plain", FontColor -> GrayLevel[1], Background -> RGBColor[0.408011, 0.440726, 0.8]], Cell[ StyleData["SlideShowSection", "Presentation"], CellFrameMargins -> {{20, 10}, {10, 18}}, FontSize -> 27], Cell[ StyleData["SlideShowSection", "SlideShow"], ShowCellBracket -> False, PageBreakAbove -> True], Cell[ StyleData["SlideShowSection", "Printout"], CellMargins -> {{18, 30}, {0, 30}}, CellFrameMargins -> 5, FontSize -> 14]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideHyperlink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontSize -> 26, FontColor -> GrayLevel[0.400015], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonMargins -> 0.5, ButtonMinHeight -> 0.85, ButtonNote -> None}], Cell[ StyleData["SlideHyperlink", "Presentation"], CellMargins -> {{14, 10}, {6, 12}}, FontSize -> 36], Cell[ StyleData["SlideHyperlink", "SlideShow"]], Cell[ StyleData["SlideHyperlink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideTOCLink"], CellMargins -> {{24, Inherited}, {Inherited, Inherited}}, StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Helvetica", ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonMargins -> 1.5, ButtonNote -> ButtonData}], Cell[ StyleData["SlideTOCLink", "Presentation"], CellMargins -> {{35, 10}, {8, 8}}, FontSize -> 18], Cell[ StyleData["SlideTOCLink", "SlideShow"]], Cell[ StyleData["SlideTOCLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SlideTOC"], CellDingbat -> "\[Bullet]", CellMargins -> {{18, Inherited}, {Inherited, Inherited}}, StyleMenuListing -> None, FontFamily -> "Helvetica"], Cell[ StyleData["SlideTOC", "Presentation"], CellMargins -> {{25, 10}, {10, 5}}, FontSize -> 18], Cell[ StyleData["SlideTOC", "SlideShow"], FontSize -> 14], Cell[ StyleData["SlideTOC", "Printout"], FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]]}, Closed]]}, Open]]}, Visible -> False, FrontEndVersion -> "7.0 for Mac OS X x86 (32-bit) (February 18, 2009)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "buttoncell"->{ Cell[3130, 100, 18464, 352, 20, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[21597, 454, 2308, 65, 42, "Output", CellTags->"buttoncell"], Cell[25933, 579, 20285, 427, 20, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[46221, 1008, 27495, 667, 78, "Output", CellTags->"buttoncell"], Cell[87658, 2065, 15417, 289, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[103078, 2356, 7183, 187, 106, "Output", CellTags->"buttoncell"], Cell[110487, 2555, 15435, 291, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[125925, 2848, 3588, 97, 42, "Output", CellTags->"buttoncell"], Cell[210537, 6278, 12113, 218, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[222653, 6498, 4819, 125, 74, "Output", CellTags->"buttoncell"], Cell[241563, 7057, 25287, 513, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[266853, 7572, 3990, 96, 42, "Output", CellTags->"buttoncell"], Cell[467310, 21079, 22356, 445, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[489669, 21526, 2765, 69, 77, "Output", CellTags->"buttoncell"]}, "payofffunction"->{ Cell[23917, 522, 774, 19, 40, "Input", CellTags->"payofffunction"]}, "payoffmatrix"->{ Cell[73750, 1680, 3397, 83, 44, "Input", CellTags->"payoffmatrix"], Cell[77564, 1781, 1788, 42, 76, "Input", CellTags->"payoffmatrix"], Cell[80304, 1854, 3337, 85, 76, "Input", CellTags->"payoffmatrix"]}, "meandynamic"->{ Cell[129537, 2949, 397, 8, 21, "Input", CellTags->"meandynamic"]}, "dynamicslibrary"->{ Cell[140715, 3300, 143, 3, 24, "SmallText", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[140861, 3305, 731, 21, 19, "Input", CellOpen->False, InitializationCell->True, CellTags->"dynamicslibrary"], Cell[141617, 3330, 133, 3, 27, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[141753, 3335, 1436, 36, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[143192, 3373, 235, 7, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[143464, 3385, 173, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[143640, 3390, 1998, 52, 124, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[145641, 3444, 237, 7, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[145915, 3456, 164, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[146082, 3461, 4005, 109, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[150090, 3572, 263, 8, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[150390, 3585, 128, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[150521, 3590, 3074, 85, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[153598, 3677, 259, 8, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[153894, 3690, 145, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[154042, 3695, 2787, 77, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[156832, 3774, 222, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[157091, 3786, 180, 4, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[157274, 3792, 2370, 70, 50, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[159647, 3864, 2038, 62, 50, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[161688, 3928, 229, 7, 29, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[168003, 4123, 2372, 70, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[170378, 4195, 2057, 62, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[172438, 4259, 243, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[172718, 4271, 135, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[181506, 4505, 234, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[181777, 4517, 147, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[181927, 4522, 264, 6, 77, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[182194, 4530, 1426, 36, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"]}, "contourfunction"->{ Cell[227484, 6626, 307, 6, 24, "Input", CellTags->"contourfunction"]}, "contourfunctions"->{ Cell[227816, 6636, 153, 3, 26, "SmallText", InitializationCell->True, CellTags->"contourfunctions"], Cell[227994, 6643, 71, 1, 27, "Subsubsection", CellTags->"contourfunctions"], Cell[228068, 6646, 282, 8, 27, "Text", Evaluatable->False, InitializationCell->True, CellTags->"contourfunctions"], Cell[230067, 6710, 75, 1, 21, "Subsubsection", CellTags->"contourfunctions"], Cell[230436, 6726, 77, 1, 21, "Subsubsection", CellTags->"contourfunctions"], Cell[238778, 6980, 97, 1, 21, "Subsubsection", CellTags->{"contourfunctions", "othercontour"}], Cell[238878, 6983, 128, 2, 27, "Text", CellTags->{"contourfunctions", "othercontour"}]}, "othercontour"->{ Cell[238778, 6980, 97, 1, 21, "Subsubsection", CellTags->{"contourfunctions", "othercontour"}], Cell[238878, 6983, 128, 2, 27, "Text", CellTags->{"contourfunctions", "othercontour"}]}, "degisken"->{ Cell[273185, 7737, 1987, 53, 67, "Input", CellTags->{"degisken", "trajectoryspecs"}]}, "trajectoryspecs"->{ Cell[273185, 7737, 1987, 53, 67, "Input", CellTags->{"degisken", "trajectoryspecs"}]}, "extragraphicselements"->{ Cell[290337, 8218, 86, 1, 24, "SmallText", CellTags->"extragraphicselements"], Cell[290426, 8221, 3410, 60, 77, "Text", CellTags->"extragraphicselements"], Cell[293839, 8283, 761, 13, 77, "Text", CellTags->"extragraphicselements"], Cell[294603, 8298, 569, 16, 77, "Input", CellTags->"extragraphicselements"], Cell[295175, 8316, 6905, 161, 77, "Input", CellTags->"extragraphicselements"]}, "vectorfieldspecs"->{ Cell[492449, 21598, 1535, 41, 52, "Input", CellTags->"vectorfieldspecs"]}, "printingcell"->{ Cell[583454, 23813, 5645, 157, 340, "Input", CellTags->"printingcell"]}, "maintenance"->{ Cell[665192, 25917, 1202, 24, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"], Cell[666419, 25945, 1203, 24, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"], Cell[668839, 25999, 1223, 27, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"]} } *) (*CellTagsIndex CellTagsIndex->{ {"buttoncell", 787274, 28455}, {"payofffunction", 788624, 28498}, {"payoffmatrix", 788717, 28501}, {"meandynamic", 788955, 28508}, {"dynamicslibrary", 789049, 28511}, {"contourfunction", 792126, 28600}, {"contourfunctions", 792225, 28603}, {"othercontour", 792924, 28621}, {"degisken", 793134, 28626}, {"trajectoryspecs", 793248, 28629}, {"extragraphicselements", 793368, 28632}, {"vectorfieldspecs", 793805, 28643}, {"printingcell", 793904, 28646}, {"maintenance", 794000, 28649} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 341, 10, 132, "Title"], Cell[CellGroupData[{ Cell[933, 36, 63, 1, 46, "Subtitle"], Cell[CellGroupData[{ Cell[1021, 41, 221, 6, 30, "Text", Evaluatable->False], Cell[1245, 49, 260, 7, 20, "Input", CellOpen->False, InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[1542, 61, 194, 3, 37, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[1761, 68, 158, 3, 37, "Subsection"], Cell[1922, 73, 1183, 23, 43, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[3130, 100, 18464, 352, 20, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[21597, 454, 2308, 65, 42, "Output", CellTags->"buttoncell"] }, {2}]], Cell[23917, 522, 774, 19, 40, "Input", CellTags->"payofffunction"] }, Closed]], Cell[CellGroupData[{ Cell[24728, 546, 366, 6, 29, "Subsection"], Cell[CellGroupData[{ Cell[25119, 556, 340, 5, 27, "Subsubsection"], Cell[25462, 563, 446, 12, 27, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[25933, 579, 20285, 427, 20, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[46221, 1008, 27495, 667, 78, "Output", CellTags->"buttoncell"] }, {2}]], Cell[CellGroupData[{ Cell[73750, 1680, 3397, 83, 44, "Input", CellTags->"payoffmatrix"], Cell[77150, 1765, 411, 14, 27, "Text", Evaluatable->False], Cell[77564, 1781, 1788, 42, 76, "Input", CellTags->"payoffmatrix"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[79401, 1829, 426, 6, 27, "Subsubsection"], Cell[79830, 1837, 471, 15, 27, "Text", Evaluatable->False], Cell[80304, 1854, 3337, 85, 76, "Input", CellTags->"payoffmatrix"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[83690, 1945, 360, 5, 37, "Subsection"], Cell[84053, 1952, 489, 17, 43, "Text"], Cell[84545, 1971, 521, 18, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[85103, 1994, 415, 6, 29, "Subsection"], Cell[85521, 2002, 505, 13, 59, "Text"], Cell[86029, 2017, 89, 2, 24, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[86167, 2025, 89, 2, 67, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[86281, 2031, 552, 8, 37, "Subsection"], Cell[86836, 2041, 729, 16, 60, "Text"], Cell[CellGroupData[{ Cell[87590, 2061, 43, 0, 26, "SmallText"], Cell[CellGroupData[{ Cell[87658, 2065, 15417, 289, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[103078, 2356, 7183, 187, 106, "Output", CellTags->"buttoncell"] }, {2}]] }, Open ]], Cell[CellGroupData[{ Cell[110307, 2549, 155, 2, 26, "SmallText"], Cell[CellGroupData[{ Cell[110487, 2555, 15435, 291, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[125925, 2848, 3588, 97, 42, "Output", CellTags->"buttoncell"] }, {2}]] }, Closed]], Cell[129537, 2949, 397, 8, 21, "Input", CellTags->"meandynamic"], Cell[CellGroupData[{ Cell[129959, 2961, 126, 1, 26, "SmallText"], Cell[CellGroupData[{ Cell[130110, 2966, 62, 0, 27, "Text"], Cell[130175, 2968, 89, 2, 24, "Input"] }, Closed]] }, Closed]], Cell[130291, 2974, 157, 4, 19, "Input", CellOpen->False] }, Open ]], Cell[CellGroupData[{ Cell[130485, 2983, 541, 8, 37, "Subsection"], Cell[131029, 2993, 558, 14, 43, "Text"], Cell[131590, 3009, 199, 4, 24, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[131826, 3018, 514, 7, 29, "Subsection"], Cell[CellGroupData[{ Cell[132365, 3029, 89, 1, 26, "SmallText"], Cell[132457, 3032, 336, 7, 24, "Input", InitializationCell->True], Cell[CellGroupData[{ Cell[132818, 3043, 185, 3, 27, "Text", InitializationCell->True], Cell[133006, 3048, 296, 10, 24, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[133339, 3063, 143, 2, 27, "Text", InitializationCell->True], Cell[133485, 3067, 1104, 33, 139, "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[134626, 3105, 106, 2, 27, "Text", InitializationCell->True], Cell[134735, 3109, 837, 26, 70, "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[135609, 3140, 128, 2, 27, "Text", InitializationCell->True], Cell[135740, 3144, 1595, 46, 70, "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[137372, 3195, 39, 0, 27, "Text"], Cell[137414, 3197, 1269, 40, 83, "Input", InitializationCell->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[138732, 3243, 104, 1, 24, "SmallText"], Cell[138839, 3246, 751, 12, 91, "Text"], Cell[139593, 3260, 1085, 35, 100, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[140715, 3300, 143, 3, 24, "SmallText", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[140861, 3305, 731, 21, 19, "Input", CellOpen->False, InitializationCell->True, CellTags->"dynamicslibrary"], Cell[CellGroupData[{ Cell[141617, 3330, 133, 3, 27, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[141753, 3335, 1436, 36, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[143192, 3373, 235, 7, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[143464, 3385, 173, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[143640, 3390, 1998, 52, 124, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[145641, 3444, 237, 7, 40, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[145915, 3456, 164, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[146082, 3461, 4005, 109, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[150090, 3572, 263, 8, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[150390, 3585, 128, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[150521, 3590, 3074, 85, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[153598, 3677, 259, 8, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[153894, 3690, 145, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[154042, 3695, 2787, 77, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[156832, 3774, 222, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[157091, 3786, 180, 4, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[157274, 3792, 2370, 70, 50, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[159647, 3864, 2038, 62, 50, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[161688, 3928, 229, 7, 29, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[161954, 3940, 129, 2, 24, "Text", InitializationCell->True], Cell[162086, 3944, 971, 35, 77, "Text", InitializationCell->True], Cell[163060, 3981, 1576, 45, 77, "Input", InitializationCell->True], Cell[164639, 4028, 2635, 69, 77, "Input", InitializationCell->True], Cell[167277, 4099, 205, 6, 77, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[167519, 4110, 164, 3, 24, "Text", InitializationCell->True], Cell[167686, 4115, 314, 6, 77, "Text", InitializationCell->True], Cell[168003, 4123, 2372, 70, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[170378, 4195, 2057, 62, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[172438, 4259, 243, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[172718, 4271, 135, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[172856, 4276, 180, 6, 77, "Input", InitializationCell->True], Cell[173039, 4284, 8464, 219, 77, "Input", InitializationCell->True], Cell[181506, 4505, 234, 7, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"] }, Closed]], Cell[CellGroupData[{ Cell[181777, 4517, 147, 3, 24, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[181927, 4522, 264, 6, 77, "Text", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[182194, 4530, 1426, 36, 77, "Input", InitializationCell->True, CellTags->"dynamicslibrary"], Cell[183623, 4568, 161, 5, 77, "Input", InitializationCell->True] }, Closed]] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[183857, 4581, 152, 3, 67, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[184034, 4588, 203, 3, 37, "Subsection"], Cell[184240, 4593, 1508, 31, 155, "Text"], Cell[185751, 4626, 23156, 1602, 73, "Text"], Cell[208910, 6230, 878, 20, 115, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[209825, 6255, 101, 2, 37, "Subsection", Evaluatable->False], Cell[209929, 6259, 583, 15, 43, "Text"], Cell[CellGroupData[{ Cell[210537, 6278, 12113, 218, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[222653, 6498, 4819, 125, 74, "Output", CellTags->"buttoncell"] }, {2}]], Cell[227484, 6626, 307, 6, 24, "Input", CellTags->"contourfunction"], Cell[CellGroupData[{ Cell[227816, 6636, 153, 3, 26, "SmallText", InitializationCell->True, CellTags->"contourfunctions"], Cell[CellGroupData[{ Cell[227994, 6643, 71, 1, 27, "Subsubsection", CellTags->"contourfunctions"], Cell[228068, 6646, 282, 8, 27, "Text", Evaluatable->False, InitializationCell->True, CellTags->"contourfunctions"], Cell[228353, 6656, 1141, 31, 54, "Input", InitializationCell->True], Cell[229497, 6689, 533, 16, 54, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[230067, 6710, 75, 1, 21, "Subsubsection", CellTags->"contourfunctions"], Cell[230145, 6713, 254, 8, 24, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[230436, 6726, 77, 1, 21, "Subsubsection", CellTags->"contourfunctions"], Cell[CellGroupData[{ Cell[230538, 6731, 244, 7, 24, "Input"], Cell[230785, 6740, 868, 15, 70, "Message"] }, Open ]], Cell[231668, 6758, 926, 28, 54, "Input", InitializationCell->True], Cell[232597, 6788, 2455, 74, 122, "Input", InitializationCell->True], Cell[235055, 6864, 999, 30, 54, "Input", InitializationCell->True], Cell[236057, 6896, 852, 25, 54, "Input", InitializationCell->True], Cell[236912, 6923, 1829, 52, 74, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[238778, 6980, 97, 1, 21, "Subsubsection", CellTags->{"contourfunctions", "othercontour"}], Cell[238878, 6983, 128, 2, 27, "Text", CellTags->{"contourfunctions", "othercontour"}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[239067, 6992, 179, 2, 29, "Subsection"], Cell[CellGroupData[{ Cell[239271, 6998, 98, 2, 26, "SmallText"], Cell[239372, 7002, 1566, 32, 203, "Text"] }, Closed]], Cell[240953, 7037, 585, 16, 97, "Input"], Cell[CellGroupData[{ Cell[241563, 7057, 25287, 513, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[266853, 7572, 3990, 96, 42, "Output", CellTags->"buttoncell"] }, {2}]], Cell[CellGroupData[{ Cell[270877, 7673, 95, 2, 26, "SmallText"], Cell[270975, 7677, 2195, 57, 203, "Text"] }, Closed]], Cell[273185, 7737, 1987, 53, 67, "Input", CellTags->{"degisken", "trajectoryspecs"}] }, Closed]], Cell[CellGroupData[{ Cell[275209, 7795, 159, 2, 29, "Subsection"], Cell[CellGroupData[{ Cell[275393, 7801, 45, 0, 26, "SmallText"], Cell[275441, 7803, 729, 14, 77, "Text"], Cell[276173, 7819, 11297, 315, 77, "Input"], Cell[287473, 8136, 86, 2, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[287596, 8143, 43, 0, 24, "SmallText"], Cell[287642, 8145, 723, 20, 77, "Text"], Cell[288368, 8167, 401, 12, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[288806, 8184, 69, 0, 24, "SmallText"], Cell[288878, 8186, 1243, 21, 77, "Text"], Cell[290124, 8209, 176, 4, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[290337, 8218, 86, 1, 24, "SmallText", CellTags->"extragraphicselements"], Cell[290426, 8221, 3410, 60, 77, "Text", CellTags->"extragraphicselements"], Cell[293839, 8283, 761, 13, 77, "Text", CellTags->"extragraphicselements"], Cell[294603, 8298, 569, 16, 77, "Input", CellTags->"extragraphicselements"], Cell[295175, 8316, 6905, 161, 77, "Input", CellTags->"extragraphicselements"], Cell[CellGroupData[{ Cell[302105, 8481, 968, 17, 77, "Text"], Cell[303076, 8500, 587, 10, 77, "Input"] }, Closed]] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[303736, 8518, 150, 2, 67, "Section"], Cell[CellGroupData[{ Cell[303911, 8524, 42, 0, 37, "Subsection"], Cell[303956, 8526, 434, 10, 59, "Text"], Cell[304393, 8538, 239, 5, 40, "Input"], Cell[CellGroupData[{ Cell[304657, 8547, 68, 0, 26, "SmallText"], Cell[304728, 8549, 1430, 34, 77, "Text"], Cell[306161, 8585, 158666, 12426, 77, "Text"], Cell[464830, 21013, 882, 17, 77, "Text"] }, Closed]], Cell[465727, 21033, 556, 14, 97, "Input"], Cell[466286, 21049, 999, 26, 175, "Input"], Cell[CellGroupData[{ Cell[467310, 21079, 22356, 445, 19, "Input", Evaluatable->False, CellOpen->False, CellTags->"buttoncell"], Cell[489669, 21526, 2765, 69, 77, "Output", CellTags->"buttoncell"] }, Closed]], Cell[492449, 21598, 1535, 41, 52, "Input", CellTags->"vectorfieldspecs"] }, Open ]], Cell[CellGroupData[{ Cell[494021, 21644, 54, 0, 37, "Subsection"], Cell[494078, 21646, 1840, 52, 174, "Text"], Cell[495921, 21700, 741, 22, 100, "Input"] }, Closed]] }, Closed]] }, Open ]], Cell[496701, 21727, 108, 2, 40, "Input", Evaluatable->False], Cell[CellGroupData[{ Cell[496834, 21733, 52, 1, 46, "Subtitle"], Cell[CellGroupData[{ Cell[496911, 21738, 84, 1, 67, "Section"], Cell[496998, 21741, 155, 4, 77, "Input"], Cell[497156, 21747, 520, 18, 77, "Input"], Cell[497679, 21767, 2416, 59, 77, "Input"], Cell[500098, 21828, 2806, 68, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[502941, 21901, 73, 1, 37, "Section"], Cell[503017, 21904, 513, 14, 77, "Input"], Cell[CellGroupData[{ Cell[503555, 21922, 52, 0, 77, "Subsection"], Cell[503610, 21924, 891, 25, 77, "Input"], Cell[504504, 21951, 739, 18, 77, "Input"] }, Closed]], Cell[505258, 21972, 58, 0, 77, "Subsection"], Cell[505319, 21974, 6603, 128, 77, "Input"], Cell[511925, 22104, 17995, 392, 77, "Input"], Cell[CellGroupData[{ Cell[529945, 22500, 111, 1, 77, "Subsection"], Cell[530059, 22503, 1846, 48, 77, "Input"], Cell[531908, 22553, 2277, 59, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[534222, 22617, 55, 0, 77, "Subsection"], Cell[534280, 22619, 181, 4, 77, "Text"], Cell[534464, 22625, 11800, 308, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[546301, 22938, 110, 1, 77, "Subsection"], Cell[546414, 22941, 2976, 79, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[549427, 23025, 57, 0, 77, "Subsection"], Cell[549487, 23027, 9942, 223, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[559466, 23255, 79, 1, 77, "Subsection"], Cell[559548, 23258, 134, 3, 77, "Text"], Cell[559685, 23263, 541, 18, 77, "Input"], Cell[CellGroupData[{ Cell[560251, 23285, 429, 8, 77, "Text"], Cell[560683, 23295, 2175, 58, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[562895, 23358, 108, 3, 77, "Text"], Cell[563006, 23363, 5643, 131, 77, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[568698, 23500, 60, 1, 77, "Subsection"], Cell[568761, 23503, 7135, 145, 77, "Input"], Cell[575899, 23650, 7146, 148, 77, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[583094, 23804, 49, 0, 37, "Section"], Cell[583146, 23806, 305, 5, 24, "Input"], Cell[583454, 23813, 5645, 157, 340, "Input", CellTags->"printingcell"], Cell[589102, 23972, 711, 17, 40, "Input"], Cell[CellGroupData[{ Cell[589838, 23993, 38, 0, 27, "Text"], Cell[CellGroupData[{ Cell[589901, 23997, 5921, 142, 77, "Input"], Cell[595825, 24141, 803, 14, 70, "Message"], Cell[596631, 24157, 801, 14, 70, "Message"], Cell[597435, 24173, 801, 14, 70, "Message"], Cell[598239, 24189, 633, 11, 70, "Message"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[598921, 24206, 41, 0, 24, "Text"], Cell[598965, 24208, 2174, 59, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[601176, 24272, 54, 0, 24, "Text"], Cell[601233, 24274, 4578, 109, 77, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[605848, 24388, 50, 0, 24, "Text"], Cell[605901, 24390, 3788, 95, 77, "Input"] }, Closed]], Cell[609704, 24488, 51, 0, 24, "Text"], Cell[609758, 24490, 2854, 72, 190, "Input"], Cell[CellGroupData[{ Cell[612637, 24566, 56, 0, 27, "Text"], Cell[612696, 24568, 2224, 58, 77, "Input"] }, Closed]], Cell[614935, 24629, 62, 0, 24, "Text"], Cell[615000, 24631, 4390, 99, 160, "Input"], Cell[619393, 24732, 2855, 74, 160, "Input"], Cell[622251, 24808, 2764, 81, 175, "Input"] }, Closed]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[625076, 24896, 125, 1, 46, "Subtitle"], Cell[625204, 24899, 86, 1, 67, "Section", InitializationCell->True], Cell[CellGroupData[{ Cell[625315, 24904, 103, 1, 37, "Section", InitializationCell->True], Cell[625421, 24907, 14774, 363, 77, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[640232, 25275, 90, 1, 37, "Section", InitializationCell->True], Cell[640325, 25278, 9049, 225, 77, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[649411, 25508, 74, 1, 37, "Section", InitializationCell->True], Cell[649488, 25511, 1451, 39, 77, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[650976, 25555, 78, 1, 37, "Section", InitializationCell->True], Cell[651057, 25558, 13975, 349, 77, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[665069, 25912, 98, 1, 37, "Section"], Cell[CellGroupData[{ Cell[665192, 25917, 1202, 24, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"], Cell[CellGroupData[{ Cell[666419, 25945, 1203, 24, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"], Cell[667625, 25971, 1165, 22, 77, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[668839, 25999, 1223, 27, 77, "Input", Evaluatable->True, CellOpen->True, CellTags->"maintenance"], Cell[670065, 26028, 1112, 21, 77, "Input"], Cell[671180, 26051, 1113, 21, 77, "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[672354, 26079, 27, 0, 46, "Subtitle"], Cell[672384, 26081, 1366, 28, 331, "Text"] }, Closed]] } ] *) (* End of internal cache information *)