(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 12.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 98276, 2280] NotebookOptionsPosition[ 95330, 2226] NotebookOutlinePosition[ 95731, 2242] CellTagsIndexPosition[ 95688, 2239] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["\<\ Go to the line \[OpenCurlyDoubleQuote]G=GramMaker[myAntiPyramid[4],14,10000]\ \[CloseCurlyDoubleQuote] and change the 4 to anything you want, then run the \ note book. \ \>", "Text", CellChangeTimes->{{3.834179751045641*^9, 3.834179804320656*^9}},ExpressionUUID->"73b90f40-aa75-45cc-9624-\ 86406ff3f05e"], Cell[BoxData[ RowBox[{ RowBox[{"P", "[", "n_", "]"}], ":=", RowBox[{"ArrayFlatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "2"}], ",", "0"}], "}"}]}], "}"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"IdentityMatrix", "[", RowBox[{"n", "-", "2"}], "]"}]}], "}"}]}], "}"}], "]"}]}]], "Input", CellChangeTimes->{{3.830960179328179*^9, 3.830960326652483*^9}, { 3.8309604817304897`*^9, 3.830960491478415*^9}, {3.830960625774377*^9, 3.8309610006696243`*^9}, {3.8309610406625767`*^9, 3.830961145400291*^9}, { 3.830974193183652*^9, 3.8309745378615713`*^9}, {3.831070955808754*^9, 3.831070961297104*^9}, {3.834179746565708*^9, 3.8341797491247168`*^9}}, CellLabel-> "In[255]:=",ExpressionUUID->"42bda541-275e-4fa8-ad0f-dff973087409"], Cell[BoxData[{ RowBox[{ RowBox[{"object", "[", RowBox[{"v_", ",", "f_"}], "]"}], ":=", RowBox[{"Polygon", "/@", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"v", "[", RowBox[{"[", "#1", "]"}], "]"}], "&"}], ",", "f", ",", RowBox[{"{", "2", "}"}]}], "]"}]}]}], "\n", RowBox[{ RowBox[{"face2edges", "[", "face_", "]"}], ":=", RowBox[{"MapThread", "[", RowBox[{ RowBox[{ RowBox[{"Sort", "[", RowBox[{"{", RowBox[{"#1", ",", "#2"}], "}"}], "]"}], "&"}], ",", RowBox[{"{", RowBox[{"face", ",", RowBox[{"RotateLeft", "[", "face", "]"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"f2e", "[", "f_", "]"}], ":=", RowBox[{"Union", "@@", RowBox[{"face2edges", "/@", "f"}]}]}], "\n", RowBox[{ RowBox[{"closest", "[", RowBox[{"{", RowBox[{"P1_", ",", "P2_"}], "}"}], "]"}], ":=", RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"L", "=", RowBox[{"P2", "-", "P1"}]}], "}"}], ",", RowBox[{"P1", "-", FractionBox[ RowBox[{ RowBox[{"L", ".", "P1"}], " ", "L"}], RowBox[{"L", ".", "L"}]]}]}], "]"}]}], "\n", RowBox[{ RowBox[{ RowBox[{"tangentify", "[", RowBox[{"v_", ",", "e_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"newV", "=", "v"}], ",", "t", ",", "c"}], "}"}], ",", RowBox[{ RowBox[{"Scan", "[", RowBox[{ RowBox[{ RowBox[{"(", "\[IndentingNewLine]", RowBox[{ RowBox[{"t", "=", RowBox[{"closest", "[", RowBox[{"v", "[", RowBox[{"[", "#1", "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"c", "=", RowBox[{"0.5", "*", RowBox[{"(", RowBox[{"1", "-", RowBox[{"Sqrt", "[", RowBox[{"t", ".", "t"}], "]"}]}], ")"}], "*", "t"}]}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"newV", "[", RowBox[{"[", RowBox[{"#1", "[", RowBox[{"[", "1", "]"}], "]"}], "]"}], "]"}], "+=", "c"}], ";", "\[IndentingNewLine]", RowBox[{ RowBox[{"newV", "[", RowBox[{"[", RowBox[{"#1", "[", RowBox[{"[", "2", "]"}], "]"}], "]"}], "]"}], "+=", "c"}], ";"}], "\[IndentingNewLine]", ")"}], "&"}], ",", "e"}], "]"}], ";", "newV"}]}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"recenter", "[", RowBox[{"v_", ",", "e_"}], "]"}], ":=", RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"centroid", "=", RowBox[{ RowBox[{"Plus", "@@", RowBox[{"closest", "/@", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"v", "[", RowBox[{"[", "#1", "]"}], "]"}], "&"}], ",", "e", ",", RowBox[{"{", "2", "}"}]}], "]"}]}]}], "/", RowBox[{"Length", "[", "e", "]"}]}]}], "}"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#1", "-", "centroid"}], "&"}], ")"}], "/@", "v"}]}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"unit", "[", "x_", "]"}], ":=", RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"mag2", "=", RowBox[{"x", ".", "x"}]}], "}"}], ",", RowBox[{"If", "[", RowBox[{ RowBox[{"mag2", "\[NotEqual]", "0"}], ",", RowBox[{"x", "/", RowBox[{"Sqrt", "[", "mag2", "]"}]}], ",", "x"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cross", "[", RowBox[{ RowBox[{"{", RowBox[{"ax_", ",", "ay_", ",", "az_"}], "}"}], ",", RowBox[{"{", RowBox[{"bx_", ",", "by_", ",", "bz_"}], "}"}]}], "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"ay", "*", "bz"}], "-", RowBox[{"az", "*", "by"}]}], ",", RowBox[{ RowBox[{"az", "*", "bx"}], "-", RowBox[{"ax", "*", "bz"}]}], ",", RowBox[{ RowBox[{"ax", "*", "by"}], "-", RowBox[{"ay", "*", "bx"}]}]}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"approxNormal", "[", "face_", "]"}], ":=", RowBox[{"unit", "[", RowBox[{"Plus", "@@", RowBox[{"MapThread", "[", RowBox[{ RowBox[{ RowBox[{"unit", "[", RowBox[{"cross", "[", RowBox[{ RowBox[{"#1", "-", "#2"}], ",", RowBox[{"#2", "-", "#3"}]}], "]"}], "]"}], "&"}], ",", RowBox[{"{", RowBox[{"face", ",", RowBox[{"RotateLeft", "[", RowBox[{"face", ",", "1"}], "]"}], ",", RowBox[{"RotateLeft", "[", RowBox[{"face", ",", "2"}], "]"}]}], "}"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"planarize", "[", RowBox[{"v_", ",", "f_"}], "]"}], ":=", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"newV", "=", "v"}], ",", "faceXYZ", ",", "n", ",", "centroid"}], "}"}], ",", RowBox[{ RowBox[{"Scan", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"faceXYZ", "=", RowBox[{"v", "[", RowBox[{"[", "#1", "]"}], "]"}]}], ";", RowBox[{"n", "=", RowBox[{"approxNormal", "[", "faceXYZ", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"centroid", "=", RowBox[{ RowBox[{"Plus", "@@", "faceXYZ"}], "/", RowBox[{"Length", "[", "faceXYZ", "]"}]}]}], ";", "\[IndentingNewLine]", RowBox[{"if", "[", RowBox[{ RowBox[{ RowBox[{"n", ".", "centroid"}], "<", "0"}], ",", RowBox[{"n", "=", RowBox[{"-", "n"}]}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Scan", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"newV", "[", RowBox[{"[", "#1", "]"}], "]"}], "+=", RowBox[{"0.2", "*", RowBox[{"n", ".", RowBox[{"(", RowBox[{"centroid", "-", RowBox[{"v", "[", RowBox[{"[", "#1", "]"}], "]"}]}], ")"}]}], "*", "n"}]}], "&"}], ",", "#1"}], "]"}], ";"}], ")"}], "&"}], ",", "f"}], "]"}], ";", "\[IndentingNewLine]", "newV"}]}], "]"}]}], "\n", RowBox[{ RowBox[{"canonicalize", "[", RowBox[{"v_", ",", " ", "f_", ",", "prec_", ",", "stop_"}], "]"}], " ", ":=", " ", "\n", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"newV", " ", "=", " ", RowBox[{"N", "[", "v", "]"}]}], ",", " ", RowBox[{"e", " ", "=", " ", RowBox[{"f2e", "[", "f", "]"}]}], ",", " ", "oldV", ",", " ", "maxChange"}], "}"}], ",", " ", "\n", " ", RowBox[{ RowBox[{"Do", "[", RowBox[{ RowBox[{ RowBox[{"oldV", " ", "=", " ", "newV"}], ";", " ", RowBox[{"newV", " ", "=", " ", RowBox[{"tangentify", "[", RowBox[{"newV", ",", " ", "e"}], "]"}]}], ";", " ", RowBox[{"newV", " ", "=", " ", RowBox[{"recenter", "[", RowBox[{"newV", ",", " ", "e"}], "]"}]}], ";", " ", "\n", " ", RowBox[{"newV", " ", "=", " ", RowBox[{"planarize", "[", RowBox[{"newV", ",", " ", "f"}], "]"}]}], ";", " ", RowBox[{"maxChange", " ", "=", " ", RowBox[{"Max", "[", RowBox[{"Abs", "[", RowBox[{"oldV", " ", "-", " ", "newV"}], "]"}], "]"}]}], ";", " ", "\n", " ", RowBox[{"If", "[", RowBox[{ RowBox[{"maxChange", " ", "<", " ", RowBox[{"10.", "^", RowBox[{"(", RowBox[{"-", "prec"}], ")"}]}]}], ",", " ", RowBox[{"Break", "[", "]"}]}], "]"}]}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", "stop"}], "}"}]}], "]"}], ";", " ", "\n", " ", "newV"}]}], "]"}]}], "\n", RowBox[{ RowBox[{"vPyramid", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0", ",", "2"}], "}"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fPyramid", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"Range", "[", "n", "]"}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"n", "+", "1"}]}], "}"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"myPyramid", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vPyramid", "[", "n", "]"}], ",", RowBox[{"fPyramid", "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vBiPyramid", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0", ",", "2"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "2"}]}], "}"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fBiPyramid", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"Range", "[", "n", "]"}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"n", "+", "1"}]}], "}"}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"n", "+", "2"}]}], "}"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"myBiPyramid", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vBiPyramid", "[", "n", "]"}], ",", RowBox[{"fBiPyramid", "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vAntiPyramid", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", RowBox[{"-", "0.5"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", "0.5"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}]}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fAntiPyramid", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ",", "n", ",", RowBox[{"n", "+", "1"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", "n"}], "+", "2"}], ",", RowBox[{"2", "n"}], ",", "n", ",", RowBox[{"n", "+", "1"}]}], "}"}]}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", "n"}], "+", "1"}], ",", "i", ",", RowBox[{"n", "+", "i", "+", "1"}], ",", RowBox[{"i", "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"2", "n"}], "+", "2"}], ",", RowBox[{"n", "+", "i"}], ",", "i", ",", RowBox[{"n", "+", "i", "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"myAntiPyramid", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vAntiPyramid", "[", "n", "]"}], ",", RowBox[{"fAntiPyramid", "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"vKPrism", "[", "k_", "]"}], "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", "*", RowBox[{"j", "/", "k"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "k"}], "}"}]}], "]"}], ",", "1"}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"fKPrism", "[", "k_", "]"}], "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{ RowBox[{"Range", "[", "n", "]"}], "+", RowBox[{"i", "*", "n"}]}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "k"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"i", "*", "n"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"i", "-", "1"}], ")"}], "*", "n"}], "+", "1"}], ",", RowBox[{ RowBox[{"i", "*", "n"}], "+", "1"}], ",", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "1"}], ")"}], "*", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "k"}], "}"}]}], "]"}], ",", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], "*", "n"}], "+", "i"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"j", "-", "1"}], ")"}], "*", "n"}], "+", "i", "+", "1"}], ",", RowBox[{ RowBox[{"j", "*", "n"}], "+", "i", "+", "1"}], ",", RowBox[{ RowBox[{"j", "*", "n"}], "+", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "k"}], "}"}]}], "]"}], ",", "1"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"myKPrism", "[", "k_", "]"}], "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"vKPrism", "[", "k", "]"}], "[", "n", "]"}], ",", RowBox[{ RowBox[{"fKPrism", "[", "k", "]"}], "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vAntiPrism", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fAntiPrism", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Range", "[", "n", "]"}], ",", RowBox[{ RowBox[{"Range", "[", "n", "]"}], "+", "n"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"2", "*", "n"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"2", "*", "n"}], ",", "1", ",", RowBox[{"n", "+", "1"}]}], "}"}]}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "+", "i", "-", "1"}], ",", "i", ",", RowBox[{"n", "+", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "2", ",", "n"}], "}"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"myAntiPrism", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vAntiPrism", "[", "n", "]"}], ",", RowBox[{"fAntiPrism", "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{ RowBox[{"(", RowBox[{"2", "*", "Pi", "*", "i"}], ")"}], "/", "n"}], "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Range", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"n", "+", "1"}], ",", RowBox[{"2", "*", "n"}], ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"n", "+", "1"}], ",", RowBox[{"2", "*", "n"}], ",", RowBox[{ RowBox[{"2", "*", "n"}], "+", "1"}]}], "}"}]}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "i", "+", "1"}], ",", RowBox[{"n", "+", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"n", "+", "i"}], ",", RowBox[{"n", "+", "i", "+", "1"}], ",", RowBox[{ RowBox[{"2", "*", "n"}], "+", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"myHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vHermaphrodite", "[", "n", "]"}], ",", RowBox[{"fHermaphrodite", "[", "n", "]"}]}], "}"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"vAntiHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"N", "[", RowBox[{"Join", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{"i", "/", "n"}]}], "]"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Cos", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", RowBox[{"Sin", "[", RowBox[{"2", "*", "Pi", "*", RowBox[{ RowBox[{"(", RowBox[{"i", "+", "0.5"}], ")"}], "/", "n"}]}], "]"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], "}"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fAntiHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Range", "[", "n", "]"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"2", "*", "n"}], ",", "n"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"n", "+", "1"}], ",", RowBox[{ RowBox[{"2", "*", "n"}], "+", "1"}], ",", RowBox[{"2", "*", "n"}]}], "}"}]}], "}"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"i", "+", "1"}], ",", RowBox[{"n", "+", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "-", "1"}]}], "}"}]}], "]"}], ",", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"i", ",", RowBox[{"n", "+", "i"}], ",", RowBox[{ RowBox[{"2", "*", "n"}], "+", "1"}], ",", RowBox[{"n", "+", "i", "-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "2", ",", "n"}], "}"}]}], "]"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"myAntiHermaphrodite", "[", "n_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"vAntiHermaphrodite", "[", "n", "]"}], ",", RowBox[{"fAntiHermaphrodite", "[", "n", "]"}]}], "}"}]}], "\n", RowBox[{ RowBox[{"vNew", "[", RowBox[{"myShape_", ",", "prec_", ",", "stop_"}], "]"}], ":=", RowBox[{"canonicalize", "[", RowBox[{ RowBox[{"myShape", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"myShape", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "prec", ",", "stop"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"spherebbhhhCoords", "[", "point_", "]"}], ":=", RowBox[{"{", RowBox[{ RowBox[{"1", "/", SqrtBox[ RowBox[{ RowBox[{"point", ".", "point"}], "-", "1"}]]}], ",", RowBox[{"1", "/", SqrtBox[ RowBox[{ RowBox[{"point", ".", "point"}], "-", "1"}]]}], ",", RowBox[{ RowBox[{"point", "[", RowBox[{"[", "1", "]"}], "]"}], "/", SqrtBox[ RowBox[{ RowBox[{"point", ".", "point"}], "-", "1"}]]}], ",", RowBox[{ RowBox[{"point", "[", RowBox[{"[", "2", "]"}], "]"}], "/", SqrtBox[ RowBox[{ RowBox[{"point", ".", "point"}], "-", "1"}]]}], ",", RowBox[{ RowBox[{"point", "[", RowBox[{"[", "3", "]"}], "]"}], "/", SqrtBox[ RowBox[{ RowBox[{"point", ".", "point"}], "-", "1"}]]}]}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cMatrix", "[", RowBox[{"myShape_", ",", "prec_", ",", "stop_"}], "]"}], ":=", RowBox[{"Transpose", "[", RowBox[{"Map", "[", RowBox[{"spherebbhhhCoords", ",", RowBox[{"vNew", "[", RowBox[{"myShape", ",", "prec", ",", "stop"}], "]"}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"GramMaker", "[", RowBox[{"myShape_", ",", "prec_", ",", "stop_"}], "]"}], ":=", " ", RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"cFin", " ", "=", RowBox[{"cMatrix", "[", RowBox[{"myShape", ",", "prec", ",", "stop"}], "]"}]}], "}"}], ",", " ", RowBox[{ RowBox[{"Transpose", "[", "cFin", "]"}], ".", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "1"}], "/", "2"}], ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", "2"}], ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "1"}], "}"}]}], "}"}], ".", "cFin"}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.834179528431576*^9, 3.8341796307976007`*^9}}, CellLabel-> "In[256]:=",ExpressionUUID->"c77ea1b4-464a-475d-935a-6ddd3139e407"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"G", "=", RowBox[{"GramMaker", "[", RowBox[{ RowBox[{"myAntiPyramid", "[", "5", "]"}], ",", "14", ",", "10000"}], "]"}]}]], "Input", CellChangeTimes->{{3.8341795407019453`*^9, 3.834179541264065*^9}, { 3.834179796934347*^9, 3.834179809094207*^9}}, CellLabel-> "In[292]:=",ExpressionUUID->"2acb2df6-0250-4f93-a487-d393ec6948a7"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1.0000000000000009`", ",", RowBox[{"-", "4.2360679774997845`"}], ",", RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "12.708203932499343`"}], ",", RowBox[{"-", "4.23606797749978`"}], ",", RowBox[{"-", "1.000000000000066`"}], ",", RowBox[{"-", "1.0000000000000626`"}], ",", RowBox[{"-", "9.47213595499963`"}], ",", RowBox[{"-", "14.708203932499408`"}], ",", RowBox[{"-", "9.472135954999644`"}], ",", RowBox[{"-", "1.0000000000000089`"}], ",", RowBox[{"-", "2.236067977499884`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4.2360679774997845`"}], ",", "1.0000000000000009`", ",", RowBox[{"-", "4.236067977499781`"}], ",", RowBox[{"-", "12.70820393249936`"}], ",", RowBox[{"-", "12.70820393249936`"}], ",", RowBox[{"-", "9.472135954999644`"}], ",", RowBox[{"-", "1.0000000000000655`"}], ",", RowBox[{"-", "1.0000000000000668`"}], ",", RowBox[{"-", "9.472135954999642`"}], ",", RowBox[{"-", "14.70820393249945`"}], ",", RowBox[{"-", "1.0000000000000098`"}], ",", RowBox[{"-", "2.236067977499888`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "4.236067977499781`"}], ",", "0.9999999999999996`", ",", RowBox[{"-", "4.236067977499778`"}], ",", RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "14.708203932499396`"}], ",", RowBox[{"-", "9.47213595499961`"}], ",", RowBox[{"-", "1.0000000000000635`"}], ",", RowBox[{"-", "1.000000000000064`"}], ",", RowBox[{"-", "9.472135954999635`"}], ",", RowBox[{"-", "1.0000000000000084`"}], ",", RowBox[{"-", "2.236067977499882`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "12.708203932499343`"}], ",", RowBox[{"-", "12.70820393249936`"}], ",", RowBox[{"-", "4.236067977499778`"}], ",", "0.9999999999999993`", ",", RowBox[{"-", "4.236067977499778`"}], ",", RowBox[{"-", "9.472135954999626`"}], ",", RowBox[{"-", "14.708203932499394`"}], ",", RowBox[{"-", "9.472135954999635`"}], ",", RowBox[{"-", "1.0000000000000648`"}], ",", RowBox[{"-", "1.0000000000000657`"}], ",", RowBox[{"-", "1.0000000000000093`"}], ",", RowBox[{"-", "2.236067977499884`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "4.23606797749978`"}], ",", RowBox[{"-", "12.70820393249936`"}], ",", RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "4.236067977499778`"}], ",", "0.9999999999999994`", ",", RowBox[{"-", "1.000000000000063`"}], ",", RowBox[{"-", "9.47213595499962`"}], ",", RowBox[{"-", "14.708203932499417`"}], ",", RowBox[{"-", "9.472135954999626`"}], ",", RowBox[{"-", "1.0000000000000673`"}], ",", RowBox[{"-", "1.0000000000000093`"}], ",", RowBox[{"-", "2.236067977499884`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.000000000000066`"}], ",", RowBox[{"-", "9.472135954999644`"}], ",", RowBox[{"-", "14.708203932499396`"}], ",", RowBox[{"-", "9.472135954999626`"}], ",", RowBox[{"-", "1.000000000000063`"}], ",", "0.9999999999999998`", ",", RowBox[{"-", "4.236067977499778`"}], ",", RowBox[{"-", "12.70820393249935`"}], ",", RowBox[{"-", "12.708203932499341`"}], ",", RowBox[{"-", "4.236067977499785`"}], ",", RowBox[{"-", "2.236067977499885`"}], ",", RowBox[{"-", "1.0000000000000089`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.0000000000000626`"}], ",", RowBox[{"-", "1.0000000000000655`"}], ",", RowBox[{"-", "9.47213595499961`"}], ",", RowBox[{"-", "14.708203932499394`"}], ",", RowBox[{"-", "9.47213595499962`"}], ",", RowBox[{"-", "4.236067977499778`"}], ",", "0.9999999999999986`", ",", RowBox[{"-", "4.236067977499777`"}], ",", RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "12.708203932499352`"}], ",", RowBox[{"-", "2.2360679774998817`"}], ",", RowBox[{"-", "1.0000000000000089`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "9.47213595499963`"}], ",", RowBox[{"-", "1.0000000000000668`"}], ",", RowBox[{"-", "1.0000000000000635`"}], ",", RowBox[{"-", "9.472135954999635`"}], ",", RowBox[{"-", "14.708203932499417`"}], ",", RowBox[{"-", "12.70820393249935`"}], ",", RowBox[{"-", "4.236067977499777`"}], ",", "1.`", ",", RowBox[{"-", "4.236067977499784`"}], ",", RowBox[{"-", "12.70820393249937`"}], ",", RowBox[{"-", "2.2360679774998853`"}], ",", RowBox[{"-", "1.0000000000000102`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "14.708203932499408`"}], ",", RowBox[{"-", "9.472135954999642`"}], ",", RowBox[{"-", "1.000000000000064`"}], ",", RowBox[{"-", "1.0000000000000648`"}], ",", RowBox[{"-", "9.472135954999626`"}], ",", RowBox[{"-", "12.708203932499341`"}], ",", RowBox[{"-", "12.708203932499332`"}], ",", RowBox[{"-", "4.236067977499784`"}], ",", "1.000000000000001`", ",", RowBox[{"-", "4.2360679774997845`"}], ",", RowBox[{"-", "2.236067977499885`"}], ",", RowBox[{"-", "1.0000000000000089`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "9.472135954999644`"}], ",", RowBox[{"-", "14.70820393249945`"}], ",", RowBox[{"-", "9.472135954999635`"}], ",", RowBox[{"-", "1.0000000000000657`"}], ",", RowBox[{"-", "1.0000000000000673`"}], ",", RowBox[{"-", "4.236067977499785`"}], ",", RowBox[{"-", "12.708203932499352`"}], ",", RowBox[{"-", "12.70820393249937`"}], ",", RowBox[{"-", "4.2360679774997845`"}], ",", "1.0000000000000002`", ",", RowBox[{"-", "2.2360679774998875`"}], ",", RowBox[{"-", "1.0000000000000107`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.0000000000000089`"}], ",", RowBox[{"-", "1.0000000000000098`"}], ",", RowBox[{"-", "1.0000000000000084`"}], ",", RowBox[{"-", "1.0000000000000093`"}], ",", RowBox[{"-", "1.0000000000000093`"}], ",", RowBox[{"-", "2.236067977499885`"}], ",", RowBox[{"-", "2.2360679774998817`"}], ",", RowBox[{"-", "2.2360679774998853`"}], ",", RowBox[{"-", "2.236067977499885`"}], ",", RowBox[{"-", "2.2360679774998875`"}], ",", "1.`", ",", RowBox[{"-", "1.7639320225002568`"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2.236067977499884`"}], ",", RowBox[{"-", "2.236067977499888`"}], ",", RowBox[{"-", "2.236067977499882`"}], ",", RowBox[{"-", "2.236067977499884`"}], ",", RowBox[{"-", "2.236067977499884`"}], ",", RowBox[{"-", "1.0000000000000089`"}], ",", RowBox[{"-", "1.0000000000000089`"}], ",", RowBox[{"-", "1.0000000000000102`"}], ",", RowBox[{"-", "1.0000000000000089`"}], ",", RowBox[{"-", "1.0000000000000107`"}], ",", RowBox[{"-", "1.7639320225002568`"}], ",", "0.9999999999999997`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.8341795446742983`*^9, 3.8341796342153883`*^9, 3.8341797131672173`*^9, 3.834179811383936*^9, {3.834501061390765*^9, 3.834501076103367*^9}, 3.834501229114954*^9, 3.834502882776107*^9, 3.834568960544511*^9, 3.83456904188068*^9, {3.83460821719843*^9, 3.8346082773639317`*^9}, 3.8346132595491343`*^9}, CellLabel-> "Out[292]=",ExpressionUUID->"00f58963-1bec-4f17-b581-aff807028e0f"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"G", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}]], "Input", CellChangeTimes->{{3.834501067162672*^9, 3.8345010680342617`*^9}, 3.83460821356898*^9, 3.834608254494473*^9, 3.834613256684762*^9}, CellLabel-> "In[293]:=",ExpressionUUID->"1616f30b-f817-4bed-8186-0f3e4b738bac"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}], ",", "1", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.8345010712331038`*^9, 3.834501076129974*^9}, 3.834501229130864*^9, 3.834502882798918*^9, 3.8345689605886927`*^9, 3.834569041895773*^9, {3.83460821722288*^9, 3.834608277378764*^9}, 3.834613259571035*^9}, CellLabel-> "Out[293]=",ExpressionUUID->"71b7f1a7-5e88-4605-9406-a449116256ae"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"vertices", "=", RowBox[{"Length", "[", "G", "]"}]}]], "Input", CellChangeTimes->{{3.831068421040749*^9, 3.831068438134652*^9}, { 3.831068556911811*^9, 3.831068559962613*^9}, {3.83106866537999*^9, 3.83106867535107*^9}, {3.8310708651242313`*^9, 3.831070882631831*^9}, { 3.831070938090979*^9, 3.8310709389375887`*^9}, {3.831071070042544*^9, 3.831071070877789*^9}, {3.83113873699689*^9, 3.831138763545807*^9}, 3.8311389908302593`*^9, {3.8311391357726994`*^9, 3.83113917659623*^9}, { 3.8315528082278433`*^9, 3.831552809049559*^9}, 3.831553416566492*^9, 3.831553450056925*^9, 3.832068143395343*^9, 3.832070674353347*^9, 3.832070883739078*^9, {3.832071008571824*^9, 3.832071026710023*^9}, 3.832071167570911*^9, 3.8320712911138363`*^9, 3.832071364059092*^9, { 3.832075225240695*^9, 3.832075250655039*^9}, 3.832154275791316*^9, { 3.834150652562565*^9, 3.8341506602368183`*^9}, {3.834179514150607*^9, 3.834179527454651*^9}}, CellLabel-> "In[294]:=",ExpressionUUID->"ced1cd28-39c9-46f3-906f-472b911c83b5"], Cell[BoxData["5"], "Output", CellChangeTimes->{ 3.8311389995758657`*^9, 3.8311390332247753`*^9, {3.831139077841172*^9, 3.8311390946047153`*^9}, {3.831139139540516*^9, 3.8311391502889767`*^9}, { 3.831139185172961*^9, 3.831139214778775*^9}, 3.831552872925318*^9, { 3.83155345133862*^9, 3.831553481569771*^9}, {3.832068144503533*^9, 3.832068148317852*^9}, 3.832068237659737*^9, 3.832068320014284*^9, 3.832069208303895*^9, 3.832069241712646*^9, 3.832069415660672*^9, 3.832069465456599*^9, {3.832070658973015*^9, 3.832070679862513*^9}, { 3.83207102739043*^9, 3.832071035233778*^9}, {3.83207116862951*^9, 3.832071174680533*^9}, 3.832071292981135*^9, 3.832071365877555*^9, 3.832071411308194*^9, {3.832075226083325*^9, 3.832075229578257*^9}, 3.832075261919179*^9, 3.832154278676079*^9, 3.832154312567971*^9, 3.8341506641986094`*^9, 3.834150717757927*^9, 3.834179634237877*^9, 3.8341797131884813`*^9, 3.834179811405641*^9, {3.834501061407423*^9, 3.834501076151882*^9}, 3.8345012291462593`*^9, 3.834502882817725*^9, 3.834568960611871*^9, 3.834569041953014*^9, {3.834608217314954*^9, 3.83460827739392*^9}, 3.8346132595933733`*^9}, CellLabel-> "Out[294]=",ExpressionUUID->"7d1068cd-4185-4697-a370-98c58525919d"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MatrixForm", "[", "G", "]"}]], "Input", CellChangeTimes->{{3.8310684245019207`*^9, 3.831068430589032*^9}, 3.831070943176569*^9}, CellLabel-> "In[295]:=",ExpressionUUID->"c3856cfc-8a90-4b2e-a7f8-03f066ea4f67"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], RowBox[{"-", "3"}], RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}], RowBox[{"-", "3"}]}, { RowBox[{"-", "1"}], RowBox[{"-", "3"}], RowBox[{"-", "1"}], "1", RowBox[{"-", "1"}]}, { RowBox[{"-", "1"}], RowBox[{"-", "1"}], RowBox[{"-", "3"}], RowBox[{"-", "1"}], "1"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.831113731311738*^9, 3.831113772992929*^9, 3.831114119311471*^9, 3.8311146005904016`*^9, {3.831114632193636*^9, 3.831114644834837*^9}, 3.831114778940421*^9, {3.831116160766554*^9, 3.831116181220832*^9}, 3.8311168471274223`*^9, 3.8311168779294567`*^9, {3.8311220848380127`*^9, 3.831122097327479*^9}, {3.831122161542061*^9, 3.83112217077485*^9}, { 3.831122217902728*^9, 3.8311222563554697`*^9}, 3.8311223010771637`*^9, 3.8311224108541594`*^9, 3.83112246199374*^9, 3.8311225339162416`*^9, 3.8311225999972982`*^9, {3.831122707949477*^9, 3.831122727539935*^9}, 3.831125948638878*^9, {3.831126079496434*^9, 3.8311260996313553`*^9}, { 3.831126158496183*^9, 3.831126170692679*^9}, 3.831126267631433*^9, 3.831138999660606*^9, 3.831139033309568*^9, {3.831139077926798*^9, 3.831139094687868*^9}, 3.83113915037433*^9, {3.831139185257388*^9, 3.831139214863204*^9}, 3.831552872943748*^9, {3.8315534554759617`*^9, 3.831553481591659*^9}, 3.832068148328765*^9, 3.832068237670595*^9, 3.8320683200251417`*^9, 3.8320692083412857`*^9, 3.832069241723998*^9, 3.8320694156755123`*^9, 3.832069465469358*^9, {3.8320706589863863`*^9, 3.83207067987668*^9}, 3.832071035254932*^9, 3.8320711747006607`*^9, 3.83207129300419*^9, 3.832071365897861*^9, 3.832071411328372*^9, 3.832075229728857*^9, 3.832075261941083*^9, 3.832154278692697*^9, 3.832154312584054*^9, 3.834150664215773*^9, 3.834150717774004*^9, 3.834179634265574*^9, 3.834179713243734*^9, 3.8341798114593563`*^9, { 3.834501061427705*^9, 3.834501076174374*^9}, 3.8345012291623507`*^9, 3.8345028828382463`*^9, 3.834568960652845*^9, {3.834569033461903*^9, 3.834569041971336*^9}, {3.834608217364354*^9, 3.834608277409753*^9}, 3.834613259617034*^9}, CellLabel-> "Out[295]//MatrixForm=",ExpressionUUID->"45374975-4620-44a5-bf25-\ 34b9631e9eef"] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.8310924022859507`*^9, 3.831092406878796*^9}, { 3.8311137278056173`*^9, 3.8311137280579557`*^9}, 3.831552904141026*^9}, CellLabel-> "In[296]:=",ExpressionUUID->"c0fe9f2e-e239-4938-84cd-0e217d1ee57c"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"d", "=", "4"}]], "Input", CellChangeTimes->{{3.8310776138956413`*^9, 3.831077634033587*^9}, { 3.831085474436421*^9, 3.831085474482007*^9}, {3.831086409937026*^9, 3.8310864103382587`*^9}, {3.831086556306321*^9, 3.831086556662953*^9}, { 3.831114629667485*^9, 3.831114629950506*^9}, {3.831126153373056*^9, 3.831126153456332*^9}, {3.831138701611702*^9, 3.831138701838715*^9}, { 3.831139071114275*^9, 3.8311390712579117`*^9}, {3.831139182740775*^9, 3.831139182989287*^9}, {3.8315534621430817`*^9, 3.8315534622203608`*^9}}, CellLabel-> "In[297]:=",ExpressionUUID->"0fcfbb19-b2bd-4a52-925c-ac50bcdaec4f"], Cell[BoxData["4"], "Output", CellChangeTimes->{{3.831077658967082*^9, 3.831077690109293*^9}, 3.831077733656962*^9, 3.831077778579384*^9, 3.831077813266864*^9, { 3.831077864073882*^9, 3.831077873816915*^9}, {3.831077910730093*^9, 3.8310779230026693`*^9}, 3.831077974813656*^9, {3.831078043889035*^9, 3.831078113327784*^9}, 3.8310781750941343`*^9, {3.831078217108872*^9, 3.83107824437598*^9}, 3.831078383612719*^9, {3.831078587956915*^9, 3.831078613683185*^9}, 3.831078671081244*^9, 3.8310789098145742`*^9, 3.831078979319487*^9, {3.831079047294744*^9, 3.831079074744776*^9}, { 3.831079226947139*^9, 3.831079246400888*^9}, 3.83107931088827*^9, { 3.8310793593334513`*^9, 3.8310793800506687`*^9}, 3.831079451457137*^9, 3.8310795111036386`*^9, {3.831079556051539*^9, 3.831079569635724*^9}, { 3.83107961406079*^9, 3.8310796563137417`*^9}, {3.8310797108951683`*^9, 3.831079753550872*^9}, {3.8310798043614407`*^9, 3.8310798216331167`*^9}, { 3.831079859525929*^9, 3.831079875498805*^9}, 3.831079967398101*^9, 3.831080039189786*^9, 3.8310801269841547`*^9, 3.831080320856745*^9, 3.831080483742866*^9, {3.831080546374776*^9, 3.831080657325653*^9}, 3.8310807279863873`*^9, {3.831080777231256*^9, 3.83108081503274*^9}, 3.831080857862154*^9, {3.831080944097547*^9, 3.831080961988565*^9}, { 3.831081001518919*^9, 3.8310810201704082`*^9}, {3.831081054451872*^9, 3.831081080505817*^9}, {3.831081134994418*^9, 3.831081148976095*^9}, { 3.831081224940263*^9, 3.831081309382938*^9}, {3.831081347278316*^9, 3.831081372247065*^9}, {3.8310814328871813`*^9, 3.831081455401924*^9}, 3.831081502910358*^9, 3.831081549132598*^9, {3.831081659131331*^9, 3.831081744479577*^9}, 3.8310817837213163`*^9, 3.831081914374284*^9, { 3.831082144186009*^9, 3.8310821563578587`*^9}, 3.831082835274742*^9, { 3.8310829488837547`*^9, 3.8310830510527277`*^9}, {3.831083086790802*^9, 3.831083127197052*^9}, {3.8310831873907557`*^9, 3.8310831999266*^9}, 3.8310835160563917`*^9, 3.831083587252075*^9, 3.8310836341204557`*^9, 3.83108381618281*^9, 3.831083849485272*^9, 3.8310839271915007`*^9, 3.831083960923689*^9, {3.83108400339469*^9, 3.8310840195323133`*^9}, { 3.831084124237936*^9, 3.8310841444301577`*^9}, 3.8310843773986187`*^9, { 3.831084495212154*^9, 3.831084514783704*^9}, 3.831084596382153*^9, { 3.831084640172618*^9, 3.831084681007483*^9}, 3.831084722171508*^9, 3.831085322915217*^9, 3.831085357432289*^9, 3.831085409940709*^9, { 3.831085463293128*^9, 3.831085499277111*^9}, {3.831085612156795*^9, 3.831085631938157*^9}, 3.831085670134282*^9, 3.8310857436175747`*^9, 3.831085797298798*^9, {3.831085859622034*^9, 3.831085871450782*^9}, 3.831086177337042*^9, 3.8310862827407913`*^9, 3.831086352211237*^9, { 3.831086412827619*^9, 3.831086437221917*^9}, 3.8310865087551327`*^9, { 3.831086562348138*^9, 3.831086601834384*^9}, 3.831086674416045*^9, 3.831088396860242*^9, 3.831089431159539*^9, 3.831089552478197*^9, { 3.8310900441401567`*^9, 3.831090052949997*^9}, {3.831090104803471*^9, 3.831090133738884*^9}, {3.8310901942400713`*^9, 3.8310902054645243`*^9}, 3.831091157083054*^9, 3.8311137315379267`*^9, 3.831113773149817*^9, 3.831114119484942*^9, 3.831114600782851*^9, {3.8311146323626013`*^9, 3.831114645012108*^9}, 3.831114779097286*^9, {3.831116160942577*^9, 3.831116181384281*^9}, 3.8311168473362513`*^9, 3.831116878102932*^9, { 3.831122085001936*^9, 3.831122097494439*^9}, {3.831122161704962*^9, 3.831122170941372*^9}, {3.831122218070804*^9, 3.83112225652144*^9}, 3.831122301254896*^9, 3.8311224110292387`*^9, 3.831122462163929*^9, 3.831122534084831*^9, 3.831122600174018*^9, {3.8311227081143227`*^9, 3.831122727703231*^9}, 3.8311259488139133`*^9, {3.831126079676717*^9, 3.8311260998376503`*^9}, {3.831126158680934*^9, 3.831126170875133*^9}, 3.831126267799159*^9, 3.8311389998357077`*^9, 3.831139033483056*^9, { 3.831139078111813*^9, 3.831139094878602*^9}, 3.831139150568006*^9, { 3.8311391854492207`*^9, 3.831139215038693*^9}, 3.831552873017661*^9, { 3.83155345553802*^9, 3.831553481650535*^9}, 3.832068148383144*^9, 3.832068237711174*^9, 3.8320683200637836`*^9, 3.832069208386382*^9, 3.832069241761348*^9, 3.832069415737545*^9, 3.832069465504928*^9, { 3.832070659039729*^9, 3.8320706799287*^9}, 3.8320710353038473`*^9, 3.8320711747467422`*^9, 3.832071293055305*^9, 3.8320713659445143`*^9, 3.8320714113800497`*^9, 3.832075229872122*^9, 3.832075261990219*^9, 3.832154278741716*^9, 3.8321543126328583`*^9, 3.8341506642636967`*^9, 3.8341507178212643`*^9, 3.834179634318242*^9, 3.834179713300296*^9, 3.8341798115140533`*^9, {3.8345010614473867`*^9, 3.834501076200571*^9}, 3.834501229181724*^9, 3.834502882864852*^9, 3.834568960687703*^9, 3.834569041992879*^9, {3.8346082174024277`*^9, 3.834608277428707*^9}, 3.8346132596494503`*^9}, CellLabel-> "Out[297]=",ExpressionUUID->"c7ca20bd-4c9c-483c-b50b-5698dafd9f80"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", RowBox[{"P", "[", "d", "]"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.8310687914533653`*^9, 3.831068852426504*^9}, { 3.831069579236924*^9, 3.831069580068521*^9}, {3.831077557179717*^9, 3.8310775573141937`*^9}, {3.831077610720077*^9, 3.8310776304729652`*^9}}, CellLabel-> "In[298]:=",ExpressionUUID->"66dee78e-384d-4588-9d25-04b3c7b1aea7"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "1", ",", RowBox[{"-", "1"}], ",", "1"}], "}"}]], "Output", CellChangeTimes->{{3.831068803363933*^9, 3.83106885000737*^9}, { 3.831069028688038*^9, 3.8310690416517067`*^9}, {3.8310690884430037`*^9, 3.83106913186709*^9}, {3.8310691974094563`*^9, 3.831069262025526*^9}, { 3.83106931298415*^9, 3.831069325285467*^9}, 3.8310694948179703`*^9, 3.831069530691061*^9, 3.831069592651828*^9, 3.8310696553133307`*^9, { 3.831069731527321*^9, 3.831069742343192*^9}, 3.831069792227182*^9, { 3.831069846686751*^9, 3.831069895626308*^9}, {3.831070151217969*^9, 3.83107019034741*^9}, 3.831070239199666*^9, {3.8310702786295767`*^9, 3.831070422738036*^9}, {3.831070508115368*^9, 3.8310705515547333`*^9}, 3.831070582010604*^9, {3.8310706415191402`*^9, 3.831070656317865*^9}, 3.831070714419696*^9, {3.831070784942418*^9, 3.831070799448985*^9}, { 3.8310708902875757`*^9, 3.8310709468508368`*^9}, {3.831070985556386*^9, 3.831071012311507*^9}, {3.831071074570899*^9, 3.831071099081758*^9}, { 3.831075176590795*^9, 3.831075187241228*^9}, 3.831075267118023*^9, { 3.831075317938847*^9, 3.831075349881082*^9}, {3.831075414802733*^9, 3.831075537871869*^9}, {3.831075570740234*^9, 3.831075583132401*^9}, { 3.8310756388718157`*^9, 3.831075662777749*^9}, 3.831075742400702*^9, 3.831075774501356*^9, 3.831075829128186*^9, 3.831075897325326*^9, 3.831075963738758*^9, 3.831076020813298*^9, 3.831076087624449*^9, { 3.8310761258852797`*^9, 3.831076147905953*^9}, 3.831076285225354*^9, 3.831076320555789*^9, 3.831076358288659*^9, {3.831076404900782*^9, 3.8310764635949183`*^9}, 3.831076510336896*^9, 3.8310765472324266`*^9, { 3.831076595630175*^9, 3.831076618668092*^9}, {3.831076655119701*^9, 3.831076711528955*^9}, {3.8310767589374866`*^9, 3.831076795510066*^9}, 3.831076855037743*^9, {3.8310769466726437`*^9, 3.8310769541384478`*^9}, { 3.8310769893100452`*^9, 3.8310770158363943`*^9}, 3.831077086467978*^9, 3.831077141389928*^9, 3.831077208317356*^9, 3.831077499081492*^9, { 3.831077547189341*^9, 3.831077593100355*^9}, {3.831077659049283*^9, 3.831077690197226*^9}, 3.831077733733485*^9, 3.8310777786528788`*^9, 3.8310778133463297`*^9, {3.831077864125955*^9, 3.831077873895648*^9}, { 3.831077910816896*^9, 3.831077923081874*^9}, 3.8310779748963757`*^9, { 3.831078043950102*^9, 3.8310781134145803`*^9}, 3.8310781751789227`*^9, { 3.831078217196581*^9, 3.831078244461989*^9}, 3.831078383705928*^9, { 3.83107858804125*^9, 3.831078613777569*^9}, 3.831078671142501*^9, 3.8310789098883142`*^9, 3.831078979387238*^9, {3.831079047350108*^9, 3.8310790748115587`*^9}, {3.8310792270273533`*^9, 3.8310792464768887`*^9}, 3.8310793109605207`*^9, {3.831079359399391*^9, 3.831079380115336*^9}, 3.831079451526115*^9, 3.831079511178684*^9, {3.83107955612757*^9, 3.831079569700919*^9}, {3.8310796141450567`*^9, 3.831079656389378*^9}, { 3.8310797109717484`*^9, 3.831079753625214*^9}, {3.83107980444046*^9, 3.831079821710692*^9}, {3.831079859608279*^9, 3.831079875577162*^9}, 3.8310799674791613`*^9, 3.831080039274103*^9, 3.831080127055891*^9, 3.831080320920989*^9, 3.831080483813675*^9, {3.831080546448228*^9, 3.8310806574063787`*^9}, 3.8310807280617037`*^9, {3.831080777314292*^9, 3.831080815119005*^9}, 3.831080857949409*^9, {3.8310809441774883`*^9, 3.8310809620790443`*^9}, {3.831081001602944*^9, 3.831081020252708*^9}, { 3.831081054532878*^9, 3.831081080587627*^9}, {3.831081135074891*^9, 3.831081149057116*^9}, {3.831081225068304*^9, 3.831081309480452*^9}, { 3.831081347361559*^9, 3.831081372333157*^9}, {3.831081432975114*^9, 3.831081455494761*^9}, 3.8310815029954767`*^9, 3.8310815492204103`*^9, { 3.8310816592178698`*^9, 3.831081744569416*^9}, 3.831081783811069*^9, 3.831081914459962*^9, {3.8310821442795563`*^9, 3.8310821564466667`*^9}, 3.831082835368518*^9, {3.831082948979497*^9, 3.831083051151186*^9}, { 3.831083086881266*^9, 3.831083127306148*^9}, {3.8310831874818068`*^9, 3.831083200021138*^9}, 3.8310835161476316`*^9, 3.831083587342951*^9, 3.83108363421138*^9, 3.831083816278112*^9, 3.8310838495929127`*^9, 3.8310839272770348`*^9, 3.831083961011763*^9, {3.831084003483045*^9, 3.83108401965979*^9}, {3.831084124344179*^9, 3.831084144530644*^9}, 3.8310843774928637`*^9, {3.8310844953186502`*^9, 3.831084514881317*^9}, 3.831084596480114*^9, {3.831084640272088*^9, 3.831084681108876*^9}, 3.8310847222887373`*^9, 3.831085323025505*^9, 3.831085357536736*^9, 3.831085410036068*^9, {3.831085463418747*^9, 3.831085499387247*^9}, { 3.831085612254614*^9, 3.831085632040267*^9}, 3.831085670240221*^9, 3.831085743715929*^9, 3.831085797406872*^9, {3.831085859730665*^9, 3.831085871559651*^9}, 3.831086177442246*^9, 3.831086282851125*^9, 3.8310863523130503`*^9, {3.831086412933577*^9, 3.8310864373363667`*^9}, 3.831086508853647*^9, {3.831086562455793*^9, 3.831086601935947*^9}, 3.831086674522703*^9, 3.83108839698092*^9, 3.831089431258123*^9, 3.831089552573764*^9, {3.83109004425182*^9, 3.831090053043117*^9}, { 3.83109010492227*^9, 3.831090133859674*^9}, {3.831090194354433*^9, 3.8310902055687647`*^9}, 3.83109115721312*^9, 3.83111373165549*^9, 3.8311137732308807`*^9, 3.831114119563757*^9, 3.83111460086872*^9, { 3.831114632438829*^9, 3.831114645088572*^9}, 3.831114779172229*^9, { 3.8311161610498857`*^9, 3.8311161814622602`*^9}, 3.831116847415412*^9, 3.8311168781848097`*^9, {3.831122085105588*^9, 3.831122097573892*^9}, { 3.831122161783801*^9, 3.831122171022398*^9}, {3.8311222181494617`*^9, 3.83112225659938*^9}, 3.831122301334229*^9, 3.831122411107917*^9, 3.8311224622466373`*^9, 3.831122534165197*^9, 3.831122600261423*^9, { 3.831122708196787*^9, 3.831122727783492*^9}, 3.831125948893791*^9, { 3.831126079757305*^9, 3.8311260999339848`*^9}, {3.831126158766491*^9, 3.8311261709546623`*^9}, 3.831126267884177*^9, 3.831138999947844*^9, 3.8311390335929832`*^9, {3.8311390782237883`*^9, 3.831139095008959*^9}, 3.8311391506898203`*^9, {3.8311391855640707`*^9, 3.831139215148542*^9}, 3.8315528730744667`*^9, {3.831553455592843*^9, 3.8315534816990013`*^9}, 3.832068148424966*^9, 3.832068237746542*^9, 3.832068320096835*^9, 3.832069208397925*^9, 3.832069241794717*^9, 3.832069415789654*^9, 3.83206946553625*^9, {3.832070659084938*^9, 3.832070679970484*^9}, 3.8320710353434887`*^9, 3.8320711747816563`*^9, 3.832071293098208*^9, 3.8320713659792213`*^9, 3.8320714114220943`*^9, 3.832075262035531*^9, 3.832154278782291*^9, 3.832154312670209*^9, 3.834150664304747*^9, 3.8341507178610277`*^9, 3.8341796343412113`*^9, 3.834179713320942*^9, 3.834179811535512*^9, {3.834501061468029*^9, 3.83450107622572*^9}, 3.8345012291977587`*^9, 3.834502882881853*^9, 3.834568960712244*^9, 3.834569042005877*^9, {3.834608217439719*^9, 3.834608277444111*^9}, 3.83461325967183*^9}, CellLabel-> "Out[298]=",ExpressionUUID->"4d944208-efd8-4bf9-8571-ed7c9065db41"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", "G", "]"}], "]"}]], "Input", CellChangeTimes->{ 3.831068864549449*^9, {3.831068913060398*^9, 3.831068913704132*^9}, { 3.831070982047958*^9, 3.8310709823617363`*^9}, {3.8341797067716312`*^9, 3.8341797075825768`*^9}}, CellLabel-> "In[299]:=",ExpressionUUID->"6c7429b3-1587-4d20-991f-d99f45021537"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1", ",", "1", ",", "1", ",", "0"}], "}"}]], "Output", CellChangeTimes->{ 3.831069655368197*^9, {3.831069731555151*^9, 3.8310697423741207`*^9}, 3.831069792282263*^9, {3.8310698467388144`*^9, 3.831069895675623*^9}, { 3.8310701512690077`*^9, 3.831070190400093*^9}, 3.831070239257474*^9, { 3.8310702786912518`*^9, 3.831070422799748*^9}, {3.831070508178976*^9, 3.831070551619849*^9}, 3.831070582092524*^9, {3.831070641587496*^9, 3.8310706563556633`*^9}, 3.831070714479004*^9, {3.831070784978848*^9, 3.8310707994886913`*^9}, {3.831070890324595*^9, 3.831070946888949*^9}, { 3.83107098562829*^9, 3.8310710123816433`*^9}, {3.831071074607935*^9, 3.831071099119403*^9}, {3.831075176656003*^9, 3.831075187281822*^9}, 3.83107526715866*^9, {3.8310753179778233`*^9, 3.8310753499504633`*^9}, { 3.831075414869905*^9, 3.831075537936016*^9}, {3.8310755708103533`*^9, 3.8310755831768017`*^9}, {3.831075638945064*^9, 3.831075662846138*^9}, 3.831075742461596*^9, 3.831075774570422*^9, 3.8310758291709633`*^9, 3.8310758973678417`*^9, 3.831075963814969*^9, 3.831076020857087*^9, 3.83107608767295*^9, {3.8310761259543858`*^9, 3.831076147980194*^9}, 3.831076285282036*^9, 3.8310763205993834`*^9, 3.831076358346161*^9, { 3.8310764049613667`*^9, 3.831076463654627*^9}, 3.831076510381597*^9, 3.831076547292337*^9, {3.831076595673067*^9, 3.8310766187340527`*^9}, { 3.8310766551654377`*^9, 3.83107671157808*^9}, {3.8310767591001062`*^9, 3.831076795672284*^9}, 3.831076855197773*^9, {3.831076946732779*^9, 3.831076954184325*^9}, {3.831076989387567*^9, 3.831077015913034*^9}, 3.8310770865311728`*^9, 3.831077141437736*^9, 3.83107720837549*^9, 3.831077499153816*^9, {3.831077547234572*^9, 3.831077593172073*^9}, { 3.831077659097555*^9, 3.831077690245576*^9}, 3.831077733779563*^9, 3.831077778699988*^9, 3.831077813395301*^9, {3.8310778642006273`*^9, 3.831077873945067*^9}, {3.831077910865962*^9, 3.831077923129714*^9}, 3.8310779749444733`*^9, {3.831078043997691*^9, 3.831078113462758*^9}, 3.831078175230336*^9, {3.831078217246277*^9, 3.831078244510528*^9}, 3.83107838379058*^9, {3.831078588092939*^9, 3.8310786138271437`*^9}, 3.831078671189645*^9, 3.831078909937131*^9, 3.8310789794396133`*^9, { 3.831079047410034*^9, 3.8310790748611794`*^9}, {3.831079227077423*^9, 3.8310792465302353`*^9}, 3.831079311010686*^9, {3.831079359450713*^9, 3.831079380166844*^9}, 3.831079451575468*^9, 3.831079511228915*^9, { 3.831079556178801*^9, 3.831079569751449*^9}, {3.831079614198246*^9, 3.8310796564422626`*^9}, {3.831079711023823*^9, 3.8310797536768637`*^9}, { 3.831079804492696*^9, 3.831079821760157*^9}, {3.831079859661373*^9, 3.83107987562963*^9}, 3.831079967529875*^9, 3.831080039325128*^9, 3.831080127105812*^9, 3.831080320982728*^9, 3.83108048386581*^9, { 3.8310805464995413`*^9, 3.831080657457603*^9}, 3.831080728115947*^9, { 3.831080777368067*^9, 3.831080815173826*^9}, 3.8310808579984407`*^9, { 3.831080944228509*^9, 3.831080962132187*^9}, {3.8310810016540337`*^9, 3.8310810203025513`*^9}, {3.831081054586232*^9, 3.831081080640904*^9}, { 3.831081135127688*^9, 3.8310811491105967`*^9}, {3.831081225138783*^9, 3.831081309538619*^9}, {3.831081347419499*^9, 3.8310813723919697`*^9}, { 3.831081433034418*^9, 3.831081455548573*^9}, 3.831081503055414*^9, 3.831081549275134*^9, {3.8310816592756653`*^9, 3.8310817446263523`*^9}, 3.8310817838697033`*^9, 3.8310819145165157`*^9, {3.8310821443396378`*^9, 3.831082156506336*^9}, 3.831082835427273*^9, {3.831082949040565*^9, 3.831083051208815*^9}, {3.8310830869396353`*^9, 3.831083127375123*^9}, { 3.83108318754291*^9, 3.8310832000813093`*^9}, 3.831083516205159*^9, 3.831083587399774*^9, 3.8310836342696733`*^9, 3.831083816335678*^9, 3.831083849653439*^9, 3.831083927336383*^9, 3.831083961070106*^9, { 3.831084003541054*^9, 3.831084019753126*^9}, {3.831084124444031*^9, 3.8310841445907087`*^9}, 3.831084377553594*^9, {3.8310844953781023`*^9, 3.831084514942717*^9}, 3.8310845965400553`*^9, {3.83108464033323*^9, 3.831084681167437*^9}, 3.831084722353668*^9, 3.83108532308632*^9, 3.831085357596037*^9, 3.83108541009603*^9, {3.831085463477619*^9, 3.831085499446682*^9}, {3.831085612315235*^9, 3.8310856321001177`*^9}, 3.831085670302368*^9, 3.831085743776698*^9, 3.831085797469809*^9, { 3.831085859829314*^9, 3.831085871620442*^9}, 3.831086177501854*^9, 3.831086282912528*^9, 3.831086352374248*^9, {3.831086412996358*^9, 3.8310864373969793`*^9}, 3.8310865089165297`*^9, {3.8310865625155153`*^9, 3.831086601999567*^9}, 3.831086674586659*^9, 3.831088397046365*^9, 3.831089431322687*^9, 3.831089552638441*^9, {3.831090044314065*^9, 3.831090053106535*^9}, {3.831090104985931*^9, 3.831090133925021*^9}, { 3.8310901944157867`*^9, 3.83109020562964*^9}, 3.8310911572774076`*^9, 3.8311137317185163`*^9, 3.831113773306253*^9, 3.83111411965912*^9, 3.8311146009660187`*^9, {3.831114632529933*^9, 3.8311146451862707`*^9}, 3.8311147792488203`*^9, {3.831116161112501*^9, 3.831116181549169*^9}, 3.831116847514269*^9, 3.831116878288761*^9, {3.831122085170596*^9, 3.831122097658691*^9}, {3.831122161868206*^9, 3.831122171109209*^9}, { 3.831122218241169*^9, 3.8311222566857023`*^9}, 3.8311223014216537`*^9, 3.831122411193157*^9, 3.83112246232994*^9, 3.831122534250416*^9, 3.8311226003505507`*^9, {3.831122708282034*^9, 3.831122727866929*^9}, 3.8311259489832497`*^9, {3.831126079853568*^9, 3.831126100044654*^9}, { 3.831126158865193*^9, 3.831126171054523*^9}, 3.83112626796636*^9, 3.831139000040764*^9, 3.831139033657256*^9, {3.831139078287389*^9, 3.831139095073455*^9}, 3.831139150755673*^9, {3.831139185655446*^9, 3.8311392152126904`*^9}, 3.8315528730935297`*^9, {3.8315534557219553`*^9, 3.831553481787972*^9}, 3.832068148435656*^9, 3.832068237757374*^9, 3.832068320108164*^9, 3.83206920843394*^9, 3.832069241807156*^9, 3.832069415804693*^9, 3.8320694655498857`*^9, {3.832070659096758*^9, 3.832070680069398*^9}, 3.832071035389688*^9, 3.832071174823353*^9, 3.8320712931145287`*^9, 3.832071366648343*^9, 3.8320714120817337`*^9, { 3.8320752398176622`*^9, 3.8320752620829077`*^9}, 3.832154278794956*^9, 3.832154312683844*^9, 3.83415066502416*^9, 3.834150718573269*^9, 3.834179635038335*^9, 3.834179714041378*^9, 3.834179811582711*^9, { 3.8345010615381107`*^9, 3.834501076421116*^9}, 3.8345012292720633`*^9, 3.8345028829639797`*^9, 3.834568961033568*^9, 3.834569042385539*^9, { 3.834608217835533*^9, 3.83460827747479*^9}, 3.8346132596995*^9}, CellLabel-> "Out[299]=",ExpressionUUID->"b86716b8-cefa-481e-bf7a-e62f17d96863"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"Perm", "=", RowBox[{ RowBox[{"IdentityMatrix", "[", "d", "]"}], "[", RowBox[{"[", RowBox[{"All", ",", RowBox[{"Ordering", "@", RowBox[{"{", RowBox[{"3", ",", "2", ",", "1", ",", "4"}], "}"}]}]}], "]"}], "]"}]}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.831070517601385*^9, 3.831070517602683*^9}, { 3.8310706361907797`*^9, 3.831070652509316*^9}, {3.83107516698969*^9, 3.831075182625458*^9}, {3.8310752139566936`*^9, 3.831075214492215*^9}, { 3.831075308983886*^9, 3.83107534681105*^9}, {3.831075445123208*^9, 3.8310754458798113`*^9}, {3.831076119680711*^9, 3.831076122616803*^9}, { 3.831077136570435*^9, 3.831077137391184*^9}, {3.831077567865345*^9, 3.8310775889451714`*^9}, {3.831077636484318*^9, 3.831077636534939*^9}, { 3.83107787077623*^9, 3.831077871752643*^9}, {3.831077918667498*^9, 3.831077920882162*^9}, {3.831084131296829*^9, 3.831084138290951*^9}, { 3.831084502962081*^9, 3.8310845121637278`*^9}, {3.8310846738761683`*^9, 3.8310846783266068`*^9}, {3.8310853495975733`*^9, 3.8310853554146023`*^9}, {3.831085491343258*^9, 3.831085496889612*^9}, { 3.831086430587381*^9, 3.8310864348227158`*^9}, {3.831086558861578*^9, 3.831086575034587*^9}, {3.831090124659238*^9, 3.831090131303933*^9}, { 3.831090198771377*^9, 3.831090202795731*^9}, {3.8311146386291122`*^9, 3.831114642242487*^9}, {3.8311161747294397`*^9, 3.831116179220029*^9}, { 3.831116854594701*^9, 3.8311168579666967`*^9}, {3.83112616447381*^9, 3.831126166776269*^9}, {3.83113900769049*^9, 3.831139025917798*^9}, { 3.831139083258071*^9, 3.831139092421317*^9}, {3.831139192060491*^9, 3.831139212300468*^9}, {3.831553470591372*^9, 3.831553478545971*^9}, 3.83417970530786*^9}, CellLabel-> "In[300]:=",ExpressionUUID->"dd7b3324-1ab6-43b0-9e24-406f40fb34ba"], Cell[BoxData[{ RowBox[{ RowBox[{"V1a", "=", RowBox[{"(", RowBox[{ RowBox[{"DiagonalMatrix", "[", RowBox[{"Abs", "[", RowBox[{ RowBox[{"Eigenvalues", "[", RowBox[{"P", "[", "d", "]"}], "]"}], "^", "0.5"}], "]"}], "]"}], ".", RowBox[{"DiagonalMatrix", "[", RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", RowBox[{"P", "[", "d", "]"}], "]"}], "]"}], "]"}]}], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"V1b", "=", RowBox[{"Orthogonalize", "[", RowBox[{"Eigenvectors", "[", RowBox[{"P", "[", "d", "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"V1", "=", RowBox[{"Perm", ".", "V1a", ".", "V1b"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"T1", "=", RowBox[{"Perm", ".", RowBox[{"DiagonalMatrix", "[", RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", RowBox[{"P", "[", "d", "]"}], "]"}], "]"}], "]"}], ".", "Perm"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{ RowBox[{"Transpose", "[", "V1", "]"}], ".", "T1", ".", "V1"}], "]"}], ";"}]}], "Input", CellChangeTimes->{{3.831070223031583*^9, 3.831070235378611*^9}, { 3.831070565111226*^9, 3.831070577654736*^9}, {3.831071006844528*^9, 3.831071007142*^9}, 3.831075198677891*^9, {3.8310752389966803`*^9, 3.831075261730558*^9}, {3.831075300950989*^9, 3.831075314345291*^9}, { 3.8310753969863*^9, 3.8310754355642138`*^9}, {3.831075470250301*^9, 3.831075579944098*^9}, {3.831077639267008*^9, 3.8310776441227293`*^9}, { 3.8310843677991743`*^9, 3.8310843903198833`*^9}, {3.831084590240316*^9, 3.8310845937558413`*^9}, {3.831084628215064*^9, 3.831084651458681*^9}, { 3.8341797019320917`*^9, 3.834179704491941*^9}}, CellLabel-> "In[301]:=",ExpressionUUID->"9e97f31a-ffaa-4f35-bb49-127a66bb73f7"], Cell[BoxData[{ RowBox[{ RowBox[{"V2a", "=", RowBox[{"(", RowBox[{ RowBox[{"DiagonalMatrix", "[", RowBox[{"Abs", "[", RowBox[{ RowBox[{"Eigenvalues", "[", "G", "]"}], "^", "0.5"}], "]"}], "]"}], ".", RowBox[{"DiagonalMatrix", "[", RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", "G", "]"}], "]"}], "]"}]}], ")"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"V2b", "=", RowBox[{"Orthogonalize", "[", RowBox[{"N", "[", RowBox[{ RowBox[{"Eigenvectors", "[", "G", "]"}], ",", "100"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"V2", "=", RowBox[{"V2a", ".", "V2b"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"T2", "=", RowBox[{"DiagonalMatrix", "[", RowBox[{"Sign", "[", RowBox[{"Eigenvalues", "[", "G", "]"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{ RowBox[{"Transpose", "[", "V2", "]"}], ".", "T2", ".", "V2"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", "V2", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"reducer", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{"i", "\[Equal]", "j"}], ",", "1", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "d"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "vertices"}], "}"}]}], "]"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{"c", "=", RowBox[{ RowBox[{"Inverse", "[", "V1", "]"}], ".", "reducer", ".", "V2"}]}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"MatrixForm", "[", RowBox[{ RowBox[{"Transpose", "[", "c", "]"}], ".", RowBox[{"P", "[", "d", "]"}], ".", "c"}], "]"}], ";"}]}], "Input", CellChangeTimes->CompressedData[" 1:eJwlz1sow2EABfB/vGHz4LZm0cqDpRTGWklNsqa1XIoXtVpZw8SQW2FKYmyM sMImcytbQqEkJizTygPlbomkXB6kufOdz8Pp13k7h6+qzC8JYBgmlgRGCvuS krsfJPXp//oD83TQlm6rg30mfgvUFQmoX4bQDlj4vUKNfx7MSCHWil4zYVy1 XwYvvSMKKF+eU0GXcUENcxQXZfBzI1cLexKlOvg2y1TD+x9nF/RbrQaY3bgz AtdXvVR2xfEEvFDa7bC9fn4Wmo1SB9xxy3bh85HwADrC3Ie0i9WnUHNSoEkj Vg0Vl8GJ3tYsEVG/6pLCm32ZHA635VEV2o89mC/+pW6rxJ7oHrJ3q8YL1aXl 7Cgj+XG2S3266o+G/Q2b1ITw4E6475kyQAfTbIKLzQILPH58H4U+AccK73iW afjS+0pVpgo5HOLSZBMPsh3O21DzgyRI+k1V+q5ZMcRprp4NLb6BkDWi253A ghFjM2eQO846h39Zj/tn "], CellLabel-> "In[306]:=",ExpressionUUID->"0209d30a-517c-4664-b87b-84799191f438"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"MatrixForm", "[", RowBox[{"c", "=", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Length", "[", "c", "]"}], "\[Equal]", "4"}], ",", RowBox[{"Join", "[", RowBox[{"c", ",", RowBox[{"{", RowBox[{"ConstantArray", "[", RowBox[{"0", ",", "vertices"}], "]"}], "}"}]}], "]"}], ",", "c"}], "]"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"c", "\[LeftDoubleBracket]", RowBox[{"2", ",", "All"}], "\[RightDoubleBracket]"}], "\[IndentingNewLine]", RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"InfiniteLine", "[", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "3", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", "2"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", RowBox[{"(", RowBox[{"2", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}]}], ")"}]}]}], "}"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "3", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", "2"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}], "\[Equal]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", "2"}], ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], "/", RowBox[{"(", RowBox[{"2", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}]}], ")"}]}], "-", RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "3", "]"}], "]"}], "/", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}]}]}]}], "}"}]}], "]"}]}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "3", "]"}], "]"}], "/", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "4", "]"}], "]"}], "/", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}]}], "}"}], ",", RowBox[{"Abs", "[", RowBox[{"1", "/", RowBox[{ RowBox[{"c", "[", RowBox[{"[", RowBox[{"All", ",", "i"}], "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}]}], "]"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"i", ",", "vertices"}], "}"}]}], "]"}], "]"}]}], "Input", CellChangeTimes->{ 3.831078297451989*^9, {3.831080812666642*^9, 3.831080843743086*^9}, { 3.831080931780704*^9, 3.83108096026335*^9}, {3.831080993687943*^9, 3.8310811909456863`*^9}, {3.831081277569045*^9, 3.831081452973516*^9}, { 3.8310814855152187`*^9, 3.831081499172461*^9}, {3.8310815608349247`*^9, 3.831081561056739*^9}, {3.831083616869606*^9, 3.831083630641979*^9}, 3.831083811003882*^9, {3.8310838650303373`*^9, 3.831083866153501*^9}, { 3.83108390774347*^9, 3.831083924132242*^9}, {3.831083956561339*^9, 3.831083957719562*^9}, {3.8310839998451347`*^9, 3.831084001216508*^9}, { 3.831084745345668*^9, 3.8310847721313467`*^9}, {3.831084812305414*^9, 3.831084878162966*^9}, {3.83108503234649*^9, 3.8310851793835993`*^9}, { 3.83108522028439*^9, 3.8310853200856524`*^9}, {3.831085388561405*^9, 3.831085407116714*^9}, 3.83108543714983*^9, {3.831085718889179*^9, 3.8310857413723297`*^9}, {3.831086341667169*^9, 3.8310863497302*^9}, { 3.831086495725498*^9, 3.8310865039382067`*^9}, {3.831088343678843*^9, 3.831088348509108*^9}, {3.83108838671922*^9, 3.831088391776963*^9}, { 3.831089118471314*^9, 3.831089427868104*^9}, {3.831089519249083*^9, 3.831089547971946*^9}, {3.831090914657469*^9, 3.831090956211699*^9}, { 3.83109099253691*^9, 3.831091152202259*^9}, {3.8310911914579782`*^9, 3.8310912484893436`*^9}, {3.831092078411395*^9, 3.831092093658761*^9}, { 3.8310921287931747`*^9, 3.83109214914692*^9}, {3.831113743889797*^9, 3.831113768930172*^9}, {3.831114593194087*^9, 3.831114593783296*^9}, { 3.831126219196403*^9, 3.831126229413628*^9}, {3.8346082657844973`*^9, 3.8346082869679623`*^9}}, NumberMarks->False, CellLabel-> "In[315]:=",ExpressionUUID->"3a5095fb-bef7-4905-a187-ccc481ddd9ee"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1.9486311405059253`", "0.8071494464601062`", "0.8071494464601062`", "0.8071494464601062`", "0.8071494464601062`"}, { RowBox[{"-", "0.5131807550506294`"}], "1.2389279387920946`", "1.2389279387920946`", "1.2389279387920946`", "1.2389279387920946`"}, {"0.`", "0.`", RowBox[{"-", "1.4142135623730951`"}], "0.`", "1.4142135623730951`"}, {"0.`", RowBox[{"-", "1.4142135623730951`"}], "0.`", "1.4142135623730951`", "0.`"}, {"0", "0", "0", "0", "0"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.8310808181124763`*^9, 3.831080860753619*^9, {3.8310809469470253`*^9, 3.831080964993269*^9}, {3.831081004545352*^9, 3.8310810231079683`*^9}, { 3.831081057456705*^9, 3.8310810835298233`*^9}, {3.831081138060302*^9, 3.831081152082024*^9}, {3.831081228011375*^9, 3.8310813133718987`*^9}, { 3.831081351183011*^9, 3.831081375990341*^9}, {3.831081436575982*^9, 3.831081459114427*^9}, 3.8310815067955008`*^9, 3.831081552992103*^9, { 3.83108166276462*^9, 3.831081748301043*^9}, 3.831081787574188*^9, 3.831081918210712*^9, {3.831082148360456*^9, 3.831082160262785*^9}, 3.831082839195043*^9, {3.831082952781499*^9, 3.831083055035534*^9}, { 3.831083090755866*^9, 3.831083131568055*^9}, {3.8310831915345984`*^9, 3.831083203976349*^9}, 3.831083520250152*^9, 3.831083591479097*^9, { 3.831083638426196*^9, 3.831083733223453*^9}, 3.831083820433951*^9, { 3.8310838540743637`*^9, 3.831083872688506*^9}, 3.831083931218514*^9, 3.831083964991393*^9, {3.831084007446355*^9, 3.8310840240544577`*^9}, { 3.831084126438016*^9, 3.8310841465491047`*^9}, 3.8310843794593287`*^9, { 3.831084496467749*^9, 3.8310845160449467`*^9}, 3.831084597631049*^9, { 3.83108464142036*^9, 3.831084683108674*^9}, 3.831084723554061*^9, 3.8310853242106657`*^9, 3.831085358717671*^9, 3.831085411190071*^9, { 3.8310854646012907`*^9, 3.8310855005741*^9}, {3.831085613523452*^9, 3.831085633371294*^9}, 3.8310856714538593`*^9, 3.831085744893196*^9, 3.8310857985908613`*^9, {3.83108586096107*^9, 3.8310858727632713`*^9}, 3.831086178663618*^9, 3.831086284067205*^9, 3.8310863535520144`*^9, { 3.83108641443573*^9, 3.831086438553163*^9}, 3.8310865100347013`*^9, { 3.831086563691814*^9, 3.831086603192316*^9}, 3.831086675762972*^9, 3.8310883982145433`*^9, 3.831089432472085*^9, 3.8310895538054*^9, { 3.831090045452672*^9, 3.831090054373206*^9}, {3.831090106351191*^9, 3.831090135089933*^9}, {3.831090195570376*^9, 3.8310902067729397`*^9}, 3.831091158467819*^9, 3.831113732950795*^9, 3.831113774456149*^9, 3.831114121816136*^9, 3.831114603012059*^9, {3.831114634767717*^9, 3.831114647267293*^9}, 3.831114781459367*^9, {3.831116162343802*^9, 3.831116182717697*^9}, 3.831116848790416*^9, 3.831116879481612*^9, { 3.831122086375164*^9, 3.831122098811386*^9}, {3.8311221630541286`*^9, 3.831122172288553*^9}, {3.831122219410223*^9, 3.831122257867687*^9}, 3.831122302607841*^9, 3.8311224123907022`*^9, 3.831122463557585*^9, 3.831122535424923*^9, 3.831122601531713*^9, {3.831122709456368*^9, 3.831122729049098*^9}, 3.831125950159609*^9, {3.8311260810683107`*^9, 3.831126101291016*^9}, {3.83112616116888*^9, 3.8311261732572937`*^9}, 3.831126270136245*^9, 3.831139001383645*^9, 3.831139034894452*^9, { 3.8311390797257853`*^9, 3.831139096495474*^9}, 3.8311391520341063`*^9, { 3.831139187064781*^9, 3.8311392165042562`*^9}, 3.831552873355103*^9, { 3.83155345791722*^9, 3.831553483767668*^9}, 3.8320681489121304`*^9, 3.8320682380737886`*^9, 3.832068320428842*^9, 3.832069208784215*^9, 3.8320692421395473`*^9, 3.832069416244701*^9, 3.832069465870864*^9, { 3.832070659471138*^9, 3.832070682242206*^9}, 3.832071035748856*^9, 3.832071175060895*^9, 3.8320712933509083`*^9, 3.832071656839703*^9, 3.8320752622828913`*^9, 3.832154278985277*^9, 3.832154312852416*^9, 3.834150722393003*^9, 3.834179638862646*^9, 3.83417971760988*^9, 3.834179811662073*^9, {3.83450106170175*^9, 3.834501078858068*^9}, 3.834502885610161*^9, 3.834568964784423*^9, 3.834569045834074*^9, { 3.834608221545703*^9, 3.834608287914912*^9}, 3.834613259816371*^9}, CellLabel-> "Out[315]//MatrixForm=",ExpressionUUID->"e0ad8c18-1b83-4146-ae6d-\ 44a1abd94479"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "0.5131807550506294`"}], ",", "1.2389279387920946`", ",", "1.2389279387920946`", ",", "1.2389279387920946`", ",", "1.2389279387920946`"}], "}"}]], "Output", CellChangeTimes->{ 3.8310808181124763`*^9, 3.831080860753619*^9, {3.8310809469470253`*^9, 3.831080964993269*^9}, {3.831081004545352*^9, 3.8310810231079683`*^9}, { 3.831081057456705*^9, 3.8310810835298233`*^9}, {3.831081138060302*^9, 3.831081152082024*^9}, {3.831081228011375*^9, 3.8310813133718987`*^9}, { 3.831081351183011*^9, 3.831081375990341*^9}, {3.831081436575982*^9, 3.831081459114427*^9}, 3.8310815067955008`*^9, 3.831081552992103*^9, { 3.83108166276462*^9, 3.831081748301043*^9}, 3.831081787574188*^9, 3.831081918210712*^9, {3.831082148360456*^9, 3.831082160262785*^9}, 3.831082839195043*^9, {3.831082952781499*^9, 3.831083055035534*^9}, { 3.831083090755866*^9, 3.831083131568055*^9}, {3.8310831915345984`*^9, 3.831083203976349*^9}, 3.831083520250152*^9, 3.831083591479097*^9, { 3.831083638426196*^9, 3.831083733223453*^9}, 3.831083820433951*^9, { 3.8310838540743637`*^9, 3.831083872688506*^9}, 3.831083931218514*^9, 3.831083964991393*^9, {3.831084007446355*^9, 3.8310840240544577`*^9}, { 3.831084126438016*^9, 3.8310841465491047`*^9}, 3.8310843794593287`*^9, { 3.831084496467749*^9, 3.8310845160449467`*^9}, 3.831084597631049*^9, { 3.83108464142036*^9, 3.831084683108674*^9}, 3.831084723554061*^9, 3.8310853242106657`*^9, 3.831085358717671*^9, 3.831085411190071*^9, { 3.8310854646012907`*^9, 3.8310855005741*^9}, {3.831085613523452*^9, 3.831085633371294*^9}, 3.8310856714538593`*^9, 3.831085744893196*^9, 3.8310857985908613`*^9, {3.83108586096107*^9, 3.8310858727632713`*^9}, 3.831086178663618*^9, 3.831086284067205*^9, 3.8310863535520144`*^9, { 3.83108641443573*^9, 3.831086438553163*^9}, 3.8310865100347013`*^9, { 3.831086563691814*^9, 3.831086603192316*^9}, 3.831086675762972*^9, 3.8310883982145433`*^9, 3.831089432472085*^9, 3.8310895538054*^9, { 3.831090045452672*^9, 3.831090054373206*^9}, {3.831090106351191*^9, 3.831090135089933*^9}, {3.831090195570376*^9, 3.8310902067729397`*^9}, 3.831091158467819*^9, 3.831113732950795*^9, 3.831113774456149*^9, 3.831114121816136*^9, 3.831114603012059*^9, {3.831114634767717*^9, 3.831114647267293*^9}, 3.831114781459367*^9, {3.831116162343802*^9, 3.831116182717697*^9}, 3.831116848790416*^9, 3.831116879481612*^9, { 3.831122086375164*^9, 3.831122098811386*^9}, {3.8311221630541286`*^9, 3.831122172288553*^9}, {3.831122219410223*^9, 3.831122257867687*^9}, 3.831122302607841*^9, 3.8311224123907022`*^9, 3.831122463557585*^9, 3.831122535424923*^9, 3.831122601531713*^9, {3.831122709456368*^9, 3.831122729049098*^9}, 3.831125950159609*^9, {3.8311260810683107`*^9, 3.831126101291016*^9}, {3.83112616116888*^9, 3.8311261732572937`*^9}, 3.831126270136245*^9, 3.831139001383645*^9, 3.831139034894452*^9, { 3.8311390797257853`*^9, 3.831139096495474*^9}, 3.8311391520341063`*^9, { 3.831139187064781*^9, 3.8311392165042562`*^9}, 3.831552873355103*^9, { 3.83155345791722*^9, 3.831553483767668*^9}, 3.8320681489121304`*^9, 3.8320682380737886`*^9, 3.832068320428842*^9, 3.832069208784215*^9, 3.8320692421395473`*^9, 3.832069416244701*^9, 3.832069465870864*^9, { 3.832070659471138*^9, 3.832070682242206*^9}, 3.832071035748856*^9, 3.832071175060895*^9, 3.8320712933509083`*^9, 3.832071656839703*^9, 3.8320752622828913`*^9, 3.832154278985277*^9, 3.832154312852416*^9, 3.834150722393003*^9, 3.834179638862646*^9, 3.83417971760988*^9, 3.834179811662073*^9, {3.83450106170175*^9, 3.834501078858068*^9}, 3.834502885610161*^9, 3.834568964784423*^9, 3.834569045834074*^9, { 3.834608221545703*^9, 3.834608287914912*^9}, 3.834613259822506*^9}, CellLabel-> "Out[316]=",ExpressionUUID->"bd55e7f1-e7ed-4687-b2e0-1b4acec683a0"], Cell[BoxData[ GraphicsBox[{CircleBox[{0., 0.}, 1.9486311405059256], CircleBox[{0., -1.1414816940458192}, 0.8071494464601066], CircleBox[{-1.1414816940458192, 0.}, 0.8071494464601066], CircleBox[{0., 1.1414816940458192}, 0.8071494464601066], CircleBox[{1.1414816940458192, 0.}, 0.8071494464601066]}, ImageSize->{443.87890625, Automatic}]], "Output", CellChangeTimes->{ 3.8310808181124763`*^9, 3.831080860753619*^9, {3.8310809469470253`*^9, 3.831080964993269*^9}, {3.831081004545352*^9, 3.8310810231079683`*^9}, { 3.831081057456705*^9, 3.8310810835298233`*^9}, {3.831081138060302*^9, 3.831081152082024*^9}, {3.831081228011375*^9, 3.8310813133718987`*^9}, { 3.831081351183011*^9, 3.831081375990341*^9}, {3.831081436575982*^9, 3.831081459114427*^9}, 3.8310815067955008`*^9, 3.831081552992103*^9, { 3.83108166276462*^9, 3.831081748301043*^9}, 3.831081787574188*^9, 3.831081918210712*^9, {3.831082148360456*^9, 3.831082160262785*^9}, 3.831082839195043*^9, {3.831082952781499*^9, 3.831083055035534*^9}, { 3.831083090755866*^9, 3.831083131568055*^9}, {3.8310831915345984`*^9, 3.831083203976349*^9}, 3.831083520250152*^9, 3.831083591479097*^9, { 3.831083638426196*^9, 3.831083733223453*^9}, 3.831083820433951*^9, { 3.8310838540743637`*^9, 3.831083872688506*^9}, 3.831083931218514*^9, 3.831083964991393*^9, {3.831084007446355*^9, 3.8310840240544577`*^9}, { 3.831084126438016*^9, 3.8310841465491047`*^9}, 3.8310843794593287`*^9, { 3.831084496467749*^9, 3.8310845160449467`*^9}, 3.831084597631049*^9, { 3.83108464142036*^9, 3.831084683108674*^9}, 3.831084723554061*^9, 3.8310853242106657`*^9, 3.831085358717671*^9, 3.831085411190071*^9, { 3.8310854646012907`*^9, 3.8310855005741*^9}, {3.831085613523452*^9, 3.831085633371294*^9}, 3.8310856714538593`*^9, 3.831085744893196*^9, 3.8310857985908613`*^9, {3.83108586096107*^9, 3.8310858727632713`*^9}, 3.831086178663618*^9, 3.831086284067205*^9, 3.8310863535520144`*^9, { 3.83108641443573*^9, 3.831086438553163*^9}, 3.8310865100347013`*^9, { 3.831086563691814*^9, 3.831086603192316*^9}, 3.831086675762972*^9, 3.8310883982145433`*^9, 3.831089432472085*^9, 3.8310895538054*^9, { 3.831090045452672*^9, 3.831090054373206*^9}, {3.831090106351191*^9, 3.831090135089933*^9}, {3.831090195570376*^9, 3.8310902067729397`*^9}, 3.831091158467819*^9, 3.831113732950795*^9, 3.831113774456149*^9, 3.831114121816136*^9, 3.831114603012059*^9, {3.831114634767717*^9, 3.831114647267293*^9}, 3.831114781459367*^9, {3.831116162343802*^9, 3.831116182717697*^9}, 3.831116848790416*^9, 3.831116879481612*^9, { 3.831122086375164*^9, 3.831122098811386*^9}, {3.8311221630541286`*^9, 3.831122172288553*^9}, {3.831122219410223*^9, 3.831122257867687*^9}, 3.831122302607841*^9, 3.8311224123907022`*^9, 3.831122463557585*^9, 3.831122535424923*^9, 3.831122601531713*^9, {3.831122709456368*^9, 3.831122729049098*^9}, 3.831125950159609*^9, {3.8311260810683107`*^9, 3.831126101291016*^9}, {3.83112616116888*^9, 3.8311261732572937`*^9}, 3.831126270136245*^9, 3.831139001383645*^9, 3.831139034894452*^9, { 3.8311390797257853`*^9, 3.831139096495474*^9}, 3.8311391520341063`*^9, { 3.831139187064781*^9, 3.8311392165042562`*^9}, 3.831552873355103*^9, { 3.83155345791722*^9, 3.831553483767668*^9}, 3.8320681489121304`*^9, 3.8320682380737886`*^9, 3.832068320428842*^9, 3.832069208784215*^9, 3.8320692421395473`*^9, 3.832069416244701*^9, 3.832069465870864*^9, { 3.832070659471138*^9, 3.832070682242206*^9}, 3.832071035748856*^9, 3.832071175060895*^9, 3.8320712933509083`*^9, 3.832071656839703*^9, 3.8320752622828913`*^9, 3.832154278985277*^9, 3.832154312852416*^9, 3.834150722393003*^9, 3.834179638862646*^9, 3.83417971760988*^9, 3.834179811662073*^9, {3.83450106170175*^9, 3.834501078858068*^9}, 3.834502885610161*^9, 3.834568964784423*^9, 3.834569045834074*^9, { 3.834608221545703*^9, 3.834608287914912*^9}, 3.834613259845879*^9}, CellLabel-> "Out[317]=",ExpressionUUID->"666c0c41-6bfc-4847-a5d2-14880c7266f6"] }, Open ]] }, WindowSize->{1425., 776.25}, WindowMargins->{{7.5, Automatic}, {7.5, Automatic}}, FrontEndVersion->"12.2 for Linux x86 (64-bit) (December 12, 2020)", StyleDefinitions->"Default.nb", ExpressionUUID->"cb87b367-1e4a-4501-8bdc-8262517a501c" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 318, 8, 58, "Text",ExpressionUUID->"73b90f40-aa75-45cc-9624-86406ff3f05e"], Cell[879, 30, 1102, 29, 29, "Input",ExpressionUUID->"42bda541-275e-4fa8-ad0f-dff973087409"], Cell[1984, 61, 28640, 879, 1293, "Input",ExpressionUUID->"c77ea1b4-464a-475d-935a-6ddd3139e407"], Cell[CellGroupData[{ Cell[30649, 944, 370, 9, 29, "Input",ExpressionUUID->"2acb2df6-0250-4f93-a487-d393ec6948a7"], Cell[31022, 955, 7643, 167, 261, "Output",ExpressionUUID->"00f58963-1bec-4f17-b581-aff807028e0f"] }, Open ]], Cell[CellGroupData[{ Cell[38702, 1127, 1191, 37, 29, "Input",ExpressionUUID->"1616f30b-f817-4bed-8186-0f3e4b738bac"], Cell[39896, 1166, 1238, 38, 33, "Output",ExpressionUUID->"71b7f1a7-5e88-4605-9406-a449116256ae"] }, Open ]], Cell[CellGroupData[{ Cell[41171, 1209, 1068, 17, 29, "Input",ExpressionUUID->"ced1cd28-39c9-46f3-906f-472b911c83b5"], Cell[42242, 1228, 1262, 19, 33, "Output",ExpressionUUID->"7d1068cd-4185-4697-a370-98c58525919d"] }, Open ]], Cell[CellGroupData[{ Cell[43541, 1252, 240, 5, 29, "Input",ExpressionUUID->"c3856cfc-8a90-4b2e-a7f8-03f066ea4f67"], Cell[43784, 1259, 2933, 67, 113, "Output",ExpressionUUID->"45374975-4620-44a5-bf25-34b9631e9eef"] }, Open ]], Cell[46732, 1329, 253, 4, 29, "Input",ExpressionUUID->"c0fe9f2e-e239-4938-84cd-0e217d1ee57c"], Cell[CellGroupData[{ Cell[47010, 1337, 640, 10, 29, "Input",ExpressionUUID->"0fcfbb19-b2bd-4a52-925c-ac50bcdaec4f"], Cell[47653, 1349, 5021, 70, 33, "Output",ExpressionUUID->"c7ca20bd-4c9c-483c-b50b-5698dafd9f80"] }, Open ]], Cell[CellGroupData[{ Cell[52711, 1424, 423, 8, 29, "Input",ExpressionUUID->"66dee78e-384d-4588-9d25-04b3c7b1aea7"], Cell[53137, 1434, 7084, 100, 33, "Output",ExpressionUUID->"4d944208-efd8-4bf9-8571-ed7c9065db41"] }, Open ]], Cell[CellGroupData[{ Cell[60258, 1539, 375, 8, 29, "Input",ExpressionUUID->"6c7429b3-1587-4d20-991f-d99f45021537"], Cell[60636, 1549, 6802, 97, 33, "Output",ExpressionUUID->"b86716b8-cefa-481e-bf7a-e62f17d96863"] }, Open ]], Cell[67453, 1649, 1916, 34, 29, "Input",ExpressionUUID->"dd7b3324-1ab6-43b0-9e24-406f40fb34ba"], Cell[69372, 1685, 1948, 48, 113, "Input",ExpressionUUID->"9e97f31a-ffaa-4f35-bb49-127a66bb73f7"], Cell[71323, 1735, 2603, 74, 195, "Input",ExpressionUUID->"0209d30a-517c-4664-b87b-84799191f438"], Cell[CellGroupData[{ Cell[73951, 1813, 8586, 209, 408, "Input",ExpressionUUID->"3a5095fb-bef7-4905-a187-ccc481ddd9ee"], Cell[82540, 2024, 4709, 78, 113, "Output",ExpressionUUID->"e0ad8c18-1b83-4146-ae6d-44a1abd94479"], Cell[87252, 2104, 3956, 58, 56, "Output",ExpressionUUID->"bd55e7f1-e7ed-4687-b2e0-1b4acec683a0"], Cell[91211, 2164, 4103, 59, 460, "Output",ExpressionUUID->"666c0c41-6bfc-4847-a5d2-14880c7266f6"] }, Open ]] } ] *)