1101 lines
37 KiB
Mathematica
1101 lines
37 KiB
Mathematica
|
|
(* Content-type: application/vnd.wolfram.mathematica *)
|
||
|
|
|
||
|
|
(*** Wolfram Notebook File ***)
|
||
|
|
(* http://www.wolfram.com/nb *)
|
||
|
|
|
||
|
|
(* CreatedBy='Mathematica 12.3' *)
|
||
|
|
|
||
|
|
(*CacheID: 234*)
|
||
|
|
(* Internal cache information:
|
||
|
|
NotebookFileLineBreakTest
|
||
|
|
NotebookFileLineBreakTest
|
||
|
|
NotebookDataPosition[ 158, 7]
|
||
|
|
NotebookDataLength[ 37943, 1092]
|
||
|
|
NotebookOptionsPosition[ 36764, 1066]
|
||
|
|
NotebookOutlinePosition[ 37157, 1082]
|
||
|
|
CellTagsIndexPosition[ 37114, 1079]
|
||
|
|
WindowFrame->Normal*)
|
||
|
|
|
||
|
|
(* Beginning of Notebook Content *)
|
||
|
|
Notebook[{
|
||
|
|
Cell["\<\
|
||
|
|
My growing list of utility functions I keep copy and pasting everywhere\
|
||
|
|
\>", "Text",
|
||
|
|
CellChangeTimes->{{3.836775550885043*^9,
|
||
|
|
3.8367755620440617`*^9}},ExpressionUUID->"30527bb2-1c83-410b-a9c3-\
|
||
|
|
cd217fac9ba3"],
|
||
|
|
|
||
|
|
Cell[BoxData[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"xyrtoabbc", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"x_", ",", "y_", ",", "r_"}], "}"}], "]"}], ":=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"r",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["x", "2"],
|
||
|
|
SuperscriptBox["r", "2"]], "+",
|
||
|
|
FractionBox[
|
||
|
|
SuperscriptBox["y", "2"],
|
||
|
|
SuperscriptBox["r", "2"]], "-", "1"}], ")"}]}], ",",
|
||
|
|
RowBox[{"1", "/", "r"}], ",",
|
||
|
|
RowBox[{"x", "/", "r"}], ",",
|
||
|
|
RowBox[{"y", "/", "r"}]}], "}"}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"graphFromG", "[", "G_", "]"}], ":=",
|
||
|
|
RowBox[{"PlanarGraph", "[",
|
||
|
|
RowBox[{"AdjacencyGraph", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"If", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"#", "\[Equal]",
|
||
|
|
RowBox[{"-", "1"}]}], ",", "1", ",", "0"}], "]"}], "&"}], "/@",
|
||
|
|
"#"}], "&"}], "/@", "G"}], ",",
|
||
|
|
RowBox[{"VertexLabels", "\[Rule]", "\"\<Name\>\""}]}], "]"}],
|
||
|
|
"]"}]}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"abbctoxyr", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"bt_", ",", "b_", ",", "h1_", ",", "h2_"}], "}"}], "]"}], ":=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"h1", "/", "b"}], ",",
|
||
|
|
RowBox[{"h2", "/", "b"}], ",",
|
||
|
|
RowBox[{"1", "/", "b"}]}], "}"}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"graphDuals", "[", "circs_", "]"}], ":=",
|
||
|
|
RowBox[{"Graphics", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"Red", ",", "Dashed", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Circle", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
"#", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
"#", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}],
|
||
|
|
"}"}], ",",
|
||
|
|
RowBox[{"Abs", "[",
|
||
|
|
RowBox[{"#", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}],
|
||
|
|
"]"}]}], "]"}], "&"}], "/@", "circs"}]}], "}"}],
|
||
|
|
"]"}]}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"graphCircles", "[", "circs_", "]"}], ":=",
|
||
|
|
RowBox[{"Graphics", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Circle", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"#", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}],
|
||
|
|
",",
|
||
|
|
RowBox[{
|
||
|
|
"#", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}]}], "}"}],
|
||
|
|
",",
|
||
|
|
RowBox[{"Abs", "[",
|
||
|
|
RowBox[{"#", "\[LeftDoubleBracket]", "3", "\[RightDoubleBracket]"}],
|
||
|
|
"]"}]}], "]"}], "&"}], "/@", "circs"}], "]"}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"graphAbbc", "[", "circs_", "]"}], ":=",
|
||
|
|
RowBox[{"graphCircles", "[",
|
||
|
|
RowBox[{"abbctoxyr", "/@", "circs"}], "]"}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"graphDualAbbc", "[", "circs_", "]"}], ":=",
|
||
|
|
RowBox[{"graphDuals", "[",
|
||
|
|
RowBox[{"abbctoxyr", "/@", "circs"}], "]"}]}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"findRoot", "[",
|
||
|
|
RowBox[{"tuple_", ",", "sigmas_"}], "]"}], ":=",
|
||
|
|
RowBox[{"Block", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{", "candidates", "}"}], ",", "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"candidates", "=",
|
||
|
|
RowBox[{"Select", "[",
|
||
|
|
RowBox[{"sigmas", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Total", "[",
|
||
|
|
RowBox[{"#", ".", "tuple"}], "]"}], "<",
|
||
|
|
RowBox[{"Total", "[", "tuple", "]"}]}], "&"}]}], "]"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"If", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Length", "[", "candidates", "]"}], "\[Equal]", "0"}], ",",
|
||
|
|
"tuple", ",",
|
||
|
|
RowBox[{"findRoot", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
"candidates", "\[LeftDoubleBracket]", "1",
|
||
|
|
"\[RightDoubleBracket]"}], ".", "tuple"}], ",", "sigmas"}],
|
||
|
|
"]"}]}], "]"}]}]}], "]"}]}], "\n",
|
||
|
|
RowBox[{"reflectx", ":=", GridBox[{
|
||
|
|
{"1", "0", "0", "0"},
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"0", "0",
|
||
|
|
RowBox[{"-", "1"}], "0"},
|
||
|
|
{"0", "0", "0", "1"}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{"reflecty", ":=", GridBox[{
|
||
|
|
{"1", "0", "0", "0"},
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"0", "0", "1", "0"},
|
||
|
|
{"0", "0", "0",
|
||
|
|
RowBox[{"-", "1"}]}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"scale", "[", "a_", "]"}], ":=", GridBox[{
|
||
|
|
{"a", "0", "0", "0"},
|
||
|
|
{"0",
|
||
|
|
RowBox[{"1", "/", "a"}], "0", "0"},
|
||
|
|
{"0", "0", "1", "0"},
|
||
|
|
{"0", "0", "0", "1"}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"rotate", "[", "\[Theta]_", "]"}], ":=", GridBox[{
|
||
|
|
{"1", "0", "0", "0"},
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"0", "0",
|
||
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}],
|
||
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]},
|
||
|
|
{"0", "0",
|
||
|
|
RowBox[{"-",
|
||
|
|
RowBox[{"Sin", "[", "\[Theta]", "]"}]}],
|
||
|
|
RowBox[{"Cos", "[", "\[Theta]", "]"}]}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"translate", "[",
|
||
|
|
RowBox[{"s_", ",", "t_"}], "]"}], ":=", GridBox[{
|
||
|
|
{"1",
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["s", "2"], "+",
|
||
|
|
SuperscriptBox["t", "2"]}],
|
||
|
|
RowBox[{"2", "s"}],
|
||
|
|
RowBox[{"2", "t"}]},
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"0", "s", "1", "0"},
|
||
|
|
{"0", "t", "0", "1"}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{"invert", ":=", GridBox[{
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"1", "0", "0", "0"},
|
||
|
|
{"0", "0", "1", "0"},
|
||
|
|
{"0", "0", "0", "1"}
|
||
|
|
}]}], "\n",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"invertAboutCircle", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"x_", ",", "y_", ",", "r_"}], "}"}], "]"}], ":=",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"translate", "[",
|
||
|
|
RowBox[{"x", ",", "y"}], "]"}], ".",
|
||
|
|
RowBox[{"scale", "[", "r", "]"}], ".", GridBox[{
|
||
|
|
{"0", "1", "0", "0"},
|
||
|
|
{"1", "0", "0", "0"},
|
||
|
|
{"0", "0", "1", "0"},
|
||
|
|
{"0", "0", "0", "1"}
|
||
|
|
}], ".",
|
||
|
|
RowBox[{"scale", "[",
|
||
|
|
RowBox[{"1", "/", "r"}], "]"}], ".",
|
||
|
|
RowBox[{"translate", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "x"}], ",",
|
||
|
|
RowBox[{"-", "y"}]}], "]"}]}]}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"invertAboutAbbc", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"bt_", ",", "b_", ",", "h1_", ",", "h2_"}], "}"}], "]"}], ":=",
|
||
|
|
RowBox[{"invertAboutCircle", "[",
|
||
|
|
RowBox[{"abbctoxyr", "[",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"bt", ",", "b", ",", "h1", ",", "h2"}], "}"}], "]"}],
|
||
|
|
"]"}]}]}], "Input",
|
||
|
|
CellChangeTimes->{{3.83518188899883*^9, 3.83518196723921*^9}, {
|
||
|
|
3.835189667119636*^9, 3.835189672844467*^9}, 3.8351900823026648`*^9, {
|
||
|
|
3.835190500475547*^9, 3.8351905140234118`*^9}, {3.835273965292259*^9,
|
||
|
|
3.8352739991796618`*^9}, {3.835274036684937*^9, 3.835274038678647*^9}, {
|
||
|
|
3.836773826590536*^9, 3.836773850497075*^9}, {3.83677440688564*^9,
|
||
|
|
3.836774407282791*^9}, {3.836775272970418*^9, 3.836775286241686*^9},
|
||
|
|
3.836775349044335*^9},
|
||
|
|
CellLabel->"In[1]:=",ExpressionUUID->"712f1eee-ffe3-4442-b0ef-88c55ebe5557"],
|
||
|
|
|
||
|
|
Cell["\<\
|
||
|
|
Function to find root tuple just given G. It needs to know three rows of G \
|
||
|
|
corresponding to three circles on a face. It defaults to {1, 2, 3}, but you \
|
||
|
|
can change that with Face->whatever. Likewise, it will default to inverting \
|
||
|
|
through circle 4 to make the bounded packing, but you can change that with \
|
||
|
|
Invert->whatever. I\[CloseCurlyQuote]d recommend not picking anything on the \
|
||
|
|
face, since two of them don\[CloseCurlyQuote]t work as they are lines and the \
|
||
|
|
other can often give extra unwanted symmetry. Finally, it defaults to doing \
|
||
|
|
everything numerically, but you can make it exact by specifying Exact->True.\
|
||
|
|
\>", "Text",
|
||
|
|
CellChangeTimes->{{3.836775573543792*^9, 3.836775580674549*^9}, {
|
||
|
|
3.836781087527965*^9, 3.836781202947666*^9}, {3.836781271184314*^9,
|
||
|
|
3.836781281672988*^9}},ExpressionUUID->"9ac07c3a-f945-48dc-946f-\
|
||
|
|
d840bb5c11e3"],
|
||
|
|
|
||
|
|
Cell[BoxData[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Options", "[", "rootTupleFromG", "]"}], "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"\"\<Face\>\"", "->",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], ",",
|
||
|
|
RowBox[{"\"\<Invert\>\"", "->", "4"}], ",",
|
||
|
|
RowBox[{"\"\<Exact\>\"", "->", "False"}]}], "}"}]}],
|
||
|
|
";"}], "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"rootTupleFromG", "[",
|
||
|
|
RowBox[{"G_", ",",
|
||
|
|
RowBox[{"OptionsPattern", "[", "]"}]}], "]"}], ":=",
|
||
|
|
RowBox[{"Block", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
"circs", ",", "P", ",", "v", ",", "c1", ",", "c2", ",", "c3", ",",
|
||
|
|
"face", ",", "invert", ",", "exact"}], "}"}], ",",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"P", "=", GridBox[{
|
||
|
|
{"0",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "/", "2"}], "0", "0"},
|
||
|
|
{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], "/", "2"}], "0", "0", "0"},
|
||
|
|
{"0", "0", "1", "0"},
|
||
|
|
{"0", "0", "0", "1"}
|
||
|
|
}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{"face", "=",
|
||
|
|
RowBox[{"OptionValue", "[", "\"\<Face\>\"", "]"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"invert", "=",
|
||
|
|
RowBox[{"OptionValue", "[", "\"\<Invert\>\"", "]"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"exact", "=",
|
||
|
|
RowBox[{"OptionValue", "[", "\"\<Exact\>\"", "]"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"v", "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"bt", ",", "b", ",", "h1", ",", "h2"}], "}"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"c1", "=",
|
||
|
|
RowBox[{"face", "[",
|
||
|
|
RowBox[{"[", "1", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{"c2", "=",
|
||
|
|
RowBox[{"face", "[",
|
||
|
|
RowBox[{"[", "2", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{"c3", "=",
|
||
|
|
RowBox[{"face", "[",
|
||
|
|
RowBox[{"[", "3", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{"circs", "=",
|
||
|
|
RowBox[{"Range", "[",
|
||
|
|
RowBox[{"Length", "[", "G", "]"}], "]"}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c1", "]"}], "]"}], "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"2", ",", "0", ",", "0", ",", "1"}], "}"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c2", "]"}], "]"}], "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"0", ",", "0", ",", "0", ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}]}], ";", "\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c3", "]"}], "]"}], "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
FractionBox[
|
||
|
|
RowBox[{"1", "-",
|
||
|
|
SuperscriptBox[
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c2", ",", "c3"}], "]"}], "]"}], "2"]}],
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c1", ",", "c3"}], "]"}], "]"}], "+",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c2", ",", "c3"}], "]"}], "]"}]}]], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c1", ",", "c3"}], "]"}], "]"}]}], "-",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c2", ",", "c3"}], "]"}], "]"}]}], ",", "0", ",",
|
||
|
|
RowBox[{"-",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c2", ",", "c3"}], "]"}], "]"}]}]}], "}"}]}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{"For", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"i", "=", "1"}], ",",
|
||
|
|
RowBox[{"i", "<=",
|
||
|
|
RowBox[{"Length", "[", "G", "]"}]}], ",",
|
||
|
|
RowBox[{"i", "++"}], ",", "\[IndentingNewLine]",
|
||
|
|
RowBox[{"If", "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"Not", "[",
|
||
|
|
RowBox[{"MemberQ", "[",
|
||
|
|
RowBox[{"i", ",", "face"}], "]"}], "]"}], ",",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "i", "]"}], "]"}], "=",
|
||
|
|
RowBox[{"v", "/.",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"If", "[",
|
||
|
|
RowBox[{"exact", ",", "Solve", ",", "NSolve"}], "]"}], "[",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c1", "]"}], "]"}], ".", "P", ".", "v"}], "==",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c1", ",", "i"}], "]"}], "]"}]}], "&&",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c2", "]"}], "]"}], ".", "P", ".", "v"}], "==",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c2", ",", "i"}], "]"}], "]"}]}], "&&",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "c3", "]"}], "]"}], ".", "P", ".", "v"}], "==",
|
||
|
|
RowBox[{"G", "[",
|
||
|
|
RowBox[{"[",
|
||
|
|
RowBox[{"c3", ",", "i"}], "]"}], "]"}]}], "&&",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
SuperscriptBox["h1", "2"], "+",
|
||
|
|
SuperscriptBox["h2", "2"], "-",
|
||
|
|
RowBox[{"b", " ", "bt"}]}], "==", "1"}]}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"bt", ",", "b", ",", "h1", ",", "h2"}], "}"}]}],
|
||
|
|
"]"}], "[",
|
||
|
|
RowBox[{"[", "1", "]"}], "]"}], ")"}]}]}], ";"}]}],
|
||
|
|
"\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}], ";",
|
||
|
|
"\[IndentingNewLine]",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"invertAboutAbbc", "[",
|
||
|
|
RowBox[{"circs", "[",
|
||
|
|
RowBox[{"[", "invert", "]"}], "]"}], "]"}], ".", "#"}], "&"}], "/@",
|
||
|
|
"circs"}]}]}], "\[IndentingNewLine]", "]"}]}]}], "Input",
|
||
|
|
CellChangeTimes->{{3.836772368781335*^9, 3.836772448964113*^9}, {
|
||
|
|
3.83677286709816*^9, 3.83677289675002*^9}, {3.83677333408657*^9,
|
||
|
|
3.836773426440043*^9}, {3.836773464273794*^9, 3.836773506259012*^9}, {
|
||
|
|
3.8367735508177977`*^9, 3.836773588147397*^9}, {3.836773868945211*^9,
|
||
|
|
3.836773888576144*^9}, {3.836774011684956*^9, 3.836774013795322*^9}, {
|
||
|
|
3.8367742134127903`*^9, 3.836774354444405*^9}, {3.836774442009274*^9,
|
||
|
|
3.836774451232985*^9}, {3.836774606345356*^9, 3.836774769320375*^9}, {
|
||
|
|
3.836774802029441*^9, 3.836774842000496*^9}, {3.836774975692432*^9,
|
||
|
|
3.836774977916898*^9}, {3.836775038086772*^9, 3.8367750548327227`*^9}, {
|
||
|
|
3.8367750936076937`*^9, 3.836775095953889*^9}, {3.836775197895112*^9,
|
||
|
|
3.836775247540461*^9}, {3.836775298645521*^9, 3.836775315775177*^9}, {
|
||
|
|
3.836775378516039*^9, 3.836775382545352*^9}, {3.8367820316307087`*^9,
|
||
|
|
3.836782036214923*^9}, 3.8367825449307203`*^9},
|
||
|
|
CellLabel->
|
||
|
|
"In[107]:=",ExpressionUUID->"8619e990-8f3c-4557-a370-b0aceddab3a5"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"icos", "=",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"1", ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1", ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",",
|
||
|
|
RowBox[{"-", "1"}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
RowBox[{"Sqrt", "[", "5", "]"}]}], ",", "1"}], "}"}]}], "}"}]}],
|
||
|
|
";"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.836773637317699*^9, 3.836773716053958*^9}, {
|
||
|
|
3.836773771358551*^9, 3.836773778846367*^9}, {3.836773915102661*^9,
|
||
|
|
3.83677398119965*^9}, {3.8367740492110558`*^9, 3.836774049587277*^9}, {
|
||
|
|
3.8367754625701113`*^9, 3.836775462934154*^9}, {3.8367812198847322`*^9,
|
||
|
|
3.836781220047799*^9}, {3.836781379804858*^9, 3.836781390355057*^9}},
|
||
|
|
CellLabel->"In[19]:=",ExpressionUUID->"e8ee6a05-c4eb-478e-af98-5d6b7fbfa46a"],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"root", "=",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"rootTupleFromG", "[",
|
||
|
|
RowBox[{"icos", ",",
|
||
|
|
RowBox[{"\"\<Invert\>\"", "->", "3"}], ",",
|
||
|
|
RowBox[{"\"\<Face\>\"", "->",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{"1", ",", "2", ",", "10"}], "}"}]}], ",",
|
||
|
|
RowBox[{"\"\<Exact\>\"", "->", "True"}]}], "]"}], "//",
|
||
|
|
"FullSimplify"}]}]], "Input",
|
||
|
|
CellChangeTimes->CompressedData["
|
||
|
|
1:eJxTTMoPSmViYGAQAWIQ7dJVNllg2hvH32cvgun+vNvzQPSXJY7zQbRCruVK
|
||
|
|
EP2hJxlM794evxlEH28oANOORTYHQfSJMy5nQPQiubwLIPpx7rorIHoXh8Vt
|
||
|
|
EH1m1qOHINrM/TeTIJCW+WDGDKLDGDnZQfStT0IiIJrhFJcliP6WzWUHok07
|
||
|
|
vZ1BdLpmvyuIFkpt9wLRmotKfED0jwP9cSDaPXwymBaYPKkcRO85UVEHop8X
|
||
|
|
LGsD0V1s3ztB9K7jmxaD6L6TyUtAtO/zCztA9LqmwF0g+v6h4yEiQNpobXU4
|
||
|
|
iD4xVTYORB97+CQFRCsoHckC0W2tV8A0AOvZnTQ=
|
||
|
|
"],
|
||
|
|
CellLabel->"In[20]:=",ExpressionUUID->"91e21391-15e5-4f71-a86a-70fa1b7d0f63"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"68", "+",
|
||
|
|
RowBox[{"28", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"13", "+",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"3", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"44", "+",
|
||
|
|
RowBox[{"20", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"17", "+",
|
||
|
|
RowBox[{"8", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"3", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{"2", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "2"}], "-",
|
||
|
|
SqrtBox["5"]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"39", "+",
|
||
|
|
RowBox[{"17", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"47", "+",
|
||
|
|
RowBox[{"21", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "37"}], "-",
|
||
|
|
RowBox[{"17", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"20", "+",
|
||
|
|
RowBox[{"9", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"11", "+",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"3", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "11"}], "-",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"5", "+",
|
||
|
|
RowBox[{"2", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"39", "+",
|
||
|
|
RowBox[{"17", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"46", "+",
|
||
|
|
RowBox[{"20", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "37"}], "-",
|
||
|
|
RowBox[{"17", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"19", "+",
|
||
|
|
RowBox[{"8", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"14", "+",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"3", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "6"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{"8", "+",
|
||
|
|
RowBox[{"3", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"11", "+",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"16", "+",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "11"}], "-",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"3", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"40", "+",
|
||
|
|
RowBox[{"18", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"47", "+",
|
||
|
|
RowBox[{"21", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "39"}], "-",
|
||
|
|
RowBox[{"17", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"20", "+",
|
||
|
|
RowBox[{"9", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"46", "+",
|
||
|
|
RowBox[{"20", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "4"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"9", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ")"}]}], ",",
|
||
|
|
RowBox[{"19", "+",
|
||
|
|
RowBox[{"8", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"14", "+",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"16", "+",
|
||
|
|
RowBox[{"6", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "6"}], " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{"3", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"2", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}]}], "}"}], ",",
|
||
|
|
RowBox[{"{",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"10", "+",
|
||
|
|
RowBox[{"4", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
RowBox[{"(",
|
||
|
|
RowBox[{"3", "+",
|
||
|
|
SqrtBox["5"]}], ")"}]}], ",",
|
||
|
|
RowBox[{
|
||
|
|
RowBox[{"-", "9"}], "-",
|
||
|
|
RowBox[{"5", " ",
|
||
|
|
SqrtBox["5"]}]}], ",",
|
||
|
|
RowBox[{"5", "+",
|
||
|
|
RowBox[{"2", " ",
|
||
|
|
SqrtBox["5"]}]}]}], "}"}]}], "}"}]], "Output",
|
||
|
|
CellChangeTimes->{
|
||
|
|
3.83677353485019*^9, {3.8367735702734957`*^9, 3.836773580101294*^9},
|
||
|
|
3.836773626672426*^9, 3.8367737074892073`*^9, 3.836773787882546*^9, {
|
||
|
|
3.836773892997232*^9, 3.836773986616167*^9}, {3.836774016999596*^9,
|
||
|
|
3.836774053862307*^9}, {3.836774106559168*^9, 3.836774159514324*^9},
|
||
|
|
3.8367743638879642`*^9, 3.83677442619223*^9, {3.836774457157482*^9,
|
||
|
|
3.8367745609996557`*^9}, {3.836774857772161*^9, 3.836774898603446*^9}, {
|
||
|
|
3.8367749306671677`*^9, 3.836775012834338*^9}, {3.8367750432842503`*^9,
|
||
|
|
3.836775099374961*^9}, 3.8367751571341887`*^9, {3.836775204207635*^9,
|
||
|
|
3.836775251826714*^9}, 3.836775319803225*^9, {3.836775353570438*^9,
|
||
|
|
3.83677541220298*^9}, {3.836775480754055*^9, 3.836775504168625*^9}, {
|
||
|
|
3.836775710248557*^9, 3.836775715714079*^9}, {3.836775884582399*^9,
|
||
|
|
3.836775891136197*^9}, {3.836781233827829*^9, 3.83678124429418*^9}, {
|
||
|
|
3.8367812978893347`*^9, 3.836781353440551*^9}, 3.836781399263618*^9,
|
||
|
|
3.836781439189076*^9},
|
||
|
|
CellLabel->"Out[20]=",ExpressionUUID->"38df915a-be40-4d71-b537-efd37c74906b"]
|
||
|
|
}, Open ]],
|
||
|
|
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
RowBox[{"graphAbbc", "[", "root", "]"}]], "Input",
|
||
|
|
CellChangeTimes->{{3.836781404223935*^9, 3.836781406064753*^9}},
|
||
|
|
CellLabel->"In[21]:=",ExpressionUUID->"1b485785-b18a-41cd-ae3f-e08589cba70c"],
|
||
|
|
|
||
|
|
Cell[BoxData[
|
||
|
|
GraphicsBox[{
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-4) (13 + 6 5^Rational[1, 2])/(68 + 28 5^Rational[1, 2]),
|
||
|
|
3 (9 + 4 5^Rational[1, 2])/(68 +
|
||
|
|
28 5^Rational[1, 2])}, {-0.8090169943749473, 0.41216488444600474`}],
|
||
|
|
NCache[(68 + 28 5^Rational[1, 2])^(-1), 0.00765638725853109]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-4) (9 + 4 5^Rational[1, 2])/(44 +
|
||
|
|
20 5^Rational[1, 2]), (17 + 8 5^Rational[1, 2])/(44 +
|
||
|
|
20 5^Rational[1, 2])}, {-0.8090169943749473, 0.3932372542187894}],
|
||
|
|
NCache[(44 + 20 5^Rational[1, 2])^(-1), 0.01127124296868428]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{-(2 + 5^Rational[1, 2])/(3 + 5^Rational[1, 2]),
|
||
|
|
Rational[-1, 2] (-2 - 5^Rational[1, 2])/(3 +
|
||
|
|
5^Rational[1, 2])}, {-0.8090169943749475, 0.4045084971874737}], NCache[
|
||
|
|
Rational[1, 2]/(3 + 5^Rational[1, 2]), 0.09549150281252629]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-37 - 17 5^Rational[1, 2])/(47 +
|
||
|
|
21 5^Rational[1, 2]), (20 + 9 5^Rational[1, 2])/(47 +
|
||
|
|
21 5^Rational[1, 2])}, {-0.7983738762488434, 0.42705098312484224`}],
|
||
|
|
NCache[(47 + 21 5^Rational[1, 2])^(-1), 0.010643118126104094`]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{Rational[1, 5] (-11 - 5 5^Rational[1, 2])/(3 + 5^Rational[1, 2]),
|
||
|
|
Rational[1, 5] (3 + 5^Rational[1, 2])^(-1) (5 +
|
||
|
|
2 5^Rational[1, 2])}, {-0.847213595499958, 0.3618033988749895}],
|
||
|
|
NCache[Rational[1, 5]/(3 + 5^Rational[1, 2]), 0.03819660112501052]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-37 - 17 5^Rational[1, 2])/(46 +
|
||
|
|
20 5^Rational[1, 2]), (19 + 8 5^Rational[1, 2])/(46 +
|
||
|
|
20 5^Rational[1, 2])}, {-0.8268521987499238, 0.40661365750002176`}],
|
||
|
|
NCache[(46 + 20 5^Rational[1, 2])^(-1), 0.011022762500036259`]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{-(2 + 5^Rational[1, 2])/(3 + 5^Rational[1, 2]),
|
||
|
|
Rational[1, 6] (3 + 5^Rational[1, 2])^(-1) (8 +
|
||
|
|
3 5^Rational[1, 2])}, {-0.8090169943749475, 0.4681694990624912}],
|
||
|
|
NCache[Rational[1, 6]/(3 + 5^Rational[1, 2]), 0.03183050093750876]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-11 - 5 5^Rational[1, 2])/(16 + 6 5^Rational[1, 2]),
|
||
|
|
3 (2 + 5^Rational[1, 2])/(16 +
|
||
|
|
6 5^Rational[1, 2])}, {-0.7540125221710139, 0.4320107332894405}],
|
||
|
|
NCache[(16 + 6 5^Rational[1, 2])^(-1), 0.03399463335527976]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-39 - 17 5^Rational[1, 2])/(47 +
|
||
|
|
21 5^Rational[1, 2]), (20 + 9 5^Rational[1, 2])/(47 +
|
||
|
|
21 5^Rational[1, 2])}, {-0.8196601125010515, 0.42705098312484224`}],
|
||
|
|
NCache[(47 + 21 5^Rational[1, 2])^(-1), 0.010643118126104094`]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-4) (9 + 4 5^Rational[1, 2])/(46 +
|
||
|
|
20 5^Rational[1, 2]), (19 + 8 5^Rational[1, 2])/(46 +
|
||
|
|
20 5^Rational[1, 2])}, {-0.791181789999971, 0.40661365750002176`}],
|
||
|
|
NCache[(46 + 20 5^Rational[1, 2])^(-1), 0.011022762500036259`]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{(-6) (2 + 5^Rational[1, 2])/(16 + 6 5^Rational[1, 2]),
|
||
|
|
3 (2 + 5^Rational[1, 2])/(16 +
|
||
|
|
6 5^Rational[1, 2])}, {-0.864021466578881, 0.4320107332894405}],
|
||
|
|
NCache[(16 + 6 5^Rational[1, 2])^(-1), 0.03399463335527976]],
|
||
|
|
CircleBox[
|
||
|
|
NCache[{Rational[1, 5] (-9 - 5 5^Rational[1, 2])/(3 + 5^Rational[1, 2]),
|
||
|
|
Rational[1, 5] (3 + 5^Rational[1, 2])^(-1) (5 +
|
||
|
|
2 5^Rational[1, 2])}, {-0.7708203932499369, 0.3618033988749895}],
|
||
|
|
NCache[Rational[1, 5]/(3 + 5^Rational[1, 2]),
|
||
|
|
0.03819660112501052]]}]], "Output",
|
||
|
|
CellChangeTimes->{3.8367814063844*^9, 3.836781439334742*^9},
|
||
|
|
CellLabel->"Out[21]=",ExpressionUUID->"4132ca7b-24a6-4589-bb4c-d5b579b34549"]
|
||
|
|
}, Open ]]
|
||
|
|
},
|
||
|
|
WindowSize->{1428., 779.25},
|
||
|
|
WindowMargins->{{6, Automatic}, {6, Automatic}},
|
||
|
|
FrontEndVersion->"12.3 for Linux x86 (64-bit) (June 19, 2021)",
|
||
|
|
StyleDefinitions->"Default.nb",
|
||
|
|
ExpressionUUID->"1f3ed8ec-6103-45a7-937b-bf03bf80e817"
|
||
|
|
]
|
||
|
|
(* End of Notebook Content *)
|
||
|
|
|
||
|
|
(* Internal cache information *)
|
||
|
|
(*CellTagsOutline
|
||
|
|
CellTagsIndex->{}
|
||
|
|
*)
|
||
|
|
(*CellTagsIndex
|
||
|
|
CellTagsIndex->{}
|
||
|
|
*)
|
||
|
|
(*NotebookFileOutline
|
||
|
|
Notebook[{
|
||
|
|
Cell[558, 20, 223, 5, 35, "Text",ExpressionUUID->"30527bb2-1c83-410b-a9c3-cd217fac9ba3"],
|
||
|
|
Cell[784, 27, 6715, 205, 965, "Input",ExpressionUUID->"712f1eee-ffe3-4442-b0ef-88c55ebe5557"],
|
||
|
|
Cell[7502, 234, 868, 13, 173, "Text",ExpressionUUID->"9ac07c3a-f945-48dc-946f-d840bb5c11e3"],
|
||
|
|
Cell[8373, 249, 7062, 179, 602, "Input",ExpressionUUID->"8619e990-8f3c-4557-a370-b0aceddab3a5"],
|
||
|
|
Cell[15438, 430, 10284, 311, 257, "Input",ExpressionUUID->"e8ee6a05-c4eb-478e-af98-5d6b7fbfa46a"],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[25747, 745, 835, 19, 29, "Input",ExpressionUUID->"91e21391-15e5-4f71-a86a-70fa1b7d0f63"],
|
||
|
|
Cell[26585, 766, 6459, 223, 103, "Output",ExpressionUUID->"38df915a-be40-4d71-b537-efd37c74906b"]
|
||
|
|
}, Open ]],
|
||
|
|
Cell[CellGroupData[{
|
||
|
|
Cell[33081, 994, 210, 3, 29, "Input",ExpressionUUID->"1b485785-b18a-41cd-ae3f-e08589cba70c"],
|
||
|
|
Cell[33294, 999, 3454, 64, 376, "Output",ExpressionUUID->"4132ca7b-24a6-4589-bb4c-d5b579b34549"]
|
||
|
|
}, Open ]]
|
||
|
|
}
|
||
|
|
]
|
||
|
|
*)
|
||
|
|
|