mirror of
http://CODE.RHODECODE.COM/u/O/O/O
synced 2024-09-20 02:56:42 -04:00
730 lines
29 KiB
Mathematica
730 lines
29 KiB
Mathematica
(* 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[ 28894, 721]
|
|
NotebookOptionsPosition[ 27728, 692]
|
|
NotebookOutlinePosition[ 28613, 718]
|
|
CellTagsIndexPosition[ 28570, 715]
|
|
WindowFrame->Normal*)
|
|
|
|
(* Beginning of Notebook Content *)
|
|
Notebook[{
|
|
Cell[BoxData[{
|
|
RowBox[{"ClearAll", "[",
|
|
RowBox[{"iCurvaturePlotHelper", ",", " ", "CurvaturePlot"}], "]"}], "\n",
|
|
RowBox[{
|
|
RowBox[{"iCurvaturePlotHelper", "[",
|
|
RowBox[{
|
|
RowBox[{"f_", "?",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Head", "[", "#", "]"}], " ", "=!=", " ", "List"}], " ",
|
|
"&"}], ")"}]}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t_", ",", " ", "tmin_", ",", " ", "tmax_"}], "}"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"x0_", ",", " ", "y0_"}], "}"}], ",", " ", "\[Theta]0_"}],
|
|
"}"}], ",", " ",
|
|
RowBox[{"opts", " ", ":", " ",
|
|
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], " ", ":=", " ",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"sol", ",", " ", "\[Theta]", ",", " ", "x", ",", " ", "y", ",", " ",
|
|
"if"}], "}"}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"sol", " ", "=", " ",
|
|
RowBox[{"NDSolve", "[",
|
|
RowBox[{
|
|
RowBox[{"{", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\[Theta]", "'"}], "[", "t", "]"}], " ", "==", " ", "f"}],
|
|
",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"x", "'"}], "[", "t", "]"}], " ", "==", " ",
|
|
RowBox[{"Cos", "[",
|
|
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"y", "'"}], "[", "t", "]"}], " ", "==", " ",
|
|
RowBox[{"Sin", "[",
|
|
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"\[Theta]", "[", "tmin", "]"}], " ", "==", " ",
|
|
"\[Theta]0"}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"x", "[", "tmin", "]"}], " ", "==", " ", "x0"}], ",", "\n",
|
|
" ",
|
|
RowBox[{
|
|
RowBox[{"y", "[", "tmin", "]"}], " ", "==", " ", "y0"}]}], "\n",
|
|
" ", "}"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"x", ",", " ", "y"}], "}"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",", " ",
|
|
"opts"}], "]"}]}], ";", "\n", " ",
|
|
RowBox[{"if", " ", "=", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"x", "[", "#", "]"}], ",", " ",
|
|
RowBox[{"y", "[", "#", "]"}]}], "}"}], " ", "&"}], " ", "/.", " ",
|
|
RowBox[{"First", "[", "sol", "]"}]}]}], ";", "\n", " ", "if"}]}],
|
|
"\n", " ", "]"}]}], "\n",
|
|
RowBox[{
|
|
RowBox[{"CurvaturePlot", "[",
|
|
RowBox[{"f_", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t_", ",", " ", "tmin_", ",", " ", "tmax_"}], "}"}], ",", " ",
|
|
RowBox[{"opts", " ", ":", " ",
|
|
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], " ", ":=", " ",
|
|
RowBox[{"CurvaturePlot", "[",
|
|
RowBox[{"f", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"0", ",", " ", "0"}], "}"}], ",", " ", "0"}], "}"}], ",", " ",
|
|
"opts"}], "]"}]}], "\n",
|
|
RowBox[{
|
|
RowBox[{"CurvaturePlot", "[",
|
|
RowBox[{"f_", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t_", ",", " ", "tmin_", ",", " ", "tmax_"}], "}"}], ",", " ",
|
|
RowBox[{"p", " ", ":", " ",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"x0_", ",", " ", "y0_"}], "}"}], ",", " ", "\[Theta]0_"}],
|
|
"}"}]}], ",", " ",
|
|
RowBox[{"opts", " ", ":", " ",
|
|
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], " ", ":=", " ",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
"\[Theta]", ",", " ", "x", ",", " ", "y", ",", " ", "sol", ",", " ",
|
|
"rlsplot", ",", " ", "rlsndsolve", ",", " ", "if", ",", " ", "ifs"}],
|
|
"}"}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"rlsplot", " ", "=", " ",
|
|
RowBox[{"FilterRules", "[",
|
|
RowBox[{
|
|
RowBox[{"{", "opts", "}"}], ",", " ",
|
|
RowBox[{"Options", "[", "ParametricPlot", "]"}]}], "]"}]}], ";", "\n",
|
|
" ",
|
|
RowBox[{"rlsndsolve", " ", "=", " ",
|
|
RowBox[{"FilterRules", "[",
|
|
RowBox[{
|
|
RowBox[{"{", "opts", "}"}], ",", " ",
|
|
RowBox[{"Options", "[", "NDSolve", "]"}]}], "]"}]}], ";", "\n", " ",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Head", "[", "f", "]"}], " ", "===", " ", "List"}], ",", "\n",
|
|
" ",
|
|
RowBox[{
|
|
RowBox[{"ifs", " ", "=", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"iCurvaturePlotHelper", "[",
|
|
RowBox[{"#", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
|
|
" ", "p", ",", " ",
|
|
RowBox[{"Evaluate", "@",
|
|
RowBox[{"(",
|
|
RowBox[{"Sequence", " ", "@@", " ", "rlsndsolve"}], ")"}]}]}],
|
|
"]"}], " ", "&"}], " ", "/@", " ", "f"}]}], ";", "\n", " ",
|
|
RowBox[{"ParametricPlot", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"#", "[", "tplot", "]"}], " ", "&"}], " ", "/@", " ",
|
|
"ifs"}], "]"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"tplot", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
|
|
" ",
|
|
RowBox[{"Evaluate", "@",
|
|
RowBox[{"(",
|
|
RowBox[{"Sequence", " ", "@@", " ", "rlsplot"}], ")"}]}]}],
|
|
"]"}]}], "\n", " ", ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"if", " ", "=", " ",
|
|
RowBox[{"iCurvaturePlotHelper", "[",
|
|
RowBox[{"f", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
|
|
" ", "p", ",", " ",
|
|
RowBox[{"Evaluate", "@",
|
|
RowBox[{"(",
|
|
RowBox[{"Sequence", " ", "@@", " ", "rlsndsolve"}], ")"}]}]}],
|
|
"]"}]}], ";", "\n", " ",
|
|
RowBox[{"ParametricPlot", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{"if", "[", "tplot", "]"}], "]"}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"tplot", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
|
|
" ",
|
|
RowBox[{"Evaluate", "@",
|
|
RowBox[{"(",
|
|
RowBox[{"Sequence", " ", "@@", " ", "rlsplot"}], ")"}]}]}],
|
|
"]"}]}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}]}], "Input",
|
|
TextAlignment->Center,
|
|
FontFamily->"Go Noto Current-Regular",
|
|
FontSize->10,
|
|
FontWeight->"Normal",
|
|
CellLabel->
|
|
"4/3/24 21:38:11 \
|
|
In[5275]:=",ExpressionUUID->"670c0d5c-4772-49bb-b74f-ae6a69be9ed0"],
|
|
|
|
Cell[BoxData[
|
|
RowBox[{"\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"ariasD", "[", "0", "]"}], " ", "=", " ", "1"}], ";"}], "\n",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"ariasD", "[",
|
|
RowBox[{"n_Integer", "?", "Positive"}], "]"}], " ", ":=", " ",
|
|
RowBox[{
|
|
RowBox[{"ariasD", "[", "n", "]"}], " ", "=", " ",
|
|
RowBox[{
|
|
RowBox[{"Sum", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"2", "^",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"k", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"k", " ", "-", " ", "1"}], ")"}]}], " ", "-", " ",
|
|
RowBox[{"n", " ",
|
|
RowBox[{"(",
|
|
RowBox[{"n", " ", "-", " ", "1"}], ")"}]}]}], ")"}], "/",
|
|
"2"}], ")"}]}], " ",
|
|
RowBox[{
|
|
RowBox[{"ariasD", "[", "k", "]"}], "/",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"n", " ", "-", " ", "k", " ", "+", " ", "1"}], ")"}],
|
|
"!"}]}]}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"k", ",", " ", "0", ",", " ",
|
|
RowBox[{"n", " ", "-", " ", "1"}]}], "}"}]}], "]"}], "/",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"2", "^", "n"}], " ", "-", " ", "1"}], ")"}]}]}]}], ";"}],
|
|
"\n",
|
|
RowBox[{
|
|
RowBox[{"iFabiusF", "[", "x_", "]"}], " ", ":=", " ",
|
|
RowBox[{"Module", "[",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"prec", " ", "=", " ",
|
|
RowBox[{"Precision", "[", "x", "]"}]}], ",", " ", "n", ",", " ", "p",
|
|
",", " ", "q", ",", " ", "s", ",", " ", "tol", ",", " ", "w", ",",
|
|
" ", "y", ",", " ", "z"}], "}"}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{"x", " ", "<", " ", "0"}], ",", " ",
|
|
RowBox[{"Return", "[",
|
|
RowBox[{"0", ",", " ", "Module"}], "]"}]}], "]"}], ";", " ",
|
|
RowBox[{"tol", " ", "=", " ",
|
|
RowBox[{"10", "^",
|
|
RowBox[{"(",
|
|
RowBox[{"-", "prec"}], ")"}]}]}], ";", "\n", " ",
|
|
RowBox[{"z", " ", "=", " ",
|
|
RowBox[{"SetPrecision", "[",
|
|
RowBox[{"x", ",", " ", "Infinity"}], "]"}]}], ";", " ",
|
|
RowBox[{"s", " ", "=", " ", "1"}], ";", " ",
|
|
RowBox[{"y", " ", "=", " ", "0"}], ";", "\n", " ",
|
|
RowBox[{"z", " ", "=", " ",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{"0", " ", "<=", " ", "z", " ", "<=", " ", "2"}], ",", " ",
|
|
RowBox[{"1", " ", "-", " ",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"1", " ", "-", " ", "z"}], "]"}]}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"q", " ", "=", " ",
|
|
RowBox[{"Quotient", "[",
|
|
RowBox[{"z", ",", " ", "2"}], "]"}]}], ";", "\n", " ",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"ThueMorse", "[", "q", "]"}], " ", "==", " ", "1"}],
|
|
",", " ",
|
|
RowBox[{"s", " ", "=", " ",
|
|
RowBox[{"-", "1"}]}]}], "]"}], ";", "\n", " ",
|
|
RowBox[{"1", " ", "-", " ",
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"1", " ", "-", " ", "z", " ", "+", " ",
|
|
RowBox[{"2", " ", "q"}]}], "]"}]}]}]}], "]"}]}], ";", "\n",
|
|
" ",
|
|
RowBox[{"While", "[",
|
|
RowBox[{
|
|
RowBox[{"z", " ", ">", " ", "0"}], ",", "\n", " ",
|
|
RowBox[{
|
|
RowBox[{"n", " ", "=", " ",
|
|
RowBox[{"-",
|
|
RowBox[{"Floor", "[",
|
|
RowBox[{"RealExponent", "[",
|
|
RowBox[{"z", ",", " ", "2"}], "]"}], "]"}]}]}], ";", " ",
|
|
RowBox[{"p", " ", "=", " ",
|
|
RowBox[{"2", "^", "n"}]}], ";", "\n", " ",
|
|
RowBox[{"z", " ", "-=", " ",
|
|
RowBox[{"1", "/", "p"}]}], ";", " ",
|
|
RowBox[{"w", " ", "=", " ", "1"}], ";", "\n", " ",
|
|
RowBox[{"Do", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"w", " ", "=", " ",
|
|
RowBox[{
|
|
RowBox[{"ariasD", "[", "m", "]"}], " ", "+", " ",
|
|
RowBox[{"p", " ", "z", " ",
|
|
RowBox[{"w", "/",
|
|
RowBox[{"(",
|
|
RowBox[{"n", " ", "-", " ", "m", " ", "+", " ", "1"}],
|
|
")"}]}]}]}]}], ";", " ",
|
|
RowBox[{"p", " ", "/=", " ", "2"}]}], ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"m", ",", " ", "n"}], "}"}]}], "]"}], ";", "\n", " ",
|
|
RowBox[{"y", " ", "=", " ",
|
|
RowBox[{"w", " ", "-", " ", "y"}]}], ";", "\n", " ",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Abs", "[", "w", "]"}], " ", "<", " ",
|
|
RowBox[{
|
|
RowBox[{"Abs", "[", "y", "]"}], " ", "tol"}]}], ",", " ",
|
|
RowBox[{"Break", "[", "]"}]}], "]"}]}]}], "]"}], ";", "\n", " ",
|
|
RowBox[{"SetPrecision", "[",
|
|
RowBox[{
|
|
RowBox[{"s", " ",
|
|
RowBox[{"Abs", "[", "y", "]"}]}], ",", " ", "prec"}], "]"}]}]}],
|
|
"]"}]}], "\n",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"FabiusF", "[", "Infinity", "]"}], " ", "=", " ",
|
|
RowBox[{"Interval", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], "]"}]}], ";"}], "\n",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"FabiusF", "[",
|
|
RowBox[{"x_", "?", "NumberQ"}], "]"}], " ", "/;", " ",
|
|
RowBox[{"If", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Im", "[", "x", "]"}], " ", "==", " ", "0"}], ",", " ",
|
|
RowBox[{"TrueQ", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Composition", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"BitAnd", "[",
|
|
RowBox[{"#", ",", " ",
|
|
RowBox[{"#", " ", "-", " ", "1"}]}], "]"}], " ", "&"}], ",",
|
|
" ", "Denominator"}], "]"}], "[", "x", "]"}], " ", "==", " ",
|
|
"0"}], "]"}], ",", " ", "False"}], "]"}]}], " ", ":=", " ",
|
|
RowBox[{"iFabiusF", "[", "x", "]"}]}], "\n",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"Derivative", "[", "n_Integer", "]"}], "[", "FabiusF", "]"}],
|
|
" ", ":=", " ",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"2", "^",
|
|
RowBox[{"(",
|
|
RowBox[{"n", " ",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"n", " ", "+", " ", "1"}], ")"}], "/", "2"}]}], ")"}]}],
|
|
" ",
|
|
RowBox[{"FabiusF", "[",
|
|
RowBox[{
|
|
RowBox[{"2", "^", "n"}], " ", "#"}], "]"}]}], " ", "&"}]}], "\n",
|
|
RowBox[{
|
|
RowBox[{"SetAttributes", "[",
|
|
RowBox[{"FabiusF", ",", " ",
|
|
RowBox[{"{",
|
|
RowBox[{"NumericFunction", ",", " ", "Listable"}], "}"}]}], "]"}],
|
|
";"}]}]}]], "Input",
|
|
FontFamily->"Go Noto Current-Regular",
|
|
FontSize->10,
|
|
FontWeight->"Normal",
|
|
CellLabel->
|
|
"4/3/24 21:38:11 \
|
|
In[5279]:=",ExpressionUUID->"a4addeb7-2708-41df-8367-f56fd1c4c60d"],
|
|
|
|
Cell[CellGroupData[{
|
|
|
|
Cell[BoxData[{
|
|
RowBox[{
|
|
RowBox[{"\:15e9", "=", "90"}], ";",
|
|
RowBox[{"\:042fR", "=",
|
|
RowBox[{"(",
|
|
RowBox[{"4", "/", "8"}], ")"}]}], ";"}], "\[IndentingNewLine]",
|
|
RowBox[{"Grid", "[",
|
|
RowBox[{"{",
|
|
RowBox[{"{", "\[IndentingNewLine]",
|
|
RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"\:1513\:1515", "=",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"WorkingPrecision", "\[Rule]", "\:041fW\:041f"}], ",",
|
|
RowBox[{"ImageSize", "\[Rule]", "256"}], ",",
|
|
RowBox[{"Axes", "\[Rule]", "True"}], ",",
|
|
RowBox[{"MaxRecursion", "\[Rule]", "0"}], ",",
|
|
RowBox[{"PlotPoints", "\[Rule]",
|
|
RowBox[{"1", "+",
|
|
SuperscriptBox["2", "\[CapitalPi]\[CapitalPi]"]}]}], ",",
|
|
RowBox[{"PlotStyle", "\[Rule]",
|
|
RowBox[{"Thickness", "[", "0.00001", "]"}]}], ",",
|
|
RowBox[{"PlotLegends", "\[Rule]", " ",
|
|
RowBox[{"Placed", "[",
|
|
RowBox[{"\"\<Expressions\>\"", ",",
|
|
RowBox[{"{",
|
|
RowBox[{"Center", ",", "Top"}], "}"}]}], "]"}]}], ",",
|
|
RowBox[{"PlotRangePadding", "\[Rule]",
|
|
RowBox[{"4", "/", "256"}]}], ",",
|
|
RowBox[{"PlotRange", "\[Rule]", " ", "Full"}], ",",
|
|
RowBox[{"Frame", "\[Rule]", " ", "True"}], ",",
|
|
RowBox[{"Axes", "\[Rule]", " ", "False"}], ",",
|
|
RowBox[{"GridLines", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{", "0", "}"}], ",",
|
|
RowBox[{"{", "0", "}"}]}], "}"}]}], " ", ",",
|
|
RowBox[{"PlotStyle", "\[Rule]",
|
|
RowBox[{"GrayLevel", "[",
|
|
RowBox[{"168", "/", "256"}], "]"}]}], ",",
|
|
RowBox[{"FrameStyle", "\[Rule]", " ",
|
|
RowBox[{"GrayLevel", "[",
|
|
RowBox[{"178", "/", "256"}], "]"}]}]}], "}"}]}], ";",
|
|
"\[IndentingNewLine]",
|
|
RowBox[{"\:1586\:1587", "=",
|
|
RowBox[{"{",
|
|
RowBox[{"x", ",", "0", ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi"}]}], "}"}]}],
|
|
";", "\[IndentingNewLine]",
|
|
RowBox[{"\:a5f3", "=",
|
|
RowBox[{"Piecewise", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"FabiusF", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"x", "/", "\:042fR"}], "/", "Pi"}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"360", "/", "\:15e9"}], ")"}], "/", "4"}]}], "]"}],
|
|
"]"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
|
|
"\:042fR", "*", "0"}], "<", "x", "<",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
|
|
"\:042fR"}]}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Abs", "[",
|
|
RowBox[{"FabiusF", "[",
|
|
RowBox[{"1", "-",
|
|
RowBox[{"(",
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{
|
|
RowBox[{"x", "/", "Pi"}],
|
|
RowBox[{
|
|
RowBox[{"(",
|
|
RowBox[{"360", "/", "\:15e9"}], ")"}], "/", "4"}]}],
|
|
")"}], "-", "\:042fR"}], ")"}], "/",
|
|
RowBox[{"(",
|
|
RowBox[{"1", "-", "\:042fR"}], ")"}]}], ")"}], ")"}]}],
|
|
"]"}], "]"}], ",",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
|
|
"\:042fR"}], "<", "x", "<",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
|
|
"1"}]}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]",
|
|
RowBox[{"Column", "[",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"CurvaturePlot", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{"SetPrecision", "[",
|
|
RowBox[{
|
|
RowBox[{"SetAccuracy", "[",
|
|
RowBox[{"\:a5f3", ",", "\:041fW\:041f"}], "]"}], ",",
|
|
"\:041fW\:041f"}], "]"}], "]"}], ",",
|
|
RowBox[{"Evaluate", "[", "\:1586\:1587", "]"}], ",",
|
|
RowBox[{"Evaluate", "[", "\:1513\:1515", "]"}], ",",
|
|
RowBox[{"FrameTicks", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Range", "[",
|
|
RowBox[{
|
|
RowBox[{"-", "16"}], ",", "16", ",",
|
|
RowBox[{"1", "/", "2"}]}], "]"}], ",",
|
|
RowBox[{"Range", "[",
|
|
RowBox[{
|
|
RowBox[{"-", "4"}], ",", "4", ",",
|
|
RowBox[{"1", "/", "2"}]}], "]"}]}], "}"}]}]}], " ", "]"}],
|
|
",",
|
|
RowBox[{"Plot", "[",
|
|
RowBox[{
|
|
RowBox[{"Evaluate", "[",
|
|
RowBox[{"SetPrecision", "[",
|
|
RowBox[{
|
|
RowBox[{"SetAccuracy", "[",
|
|
RowBox[{"\:a5f3", ",", "\:041fW\:041f"}], "]"}], ",",
|
|
"\:041fW\:041f"}], "]"}], "]"}], ",",
|
|
RowBox[{"Evaluate", "[", "\:1586\:1587", "]"}], ",",
|
|
RowBox[{"Evaluate", "[", "\:1513\:1515", "]"}], ",",
|
|
RowBox[{"FrameTicks", "\[Rule]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"Range", "[",
|
|
RowBox[{
|
|
RowBox[{
|
|
RowBox[{"-", "16"}], "*", "Pi"}], ",",
|
|
RowBox[{"16", "*", "Pi"}], ",",
|
|
RowBox[{"Pi", "/", "2"}]}], "]"}], ",",
|
|
RowBox[{"Range", "[",
|
|
RowBox[{
|
|
RowBox[{"-", "1"}], ",", "1", ",",
|
|
RowBox[{"1", "/", "2"}]}], "]"}]}], "}"}]}]}], " ", "]"}]}],
|
|
"}"}], "]"}]}], "\[IndentingNewLine]", ",", "\[IndentingNewLine]",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\:15e9", ",", "90"}], "}"}], ",", "0", ",", "360", ",",
|
|
RowBox[{"1", "/", "256"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\:042fR", ",",
|
|
RowBox[{"4", "/", "8"}], ",", "\"\<\[CenterDot]|\[CenterDot]\>\""}],
|
|
"}"}], ",", "0", ",", "1", ",",
|
|
RowBox[{"1", "/", "256"}]}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\[CapitalPi]\[CapitalPi]", ",", "8"}], "}"}], ",", "0", ",",
|
|
"16", ",", "1"}], "}"}], ",",
|
|
RowBox[{"{",
|
|
RowBox[{
|
|
RowBox[{"{",
|
|
RowBox[{"\:041fW\:041f", ",", "16"}], "}"}], ",", "0", ",", "64",
|
|
",", "1"}], "}"}], "\[IndentingNewLine]", ",",
|
|
RowBox[{"FrameMargins", "\[Rule]", "0"}]}], "\[IndentingNewLine]",
|
|
"]"}], "\[IndentingNewLine]", "}"}], "}"}], "]"}]}], "Input",
|
|
FontFamily->"Go Noto Current-Regular",
|
|
FontSize->10,
|
|
FontWeight->"Normal",ExpressionUUID->"adf5a779-403a-4c2b-985b-3306f9c44e28"],
|
|
|
|
Cell[BoxData[
|
|
TagBox[GridBox[{
|
|
{
|
|
TagBox[
|
|
StyleBox[
|
|
DynamicModuleBox[{XMPTools`Wrappers`Private`\:15e9$$ = 90,
|
|
XMPTools`Wrappers`Private`\:042fR$$ = Rational[1, 2],
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$ = 16,
|
|
XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$ = 8,
|
|
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
|
|
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$,
|
|
Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"",
|
|
Typeset`specs$$ = {{{
|
|
Hold[XMPTools`Wrappers`Private`\:15e9$$], 90}, 0, 360,
|
|
Rational[1, 256]}, {{
|
|
Hold[XMPTools`Wrappers`Private`\:042fR$$],
|
|
Rational[1, 2], "\[CenterDot]|\[CenterDot]"}, 0, 1,
|
|
Rational[1, 256]}, {{
|
|
Hold[XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$], 8}, 0,
|
|
16, 1}, {{
|
|
Hold[XMPTools`Wrappers`Private`\:041fW\:041f$$], 16}, 0, 64, 1}},
|
|
Typeset`size$$ = {256., {242., 247.}}, Typeset`update$$ = 0,
|
|
Typeset`initDone$$, Typeset`skipInitDone$$ = True},
|
|
DynamicBox[Manipulate`ManipulateBoxes[
|
|
1, StandardForm,
|
|
"Variables" :> {
|
|
XMPTools`Wrappers`Private`\:15e9$$ = 90,
|
|
XMPTools`Wrappers`Private`\:042fR$$ = Rational[1, 2],
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$ = 16,
|
|
XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$ = 8},
|
|
"ControllerVariables" :> {},
|
|
"OtherVariables" :> {
|
|
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
|
|
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
|
|
Typeset`specs$$, Typeset`size$$, Typeset`update$$,
|
|
Typeset`initDone$$, Typeset`skipInitDone$$},
|
|
"Body" :> (
|
|
XMPTools`Wrappers`Private`\:1513\:1515 = {
|
|
WorkingPrecision -> XMPTools`Wrappers`Private`\:041fW\:041f$$,
|
|
ImageSize -> 256, Axes -> True, MaxRecursion -> 0, PlotPoints ->
|
|
1 + 2^XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$,
|
|
PlotStyle -> Thickness[0.00001], PlotLegends ->
|
|
Placed["Expressions", {Center, Top}], PlotRangePadding -> 4/256,
|
|
PlotRange -> Full, Frame -> True, Axes -> False,
|
|
GridLines -> {{0}, {0}}, PlotStyle -> GrayLevel[168/256],
|
|
FrameStyle -> GrayLevel[178/256]};
|
|
XMPTools`Wrappers`Private`\:1586\:1587 = {
|
|
XMPTools`Wrappers`Private`x,
|
|
0, (XMPTools`Wrappers`Private`\:15e9$$/90) Pi};
|
|
XMPTools`Wrappers`Private`\:a5f3 = Piecewise[{{
|
|
Abs[
|
|
|
|
XMPTools`Wrappers`Private`FabiusF[((
|
|
XMPTools`Wrappers`Private`x/
|
|
XMPTools`Wrappers`Private`\:042fR$$)/
|
|
Pi) ((360/XMPTools`Wrappers`Private`\:15e9$$)/
|
|
4)]], (((XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
|
|
XMPTools`Wrappers`Private`\:042fR$$) 0 <
|
|
XMPTools`Wrappers`Private`x < ((
|
|
XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
|
|
XMPTools`Wrappers`Private`\:042fR$$}, {
|
|
Abs[
|
|
XMPTools`Wrappers`Private`FabiusF[
|
|
1 - ((XMPTools`Wrappers`Private`x/
|
|
Pi) ((360/XMPTools`Wrappers`Private`\:15e9$$)/4) -
|
|
XMPTools`Wrappers`Private`\:042fR$$)/(1 -
|
|
XMPTools`Wrappers`Private`\:042fR$$)]], ((
|
|
XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
|
|
XMPTools`Wrappers`Private`\:042fR$$ <
|
|
XMPTools`Wrappers`Private`x < ((
|
|
XMPTools`Wrappers`Private`\:15e9$$/90) Pi) 1}}]; Column[{
|
|
XMPTools`Wrappers`Private`CurvaturePlot[
|
|
Evaluate[
|
|
SetPrecision[
|
|
SetAccuracy[
|
|
XMPTools`Wrappers`Private`\:a5f3,
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$],
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$]],
|
|
Evaluate[XMPTools`Wrappers`Private`\:1586\:1587],
|
|
Evaluate[XMPTools`Wrappers`Private`\:1513\:1515], FrameTicks -> {
|
|
Range[-16, 16, 1/2],
|
|
Range[-4, 4, 1/2]}],
|
|
Plot[
|
|
Evaluate[
|
|
SetPrecision[
|
|
SetAccuracy[
|
|
XMPTools`Wrappers`Private`\:a5f3,
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$],
|
|
XMPTools`Wrappers`Private`\:041fW\:041f$$]],
|
|
Evaluate[XMPTools`Wrappers`Private`\:1586\:1587],
|
|
Evaluate[XMPTools`Wrappers`Private`\:1513\:1515], FrameTicks -> {
|
|
Range[(-16) Pi, 16 Pi, Pi/2],
|
|
Range[-1, 1, 1/2]}]}]),
|
|
"Specifications" :> {{{XMPTools`Wrappers`Private`\:15e9$$, 90}, 0,
|
|
360,
|
|
Rational[1, 256]}, {{XMPTools`Wrappers`Private`\:042fR$$,
|
|
Rational[1, 2], "\[CenterDot]|\[CenterDot]"}, 0, 1,
|
|
Rational[1, 256]}, {{
|
|
XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$, 8}, 0, 16,
|
|
1}, {{XMPTools`Wrappers`Private`\:041fW\:041f$$, 16}, 0, 64, 1}},
|
|
"Options" :> {FrameMargins -> 0}, "DefaultOptions" :> {}],
|
|
ImageSizeCache->{281., {312., 317.}},
|
|
SingleEvaluation->True],
|
|
Deinitialization:>None,
|
|
DynamicModuleValues:>{},
|
|
SynchronousInitialization->True,
|
|
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
|
|
UnsavedVariables:>{Typeset`initDone$$},
|
|
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
|
|
Deployed->True,
|
|
StripOnInput->False],
|
|
Manipulate`InterpretManipulate[1]]}
|
|
},
|
|
AutoDelete->False,
|
|
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
|
|
"Grid"]], "Output",
|
|
FontFamily->"Go Noto Current-Regular",
|
|
FontSize->10,ExpressionUUID->"87f7dffd-2a8e-4038-b9bf-2e250155a918"]
|
|
}, Open ]]
|
|
},
|
|
WindowSize->{1672, 980},
|
|
WindowMargins->{{0, Automatic}, {Automatic, 0}},
|
|
FrontEndVersion->"12.2 for Microsoft Windows (64-bit) (December 12, 2020)",
|
|
StyleDefinitions->Notebook[{
|
|
Cell[
|
|
StyleData[StyleDefinitions -> "Default.nb"]],
|
|
Cell[
|
|
StyleData[All], TextAlignment -> Center, FontFamily ->
|
|
"Go Noto Current-Regular", FontSize -> 10, FontWeight -> "Normal",
|
|
FontSlant -> "Plain", FontTracking -> "Plain",
|
|
FontVariations -> {"StrikeThrough" -> False, "Underline" -> False}]},
|
|
Visible -> False, FrontEndVersion ->
|
|
"12.2 for Microsoft Windows (64-bit) (December 12, 2020)", StyleDefinitions ->
|
|
"PrivateStylesheetFormatting.nb"],
|
|
ExpressionUUID->"87e41aa9-dea0-4ea9-92c2-e68f9a3b2137"
|
|
]
|
|
(* End of Notebook Content *)
|
|
|
|
(* Internal cache information *)
|
|
(*CellTagsOutline
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*CellTagsIndex
|
|
CellTagsIndex->{}
|
|
*)
|
|
(*NotebookFileOutline
|
|
Notebook[{
|
|
Cell[558, 20, 6723, 178, 499, "Input",ExpressionUUID->"670c0d5c-4772-49bb-b74f-ae6a69be9ed0"],
|
|
Cell[7284, 200, 6980, 185, 423, "Input",ExpressionUUID->"a4addeb7-2708-41df-8367-f56fd1c4c60d"],
|
|
Cell[CellGroupData[{
|
|
Cell[14289, 389, 7382, 181, 289, "Input",ExpressionUUID->"adf5a779-403a-4c2b-985b-3306f9c44e28"],
|
|
Cell[21674, 572, 6038, 117, 648, "Output",ExpressionUUID->"87f7dffd-2a8e-4038-b9bf-2e250155a918"]
|
|
}, Open ]]
|
|
}
|
|
]
|
|
*)
|
|
|