(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 40850, 1209] NotebookOptionsPosition[ 38859, 1143] NotebookOutlinePosition[ 39217, 1159] CellTagsIndexPosition[ 39174, 1156] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ "This", " ", "line", " ", "depends", " ", "on", " ", "your", " ", RowBox[{"directories", ".", " ", "You"}], " ", "can", " ", "just", " ", "drop", " ", RowBox[{"GREATER2", ".", "m"}], " ", "in", " ", "the", " ", "Mathematica", " ", "applications", " ", "directory", " ", "and", " ", "then", " ", "it", " ", "is", " ", "not", " ", "needed", " ", "at", " ", RowBox[{ "all", ".", "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"PrependTo", "[", RowBox[{"$Path", ",", " ", RowBox[{"ToFileName", "[", RowBox[{"{", RowBox[{ "$HomeDirectory", ",", " ", "\"\\"", ",", " ", "\"\\""}], "}"}], "]"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Needs", "[", "\"\\"", "]"}], ";"}]}]], "Input", CellChangeTimes->{{3.631696114484001*^9, 3.63169614100343*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Metric", " ", "of", " ", "Reissner"}], "-", "Nordstrom"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ds2", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"f", "[", "r", "]"}]}], RowBox[{"dt", "^", "2"}]}], " ", "+", " ", FractionBox[ RowBox[{"dr", "^", "2"}], RowBox[{"f", "[", "r", "]"}]], " ", "+", " ", RowBox[{ RowBox[{"r", "^", "2"}], " ", RowBox[{"(", RowBox[{ RowBox[{"d\[Theta]", "^", "2"}], " ", "+", " ", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "\[Theta]", "]"}], "^", "2"}], " ", RowBox[{"d\[Phi]", "^", "2"}]}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"X", " ", "=", " ", RowBox[{"{", RowBox[{"t", ",", "r", ",", "\[Theta]", ",", "\[Phi]"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Gdd", " ", "=", " ", RowBox[{"Metric", "[", RowBox[{"ds2", ",", " ", "X"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Inverse", " ", "metric"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Guu", " ", "=", " ", RowBox[{"IMetric", "[", "Gdd", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"plugf", " ", "=", " ", RowBox[{"{", RowBox[{"f", "\[Rule]", RowBox[{"Function", "[", RowBox[{ RowBox[{"{", "r", "}"}], ",", " ", RowBox[{"1", " ", "-", " ", RowBox[{"2", RowBox[{"m", "/", "r"}]}], " ", "+", " ", RowBox[{ RowBox[{"q", "^", "2"}], "/", RowBox[{"r", "^", "2"}]}]}]}], "]"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"Edd", " ", "=", " ", RowBox[{"EinsteinTensor", "[", RowBox[{"Gdd", ",", "X"}], "]"}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", " ", SubscriptBox["A", "\[Mu]"], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Ad", " ", "=", " ", RowBox[{"-", RowBox[{"{", RowBox[{ RowBox[{"q", "/", "r"}], ",", " ", "0", ",", " ", "0", ",", " ", "0"}], "}"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Fdd", " ", "=", " ", RowBox[{"FieldStrength", "[", RowBox[{"Ad", ",", " ", "X"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Tdd", " ", "=", RowBox[{ FractionBox["1", RowBox[{"4", "\[Pi]"}]], " ", RowBox[{"MaxwellStressTensor", "[", RowBox[{"Fdd", ",", " ", "Gdd"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Edd", "/.", "plugf"}], "//", "SMF"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Tdd", "/.", "plugf"}], "//", "SMF"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Edd", " ", "-", " ", RowBox[{"8", "\[Pi]", " ", "Tdd"}]}], "/.", "plugf"}], "//", "SMF"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->{{3.630933528262281*^9, 3.630933704193632*^9}, { 3.630934248257042*^9, 3.630934260808633*^9}, {3.6309342976766357`*^9, 3.6309343076611347`*^9}, {3.630934892433858*^9, 3.630934892544799*^9}, { 3.630934976583322*^9, 3.63093498247112*^9}, {3.630935117315804*^9, 3.630935141198339*^9}, {3.6309388314405527`*^9, 3.630938840014295*^9}, { 3.630938940277213*^9, 3.630938966773665*^9}, {3.6309395261066523`*^9, 3.630939538982024*^9}, {3.6316956891513147`*^9, 3.631695733280809*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}], SuperscriptBox["r", "6"]], "0", "0", "0"}, {"0", RowBox[{"-", FractionBox[ SuperscriptBox["q", "2"], RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}]]}], "0", "0"}, {"0", "0", FractionBox[ SuperscriptBox["q", "2"], SuperscriptBox["r", "2"]], "0"}, {"0", "0", "0", FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}], SuperscriptBox["r", "2"]]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.6309351214732313`*^9, 3.630935141568221*^9}, 3.630935366598802*^9, 3.630938662094602*^9, {3.630938834223134*^9, 3.630938840727396*^9}, {3.630938946946966*^9, 3.630938967093278*^9}, { 3.630939520937173*^9, 3.6309395393499002`*^9}, 3.630939874351602*^9, 3.6316437742133217`*^9, 3.63169573460979*^9, 3.631695867493219*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}], RowBox[{"8", " ", "\[Pi]", " ", SuperscriptBox["r", "6"]}]], "0", "0", "0"}, {"0", RowBox[{"-", FractionBox[ SuperscriptBox["q", "2"], RowBox[{"8", " ", "\[Pi]", " ", SuperscriptBox["r", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}]]}], "0", "0"}, {"0", "0", FractionBox[ SuperscriptBox["q", "2"], RowBox[{"8", " ", "\[Pi]", " ", SuperscriptBox["r", "2"]}]], "0"}, {"0", "0", "0", FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}], RowBox[{"8", " ", "\[Pi]", " ", SuperscriptBox["r", "2"]}]]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.6309351214732313`*^9, 3.630935141568221*^9}, 3.630935366598802*^9, 3.630938662094602*^9, {3.630938834223134*^9, 3.630938840727396*^9}, {3.630938946946966*^9, 3.630938967093278*^9}, { 3.630939520937173*^9, 3.6309395393499002`*^9}, 3.630939874351602*^9, 3.6316437742133217`*^9, 3.63169573460979*^9, 3.631695867496866*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0", "0"}, {"0", "0", "0", "0"}, {"0", "0", "0", "0"}, {"0", "0", "0", "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.6309351214732313`*^9, 3.630935141568221*^9}, 3.630935366598802*^9, 3.630938662094602*^9, {3.630938834223134*^9, 3.630938840727396*^9}, {3.630938946946966*^9, 3.630938967093278*^9}, { 3.630939520937173*^9, 3.6309395393499002`*^9}, 3.630939874351602*^9, 3.6316437742133217`*^9, 3.63169573460979*^9, 3.631695867500079*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{"Here", "'"}], "s", " ", "the", " ", "1", "st", " ", "row", " ", "of", " ", "the", " ", "Field", " ", "strength"}], ",", " ", RowBox[{"ie", " ", "the", " ", "electric", " ", "field"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Fdd", "[", RowBox[{"[", RowBox[{";;", ",", "1"}], "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.63169573883463*^9, 3.631695751481391*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", FractionBox["q", SuperscriptBox["r", "2"]], ",", "0", ",", "0"}], "}"}]], "Output", CellChangeTimes->{{3.631695739610424*^9, 3.631695751649431*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Change", " ", "coordinates", " ", "and", " ", "expand", " ", "near", " ", "the", " ", "horizon"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"X2", " ", "=", " ", RowBox[{"{", RowBox[{ "\[Eta]", ",", " ", "\[Epsilon]", ",", " ", "\[Theta]", ",", "\[Phi]"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"transformation", " ", "=", " ", RowBox[{"{", RowBox[{ RowBox[{"r", "\[Equal]", RowBox[{ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ RowBox[{"m", "^", "2"}], "-", RowBox[{"q", "^", "2"}]}]]}], ")"}], RowBox[{"(", RowBox[{"1", " ", "+", " ", RowBox[{"\[Epsilon]", "^", "2"}]}], ")"}]}]}], ",", " ", RowBox[{"\[Eta]", "\[Equal]", " ", RowBox[{"\[Lambda]", " ", "t"}]}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{"The", " ", "-", RowBox[{ RowBox[{"1", "'"}], "s", " ", "here", " ", "indicate", " ", "that", " ", "we", " ", "are", " ", "doing", " ", "a", " ", "coordinate", " ", "change", " ", "on", " ", "a", " ", "rank"}], "-", RowBox[{ RowBox[{"(", RowBox[{"0", ",", "2"}], ")"}], " ", "tensor"}]}], ",", " ", RowBox[{"ie", " ", "2", " ", "lower", " ", "indices"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ChangeCoords", "[", RowBox[{ RowBox[{"Gdd", "/.", "plugf"}], ",", " ", "X", ",", " ", "X2", ",", " ", "transformation", ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}]}], "]"}], "+", RowBox[{ RowBox[{"O", "[", "\[Epsilon]", "]"}], "^", "3"}]}], "//", "SMF"}]}]}]], "Input", CellChangeTimes->{{3.6316449342752953`*^9, 3.631645000875174*^9}, { 3.631695759204823*^9, 3.6316957978765497`*^9}}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"Solve", "::", "svars"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Equations may not give solutions for all \\\"solve\\\" \ variables. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\ \\\", ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/Solve/svars\\\", \ ButtonNote -> \\\"Solve::svars\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{{3.6316449863074007`*^9, 3.6316450010742893`*^9}, 3.6316957668649607`*^9, 3.631695798467567*^9}], Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"Solve", "::", "svars"}], "MessageName"], RowBox[{ ":", " "}], "\<\"Equations may not give solutions for all \\\"solve\\\" \ variables. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\ \\\", ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/Solve/svars\\\", \ ButtonNote -> \\\"Solve::svars\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{{3.6316449863074007`*^9, 3.6316450010742893`*^9}, 3.6316957668649607`*^9, 3.631695798511737*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"], "+", RowBox[{"m", " ", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}]}], ")"}], " ", SuperscriptBox["\[Epsilon]", "2"]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "2"], " ", SuperscriptBox["\[Lambda]", "2"]}]]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 2, 3, 1], Editable->False]}], SeriesData[$CellContext`\[Epsilon], 0, {(-2) ( GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^(-2) ( GREATER2`m^2 - GREATER2`q^2 + GREATER2`m (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2]) GREATER2`\[Lambda]^(-2)}, 2, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False]}, { InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "4"]}], RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"], "+", RowBox[{"m", " ", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["m", "2"]}], "-", RowBox[{"3", " ", SuperscriptBox["q", "2"]}], "+", RowBox[{"2", " ", "m", " ", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}]}], ")"}], " ", SuperscriptBox["\[Epsilon]", "2"]}], SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"], "+", RowBox[{"m", " ", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}]}], ")"}], "2"]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 0, 3, 1], Editable->False]}], SeriesData[$CellContext`\[Epsilon], 0, { 2 (GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^4/( GREATER2`m^2 - GREATER2`q^2 + GREATER2`m (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2]), 0, (GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^4 ( GREATER2`m^2 - GREATER2`q^2 + GREATER2`m (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^(-2) ( 2 GREATER2`m^2 - 3 GREATER2`q^2 + 2 GREATER2`m (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])}, 0, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False]}, { InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "2"], "+", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "2"], " ", SuperscriptBox["\[Epsilon]", "2"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 0, 3, 1], Editable->False]}], SeriesData[$CellContext`\[Epsilon], 0, {(GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^2, 0, 2 (GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^2}, 0, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False]}, { InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 3, 3, 1], Editable->False], InterpretationBox[ RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}], "+", RowBox[{"2", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"m", "+", SqrtBox[ RowBox[{ SuperscriptBox["m", "2"], "-", SuperscriptBox["q", "2"]}]]}], ")"}], "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"], " ", SuperscriptBox["\[Epsilon]", "2"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[Epsilon]", "]"}], "3"], SeriesData[$CellContext`\[Epsilon], 0, {}, 0, 3, 1], Editable->False]}], SeriesData[$CellContext`\[Epsilon], 0, {(GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^2 Sin[$CellContext`\[Theta]]^2, 0, 2 (GREATER2`m + (GREATER2`m^2 - GREATER2`q^2)^Rational[1, 2])^2 Sin[$CellContext`\[Theta]]^2}, 0, 3, 1], Editable->False]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.631644986390808*^9, 3.631645001591662*^9}, 3.631695766947844*^9, 3.631695798516366*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ RowBox[{"Let", "'"}], "s", " ", "check", " ", "the", " ", "Maxwell", " ", "equations"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DdFdd", " ", "=", " ", RowBox[{"CoD", "[", RowBox[{"Fdd", ",", " ", "Gdd", ",", " ", "X", ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"DdFdd", "//", "Dimensions"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Guu", " ", "=", " ", RowBox[{"IMetric", "[", "Gdd", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"DuFdd", " ", "=", " ", RowBox[{"Guu", ".", "DdFdd"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"Sum", "[", RowBox[{ RowBox[{"DuFdd", "[", RowBox[{"[", RowBox[{"\[Mu]", ",", " ", "\[Mu]", ",", " ", "\[Nu]"}], "]"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"\[Mu]", ",", "4"}], "}"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"\[Nu]", ",", "4"}], "}"}]}], "]"}], "//", "Simplify"}]}]}]], "Input", CellChangeTimes->{{3.631643980006702*^9, 3.631643997480947*^9}, { 3.631644028711145*^9, 3.63164418471557*^9}, {3.631695802931911*^9, 3.6316958094446497`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", "4", ",", "4"}], "}"}]], "Output", CellChangeTimes->{{3.631644048251389*^9, 3.631644055957999*^9}, 3.631644111251809*^9, 3.631644184930811*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]], "Output", CellChangeTimes->{{3.631644048251389*^9, 3.631644055957999*^9}, 3.631644111251809*^9, 3.631644184932664*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Some", " ", "other", " ", "curvature", " ", "functions"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"SCurvature", "[", RowBox[{"Gdd", ",", "X"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"%", "/.", "plugf"}], "//", "S"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Rdd", " ", "=", " ", RowBox[{"Ricci", "[", RowBox[{"Gdd", ",", "X"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Rdd", "/.", "plugf"}], "//", "SMF"}]}]}]], "Input", CellChangeTimes->{{3.6316442471026487`*^9, 3.631644265824581*^9}, { 3.63164433809256*^9, 3.6316443499655743`*^9}, {3.63169581824078*^9, 3.631695821931079*^9}}], Cell[BoxData[ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", " ", RowBox[{"f", "[", "r", "]"}]}], "+", RowBox[{"4", " ", "r", " ", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}], "+", RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{ SuperscriptBox["f", "\[Prime]\[Prime]", MultilineFunction->None], "[", "r", "]"}]}]}], SuperscriptBox["r", "2"]]}]], "Output", CellChangeTimes->{{3.631644253063279*^9, 3.6316442661209583`*^9}, { 3.631644346414673*^9, 3.631644350361208*^9}, 3.631695822100045*^9}], Cell[BoxData["0"], "Output", CellChangeTimes->{{3.631644253063279*^9, 3.6316442661209583`*^9}, { 3.631644346414673*^9, 3.631644350361208*^9}, 3.631695822102755*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}], SuperscriptBox["r", "6"]], "0", "0", "0"}, {"0", RowBox[{"-", FractionBox[ SuperscriptBox["q", "2"], RowBox[{ SuperscriptBox["r", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q", "2"], "+", RowBox[{"r", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", "m"}], "+", "r"}], ")"}]}]}], ")"}]}]]}], "0", "0"}, {"0", "0", FractionBox[ SuperscriptBox["q", "2"], SuperscriptBox["r", "2"]], "0"}, {"0", "0", "0", FractionBox[ RowBox[{ SuperscriptBox["q", "2"], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}], SuperscriptBox["r", "2"]]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.631644253063279*^9, 3.6316442661209583`*^9}, { 3.631644346414673*^9, 3.631644350361208*^9}, 3.631695822106443*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"\[CapitalGamma]", " ", "=", " ", RowBox[{"Christoffel", "[", RowBox[{"Gdd", ",", "X"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"ShowComponents", "[", RowBox[{"\[CapitalGamma]", ",", " ", "X", ",", " ", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "1"}], ",", RowBox[{"-", "1"}]}], "}"}], ",", " ", "\"\<\[CapitalGamma]\>\""}], "]"}]}], "Input", CellChangeTimes->{{3.6316446882326393`*^9, 3.631644712506423*^9}}], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","t"}, "Superscript"], "\<\"tr\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "r", "]"}], RowBox[{"2", " ", RowBox[{"f", "[", "r", "]"}]}]]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", GREATER2`t], "tr"], "=", Rational[1, 2] GREATER2`f[$CellContext`r]^(-1) Derivative[1][GREATER2`f][$CellContext`r]], Editable->False]], "Print", CellChangeTimes->{3.6316447147154016`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","t"}, "Superscript"], "\<\"rt\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "r", "]"}], RowBox[{"2", " ", RowBox[{"f", "[", "r", "]"}]}]]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", GREATER2`t], "rt"], "=", Rational[1, 2] GREATER2`f[$CellContext`r]^(-1) Derivative[1][GREATER2`f][$CellContext`r]], Editable->False]], "Print", CellChangeTimes->{3.6316447147181168`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","r"}, "Superscript"], "\<\"tt\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"f", "[", "r", "]"}], " ", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "r", "]"}]}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`r], "tt"], "=", Rational[1, 2] GREATER2`f[$CellContext`r] Derivative[1][GREATER2`f][$CellContext`r]], Editable->False]], "Print", CellChangeTimes->{3.631644714721683*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","r"}, "Superscript"], "\<\"rr\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{"-", FractionBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "r", "]"}], RowBox[{"2", " ", RowBox[{"f", "[", "r", "]"}]}]]}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`r], "rr"], "=", Rational[-1, 2] GREATER2`f[$CellContext`r]^(-1) Derivative[1][GREATER2`f][$CellContext`r]], Editable->False]], "Print", CellChangeTimes->{3.6316447147246923`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","r"}, "Superscript"], "\<\"\[Theta]\[Theta]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{ RowBox[{"-", "r"}], " ", RowBox[{"f", "[", "r", "]"}]}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`r], "\[Theta]\[Theta]"], "=", -$CellContext`r GREATER2`f[$CellContext`r]], Editable->False]], "Print", CellChangeTimes->{3.6316447147275867`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","r"}, "Superscript"], "\<\"\[Phi]\[Phi]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{ RowBox[{"-", "r"}], " ", RowBox[{"f", "[", "r", "]"}], " ", SuperscriptBox[ RowBox[{"Sin", "[", "\[Theta]", "]"}], "2"]}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`r], "\[Phi]\[Phi]"], "=", -$CellContext`r GREATER2`f[$CellContext`r] Sin[$CellContext`\[Theta]]^2], Editable->False]], "Print", CellChangeTimes->{3.6316447147297373`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Theta]"}, "Superscript"], "\<\"r\[Theta]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox["1", "r"]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Theta]], "r\[Theta]"], "=", $CellContext`r^(-1)], Editable->False]], "Print", CellChangeTimes->{3.631644714732443*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Theta]"}, "Superscript"], "\<\"\[Theta]r\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox["1", "r"]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Theta]], "\[Theta]r"], "=", $CellContext`r^(-1)], Editable->False]], "Print", CellChangeTimes->{3.6316447147348022`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Theta]"}, "Superscript"], "\<\"\[Phi]\[Phi]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{ RowBox[{"-", RowBox[{"Cos", "[", "\[Theta]", "]"}]}], " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Theta]], "\[Phi]\[Phi]"], "=", -Cos[$CellContext`\[Theta]] Sin[$CellContext`\[Theta]]], Editable->False]], "Print", CellChangeTimes->{3.631644714736973*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Phi]"}, "Superscript"], "\<\"r\[Phi]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox["1", "r"]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Phi]], "r\[Phi]"], "=", $CellContext`r^(-1)], Editable->False]], "Print", CellChangeTimes->{3.631644714739079*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Phi]"}, "Superscript"], "\<\"\[Theta]\[Phi]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{"Cot", "[", "\[Theta]", "]"}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Phi]], "\[Theta]\[Phi]"], "=", Cot[$CellContext`\[Theta]]], Editable->False]], "Print", CellChangeTimes->{3.63164471474117*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Phi]"}, "Superscript"], "\<\"\[Phi]r\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", FractionBox["1", "r"]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Phi]], "\[Phi]r"], "=", $CellContext`r^(-1)], Editable->False]], "Print", CellChangeTimes->{3.6316447147432528`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{ SubscriptBox[ TemplateBox[{"\"\[CapitalGamma]\"","\[Phi]"}, "Superscript"], "\<\"\[Phi]\[Theta]\"\>"], "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", RowBox[{"Cot", "[", "\[Theta]", "]"}]}], SequenceForm[ Subscript[ Superscript["\[CapitalGamma]", $CellContext`\[Phi]], "\[Phi]\[Theta]"], "=", Cot[$CellContext`\[Theta]]], Editable->False]], "Print", CellChangeTimes->{3.631644714745352*^9}] }, Open ]] }, Open ]], Cell[BoxData["\[AliasDelimiter]"], "Input", CellChangeTimes->{3.6316582352856693`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{ RowBox[{ RowBox[{ "The", " ", "\"\\"", " ", "function", " ", "is", " ", "built"}], "-", "in"}], ",", " ", RowBox[{ "but", " ", "we", " ", "could", " ", "also", " ", "compute", " ", "it", " ", "directly", " ", "as", " ", "an", " ", "antisymmetrized", " ", "partial", " ", "derivative"}]}], " ", "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"AnotherFdd", " ", "=", " ", RowBox[{"2", " ", RowBox[{"antisymmetrize", "[", RowBox[{"SimpleDeriv", "[", RowBox[{"Ad", ",", " ", "X"}], "]"}], "]"}]}]}], "\[IndentingNewLine]", "Fdd"}]}]], "Input", CellChangeTimes->{{3.631643889463455*^9, 3.631643913881877*^9}, { 3.631695831778452*^9, 3.631695863745551*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox["q", SuperscriptBox["r", "2"]]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["q", SuperscriptBox["r", "2"]], ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.631643925170394*^9, {3.6316958378428802`*^9, 3.6316958711987677`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", FractionBox["q", SuperscriptBox["r", "2"]]}], ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ FractionBox["q", SuperscriptBox["r", "2"]], ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.631643925170394*^9, {3.6316958378428802`*^9, 3.631695871201848*^9}}] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.631645223422081*^9, 3.631645226911664*^9}}] }, WindowSize->{797, 616}, WindowMargins->{{309, Automatic}, {-46, Automatic}}, FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (January 25, \ 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[557, 20, 1096, 26, 148, "Input"], Cell[CellGroupData[{ Cell[1678, 50, 3690, 97, 399, "Input"], Cell[5371, 149, 2064, 60, 158, "Output"], Cell[7438, 211, 2217, 63, 160, "Output"], Cell[9658, 276, 1016, 24, 92, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10711, 305, 482, 12, 46, "Input"], Cell[11196, 319, 207, 5, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11440, 329, 2062, 57, 132, "Input"], Cell[13505, 388, 520, 10, 24, "Message"], Cell[14028, 400, 520, 10, 24, "Message"], Cell[14551, 412, 9013, 245, 196, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23601, 662, 1417, 38, 114, "Input"], Cell[25021, 702, 197, 4, 28, "Output"], Cell[25221, 708, 207, 4, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[25465, 717, 735, 18, 97, "Input"], Cell[26203, 737, 642, 18, 50, "Output"], Cell[26848, 757, 168, 2, 28, "Output"], Cell[27019, 761, 1847, 57, 158, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[28903, 823, 493, 12, 46, "Input"], Cell[CellGroupData[{ Cell[29421, 839, 643, 19, 42, "Print"], Cell[30067, 860, 643, 19, 42, "Print"], Cell[30713, 881, 650, 19, 39, "Print"], Cell[31366, 902, 674, 20, 42, "Print"], Cell[32043, 924, 527, 15, 24, "Print"], Cell[32573, 941, 628, 18, 26, "Print"], Cell[33204, 961, 450, 13, 39, "Print"], Cell[33657, 976, 452, 13, 39, "Print"], Cell[34112, 991, 592, 16, 26, "Print"], Cell[34707, 1009, 442, 13, 39, "Print"], Cell[35152, 1024, 482, 14, 26, "Print"], Cell[35637, 1040, 444, 13, 39, "Print"], Cell[36084, 1055, 483, 14, 26, "Print"] }, Open ]] }, Open ]], Cell[36594, 1073, 87, 1, 28, "Input"], Cell[CellGroupData[{ Cell[36706, 1078, 856, 21, 114, "Input"], Cell[37565, 1101, 591, 17, 45, "Output"], Cell[38159, 1120, 589, 17, 103, "Output"] }, Open ]], Cell[38763, 1140, 92, 1, 28, "Input"] } ] *) (* End of internal cache information *)