(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 62645, 1825]*) (*NotebookOutlinePosition[ 112320, 3439]*) (* CellTagsIndexPosition[ 112276, 3435]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["Schwarzschild Metric", FontSize->36, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Subsubtitle", TextAlignment->Center, FontColor->RGBColor[0, 1, 1]], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["\<\ This notebook uses the MathTensor package(Parker&Christensen) to determine \ the geodesic equations and the constants of the motion for the Schwarzchild \ metric. MathTensor is used to calculate all relevant tensors, which is \ included in the SchwarzschildOut section. William C. Collins, Space Systems, \ USNRL(retired), bccollins1@comcast.net. \ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["MathTensor package", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Unprotect[TensorQ]\)], "Input", CellLabel->"In[1]:="], Cell[BoxData[ \({"TensorQ"}\)], "Output", CellLabel->"Out[1]="] }, Open ]], Cell[BoxData[ \(\(Off[General::"\"];\)\)], "Input", CellLabel->"In[2]:="], Cell[BoxData[ \(\(Off[General::"\"];\)\)], "Input", CellLabel->"In[3]:=", InitializationCell->True], Cell[CellGroupData[{ Cell[BoxData[ \(<< mathtensor.m\)], "Input", CellLabel->"In[4]:="], Cell[BoxData[ \("Loading MathTensor for DOS/Windows . . ."\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("\n\n"\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("==================================================="\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("MathTensor (TM) 2.2 (DOS/Windows(R)) (Jun 1, 1994)"\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("by Leonard Parker and Steven M. 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If you want one,"\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("you must edit the file called Conventions.m,"\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("or enter a command to interactively set units."\)], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ InterpretationBox[\("Units: "\[InvisibleSpace]{}\), SequenceForm[ "Units: ", {}], Editable->False]], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ InterpretationBox[\("Sign conventions: Rmsign = "\[InvisibleSpace]1\ \[InvisibleSpace]" Rcsign = "\[InvisibleSpace]1\), SequenceForm[ "Sign conventions: Rmsign = ", 1, " Rcsign = ", 1], Editable->False]], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ InterpretationBox[\("MetricgSign = "\[InvisibleSpace]1\[InvisibleSpace]" \ DetgSign = "\[InvisibleSpace]\(-1\)\), SequenceForm[ "MetricgSign = ", 1, " DetgSign = ", -1], Editable->False]], "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("TensorForm turned on,\nShowTime turned off,\nMetricgFlag = True."\)], \ "Print", CellLabel->"From In[4]:="], Cell[BoxData[ \("========================================="\)], "Print", CellLabel->"From In[4]:="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(<< SchwarzschildOut.m\)], "Input", CellLabel->"In[5]:="], Cell[BoxData[ \("MetricgFlag has been turned off."\)], "Print", CellLabel->"From In[5]:="] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["SchwarzschildOut file", "Section"], Cell["\<\ This file is generated by MathTensor given the Schwarzschild metric as \ input\ \>", "Text"], Cell[BoxData[{ \(\(\(CompSimp[a_] := Together[Expand[a //. 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IndicesAndNotOrderedQ[{b, c}]\)\(\n\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-4\), \(-3\)] = \(-\((\((M*\((2*M - r)\)* Sin[theta]^2)\)/r^2)\)\)\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-4\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-3\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-2\), \(-4\), \(-2\)] = \((\(-2\)*M^2 + M*r)\)/ r^2\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-2\), \(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-2\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-2\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-2\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-1\), \(-4\), \(-1\)] = \((\(-2\)*M)\)/ r^3\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-1\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-1\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-4\), \(-1\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-3\), \(-2\), \(-3\), \(-2\)] = 2*M*r*Sin[theta]^2\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-3\), \(-2\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-3\), \(-2\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-3\), \(-1\), \(-3\), \(-1\)] = \((M* Sin[theta]^2)\)/\((2*M - r)\)\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-3\), \(-1\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[\(-2\), \(-1\), \(-2\), \(-1\)] = M/\((2*M - r)\)\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[i_, j_, k_, l_] := RiemannR[k, l, i, j] /; i \[Equal] k && IndicesAndNotOrderedQ[{j, l}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[i_, j_, k_, l_] := 0 /; i \[Equal] j || k \[Equal] l\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := \(-RiemannR[b, a, c, d]\) /; IndicesAndNotOrderedQ[{a, b}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := \(-RiemannR[a, b, d, c]\) /; IndicesAndNotOrderedQ[{c, d}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := RiemannR[c, d, a, b] /; IndicesAndNotOrderedQ[{a, c}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[d, s199]*RiemannR[a, b, c, \(-s199\)], {s199, 1, Dimension}]] /; NegIntegerQ[a] && NegIntegerQ[b] && NegIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[c, s299]*Metricg[d, s199]* RiemannR[a, b, \(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; NegIntegerQ[a] && NegIntegerQ[b] && PosIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[b, s299]*Metricg[d, s199]* RiemannR[a, \(-s299\), c, \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; NegIntegerQ[a] && PosIntegerQ[b] && NegIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[b, s399]*Metricg[c, s299]*Metricg[d, s199]* RiemannR[a, \(-s399\), \(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}, {s399, 1, Dimension}]] /; NegIntegerQ[a] && PosIntegerQ[b] && PosIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[a, s499]*Metricg[b, s399]*Metricg[c, s299]* Metricg[d, s199]* RiemannR[\(-s499\), \(-s399\), \(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}, {s399, 1, Dimension}, {s499, 1, Dimension}]] /; PosIntegerQ[a] && PosIntegerQ[b] && PosIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RiemannR[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[b, s199]*RiemannR[a, \(-s199\), c, d], {s199, 1, Dimension}]] /; NegIntegerQ[a] && PosIntegerQ[b] && NegIntegerQ[c] && NegIntegerQ[d]\)\(\n\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-4\), \(-4\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-4\), \(-3\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-4\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-3\), \(-3\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-2\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[\(-1\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[a_, b_] := RicciR[b, a] /; IndicesAndNotOrderedQ[{a, b}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[a_, b_] := CompSimp[Sum[ Metricg[b, s199]*RicciR[a, \(-s199\)], {s199, 1, Dimension}]] /; NegIntegerQ[a] && PosIntegerQ[b]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(RicciR[a_, b_] := CompSimp[Sum[ Metricg[a, s299]*Metricg[b, s199]* RicciR[\(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; PosIntegerQ[a] && PosIntegerQ[b]\)\(\n\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(ScalarR = 0\)\(\n\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-4\), \(-4\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-4\), \(-3\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-4\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-3\), \(-3\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-2\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[\(-1\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[i_, j_] := EinsteinG[j, i] /; IndicesAndNotOrderedQ[{i, j}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[a_, b_] := CompSimp[Sum[ Metricg[b, s199]*EinsteinG[a, \(-s199\)], {s199, 1, Dimension}]] /; NegIntegerQ[a] && PosIntegerQ[b]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(EinsteinG[a_, b_] := CompSimp[Sum[ Metricg[a, s299]*Metricg[b, s199]* EinsteinG[\(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; PosIntegerQ[a] && PosIntegerQ[b]\)\(\n\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-4\), \(-3\)] = \((\(-2\)*M^2* Sin[theta]^2 + M*r*Sin[theta]^2)\)/r^2\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-4\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-3\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-2\), \(-4\), \(-2\)] = \((\(-2\)*M^2 + M*r)\)/ r^2\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-2\), \(-4\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-2\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-2\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-2\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-1\), \(-4\), \(-1\)] = \((\(-2\)*M)\)/r^3\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-1\), \(-3\), \(-2\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-1\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-4\), \(-1\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-3\), \(-2\), \(-3\), \(-2\)] = 2*M*r*Sin[theta]^2\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-3\), \(-2\), \(-3\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-3\), \(-2\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-3\), \(-1\), \(-3\), \(-1\)] = \((M* Sin[theta]^2)\)/\((2*M - r)\)\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-3\), \(-1\), \(-2\), \(-1\)] = 0\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[\(-2\), \(-1\), \(-2\), \(-1\)] = M/\((2*M - r)\)\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[i_, j_, k_, l_] := 0 /; i \[Equal] j || k \[Equal] l\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[i_, j_, k_, l_] := \(-WeylC[i, j, l, k]\) /; IndicesAndNotOrderedQ[{k, l}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[i_, j_, k_, l_] := \(-WeylC[j, i, k, l]\) /; IndicesAndNotOrderedQ[{i, j}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[i_, j_, k_, l_] := WeylC[k, l, i, j] /; IndicesAndNotOrderedQ[{i, k}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[i_, j_, k_, l_] := WeylC[k, l, i, j] /; i \[Equal] k && IndicesAndNotOrderedQ[{j, l}]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[d, s199]*WeylC[a, b, c, \(-s199\)], {s199, 1, Dimension}]] /; NegIntegerQ[a] && NegIntegerQ[b] && NegIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[c, s299]*Metricg[d, s199]* WeylC[a, b, \(-s299\), \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; NegIntegerQ[a] && NegIntegerQ[b] && PosIntegerQ[c] && PosIntegerQ[d]\)\(\n\) \)\), "\[IndentingNewLine]", \(\(\(WeylC[a_, b_, c_, d_] := CompSimp[Sum[ Metricg[b, s299]*Metricg[d, s199]* WeylC[a, \(-s299\), c, \(-s199\)], {s199, 1, Dimension}, {s299, 1, Dimension}]] /; 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Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "gridMathematica"->FormBox[ RowBox[ {"grid", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-.17499999999999999, 0}, {0, 0}}]}], TextForm], "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-.17499999999999999, 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Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a cell \ exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", 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FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Inert"], StyleMenuListing->None, Background->RGBColor[0.870588, 0.905882, 0.972549]], Cell[StyleData["Inert", "Printout"], StyleMenuListing->None, Background->GrayLevel[1]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the \ kernel. 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CellMargins->{{42, 4}, {3, 8}}, ImageSize->{250, 250}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0.2, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->14], Cell[StyleData["CellLabel", "Printout"], FontSize->7, FontSlant->"Oblique", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Unique Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["ItemizedText"], CellMargins->{{26, 4}, {0, 8}}, ShowSpecialCharacters->Automatic, LineSpacing->{1, 3}, ParagraphSpacing->{0, 8}, ParagraphIndent->-19, CounterIncrements->"Text", FontSize->14], Cell[StyleData["ItemizedText", "Presentation"], CellMargins->{{40, 8}, {2, 12}}, FontSize->21], Cell[StyleData["ItemizedText", "Printout"], CellMargins->{{20, 4}, {0, 8}}, Hyphenation->True, ParagraphIndent->-14, FontSize->11] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ItemizedTextNote"], 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Cell[StyleData["Caption", "Printout"], CellMargins->{{7, 50}, {2, 4}}, Hyphenation->True, FontSize->7, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Tables", "Section"], Cell[CellGroupData[{ Cell[StyleData["2ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, GridBoxOptions->{ColumnWidths->{0.39, 0.59}, ColumnAlignments->{Left}}], Cell[StyleData["2ColumnTable", "Presentation"], CellMargins->{{16, 8}, {2, 12}}, FontSize->18], Cell[StyleData["2ColumnTable", "Printout"], CellMargins->{{7, 4}, {0, 8}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, StyleMenuListing->None, GridBoxOptions->{ColumnWidths->0.325, ColumnAlignments->{Left}}], Cell[StyleData["3ColumnTable", "Presentation"], CellMargins->{{16, 8}, {2, 10}}, FontSize->18], Cell[StyleData["3ColumnTable", "Printout"], CellMargins->{{7, 4}, {0, 8}}, FontSize->10] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->True, FontSize->14], Cell[StyleData["ChemicalFormula", "Presentation"], CellMargins->{{82, 30}, {4, 4}}, FontSize->21], Cell[StyleData["ChemicalFormula", "Printout"], CellMargins->{{43, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, FontSize->14, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{82, 30}, {4, 8}}, FontSize->21], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{43, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellMargins->{{10, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{16, 8}, {2, 10}}, FontSize->18], Cell[StyleData["Program", "Printout"], CellMargins->{{7, Inherited}, {Inherited, Inherited}}, FontSize->9.5] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "SlideShow"]], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], 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FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "SlideShow"]], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLinkText", "SlideShow"]], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "SlideShow"]], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "SlideShow"]], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "SlideShow"]], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "SlideShow"]], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "SlideShow"]], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ 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