(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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[ 11181, 325]*) (*NotebookOutlinePosition[ 40725, 1368]*) (* CellTagsIndexPosition[ 40654, 1362]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Four tests of for a conservative force", "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox["doug "]], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "The tests\nDefinitions of quaternion operators\n1. The curl is zero\n2. \ There exists a potential function\n3. The line integral of any closed loop is \ zero\n4. The line lintegral along different paths is the same\n\ Implications"]], "Text"], Cell[CellGroupData[{ Cell[" The tests", "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "There are four well-known, equivalent tests to determine if a force is \ conservative: the curl must be zero, a potential function whose gradient is \ the force exists, all closed path integrals are zero, and the path integral \ between any two points is the same no matter what the path chosen. In this \ notebook, quaternion operators perform these tests on quaternion-valued \ forces."]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[" Definitions of quaternion operators", "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True, CellTags->"post"], Cell[TextData[StyleBox[ "Consider how a quaternion composed of differential operators acts the \ another quaternion composed of functions."]], "Text"], Cell[BoxData[ \(dq\ = \ q[d\/dt, \ d\/dx, \ d\/dy, \ d\/dz]; \n fq\ = \ q[f\_0, \ f\_1, \ f\_2, \ f\_3]; \)], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[{ \(dq\ = \ \((d\/dt, \ d\/dx, \ d\/dy, \ d\/dz)\)\), \(fq\ = \ \((f\_0, \ f\_1, \ f\_2, \ f\_3)\)\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Multiply the quaternion operator and the function together, and then \ evaluate each component."]], "Text"], Cell[BoxData[{ \(dq\ .\ fq\ .\ {1, 0, 0, 0}\), \({\(d\ f\_0\)\/dt - \(d\ f\_1\)\/dx - \(d\ f\_2\)\/dy - \(d\ f\_3\)\/dz, \(d\ f\_0\)\/dx + \(d\ f\_1\)\/dt - \(d\ f\_2\)\/dz + \(d\ f\_3\)\/dy, \n\t\(d\ f\_0\)\/dy + \(d\ f\_1\)\/dz + \(d\ f\_2\)\/dt - \(d\ f\_3\)\/dx, \(d\ f\_0\)\/dz - \(d\ f\_1\)\/dy + \(d\ f\_2\)\/dx + \(d\ f\_3\)\/dt} \)}], "Input", CellMargins->{{9, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\((\(d\ f\_0\)\/dt - \(d\ f\_1\)\/dx - \(d\ f\_2\)\/dy - \(d\ f\_3\)\/dz, \(d\ f\_0\)\/dx + \(d\ f\_1\)\/dt - \(d\ f\_2\)\/dz + \(d\ f\_3\)\/dy, \n\t\(d\ f\_0\)\/dy + \(d\ f\_1\)\/dz + \(d\ f\_2\)\/dt - \(d\ f\_3\)\/dx, \(d\ f\_0\)\/dz - \(d\ f\_1\)\/dy + \(d\ f\_2\)\/dx + \(d\ f\_3\)\/dt) \)\)], "Input", CellMargins->{{9, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "If fo = 0, then the first term is the negative of the divergence. If f is \ not a function of t, then the next three terms compose the curl. In general, \ 16 operations are required to make up the final product."]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["1. The curl is Zero", "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "To make the discussion concrete, define a force quaternion F."]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(F = \ q[0, \ \(-k\)\ x, \ \(-k\)\ y, \ 0]; \)\)], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(F = \ q[0, \ \(-k\)\ x, \ \(-k\)\ y, \ 0]; \)\)], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "The curl is the commutator of the differential operator and the force. If \ this is zero, the force is conservative."]], "Text"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["[", FontWeight->"Bold"], \(\((d\/dt, \[Del]\&\[RightVector])\), F\&\[RightVector]\), StyleBox["]", FontWeight->"Bold"]}], " ", "=", "0"}]], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["[", FontWeight->"Bold"], \(\((d\/dt, \[Del]\&\[RightVector])\), F\&\[RightVector]\), StyleBox["]", FontWeight->"Bold"]}], " ", "=", "0"}]], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}], Cell[TextData[StyleBox[ "Let the differential operator quaternion act on the force, and test if the \ vector components equal zero."]], "Text"], Cell[BoxData[{ \(oponq[D, \ F]\ .\ {1, 0, 0, 0}\), \({2\ k, 0, 0, 0}\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\((d\/dt, \[Del])\) F\ = \((2\ k, 0, 0, 0)\)\)], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ " 2. There exists a potential function for the force"]], "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Operate on force quaternion using integration. Take the negative \ of the gradient of the first component. If the field quaternion is the same, \ the force is conservative.\ \>", "Text"], Cell[BoxData[{ \(\((fint\ = \ oponq[Integrate, \ F])\).{1, 0, 0, 0}\), \({\(k\ x\^2\)\/2 + \(k\ y\^2\)\/2, \(-k\)\ t\ x + k\ y\ z, \(-k\)\ t\ y - k\ x\ z, 0}\n - opinq[D, fint[\([1, 1]\)]\ q[1, 1, 1, 1]]\ .\ {1, 0, 0, 0}\), \({0, \(-k\)\ x, \(-k\)\ y, 0}\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[{ \(F\ \ = \ \(\[Integral]\ F \((dt, dx, dy, dz)\)\n = \ \(\[Integral]\((k\ x\ dx\ + k\ y\ dy, \ \(-k\)\ x\ dt\ + \ k\ y\ dz, \n\t\t\t\ \(-k\)\ y\ dt\ - \ k\ x\ dz, 0)\)\n = \((\(k\ x\^2\)\/2 + \(k\ y\^2\)\/2, \(-k\)\ t\ x + k\ y\ z, \(-k\)\ t\ y - k\ x\ z, 0)\)\)\)\n\), \(\((d\/dt, \[Del]\&\[RightVector])\) \((\(k\ x\^2\)\/2 + \(k\ y\^2\)\/2, 0\&\[RightVector])\)\ = \ \((0, \(-k\)\ x, \(-k\)\ y, 0)\)\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell["\<\ This is the same force as we started with, so the first term of fint is the \ scalar potential of this vector field. The vector terms in fint arrise as \ constants of integration. They are zero if t=z=0. What role these vector \ terms in the potential quaternion may play, if any, is unknown to me.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell[" 3. The line integral of any closed loop is zero", "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "Use any parameterization in the line integral, making sure it comes back to \ go."]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(path\ = \ \ q[0, \ r\ Cos[t], \ r\ Sin[t], \ 0]; \n lineintegral[F, path, \ 0, \ 2\ \[Pi]]\ .\ {1, 0, 0, 0}\), \({0, 0, 0, 0}\)}], "Input", CellMargins->{{19, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[{ \(path\ = \ \ q[0, \ r\ Cos[t], \ r\ Sin[t], \ 0]\), \(\[Integral]\_0\%\(\ 2\ \[Pi]\)F\ dt = 0\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox[ " 4. The line integral along different paths is the same."]], "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Choose any two parameterizations from A to B, and test that they are the \ same. These paths are from (0, r, 0, 0) to (0, -r, 2 r, 0).\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(path1\ = \ q[0, \ r\ Cos[t], \ 2\ r\ Sin[t\/2], \ 0]; \n \(lineintegral[f\_test, \ path1, \ 0, \ \[Pi]]\)[\([1, 1]\)]\n - 2\ k\ r\^2\), \(path2\ = \ q[0, \ \(-\ t\)\ r\ + \ r, \ t\ r, \ 0]; \n \(lineintegral[f\_test, \ path2, \ 0, \ 2]\)[\([1, 1]\)]\n - 2\ k\ r\^2\)}], "Input", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[{ \(path1\ = \ q[0, \ r\ Cos[t], \ 2\ r\ Sin[t\/2], \ 0]; \n \(\[ClockwiseContourIntegral]\_0\%\[Pi]\)\+\(path\ 1\)F\ dt\ = \(-2\)\ k\ r\^2\n\), \(path2\ = \ q[0, \ \(-\ t\)\ r\ + \ r, \ t\ r, \ 0]; \n \(\[ClockwiseContourIntegral]\_0\%2\)\+\(path\ 2\)F\ dt\ = \(-2\)\ k\ r\^2\)}], "Input", CellMargins->{{17, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData["The same!"], "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[" Implications", "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}], Cell["\<\ The four standard tests for a conservative force can be done with \ operator quaternions. One new avenue opened up is for doing path integrals. \ It would be interesting to attempt four dimensional path integrals to see \ where that might lead!\ \>", "Text"] }, Open ]] }, Open ]] }, FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 640}, {0, 451}}, AutoGeneratedPackage->None, WindowToolbars->{"RulerBar", "EditBar"}, CellGrouping->Automatic, WindowSize->{591, 325}, WindowMargins->{{-7, Automatic}, {Automatic, 6}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PrintingOptions->{"PrintingMargins"->{{72, 57.5625}, {57.5625, 72}}, "PrintCellBrackets"->False, "PrintRegistrationMarks"->False, "PrintMultipleHorizontalPages"->False, "FirstPageHeader"->False}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, CharacterEncoding->"MacintoshAutomaticEncoding", StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Style Definitions"]], "Subtitle"], Cell[TextData[StyleBox[ "Modify the definitions below to change the default appearance of all cells \ in a given style. Make modifications to any definition using commands in the \ Format menu."]], "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Style Environment Names"]], "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellBracketOptions->{"Margins"->{1, 1}, "Widths"->{0, 5}}, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Notebook Options"]], "Section", FontFamily->"New York"], Cell[TextData[StyleBox[ "The options defined for the style below will be used at the Notebook \ level."]], "Text", FontFamily->"New York"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellFrameLabelMargins->6, StyleMenuListing->None, FontFamily->"New York"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Headings"]], "Section", FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{7, Inherited}, {8, 40}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 0}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->24, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontFamily->"Times New Roman", FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {12, 30}}, FontFamily->"Times New Roman", FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{7, Inherited}, {6, 15}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 10}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->18], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontFamily->"Times New Roman", FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Times New Roman", FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{7, Inherited}, {6, 15}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 20}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 8}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Times New Roman", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[GraySquare]", CellMargins->{{22, Inherited}, {8, 20}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 30}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->18, FontWeight->"Bold", FontVariations->{"Underline"->True}], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontFamily->"Times New Roman", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{19, Inherited}, {8, 15}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 40}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontFamily->"Times New Roman", FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[EmptySquare]", CellMargins->{{18, Inherited}, {8, 12}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 50}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Subsubsection", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontFamily->"Times New Roman", FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Body Text"]], "Section", FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{7, 10}, {7, 7}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 3}, CounterIncrements->"Text", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontFamily->"Times New Roman"], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontFamily->"Times New Roman"], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, FontFamily->"Times New Roman"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{7, 10}, {6, 6}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 3}, CounterIncrements->"SmallText", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->10], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontFamily->"Times New Roman", FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontFamily->"Times New Roman", FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Input/Output"]], "Section", FontSize->14, FontWeight->"Plain"], Cell[TextData[StyleBox[ "The cells in this section define styles used for input and output to the \ kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names."]], "Text", FontSize->14], Cell[CellGroupData[{ Cell[StyleData["Input"], PageWidth->Infinity, CellMargins->{{42, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", AspectRatioFixed->True, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->14, FontWeight->"Plain"] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", StyleMenuListing->None, FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[StyleData["Output"], PageWidth->Infinity, CellMargins->{{42, 10}, {7, 5}}, CellEditDuplicate->True, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output", AspectRatioFixed->True, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->14], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->14], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->14, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->14], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], PageWidth->Infinity, CellMargins->{{7, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", AspectRatioFixed->True, ImageSize->{387, 393}, ImageMargins->{{34, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}, FontSize->14], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}, FontSize->14], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["CellLabel", "Presentation"], FontSize->14], Cell[StyleData["CellLabel", "Condensed"], FontSize->14], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->14, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Formulas and Programming"]], "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Headers and Footers"]], "Section"], Cell[StyleData["Header"], CellMargins->{{7, 0}, {4, 1}}, Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{7, 0}, {0, 4}}, Evaluatable->False, PageBreakWithin->Automatic, TextAlignment->Center, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Palette Styles"]], "Section"], Cell[TextData[StyleBox[ "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], 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[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Hyperlink Styles"]], "Section"], Cell[TextData[StyleBox[ "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, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[TextData[StyleBox[ "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, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Placeholder Styles"]], "Section"], Cell[TextData[StyleBox[ "The cells below define styles useful for making placeholder objects in \ palette templates."]], "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["FormatType Styles"]], "Section"], Cell[TextData[StyleBox[ "The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options."]], "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell[TextData[StyleBox[ "The style defined below is mixed in to any cell that is in an inline cell \ within another."]], "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{ "post"->{ Cell[2856, 83, 183, 4, 42, "Subsection", CellTags->"post"]} } *) (*CellTagsIndex CellTagsIndex->{ {"post", 40558, 1355} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 106, 2, 43, "Subtitle"], Cell[1840, 55, 117, 2, 39, "Subsubtitle"], Cell[1960, 59, 268, 4, 147, "Text"], Cell[CellGroupData[{ Cell[2253, 67, 137, 3, 42, "Subsection"], Cell[2393, 72, 426, 6, 90, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[2856, 83, 183, 4, 42, "Subsection", CellTags->"post"], Cell[3042, 89, 150, 2, 33, "Text"], Cell[3195, 93, 202, 4, 74, "Input"], Cell[3400, 99, 210, 4, 74, "Input"], Cell[3613, 105, 132, 2, 33, "Text"], Cell[3748, 109, 470, 9, 117, "Input"], Cell[4221, 120, 444, 9, 92, "Input"], Cell[4668, 131, 250, 3, 52, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[4955, 139, 147, 3, 42, "Subsection"], Cell[5105, 144, 146, 3, 33, "Text"], Cell[5254, 149, 154, 3, 32, "Input"], Cell[5411, 154, 154, 3, 32, "Input"], Cell[5568, 159, 154, 2, 33, "Text"], Cell[5725, 163, 304, 8, 43, "Input"], Cell[6032, 173, 304, 8, 43, "Input"], Cell[6339, 183, 143, 2, 33, "Text"], Cell[6485, 187, 165, 4, 55, "Input"], Cell[6653, 193, 152, 3, 46, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[6842, 201, 199, 4, 42, "Subsection"], Cell[7044, 207, 198, 4, 52, "Text"], Cell[7245, 213, 373, 7, 120, "Input"], Cell[7621, 222, 605, 12, 231, "Input"], Cell[8229, 236, 325, 5, 71, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[8591, 246, 175, 3, 42, "Subsection"], Cell[8769, 251, 166, 4, 33, "Text"], Cell[8938, 257, 244, 5, 78, "Input"], Cell[9185, 264, 207, 4, 77, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[9429, 273, 204, 4, 42, "Subsection"], Cell[9636, 279, 207, 5, 52, "Text"], Cell[9846, 286, 403, 8, 161, "Input"], Cell[10252, 296, 413, 8, 213, "Input"], Cell[10668, 306, 83, 2, 33, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[10788, 313, 92, 1, 42, "Subsection"], Cell[10883, 316, 270, 5, 71, "Text"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)