Mathematica Can't calculate Determinant of Matrix?
- To: mathgroup at smc.vnet.net
- Subject: [mg45258] Mathematica Can't calculate Determinant of Matrix?
- From: Arman Khalatyan <arm2arm at thsun1.jinr.ru>
- Date: Wed, 24 Dec 2003 04:35:58 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello. I have problem with Math 3.0(UNIX) after some calculations(analitical) Its give me: Det[MyDet] "No more memory available. Mathematica kernel has shut down. Try quitting other applications and then retry." MyDet is a 16x16 Matrix. In top I can see the memory is enough. The kernel shutted down after 150Mb allocation, but I have about 1Gb RAM free. What can I do?How to solve this problem? Please help me. Thank You beforehand. Arman. (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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 at 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[ 8371, 201]*) (*NotebookOutlinePosition[ 47456, 1515]*) (* CellTagsIndexPosition[ 47412, 1511]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ "\n", StyleBox["This Program calculate the Thermodymanical potential for 4D \ Separabel(Rank I) Model for Asymmetric case.\nWith diaquark channel(2SC \ phase).\nFor more comments email to arm2arm at thsun1.jinr.ru;\nSome results are \ in http://thsun1.jinr.ru/~arm2ar", "Subtitle"], StyleBox["m", "Subtitle"] }], "Input", FormatType->TextForm], Cell[BoxData[{ \(<< LinearAlgebra`MatrixManipulation`\n (*This\ line\ also\ cant\ help\ \ to\ calculate\ Det*) \), "\[IndentingNewLine]", \(<< Utilities`MemoryConserve`\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(<< LinearAlgebra`MatrixManipulation`\), "\n", \(CFV := {\ m\_0 \[Element] Reals, \ pvec2 \[Element] Reals, \[CapitalDelta]\ \ \[Element] Reals, \ \[Omega][_] \[Element] Reals, p\_0 \[Element] Reals, p\_1 \[Element] Reals, p\_2 \[Element] Reals, p\_3 \[Element] Reals, \[Mu] \[Element] Reals, {\[Delta]\[Mu], \[Mu]\&_, \[Mu], ga, \ gb, \ ga\__, gb\__, m\__, \ \[CurlyPhi], Absg2} \[Element] Reals, Absg2 > 0, \[CapitalDelta]\ > 0, \ \[Mu] > 0, \[CurlyPhi] > 0}\), "\n", \(Rep := {p\_1\^2 + p\_2\^2 + p\_3\^2 -> \ pvec2, \(-p\_1\^2\) - p\_2\^2 - p\_3\^2 -> \ \(-pvec2\)}\n\), "\n", \(Mek2 = {{1, 0}, {0, 1}}; \), "\n", \(Mek3 = DiagonalMatrix[{1, 1, 1}]; \), "\n", \(Mek4 = DiagonalMatrix[{1, 1, 1, 1}]; \), "\n", \(sigma0 = {{1, 0}, {0, 1}}; \n (*% // MatrixForm; *) \), "\n", \(sigma1 = {{0, 1}, {1, 0}}; \n (*\ % // MatrixForm; *) \), "\n", \(sigma2 = {{0, \(-I\)}, {I, 0}}; \n (*\ % // MatrixForm; *) \), "\n", \(sigma3 = {{1, 0}, {0, \(-1\)}}; \n (*% // MatrixForm; *) \), "\n", \(Zero2 = {{0, 0}, {0, 0}}; \), "\n", \(Zero4 = DiagonalMatrix[{0, 0, 0, 0}]; \n (*% // MatrixForm; *) \), "\n", \(gamma0 = DiagonalMatrix[{1, 1, \(-1\), \(-1\)}]; \n (*% // MatrixForm*) \ \), "\n", \(gamma1 = BlockMatrix[{{Zero2, sigma1}, {\(-sigma1\), Zero2}}]; \n (*\ % // MatrixForm; *) \ \n\), "\n", \(gamma2 = BlockMatrix[{{Zero2, sigma2}, {\(-sigma2\), Zero2}}]; \n (*\ % // MatrixForm; *) \ \n\), "\n", \(gamma3 = BlockMatrix[{{Zero2, sigma3}, {\(-sigma3\), Zero2}}]; \n (*\ % // MatrixForm; *) \ \n\), "\n", \(gamma5 = \ I\ gamma0 . \ gamma1 . \ gamma2 . \ gamma3; \n (*\ % // MatrixForm*) \), "\n", \(Transpose[gamma5]; \[IndentingNewLine] (*% // MatrixForm*) \), "\n", \(Ch = I\ gamma2 . \ gamma0; \n (*\ % // MatrixForm; *) \), "\n", \(pi[i_] = p\_i; \n\), "\n", \(sigmai[i_] = Switch[i, 0, sigma0, 1, sigma1, 2, sigma2, 3, sigma3]; \), "\n", \(gmmavpv\ = \ \[Sum]\+\(i = 1\)\%3 BlockMatrix[{{Zero2, sigmai[i]\ pi[i]}, {\(-sigmai[i]\) pi[i], Zero2}}]; \n (*\ % // \ MatrixForm\ *) \[IndentingNewLine]\n (*if\ Sign \[Equal] \ \(+\(\(/\)\ \(-\ 1\)\)\)\ then\ "\<+\>"\ else\ "\<-\>"*) \), "\n", \(\ \[Mu][fc_] = Switch[\ fc, ur, \[Mu]\&_\ - \ \[Delta]\[Mu], \ dg, \[Mu]\&_\ + \ \[Delta]\[Mu], \ ug, \[Mu]\&_\ - \ \[Delta]\[Mu], \ dr, \[Mu]\&_\ + \ \[Delta]\[Mu]]\ ; \), "\n", \(\ \(m0[f_] = m\_0;\)\ \[IndentingNewLine] (*Most\ Important\ function, \ If\ I\ use\ only\ real\ part\ I\ can\ obtain\ the\ result*) \), "\n", \(g[fc_] = ga\_fc + I\ gb\_fc\ \n\), "\n", \(\(M[f_, \ fc_] = \ m0[f] + \[CurlyPhi]\ g[fc];\)\[IndentingNewLine]\), "\n", \(\(pslash[fc_] = ComplexExpand[ gamma0 \((p\_0 + \ \ \[Mu][fc])\) - gmmavpv\ ];\)\[IndentingNewLine] (*ComplexExpand[\(-gmmavpv\)\ + \ \ gamma0 \((I\ \[Omega][n] + \ \[Mu][fc])\)]; *) \), "\n", \(\(TableForm[%];\)\), "\n", \(\(pslashdega[fc_] = ComplexExpand[ gamma0 \((p\_0 - \ \ \[Mu][fc])\) - gmmavpv];\)\), "\n", \(\(TableForm[%];\)\), "\n", \(\(MatForDeltminus\ = \ BlockMatrix[{\[IndentingNewLine]{Zero4, Zero4, Zero4, \ g[ur] gamma5}, \[IndentingNewLine]{Zero4, Zero4, \(-g[ug]\) gamma5, Zero4}, \[IndentingNewLine]{Zero4, \(-g[dr]\) gamma5, Zero4, Zero4}, \[IndentingNewLine]{g[dg] gamma5, Zero4, Zero4, Zero4}}];\)\n\), "\n", \(\(Deltminus\ = \(-\ I\)\ \[CapitalDelta]\ MatForDeltminus;\)\), "\n", \(\(Deltplus = \(-\ Transpose[ Conjugate[ Deltminus]]\)\ ;\)\[IndentingNewLine]\n\[IndentingNewLine] \ (*Det[Deltminus . Deltplus]; \nFullSimplify[%, CFV]*) \n\), "\n", \(\(Gpmo[f_, fc_, \ Sign_] = If[Sign > 0, pslash[fc] - M[f, fc]\ Mek4, pslashdega[fc] - Conjugate[M[f, fc]]\ Mek4\ \ ];\)\[IndentingNewLine]\n\), "\n", \(\(Gop = BlockMatrix[{{Gpmo[u, ur, 1], Zero4, Zero4, Zero4}, {Zero4, Gpmo[u, ug, 1], Zero4, Zero4}, {Zero4, Zero4, Gpmo[d, dr, 1], Zero4}, {Zero4, Zero4, Zero4, Gpmo[d, dg, 1]}}];\)\[IndentingNewLine]\), "\n", \(\(Gom = BlockMatrix[{{Gpmo[u, ur, \(-1\)], Zero4, Zero4, Zero4}, {Zero4, Gpmo[u, ug, \(-1\)], Zero4, Zero4}, {Zero4, Zero4, Gpmo[d, dr, \(-1\)], Zero4}, {Zero4, Zero4, Zero4, Gpmo[d, dg, \(-1\)]}}];\)\[IndentingNewLine]\n (*We\ need\ to\ \ calculate\ the\ 32 x32\ matrix\ det*) \), "\[IndentingNewLine]", \(\(Grggr = BlockMatrix[{{Gop, Deltminus}, {Deltplus, Gom}}];\)\[IndentingNewLine] (*\ Or\ in\ another\ "\<word\>", \ 16 x16\ Matrix*) \), "\n", \(\(SimpleDet1 = \(-Deltplus . Deltminus\) + Deltplus . Gop . Inverse[Deltplus] . Gom;\)\[IndentingNewLine]\[IndentingNewLine] (*Another\ \ representation\ of\ determinant*) \n (*\(SimpleDet2 = \(-Deltminus . Deltplus\) + Gom . Inverse[Deltplus] . Gop . Deltplus;\)*) \[IndentingNewLine]\[IndentingNewLine]\ \[IndentingNewLine]\)}], "Input"], Cell[BoxData[ \(ga\_fc + \[ImaginaryI]\ gb\_fc\)], "Output"] }, Open ]], Cell[BoxData[ \(\(\(SimpCompExp = ComplexExpand[SimpleDet1] //. Rep;\)\(\[IndentingNewLine]\)\( (*\ \(SimpCompExp2 = Collect[ComplexExpand[SimpleDet2], \[Mu]\ ] //. Rep;\)*) \)\(\[IndentingNewLine]\)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(MyDetD = Det[SimpCompExp]\)], "Input"], Cell["\<\ No more memory available. Mathematica kernel has shut down. Try quitting other applications and then retry.\ \>", "Print"] }, Open ]] }, FrontEndVersion->"4.0 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{1147, 850}, WindowMargins->{{Automatic, 49}, {Automatic, 24}}, Visible->True, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{"usr", "users", "guests", \ "xuser7"}, "asim_new.ps", CharacterEncoding -> "ISO8859-1"], "Magnification"->1}, InputAliases->{"notation"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation>"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation<"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "symb"->RowBox[ {"Symbolize", "[", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], "]"}], "infixnotation"->RowBox[ {"InfixNotation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "addia"->RowBox[ {"AddInputAlias", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "pattwraper"->TagBox[ "\[Placeholder]", NotationPatternTag, TagStyle -> "NotationPatternWrapperStyle"], "madeboxeswraper"->TagBox[ "\[Placeholder]", NotationMadeBoxesTag, TagStyle -> "NotationMadeBoxesWrapperStyle"]}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ 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["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, CellLabelMargins->{{12, Inherited}, {Inherited, Inherited}}, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, CellLabelMargins->{{24, Inherited}, {Inherited, Inherited}}, ScriptMinSize->12], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}}, ScriptMinSize->8], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, CellLabelMargins->{{2, Inherited}, {Inherited, Inherited}}, ScriptMinSize->5, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the \ Notebook level.\ \>", "Text"], 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] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{12, Inherited}, {20, 40}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->36, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {12, 30}}, FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{12, Inherited}, {20, 15}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->24], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{12, Inherited}, {20, 15}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 8}}, FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[FilledSquare]", CellMargins->{{25, Inherited}, {8, 24}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->16, FontWeight->"Bold"], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 18}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsubsection", FontFamily->"Times", FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.35999999999999999, \ -0.10000000000000001}, {0, 0}}, BoxBaselineShift -> -0.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.074999999999999997, \ -0.085000000000000006}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, Hyphenation->True, LineSpacing->{1, 3}, CounterIncrements->"Text"], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, TextJustification->0.5, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, DefaultNewInlineCellStyle->"None", Hyphenation->True, LineSpacing->{1, 3}, LanguageCategory->"NaturalLanguage", CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, TextJustification->0.5, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ 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. Some attributes for these styles are actually set in FormatType Styles \ (in the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->11], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontSize->11, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->7, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->10], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline 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"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, 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"], Cell[StyleData["SO10", "EnhancedPrintout"], StyleMenuListing->None, FontFamily->"Futura", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, 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, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], 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, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Condensed"], FontSize->11], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, 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"], FontSize->16], Cell[StyleData["AddOnsLink", "Condensed"], FontSize->11], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, 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[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, 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"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, 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"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, 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], 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["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ 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. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ 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]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display \ of certain types of objects in typeset expressions. For example, \ \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and \ parenthesis characters are displayed (typically by coloring them to make them \ stand out).\ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Notation Package Styles", "Section", GeneratedCell->True, CellTags->"NotationPackage"], Cell["\<\ The cells below define certain styles needed by the Notation \ package. These styles serve to make visible otherwise invisible \ tagboxes.\ \>", "Text", GeneratedCell->True, CellTags->"NotationPackage"], Cell[StyleData["NotationTemplateStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 1, 0.850004], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationPatternWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 0.900008, 0.979995], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationMadeBoxesWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[0.900008, 0.889998, 1], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"] }, Closed]] }] ] (*********************************************************************** 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->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1717, 49, 364, 8, 178, "Input"], Cell[2084, 59, 191, 3, 78, "Input"], Cell[CellGroupData[{ Cell[2300, 66, 5492, 109, 2124, "Input"], Cell[7795, 177, 64, 1, 34, "Output"] }, Open ]], Cell[7874, 181, 262, 5, 78, "Input"], Cell[CellGroupData[{ Cell[8161, 190, 58, 1, 32, "Input"], Cell[8222, 193, 133, 5, 88, "Print"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)