Re: Mathematica Can't calculate Determinant of Matrix?
- To: mathgroup at smc.vnet.net
- Subject: [mg45266] Re: Mathematica Can't calculate Determinant of Matrix?
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Wed, 24 Dec 2003 17:42:21 -0500 (EST)
- References: <bsbn7v$lsu$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Just to get an idea of what you're asking Mathematica to do, I
computed leaf-counts for matrix determinants up to 11x11, where all
the entries are simple symbols:
<< "LinearAlgebra`MatrixManip\
ulation`"
sixteen = Characters[
"abcdefghijklmnop"];
many = ToExpression[
Outer[StringJoin,
sixteen, sixteen]];
mat[n_] := SubMatrix[many,
{1, 1}, {n, n}]
counts =
(LeafCount[Det[
mat[#1]]] & ) /@
Range[11]
{1, 8, 28, 133, 781, 5401,
42841, 342749, 3084764,
30847666, 339324354}
Then I extrapolated (clumsily, perhaps) to 16x16:
N[Rest[counts]/Most[counts]]
{8., 3.5, 4.75,
5.87218045112782,
6.915492957746479,
7.932049620440659,
8.000490184636213,
9.00006710449921,
10.000008428521598,
11.000000907686177}
(16!/11!)*Last[counts]
N[%]
177860253392640
1.7786025339264*^14
So...
The entries in your matrix are MUCH more complicated, so the LeafCount
of your determinant is noticeably larger than 10^14.
If your machine didn't run out of memory calculating the determinant,
and if it didn't run out of memory trying to simplify it, you'd die
watching all those characters scroll by.
On the other hand, if your symbols took on numerical values, the
leafcount would be ONE.
Bobby
Arman Khalatyan <arm2arm at thsun1.jinr.ru> wrote in message news:<bsbn7v$lsu$1 at smc.vnet.net>...
> 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.
>
>
>
>
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> 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\__,
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> \(-\ 1\)\)\)\ then\ "\<+\>"\ else\ "\<-\>"*) \), "\n",
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> \(\(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",
> \(\(Gpmo[f_, fc_, \ Sign_] =
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> pslashdega[fc] -
> Conjugate[M[f, fc]]\ Mek4\ \ ];\)\[IndentingNewLine]\n\), "\n",
> \(\(Gop =
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> Gpmo[u, ug, 1], Zero4, Zero4}, {Zero4, Zero4, Gpmo[d, dr, 1],
> Zero4}, {Zero4, Zero4, Zero4,
> Gpmo[d, dg, 1]}}];\)\[IndentingNewLine]\), "\n",
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> 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\ \
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> \(\(Grggr =
> BlockMatrix[{{Gop, Deltminus}, {Deltplus,
> Gom}}];\)\[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]\
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> Cell[BoxData[
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> ComplexExpand[SimpleDet1] //.
> Rep;\)\(\[IndentingNewLine]\)\( (*\ \(SimpCompExp2 =
> Collect[ComplexExpand[SimpleDet2], \[Mu]\ ] //.
> Rep;\)*) \)\(\[IndentingNewLine]\)\)\)], "Input"],
>
> Cell[CellGroupData[{
>
> Cell[BoxData[
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> No more memory available.
> Mathematica kernel has shut down.
> Try quitting other applications and then retry.\
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> 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[
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>
> 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]",
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> LineSpacing->{1.25, 0},
> StyleMenuListing->None,
> FontFamily->"Courier"],
>
> Cell[StyleData["TraditionalForm"],
> InputAutoReplacements->{
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> ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]",
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> 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.
> ***********************************************************************)