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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[ 20321, 692]*) (*NotebookOutlinePosition[ 94947, 3201]*) (* CellTagsIndexPosition[ 94903, 3197]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Problem Set 1", "Title", FontSize->18], StyleBox["\n", FontSize->18], "Klaus Moeltner/ APEC 720 " }], "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Start-up commands and general instructions: ", \ "Subsection"]], "Text"], Cell["\<\ Note: ignore \"possible spelling-error\" messages for similar symbols.\ \>", "Text"], Cell[BoxData[ \(\(<< Utilities`Notation`;\)\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(p\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(p\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(x\_11\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(x\_21\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(x\_22\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(x\_12\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Omega]\_11\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Omega]\_21\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Omega]\_22\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Lambda]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(t\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(t\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Alpha]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Alpha]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Beta]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Beta]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(y\_11\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(y\_21\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(y\_12\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(y\_22\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}]], "Input"], Cell[TextData[{ StyleBox["General Instructions:\n", FontVariations->{"Underline"->True}], "* Group work is encouraged, but every student needs to hand in an \ individual version.\n* In the following programming code, replace all \"your \ turn\" entries with appropriate code. \n* Unless otherwise instructed, \ execute all complete commands using Shift+Enter.\n* For ", StyleBox["some", FontWeight->"Bold"], " incomplete commands, the correct output is given for your guidance.\n* \ Use the Palette \"PS1_palette\" to enter symbols- it will make your life \ easier.\n* Some questions require a verbal explanation - please add verbal \ answers as separate cells throughout the program.\n* \ \"DisplayFunction->Identity\" for interim graphics supressed output (to \ conserve on printing resources). If for some reason you would like to see \ interim graphs, just eliminate this element from the command and re-evaluate \ the cell.\n* Save an electronic file of your work to your course folder, \ computer, or a CD-rom for your records, but please hand in a printed \ hard-copy of your work (Note: printing through the library server can be \ slow, and ", StyleBox["Mathematica", FontSlant->"Italic"], " might \"freeze up\" during printing)" }], "Text", CellDingbat->None, Background->RGBColor[0.996078, 0.905882, 0.811765]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Part 1:", "Subsection"]], "Text"], Cell["\<\ Consider a pure exchange economy with 2 agents and the following features:\ \>", "Text"], Cell[BoxData[ \(\(U\_1[\(x\_11\) : _, \(x\_21\) : _] := Log[x\_11\^\[Alpha]\_1*x\_21\^\[Alpha]\_2];\)\)], "Input"], Cell[BoxData[ \(\(U\_2[\(x\_12\) : _, \(x\_22\) : _] := Log[x\_12\^\[Beta]\_1*x\_22\^\[Beta]\_2];\)\)], "Input"], Cell[BoxData[ \(\({{\[Omega]\_11, \[Omega]\_21}, {\[Omega]\_12, \[Omega]\_22}} = {{15, 250}, {320, 40}};\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[Omega]\_1\)\&_ = \[Omega]\_11 + \[Omega]\_12\)], "Input"], Cell[BoxData[ \(335\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[Omega]\_2\)\&_ = \[Omega]\_21 + \[Omega]\_22\)], "Input"], Cell[BoxData[ \(290\)], "Output"] }, Open ]], Cell[BoxData[ \(\(p\_2 = 1;\)\)], "Input"], Cell[BoxData[ \(\({\[Alpha]\_1 = 2; \[Alpha]\_2 = 1; \[Beta]\_1 = 1, \[Beta]\_2 = 2};\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Q.1 (2 points): Solve for the equilibrium consumtion levels in \ terms of ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`p\_1\)], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[ScriptCapitalL]\_1 = your\ turn\)], "Input"], Cell[BoxData[ \(\((250 + 15\ p\_1 - p\_1\ x\_11 - x\_21)\)\ \[Lambda]\_1 + Log[x\_11\%2\ x\_21]\)], "Output"] }, Open ]], Cell[BoxData[ \(\[ScriptCapitalL]\_2 = your\ turn\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \({FOC\_1 = D[\[ScriptCapitalL]\_1, x\_11], FOC\_2 = D[\[ScriptCapitalL]\_1, x\_21], FOC\_3 = D[\[ScriptCapitalL]\_1, \[Lambda]\_1]}\)], "Input"], Cell[BoxData[ \({2\/x\_11 - p\_1\ \[Lambda]\_1, 1\/x\_21 - \[Lambda]\_1, 250 + 15\ p\_1 - p\_1\ x\_11 - x\_21}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sol1 = \(Solve[{FOC\_1 \[Equal] 0, FOC\_2 \[Equal] 0, FOC\_3 \[Equal] 0}, {x\_11, x\_21, \[Lambda]\_1}]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({x\_21 \[Rule] 5\/3\ \((50 + 3\ p\_1)\), \[Lambda]\_1 \[Rule] 3\/\(5\ \((50 + 3\ p\_1)\)\), x\_11 \[Rule] \(10\ \((50 + 3\ p\_1)\)\)\/\(3\ p\_1\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({\(x\_11\^*\), \(x\_21\^*\)} = {x\_11, x\_21} /. sol1\)], "Input"], Cell[BoxData[ \({\(10\ \((50 + 3\ p\_1)\)\)\/\(3\ p\_1\), 5\/3\ \((50 + 3\ p\_1)\)}\)], "Output"] }, Open ]], Cell[TextData[StyleBox["Solution code for the second agent: your turn!", \ "Input"]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Q.2 (2 points): Solve for the equilibrium price ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(p\_1\^*\)\)], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[", and the equilibrium consumtion levels (numerical results). Who \ is a net seller / buyer of which commodity? Explain Walras' Law and show that \ it holds.\nExplain the equation you are using to derive ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`\(p\_1\^*\)\)], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[".", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[\(Solve[your\ turn]\)[\([1]\)]]\)], "Input"], Cell[BoxData[ \({p\_1 \[Rule] 0.8244274809160306`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(p\_1\^*\) = p\_1 /. %\)], "Input"], Cell[BoxData[ \(0.8244274809160306`\)], "Output"] }, Open ]], Cell[BoxData[ \({\(x\_11\^*\), \(x\_21\^*\), \(x\_12\^*\), \(x\_22\^*\)} /. p\_1 -> \(p\_1\^*\)\)], "Input"], Cell[BoxData[ \(Determination\ of\ net\ seller\ /\ buyer\ and\ verification\ of\ Walras'\ \(Law : \ Your\ \(turn!\)\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Q.3 (2 points): Verify that both markets clear at these \ equilibrium levels, and show that the MRS's are identical for the two agents \ ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "\nNote: you may not get a precise answer of \"0\" due to rounding errors, \ but the number should be very, very small." }], "Text"], Cell[BoxData[ \(Market\ \(clearing : \ your\ turn\ for\ both\ \(\(markets\)\(.\)\)\)\)], "Input"], Cell[BoxData[ \(\(MRS\_1 = \((D[U\_1[x\_11, x\_21], x\_11])\)/\((D[U\_1[x\_11, x\_21], x\_21])\);\)\)], "Input"], Cell[BoxData[ \(MRS\_2 = your\ turn\)], "Input"], Cell[BoxData[ \(Simplify[\((MRS\_1/MRS\_2)\)\ /. {x\_11 -> \(x\_11\^*\), x\_21 -> \(x\_21\^*\), x\_12 -> \(x\_12\^*\), x\_22 -> \(x\_22\^*\)}]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Q.4 (3 points): Create a graph that shows the \ Edgeworth Box, indifference curves for both agents at endowment and \ equilibrium utility levels, the endowment and equilibrium points, the budget \ line, and the Pareto Set. On the print-out, identify the contract curve in \ the graph (by hand).", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(N[{V\_1 = U\_1[\[Omega]\_11, \[Omega]\_21], \(V\_1\^*\) = U\_1[\(x\_11\^*\), \(x\_21\^*\)]} /. p\_1 -> \(p\_1\^*\)]\)], "Input"], Cell[BoxData[ \({10.937561320066667`, 15.18581582719761`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Second\ \(agent : \ your\ turn\)\)], "Input"], Cell[BoxData[ \({13.146079904021645`, 15.432798195406626`}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(IC\_1 = ContourPlot[ U\_1[x, y], {x, 0.001, \(\[Omega]\_1\)\&_}, {y, 0.001, \(\[Omega]\_2\)\&_}, ContourShading \[Rule] False, Contours -> {V\_1, \(V\_1\^*\) /. p\_1 -> \(p\_1\^*\)}, PlotPoints \[Rule] 100, \ DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(IC\_2 = ContourPlot[ U\_2[\(\[Omega]\_1\)\&_ - x, \(\[Omega]\_2\)\&_ - y], {x, 0, \(\[Omega]\_1\)\&_ - 0.001}, {y, 0, \(\[Omega]\_2\)\&_ - 0.001}, ContourShading \[Rule] False, Contours -> {V\_2, \(V\_2\^*\) /. p\_1 -> \(p\_1\^*\)}, PlotPoints \[Rule] 100, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(<< Graphics`Graphics`\)], "Input"], Cell[BoxData[ \(\(A := LabeledListPlot[{{\(x\_11\^*\), \(x\_21\^*\), "\"} /. p\_1 -> \(p\_1\^*\), {\[Omega]\_11, \[Omega]\_21, "\"}}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell["\<\ Note: The following command is just to increase the point size for C, E, \ which is not possible using \"LabeledListPlot\".\ \>", "Text"], Cell[BoxData[ \(\(AA := ListPlot[{{\(x\_11\^*\), \(x\_21\^*\)} /. p\_1 -> \(p\_1\^*\), {\[Omega]\_11, \[Omega]\_21}}, PlotStyle \[Rule] {AbsolutePointSize[8]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[TextData[{ "Now define the budget line as a function of ", Cell[BoxData[ \(TraditionalForm\`x\_11\)]], "as we did in class" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(BC[\(x\_11\) : _] = \((your\ turn)\) /. p\_1 -> \(p\_1\^*\)\)], "Input"], Cell[BoxData[ \(\(\(262.36641221374043`\)\(\[InvisibleSpace]\)\) - 0.8244274809160306`\ x\_11\)], "Output"] }, Open ]], Cell[BoxData[ \(\(BCplot = Plot[BC[x\_11], {x\_11, 0.001, \(\[Omega]\_1\)\&_}, PlotStyle -> {RGBColor[1, 0, 0], Thickness[ .01]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell["\<\ The next command defines the pareto set implicitly as the set of all points \ where indifference curves are tangent.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(PS = \((D[U\_1[x, y], x])\)/\((D[U\_1[x, y], y])\) \[Equal] \((D[ U\_2[\(\[Omega]\_1\)\&_ - x, \(\[Omega]\_2\)\&_ - y], x])\)/\((D[ U\_2[\(\[Omega]\_1\)\&_ - x, \(\[Omega]\_2\)\&_ - y], y])\)\)], "Input"], Cell[BoxData[ \(\(2\ y\)\/x \[Equal] \(-\(\(\(-290\) + y\)\/\(2\ \((335 - x)\)\)\)\)\)], "Output"] }, Open ]], Cell[BoxData[ \(<< Graphics`ImplicitPlot`\)], "Input"], Cell[BoxData[ \(\(B := ImplicitPlot[PS, {x, 0.001, \(\[Omega]\_1\)\&_}, PlotStyle \[Rule] Dashing[{0.01}], DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[IC\_1, IC\_2, A, AA, BCplot, B, DefaultFont \[Rule] {"\", 12}, DisplayFunction \[Rule] $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[TextData[StyleBox["Don't forget to identify the contract curve on your \ print-out!", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]]], "Text"], Cell[BoxData[ StyleBox[\(\(Part\ 2\)\(:\)\), "Subsection"]], "Input"], Cell[TextData[{ "Assume a social planner would like to achieve an the following equilibrium \ consumption levels: ", Cell[BoxData[ \(TraditionalForm\`y\_11 = 150, \ y\_21 = 4350/89, y\_12 = 185, \(\(y\_22\)\(=\)\)\)]], "21460/89. (Note: preserve the seemingly weird fraction-notation for \ numerical accuracy in the following section.)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({y\_11 = 150, y\_21 = 4350/89, y\_12 = 185, y\_22 = 21460/89}\)], "Input"], Cell[BoxData[ \({150, 4350\/89, 185, 21460\/89}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Q.5 (2 points): Verify that this desired allocation \ is feasible and non-wasteful.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(Your\ turn\ for\ both\ \(\(markets\)\(.\)\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Q.6 (2 points): We know from the 2nd fundamental theorem of \ welfare economics that under some regularity conditions on preferences (which \ are satisfied in our current example), any point on the Pareto Set can be \ reached through an appropriate transfer of wealth across agents. Find these \ optimal transfers ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`t\_1\)]], StyleBox[" and ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`t\_2\)]], ". ", StyleBox["Who \"wins\"? Who \"loses\"?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell[TextData[{ "Hint: Note that the equilibrium price from Part 1 remains unchanged. \ Redefine the new budget constraints for both agents, and solve for ", Cell[BoxData[ \(TraditionalForm\`t\_1, \ t\_2\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(solt = Solve[{\(p\_1\^*\)*y\_11 + y\_21 \[Equal] your\ turn, your\ turn \[Equal] your\ turn}, {t\_1, t\_2}]\)], "Input"], Cell[BoxData[ \({{t\_1 \[Rule] 89.82588558195383`, t\_2 \[Rule] \(-89.82588558195386`\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({t\_1 = t\_1 /. solt, t\_2 = t\_2 /. solt}\)], "Input"], Cell[BoxData[ \({{89.82588558195383`}, {\(-89.82588558195386`\)}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Q.7 (2 points): Define the new budget line and add it \ to the graph from part 1. In your print-out, show the new equilibrium point \ in the graph. Is the new equilibrium Pareto-efficient? Why or why not?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(BC2[\(x\_11\) : _] = \((your\ turn)\) /. p\_1 -> \(p\_1\^*\)\)], "Input"], Cell[BoxData[ \({\(\(172.54052663178663`\)\(\[InvisibleSpace]\)\) - 0.8244274809160306`\ x\_11}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(BC2plot = Plot[BC2[x\_11], {x\_11, 0.001, \(\[Omega]\_1\)\&_}, PlotStyle -> {RGBColor[1, 0, 0], Thickness[ .01]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[IC\_1, IC\_2, A, AA, BCplot, B, BC2plot, DefaultFont \[Rule] {"\", 12}, DisplayFunction \[Rule] $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[TextData[StyleBox["Don't forget to identify the new equilibrium point on \ your print-out!", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]]], "Text"], Cell[TextData[StyleBox["Q.8 (3 points): In the \"real world\", who would be \ the \"social planner\", and how would \"transfers' be implemented? Can you \ think of examples of such \"transfers\"?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 1280}, {0, 951}}, WindowToolbars->"EditBar", CellGrouping->Manual, WindowSize->{885, 601}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, Visible->True, PrintingCopies->1, PrintingPageRange->{6, 6}, PrintingOptions->{"PrintingMargins"->{{72, 72}, {54, 54}}, "PrintCellBrackets"->True, "PrintRegistrationMarks"->True, "PrintMultipleHorizontalPages"->False}, InputAliases->{"intt"->RowBox[ {"\[Integral]", RowBox[ {"\[SelectionPlaceholder]", RowBox[ {"\[DifferentialD]", "\[Placeholder]"}]}]}], "dintt"->RowBox[ { SubsuperscriptBox[ "\[Integral]", "\[SelectionPlaceholder]", "\[Placeholder]"], RowBox[ {"\[Placeholder]", RowBox[ {"\[DifferentialD]", "\[Placeholder]"}]}]}], "sumt"->RowBox[ { UnderoverscriptBox[ "\[Sum]", RowBox[ {"\[SelectionPlaceholder]", "=", "\[Placeholder]"}], "\[Placeholder]"], "\[Placeholder]"}], "prodt"->RowBox[ { UnderoverscriptBox[ "\[Product]", RowBox[ {"\[SelectionPlaceholder]", "=", "\[Placeholder]"}], "\[Placeholder]"], "\[Placeholder]"}], "dt"->RowBox[ { SubscriptBox[ "\[PartialD]", "\[Placeholder]"], " ", "\[SelectionPlaceholder]"}], "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[ {"\"\[Placeholder]\"", "\[Rule]", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "pattwraper"->TagBox[ "\[Placeholder]", NotationPatternTag, TagStyle -> "NotationPatternWrapperStyle"], "madeboxeswraper"->TagBox[ "\[Placeholder]", NotationMadeBoxesTag, TagStyle -> "NotationMadeBoxesWrapperStyle"]}, Magnification->1.25, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Title"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. 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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[CellGroupData[{ Cell[StyleData["InputOnly"], CellMargins->{{66, 10}, {7, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Mathematica", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InputOnly", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["InputOnly", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["InputOnly", "Printout"], CellMargins->{{39, 0}, {4, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{66, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, 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->{{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, AutoStyleOptions->{"UnmatchedBracketStyle"->None}, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0.6, 0.100008, 0.100008]], 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}}, 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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"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0.269993, 0.308507, 0.6]], 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Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, 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, 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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->{{60, 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["Outline Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Outline1"], CellMargins->{{60, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, ParagraphIndent->-38, CounterIncrements->"Outline1", FontSize->18, FontWeight->"Bold", CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}], Cell[StyleData["Outline1", "Printout"], CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline2"], CellMargins->{{90, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, ParagraphIndent->-27, CounterIncrements->"Outline2", FontSize->15, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}], Cell[StyleData["Outline2", "Printout"], CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline3"], CellMargins->{{120, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, ParagraphIndent->-21, CounterIncrements->"Outline3", FontSize->12, CounterBoxOptions->{CounterFunction:>Identity}], Cell[StyleData["Outline3", "Printout"], CounterBoxOptions->{CounterFunction:>Identity}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline4"], CellMargins->{{150, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, ParagraphIndent->-18, CounterIncrements->"Outline4", FontSize->10, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["Outline4", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], 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[0.269993, 0.308507, 0.6], 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[0.269993, 0.308507, 0.6], 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["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], 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["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], 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]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "Printout"], 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[ ], #, Placeholder]}]&)}], 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}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, 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"], LanguageCategory->"Formula", ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216]] }, 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]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], FontSize->18], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{39, 0}, {0, 14}}, Hyphenation->True, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ObjectName"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["ObjectName", "Presentation"], FontSize->18], Cell[StyleData["ObjectName", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Usage"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Usage", "Presentation"], FontSize->18], Cell[StyleData["Usage", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Notes"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Notes", "Presentation"], FontSize->18], Cell[StyleData["Notes", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InlineOutput"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InlineOutput", "Presentation"], FontSize->18], Cell[StyleData["InlineOutput", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Box"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["Box", "Presentation"], FontSize->18], Cell[StyleData["Box", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DoubleBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->2, RowAlignments->Top}], Cell[StyleData["DoubleBox", "Presentation"], FontSize->18], Cell[StyleData["DoubleBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.31, 0.67}}], Cell[StyleData["2ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->9, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnEvenBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.46}], Cell[StyleData["2ColumnEvenBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnEvenBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.35, ColumnAlignments->{Right, Left}}], Cell[StyleData["2ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.32}], Cell[StyleData["3ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.24, ColumnAlignments->{Right, Center, Left}}], Cell[StyleData["3ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["4ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.13, 0.35, 0.13, 0.35}}], Cell[StyleData["4ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["4ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["5ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], 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