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{{ + AbsoluteThickness[-1]}}, "Rows" -> {{0}}}, + AllowScriptLevelChange -> False], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + TraditionalForm], HoldForm]}, { + TagBox[ + FormBox[ + TagBox[ + GridBox[{{ + PaneBox[ + StyleBox[ + TagBox[ + GridBox[{{ + StyleBox[ + TagBox[ + TagBox["\"line\"", + $CellContext`TagBoxWrapper[ + "Entity" -> {$CellContext`GeometryData, "Line"}]], + Identity], {LineIndent -> 0, + LineSpacing -> {0.9, 0, 1.5}}], + TemplateBox[{ + StyleBox[ + TagBox["\"Cartesian equation\"", Identity], { + GrayLevel[0.6], + LinebreakAdjustments -> {1, 100, 1, 0, 100}, LineIndent -> + 0}], "\" \"", + TagBox[ + RowBox[{ + RowBox[{"x", "-", + RowBox[{"3", " ", "y"}]}], "\[LongEqual]", "6"}], + HoldForm]}, "RowDefault"]}}, + GridBoxBackground -> {"Columns" -> { + GrayLevel[0.949], None}, "Rows" -> {{None}}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxDividers -> {"Columns" -> { + GrayLevel[0.84], + GrayLevel[0.84], + GrayLevel[0.84]}, "Rows" -> {{ + GrayLevel[0.84]}}, + "RowsIndexed" -> { + 1 -> GrayLevel[0.84], -1 -> GrayLevel[0.84]}}, + GridBoxSpacings -> { + "Columns" -> {1, 1, 1}, "Rows" -> {{0.3}}}, + GridBoxAlignment -> { + "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, + AllowScriptLevelChange -> False, BaselinePosition -> 1], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + LineSpacing -> {1, 0, 1.5}, LineIndent -> 0], + BaselinePosition -> Center]}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxSpacings -> {"Columns" -> {{ + AbsoluteThickness[-1]}}, "Rows" -> {{0}}}, + AllowScriptLevelChange -> False], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + TraditionalForm], HoldForm]}}, + GridBoxBackground -> { + "Columns" -> {None}, "Rows" -> {{None}}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxDividers -> {"Columns" -> { + GrayLevel[0.84], + GrayLevel[0.84]}, "Rows" -> {{ + GrayLevel[0.84]}}, + "RowsIndexed" -> { + 1 -> GrayLevel[0.84], -1 -> GrayLevel[0.84]}}, + GridBoxSpacings -> {"Columns" -> {2, 2}, "Rows" -> {{1}}}, + GridBoxAlignment -> { + "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, + AllowScriptLevelChange -> False, BaselinePosition -> + Automatic], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + LineSpacing -> {1, 0, 1.5}, LineIndent -> 0], + BaselinePosition -> Center]}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxSpacings -> {"Columns" -> {{ + AbsoluteThickness[-1]}}, "Rows" -> {{0}}}, + AllowScriptLevelChange -> False], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + TraditionalForm], + PolynomialForm[#, TraditionalOrder -> False]& ], + TraditionalForm]], "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement[ + "dataformats", {}, {"plaintext,computabledata,formatteddata"}]}], + XMLElement["expressiontypes", {"count" -> "1"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Grid"}, {}], "\n "}]}], + 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AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement["dataformats", {}, {"computabledata,formatteddata"}]}], + XMLElement["expressiontypes", {"count" -> "1"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n "}]}], + Typeset`pod4$$ = XMLElement[ + "pod", {"title" -> "Equation", "scanner" -> "Geometry", "id" -> "Equation", + "position" -> "400", "error" -> "false", "numsubpods" -> "1"}, { + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"x == 3 && y == -1"}], + XMLElement["cell", {"compressed" -> False, "string" -> True}, { + Cell[ + BoxData[ + FormBox[ + TemplateBox[{ + StyleBox["\" and \"", { + GrayLevel[0.6], LinebreakAdjustments -> {1, 100, 1, 0, 100}, + LineIndent -> 0}], + RowBox[{"x", "\[LongEqual]", "3"}], + RowBox[{"y", "\[LongEqual]", + RowBox[{"-", "1"}]}]}, "RowWithSeparator"], TraditionalForm]], + "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement["dataformats", {}, {"plaintext,minput"}]}], + XMLElement["expressiontypes", {"count" -> "1"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n "}]}], + 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False, {False}, True}, Typeset`aux12$$ = { + True, False, {False}, True}, Typeset`aux13$$ = { + True, False, {False}, True}, Typeset`aux14$$ = { + True, False, {False}, True}, Typeset`aux15$$ = { + True, False, {False}, True}, Typeset`aux16$$ = { + True, False, {False}, True}, Typeset`aux17$$ = { + True, False, {False}, True}, Typeset`aux18$$ = { + True, False, {False}, True}, Typeset`aux19$$ = { + True, False, {False}, True}, Typeset`aux20$$ = { + True, False, {False}, True}, Typeset`aux21$$ = { + True, False, {False}, True}, Typeset`aux22$$ = { + True, False, {False}, True}, Typeset`aux23$$ = { + True, False, {False}, True}, Typeset`aux24$$ = { + True, False, {False}, True}, Typeset`aux25$$ = { + True, False, {False}, True}, Typeset`aux26$$ = { + True, False, {False}, True}, Typeset`aux27$$ = { + True, False, {False}, True}, Typeset`aux28$$ = { + True, False, {False}, True}, Typeset`aux29$$ = { + True, False, {False}, True}, Typeset`aux30$$ = { + True, False, {False}, True}, 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"timedout" -> "", "timedoutpods" -> "", "timing" -> + "4.441", "parsetiming" -> "0.", "parsetimedout" -> "false", + "recalculate" -> "", "id" -> "", "parseidserver" -> "34", "host" -> + "https://www5b.wolframalpha.com", "server" -> "34", "related" -> "", + "version" -> "2.6"}}, Typeset`sessioninfo$$ = { + "TimeZone" -> 2., + "Date" -> {2020, 6, 19, 19, 19, 55.6699605`9.49819575230407}, "Line" -> 6, + "SessionID" -> 23180306378915507075}, Typeset`showpods$$ = {1, 2, 3, 4}, + Typeset`failedpods$$ = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, + 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}, + Typeset`chosen$$ = {"Result", "Result", 1, 1, "Content"}, Typeset`open$$ = + False, Typeset`newq$$ = "intersection 3x+2y=7;x-3y=6"}, + DynamicBox[ToBoxes[ + AlphaIntegration`FormatAlphaResults[ + Dynamic[{ + 2, {Typeset`pod1$$, Typeset`pod2$$, Typeset`pod3$$, Typeset`pod4$$, + Typeset`pod5$$, Typeset`pod6$$, Typeset`pod7$$, Typeset`pod8$$, + Typeset`pod9$$, Typeset`pod10$$, 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+ FrameBox[ + StyleBox[ + FormBox[ + RowBox[{"a", "\[LongEqual]", + RowBox[{"-", + FractionBox["9", "2"]}]}], + TraditionalForm], "Output", + CellSize->{550, Automatic}, + AutoStyleOptions->{"HighlightFormattingErrors"->False}, + ScriptLevel->0, + NumberPoint->".", + RenderingOptions->{"3DRenderingMethod"->"BSPTreeOrDepthBuffer"}, + FontFamily->"Times", + FontSize->14, + Background->None, + GraphicsBoxOptions->{DefaultAxesStyle->Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> 1, + "GraphicsAxes"], + DefaultBaseStyle->{FontFamily -> "Times", "Graphics"}, + DefaultFrameStyle->Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> 1, + "GraphicsFrame"], + DefaultFrameTicksStyle->Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle->Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions->{ + DefaultBaseStyle->{FontFamily -> "Times", "Graphics3D"}}], + BaseStyle->{Plain}, + FrameMargins->10, + FrameStyle->GrayLevel[0.85], + RoundingRadius->5, + StripOnInput->False], + WolframAlphaResult[ + "Solve 2^a = Sqrt[8]/4^3 for a", {{"RealSolution", 1}, + "Content"}]]], "Output", + CellChangeTimes->{3.8015789136843767`*^9, 3.801579023881501*^9}, + CellLabel->"Out[68]=",ExpressionUUID->"e20ba9bc-e19f-4111-8768-b093bee0c5e6"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"N", "[", "%", "]"}]], "Input", + CellChangeTimes->{{3.8015790323118258`*^9, 3.801579035946787*^9}}, + CellLabel->"In[69]:=",ExpressionUUID->"efb1b35e-1827-4adf-9365-d66ce2f00309"], + +Cell[BoxData[ + InterpretationBox[ + FrameBox[ + StyleBox[ + FormBox[ + RowBox[{"a", "\[LongEqual]", + RowBox[{"-", + FractionBox["9", "2"]}]}], + TraditionalForm], "Output", + CellSize->{550, Automatic}, + AutoStyleOptions->{"HighlightFormattingErrors"->False}, + ScriptLevel->0, + NumberPoint->".", + RenderingOptions->{"3DRenderingMethod"->"BSPTreeOrDepthBuffer"}, + FontFamily->"Times", + FontSize->14, + Background->None, + GraphicsBoxOptions->{DefaultAxesStyle->Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> 1, + "GraphicsAxes"], + DefaultBaseStyle->{FontFamily -> "Times", "Graphics"}, + DefaultFrameStyle->Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> 1, + "GraphicsFrame"], + DefaultFrameTicksStyle->Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle->Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions->{ + DefaultBaseStyle->{FontFamily -> "Times", "Graphics3D"}}], + BaseStyle->{Plain}, + FrameMargins->10, + FrameStyle->GrayLevel[0.85], + RoundingRadius->5, + StripOnInput->False], + WolframAlphaResult[ + "Solve 2^a = Sqrt[8]/4^3 for a", {{"RealSolution", 1}, + "Content"}]]], "Output", + CellChangeTimes->{3.801579038715397*^9}, + CellLabel->"Out[69]=",ExpressionUUID->"ae0fdc42-f7b3-40a3-850f-6b1cb914cbe5"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"N", "[", + RowBox[{ + RowBox[{"-", "9"}], "/", "2"}], "]"}]], "Input", + CellChangeTimes->{{3.8015790519287705`*^9, 3.801579061075058*^9}}, + CellLabel->"In[70]:=",ExpressionUUID->"2f957717-15c5-449a-898c-1fc4692ecda2"], + +Cell[BoxData[ + RowBox[{"-", "4.5`"}]], "Output", + CellChangeTimes->{3.801579061684697*^9}, + CellLabel->"Out[70]=",ExpressionUUID->"e170a973-f356-4f54-a4ce-fcbcbac7287d"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"Simplify", "[", + SqrtBox[ + FractionBox[ + RowBox[{ + SuperscriptBox["x", "16"], "*", + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["x", "2"]}], ")"}]}], "9"]], "]"}]], "Input", + CellChangeTimes->{{3.801579074164366*^9, 3.801579127135021*^9}}, + CellLabel->"In[71]:=",ExpressionUUID->"59d37f11-40c0-4dd9-948f-695a9fe9841c"], + +Cell[BoxData[ + RowBox[{ + FractionBox["1", "3"], " ", + SqrtBox[ + RowBox[{ + SuperscriptBox["x", "16"], "+", + SuperscriptBox["x", "18"]}]]}]], "Output", + CellChangeTimes->{3.801579128138647*^9}, + CellLabel->"Out[71]=",ExpressionUUID->"9a86d611-2859-4f9f-afdc-e2d94c9550a7"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + NamespaceBox["WolframAlphaQueryResults", + DynamicModuleBox[{Typeset`q$$ = "Simplify[Sqrt[(x^16*(1 + x^2))/9]]", + Typeset`opts$$ = { + AppearanceElements -> { + "Extrusion", "Warnings", "Assumptions", "Pods", "Unsuccessful"}, + Asynchronous -> All, + Method -> { + "ExtrusionChosen" -> { + "Fast parse", "Fast parse", 1, 0, "Input", + "Simplify[Sqrt[(x^16*(1 + x^2))/9]]"}, "ExtrusionOpen" -> True, + "Formats" -> {"cell", "minput", "moutput", "msound", "dataformats"}}}, + Typeset`elements$$ = { + "Extrusion", "Warnings", "Assumptions", "Pods", "Unsuccessful"}, + Typeset`pod1$$ = XMLElement[ + "pod", {"title" -> "Input interpretation", "scanner" -> "Identity", "id" -> + "Input", "position" -> "100", "error" -> "false", "numsubpods" -> "1"}, { + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"Simplify[Sqrt[(x^16 (1 + x^2))/9]]"}], + XMLElement["cell", {"compressed" -> False, "string" -> True}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + TagBox[ + GridBox[{{ + PaneBox[ + StyleBox[ + TagBox[ + GridBox[{{ + StyleBox[ + "\"simplify\"", { + LineIndent -> 0, LineSpacing -> {0.9, 0, 1.5}}], + StyleBox[ + SqrtBox[ + RowBox[{ + FractionBox["1", "9"], " ", + RowBox[{"(", + TagBox[ + RowBox[{ + SuperscriptBox["x", "16"], " ", + RowBox[{"(", + RowBox[{"1", "+", + SuperscriptBox["x", "2"]}], ")"}]}], + PolynomialForm[#, TraditionalOrder -> False]& ], ")"}]}]], + ScriptLevel -> 0, StripOnInput -> False]}}, + GridBoxBackground -> {"Columns" -> { + GrayLevel[0.949], None}, "Rows" -> {{None}}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxDividers -> {"Columns" -> { + GrayLevel[0.84], + GrayLevel[0.84], + GrayLevel[0.84]}, "Rows" -> {{ + GrayLevel[0.84]}}, + "RowsIndexed" -> { + 1 -> GrayLevel[0.84], -1 -> GrayLevel[0.84]}}, + GridBoxSpacings -> { + "Columns" -> {2, 2, 2}, "Rows" -> {{1}}}, + GridBoxAlignment -> { + "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, + AllowScriptLevelChange -> False, BaselinePosition -> 1], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + LineSpacing -> {1, 0, 1.5}, LineIndent -> 0], + BaselinePosition -> Center]}}, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + ColumnsEqual -> False, RowsEqual -> False, + GridBoxSpacings -> {"Columns" -> {{ + AbsoluteThickness[-1]}}, "Rows" -> {{0}}}, + AllowScriptLevelChange -> False], + $CellContext`TagBoxWrapper["Separator" -> " | "]], + PolynomialForm[#, TraditionalOrder -> False]& ], + TraditionalForm]], "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement["dataformats", {}, {"plaintext,minput"}]}], + XMLElement["expressiontypes", {"count" -> "1"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n "}]}], + Typeset`pod2$$ = XMLElement[ + "pod", {"title" -> "Result", "scanner" -> "Simplification", "id" -> + "Result", "position" -> "200", "error" -> "false", "numsubpods" -> "1", + "primary" -> "true"}, { + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"FullSimplify[Sqrt[x^16 (1 + x^2)]/3]"}], + XMLElement["moutput", {}, {"Sqrt[x^16 + x^18]/3"}], + XMLElement["cell", {"compressed" -> False, "string" -> True}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + RowBox[{ + FractionBox["1", "3"], " ", + SqrtBox[ + RowBox[{ + SuperscriptBox["x", "18"], "+", + SuperscriptBox["x", "16"]}]]}], Identity], + TraditionalForm]], "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement[ + "dataformats", {}, { + "plaintext,minput,moutput,computabledata,formatteddata,formuladata"}]}\ +], + XMLElement["expressiontypes", {"count" -> "1"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n "}]}], + Typeset`pod3$$ = XMLElement[ + "pod", {"title" -> "Alternate forms assuming x is real", "scanner" -> + "Simplification", "id" -> "RealAlternateForm", "position" -> "300", + "error" -> "false", "numsubpods" -> "2"}, { + XMLElement["subpod", {"title" -> ""}, { + XMLElement["cell", {"compressed" -> False, "string" -> True}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + RowBox[{ + FractionBox["1", "3"], " ", + SuperscriptBox["x", "8"], " ", + SqrtBox[ + RowBox[{ + SuperscriptBox["x", "2"], "+", "1"}]]}], Identity], + TraditionalForm]], "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement[ + "dataformats", {}, { + "plaintext,computabledata,formatteddata,formuladata"}]}], + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"ComplexExpand[Sqrt[x^16 (1 + x^2)]/3]"}], + XMLElement["cell", {"compressed" -> False, "string" -> True}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + RowBox[{ + FractionBox["1", "3"], " ", + SqrtBox[ + SuperscriptBox["x", "16"]], " ", + SqrtBox[ + RowBox[{ + SuperscriptBox["x", "2"], "+", "1"}]]}], Identity], + TraditionalForm]], "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement[ + "dataformats", {}, { + "plaintext,minput,computabledata,formatteddata,formuladata"}]}], + XMLElement["expressiontypes", {"count" -> "2"}, {"\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n ", + XMLElement["expressiontype", {"name" -> "Default"}, {}], "\n "}]}], + Typeset`pod4$$ = XMLElement[ + "pod", {"title" -> "Plots", "scanner" -> "Simplification", "id" -> "Plot", + "position" -> "400", "error" -> "false", "numsubpods" -> "2"}, { + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"Plot[Sqrt[x^16 + x^18]/3, {x, -12, 12}]"}], + XMLElement["cell", {"compressed" -> True, "string" -> False}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + FormBox[ + StyleBox[ + + DynamicModuleBox[{ + CalculateUtilities`GraphicsUtilities`Private`max3087$$ = 0.5, + CalculateUtilities`GraphicsUtilities`Private`min3086$$ = \ +-0.5, CalculateUtilities`GraphicsUtilities`Private`more$$ = False, + Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, + Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, + Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", + Typeset`specs$$ = {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`more$$], { + False, True}}, {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$], \ +-0.5, "min"}, -1, 1}, {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`max3087$$], + 0.5, "max"}, -1, 1}, { + Hold[ + Style[ + Overlay[{ + Dynamic[ + RawBoxes[ + FEPrivate`FrontEndResource[ + "WABitmaps", "PodInfoBackground"]]], + Pane[ + Column[{ + Grid[{{ + Manipulate`Place[1], + Manipulate`Place[2]}}]}], + ImageMargins -> {{20, 30}, {10, 10}}]}, {1, 2}, 2, + Alignment -> {Left, Top}]]], + Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = + Automatic, Typeset`update$$ = 0, Typeset`initDone$$ = False, + Typeset`skipInitDone$$ = False, + CalculateUtilities`GraphicsUtilities`Private`more$1816721$$ = + False, CalculateUtilities`GraphicsUtilities`Private`min3086$\ +1816726$$ = 0, CalculateUtilities`GraphicsUtilities`Private`max3087$1816727$$ = + 0}, + DynamicBox[ + Manipulate`ManipulateBoxes[ + 2, TraditionalForm, + "Variables" :> { + CalculateUtilities`GraphicsUtilities`Private`max3087$$ = + 0.5, CalculateUtilities`GraphicsUtilities`Private`min3086$\ +$ = -0.5, CalculateUtilities`GraphicsUtilities`Private`more$$ = False}, + "ControllerVariables" :> { + Hold[ + CalculateUtilities`GraphicsUtilities`Private`more$$, + CalculateUtilities`GraphicsUtilities`Private`more$1816721$\ +$, False], + Hold[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$, + CalculateUtilities`GraphicsUtilities`Private`min3086$\ +1816726$$, 0], + Hold[ + CalculateUtilities`GraphicsUtilities`Private`max3087$$, + CalculateUtilities`GraphicsUtilities`Private`max3087$\ +1816727$$, 0]}, "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, + Typeset`bookmarkMode$$, Typeset`animator$$, + Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, + Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> Quiet[ + Function[Null, + CalculateUtilities`GraphicsUtilities`Private`post$1816698[ + Plot[ + SlotSequence[1], AspectRatio -> If[ + TrueQ[ + CalculateUtilities`GraphicsUtilities`Private`aspect], + Automatic, 1/GoldenRatio]]], HoldAll][ + Rational[1, 3] ($CellContext`x^16 + $CellContext`x^18)^ + Rational[1, 2], {$CellContext`x, + If[ + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$], + ( + Piecewise[{{ + 0. + 12.785777813090382` Tan[1.5040801783846716` #], # < + 0}}, 0. + + 12.785777813090382` Tan[1.5040801783846716` #]]& )[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$], \ +-11.96], + If[ + And[ + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$], + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`max3087$$]], + ( + Piecewise[{{ + 0. + 12.785777813090382` Tan[1.5040801783846716` #], # < + 0}}, 0. + + 12.785777813090382` Tan[1.5040801783846716` #]]& )[ + If[ + CalculateUtilities`GraphicsUtilities`Private`min3086$$ == + CalculateUtilities`GraphicsUtilities`Private`max3087$$, + CalculateUtilities`GraphicsUtilities`Private`min3086$$ + + 0.023920000000000004`, + CalculateUtilities`GraphicsUtilities`Private`max3087$$]], + 11.96]}, + LabelStyle -> {FontFamily -> "Bitstream Charter"}, + WorkingPrecision -> 39, + PlotRange -> {Automatic, Automatic}, LabelStyle -> {}, + Ticks -> Automatic, ImageSize -> 220., AxesLabel -> { + RawBoxes[ + FormBox["x", TraditionalForm]], + RawBoxes[ + FormBox["y", TraditionalForm]]}, AxesLabel -> { + RawBoxes[ + FormBox["x", TraditionalForm]], None}]], + "Specifications" :> {{ + CalculateUtilities`GraphicsUtilities`Private`more$$, { + False, True}, ControlType -> None}, {{ + CalculateUtilities`GraphicsUtilities`Private`min3086$$, \ +-0.5, "min"}, -1, 1, ImageSize -> Tiny, ControlPlacement -> 1}, {{ + CalculateUtilities`GraphicsUtilities`Private`max3087$$, + 0.5, "max"}, -1, 1, ImageSize -> Tiny, ControlPlacement -> + 2}, + Style[ + Overlay[{ + Dynamic[ + RawBoxes[ + FEPrivate`FrontEndResource[ + "WABitmaps", "PodInfoBackground"]]], + Pane[ + Column[{ + Grid[{{ + Manipulate`Place[1], + Manipulate`Place[2]}}]}], + ImageMargins -> {{20, 30}, {10, 10}}]}, {1, 2}, 2, + Alignment -> {Left, Top}]]}, + "Options" :> { + ControlPlacement -> Bottom, + FrameMargins -> {{0, 0}, {0, 10}}, Paneled -> False, + AppearanceElements -> {}, + LabelStyle -> { + "DialogStyle", FontColor -> GrayLevel[0.25]}}, + "DefaultOptions" :> {}], SingleEvaluation -> True], + Initialization :> ({ + ReleaseHold[ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`WACleanTicks[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`res, + CalculateUtilities`GraphicsUtilities`Private`unitformat}, + CalculateUtilities`GraphicsUtilities`Private`res = + ReplaceAll[ + ReplaceAll[ + Part[ + DeleteCases[ + Replace[ + ReplaceAll[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Alternatives[ + Style, $CellContext`UnitNumberForm, NumberForm] -> (#& )], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, { + PatternTest[ + BlankSequence[], NumberQ]}] :> + Thread[{CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`t}]], { + Blank[], "", + BlankNullSequence[]}], All, + Span[1, 2]], Superscript[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[Integer]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`p, + Blank[Integer]]] :> + CalculateUtilities`GraphicsUtilities`Private`b^ + CalculateUtilities`GraphicsUtilities`Private`p], Row[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + BlankSequence[]]}, "\[Times]"] :> + Times[CalculateUtilities`GraphicsUtilities`Private`a]]; If[ + MatchQ[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 2], + Condition[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`quants, { + Alternatives[ + BlankSequence[$CellContext`ShortQuantity], + BlankSequence[Quantity]]}], Length[ + Union[ + + Map[$CellContext`UnitObjectPart, + CalculateUtilities`GraphicsUtilities`Private`quants]]] == + 1]], CalculateUtilities`GraphicsUtilities`Private`\ +unitformat = $CellContext`ToCDFQuantityFunction[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, 1, 2]]; + CalculateUtilities`GraphicsUtilities`Private`unitformat -> + Thread[{ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 1], + $CellContext`QuantityPart[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 2], + $CellContext`UnitObjectPart[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, 1, + 2]]]}], + CalculateUtilities`GraphicsUtilities`Private`res]]; + Options[ + CalculateUtilities`GraphicsUtilities`Private`post$1816698]\ + = {"ReturnInteractiveTypes" -> False, "Nearest" -> Automatic}; + CalculateUtilities`GraphicsUtilities`Private`post$1816698[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`g, + Blank[Graphics]], + OptionsPattern[]] := Check[ + + Module[{ + CalculateUtilities`GraphicsUtilities`Private`lines, + CalculateUtilities`GraphicsUtilities`Private`pts, + CalculateUtilities`GraphicsUtilities`Private`gg, + CalculateUtilities`GraphicsUtilities`Private`type, + CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r, + CalculateUtilities`GraphicsUtilities`Private`oldepilog, + CalculateUtilities`GraphicsUtilities`Private`range, + CalculateUtilities`GraphicsUtilities`Private`gridlines, + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle = OptionValue["Nearest"]}, + CalculateUtilities`GraphicsUtilities`Private`oldepilog = + Replace[ + ReplaceAll[Epilog, + Options[CalculateUtilities`GraphicsUtilities`Private`g]], + Epilog -> Sequence[]]; Switch[ + ReplaceAll[{Frame, Axes}, + Options[ + CalculateUtilities`GraphicsUtilities`Private`g]], {True, + Blank[]}, + CalculateUtilities`GraphicsUtilities`Private`type = + Frame; {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r} = + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + ReplaceAll[FrameTicks, + Options[ + CalculateUtilities`GraphicsUtilities`Private`g]]], { + Blank[], True}, + CalculateUtilities`GraphicsUtilities`Private`type = + Axes; {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l} = + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + ReplaceAll[Ticks, + Options[CalculateUtilities`GraphicsUtilities`Private`g]]], + Blank[], + CalculateUtilities`GraphicsUtilities`Private`type = None]; + If[ + And[ + CalculateUtilities`GraphicsUtilities`Private`type === + Frame, + Or[ + Not[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`t === None, + CalculateUtilities`GraphicsUtilities`Private`b === + CalculateUtilities`GraphicsUtilities`Private`t]], + Not[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`r === None, + CalculateUtilities`GraphicsUtilities`Private`l === + CalculateUtilities`GraphicsUtilities`Private`r]]]], + CalculateUtilities`GraphicsUtilities`Private`type = None]; + If[ + TrueQ[ + OptionValue["ReturnInteractiveTypes"]], + Which[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`type === + None, CalculateUtilities`GraphicsUtilities`Private`b === + None, CalculateUtilities`GraphicsUtilities`Private`l === + None], {}, + FreeQ[CalculateUtilities`GraphicsUtilities`Private`g, + Alternatives[Line, Point]], {}, True, { + "Tooltips", "Coordinates"}], If[ + FreeQ[CalculateUtilities`GraphicsUtilities`Private`g, + Alternatives[Line, Point]], + Return[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`gg = + Normal[CalculateUtilities`GraphicsUtilities`Private`g]; + CalculateUtilities`GraphicsUtilities`Private`pts = + Partition[ + Flatten[ + Cases[ + Part[CalculateUtilities`GraphicsUtilities`Private`gg, 1], + Point[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[]]] :> + CalculateUtilities`GraphicsUtilities`Private`a, + Infinity]], 2]; + If[Length[ + CalculateUtilities`GraphicsUtilities`Private`pts] < 2, + CalculateUtilities`GraphicsUtilities`Private`lines = Cases[ + Part[CalculateUtilities`GraphicsUtilities`Private`gg, 1], + Blank[Line], Infinity]; + If[CalculateUtilities`GraphicsUtilities`Private`lines === \ +{}, + Return[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`pts = Flatten[ + Cases[ + CalculateUtilities`GraphicsUtilities`Private`lines, Line[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[]]] :> + CalculateUtilities`GraphicsUtilities`Private`a, Infinity], + 1]; If[ + CalculateUtilities`GraphicsUtilities`Private`neareststyle === + Automatic, If[ + CalculateUtilities`GraphicsUtilities`Private`orderedLines[ + CalculateUtilities`GraphicsUtilities`Private`lines], + CalculateUtilities`GraphicsUtilities`Private`neareststyle = + "1D", CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle = "2D"]; Null], + If[ + CalculateUtilities`GraphicsUtilities`Private`neareststyle === + Automatic, + CalculateUtilities`GraphicsUtilities`Private`neareststyle = + "2D"]]; + CalculateUtilities`GraphicsUtilities`Private`range = + Replace[ + ReplaceAll[PlotRange, + Options[CalculateUtilities`GraphicsUtilities`Private`g]], + Except[{{ + PatternTest[ + Blank[], NumberQ], + PatternTest[ + Blank[], NumberQ]}, { + PatternTest[ + Blank[], NumberQ], + PatternTest[ + Blank[], NumberQ]}}] :> { + Through[ + {Min, Max}[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 1]]], + Through[ + {Min, Max}[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 2]]]}]; CalculateUtilities`GraphicsUtilities`Private`b = + + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[CalculateUtilities`GraphicsUtilities`Private`b, + First[CalculateUtilities`GraphicsUtilities`Private`range], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 1]]; CalculateUtilities`GraphicsUtilities`Private`l = + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[CalculateUtilities`GraphicsUtilities`Private`l, + Last[CalculateUtilities`GraphicsUtilities`Private`range], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 2]]; CalculateUtilities`GraphicsUtilities`Private`\ +oldgridlines = ReplaceAll[GridLines, + Options[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`gridlines = + With[{CalculateUtilities`GraphicsUtilities`Private`gray = + GrayLevel[0.7]}, + Replace[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines,\ + {Pattern[CalculateUtilities`GraphicsUtilities`Private`a, { + Blank[List], + Blank[List]}] :> Dynamic[ + Join[CalculateUtilities`GraphicsUtilities`Private`a, + Replace[ + MousePosition[{"Graphics", Graphics}, None], { + None -> {{}, {}}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`x, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`y, + Blank[]]} :> {{{ + CalculateUtilities`GraphicsUtilities`Private`x, + CalculateUtilities`GraphicsUtilities`Private`gray}}, {{ + CalculateUtilities`GraphicsUtilities`Private`y, + CalculateUtilities`GraphicsUtilities`Private`gray}}}}], + 2]], { + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[List]], Automatic} :> + With[{CalculateUtilities`GraphicsUtilities`Private`\ +divisions = {CalculateUtilities`GraphicsUtilities`Private`a, + FindDivisions[ + Last[CalculateUtilities`GraphicsUtilities`Private`range], + 7]}}, + Dynamic[ + Join[ + CalculateUtilities`GraphicsUtilities`Private`divisions, + Replace[ + MousePosition[{"Graphics", Graphics}, None], { + None -> {{}, {}}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`x, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`y, + Blank[]]} :> {{{ + CalculateUtilities`GraphicsUtilities`Private`x, + CalculateUtilities`GraphicsUtilities`Private`gray}}, {{ + CalculateUtilities`GraphicsUtilities`Private`y, + CalculateUtilities`GraphicsUtilities`Private`gray}}}}], + 2]]], Blank[] -> Dynamic[ + + Map[{{#, + CalculateUtilities`GraphicsUtilities`Private`gray}}& , + MousePosition[{"Graphics", Graphics}, None]]]}]]; If[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`type === + None, CalculateUtilities`GraphicsUtilities`Private`b === + None, CalculateUtilities`GraphicsUtilities`Private`l === + None], + Show[ + CalculateUtilities`GraphicsUtilities`Private`g, GridLines -> + CalculateUtilities`GraphicsUtilities`Private`gridlines, + If[ + MatchQ[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + Alternatives[None, GridLines]], + Method -> {"GridLinesInFront" -> True}, + Apply[Sequence, {}]]], + + With[{CalculateUtilities`GraphicsUtilities`Private`nf = + If[CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle === "1D", + + With[{CalculateUtilities`GraphicsUtilities`Private`n = + Nearest[Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, 1] -> + CalculateUtilities`GraphicsUtilities`Private`pts]}, + CalculateUtilities`GraphicsUtilities`Private`n[ + Part[#, 1]]& ], + + With[{CalculateUtilities`GraphicsUtilities`Private`n = + Nearest[Transpose[ + Transpose[ + CalculateUtilities`GraphicsUtilities`Private`pts]/Abs[ + Apply[ + Subtract, + CalculateUtilities`GraphicsUtilities`Private`range, { + 1}]]] -> + CalculateUtilities`GraphicsUtilities`Private`pts], + CalculateUtilities`GraphicsUtilities`Private`scale = Abs[ + Apply[ + Subtract, + CalculateUtilities`GraphicsUtilities`Private`range, { + 1}]]}, CalculateUtilities`GraphicsUtilities`Private`n[#/ + CalculateUtilities`GraphicsUtilities`Private`scale]& ]], + CalculateUtilities`GraphicsUtilities`Private`left = + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`bottom = + CalculateUtilities`GraphicsUtilities`Private`b}, + Show[ + CalculateUtilities`GraphicsUtilities`Private`g, GridLines -> + CalculateUtilities`GraphicsUtilities`Private`gridlines, + If[ + MatchQ[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + Alternatives[None, GridLines]], + Method -> {"GridLinesInFront" -> True}, + Apply[Sequence, {}]], + Epilog -> { + CalculateUtilities`GraphicsUtilities`Private`oldepilog, + Dynamic[ + + DynamicModule[{ + CalculateUtilities`GraphicsUtilities`Private`pt = + CalculateUtilities`GraphicsUtilities`Private`nf[ + MousePosition[{"Graphics", Graphics}, {0, 0}]], + CalculateUtilities`GraphicsUtilities`Private`scaled = + MousePosition[{"GraphicsScaled", Graphics}, None]}, + If[CalculateUtilities`GraphicsUtilities`Private`scaled === + None, {}, { + Text[ + Style[ + Row[{ + CalculateUtilities`GraphicsUtilities`Private`bottom[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pt, 1, 1]], + CalculateUtilities`GraphicsUtilities`Private`left[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pt, 1, 2]]}, + ","], 12], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pt, 1], { + 1.5 Sign[Part[ + CalculateUtilities`GraphicsUtilities`Private`scaled, 1] - + 0.5], 0}, Background -> White], + AbsolutePointSize[7], + Point[CalculateUtilities`GraphicsUtilities`Private`pt], + White, + AbsolutePointSize[5], + Point[ + CalculateUtilities`GraphicsUtilities`Private`pt]}]]]}]]]]]\ +, CalculateUtilities`GraphicsUtilities`Private`g]; + CalculateUtilities`GraphicsUtilities`Private`post$1816698[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`g, + Blank[]], + BlankNullSequence[]] := + CalculateUtilities`GraphicsUtilities`Private`g; + CalculateUtilities`GraphicsUtilities`Private`orderedLines[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + BlankSequence[Line]]}] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`ordered, + CalculateUtilities`GraphicsUtilities`Private`intervals}, + CalculateUtilities`GraphicsUtilities`Private`ordered = + Apply[And, + Map[OrderedQ[ + Part[#, 1, All, 1]]& , + Hold[CalculateUtilities`GraphicsUtilities`Private`l]]]; If[ + Not[ + TrueQ[ + CalculateUtilities`GraphicsUtilities`Private`ordered]], + Return[False]]; + CalculateUtilities`GraphicsUtilities`Private`intervals = + Part[{CalculateUtilities`GraphicsUtilities`Private`l}, + All, 1, {1, -1}, 1]; Length[ + Apply[ + Interval, + CalculateUtilities`GraphicsUtilities`Private`intervals]] === + Length[CalculateUtilities`GraphicsUtilities`Private`\ +intervals]]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + Alternatives[Automatic, FrameTicks]] = { + Identity, Identity, Identity, Identity}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`r, + Blank[]]}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, {{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`r, + Blank[]]}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, + Blank[]]}}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + Blank[]] = {None, None, None, None}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + Alternatives[Automatic, Ticks]] = {Identity, Identity}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`h, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`v, + Blank[]]}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`h, + CalculateUtilities`GraphicsUtilities`Private`v}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + Blank[]] = {None, None}; + CalculateUtilities`GraphicsUtilities`Private`CDFCleanTicks[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := ReplaceAll[ + ReplaceAll[ + Part[ + DeleteCases[ + ReplaceAll[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Alternatives[Style, NumberForm] -> (#& )], { + Blank[], "", + BlankNullSequence[]}], All, + Span[1, 2]], Superscript[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[Integer]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`p, + Blank[Integer]]] :> + CalculateUtilities`GraphicsUtilities`Private`b^ + CalculateUtilities`GraphicsUtilities`Private`p], Row[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + BlankSequence[]]}, "\[Times]"] :> + Times[CalculateUtilities`GraphicsUtilities`Private`a]]; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks$, + Blank[]]] := + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + CalculateUtilities`GraphicsUtilities`Private`WACleanTicks[ + CalculateUtilities`GraphicsUtilities`Private`ticks$]]; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[None] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[False] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[True] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[Automatic] = Identity; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[All] = Identity; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[Pattern[CalculateUtilities`GraphicsUtilities`Private`func, + Blank[]] -> + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := Replace[ + + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[CalculateUtilities`GraphicsUtilities`Private`ticks], + Pattern[CalculateUtilities`GraphicsUtilities`Private`f, + Except[None]] :> + Composition[ + CalculateUtilities`GraphicsUtilities`Private`func, + CalculateUtilities`GraphicsUtilities`Private`f]]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[{}] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, { + Repeated[{ + Blank[Integer], + Blank[String]}]}]] := Which[ + Quiet[ + MatchQ[ + Apply[SameQ, + Map[Part[ + DateList[#], + Span[2, All]]& , + CalculateUtilities`GraphicsUtilities`Private`ticks, { + 2}], {1}], { + Repeated[True]}]], DateString, + Apply[And, + StringMatchQ[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 2], NumberString]], + + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Transpose[{ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 1], + ToExpression[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 2]]}]], True, None]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, { + Repeated[{ + PatternTest[ + Blank[], NumericQ], + PatternTest[ + Blank[], NumericQ]}]}]] := Which[ + MatchQ[ + Apply[ + Equal, CalculateUtilities`GraphicsUtilities`Private`ticks,\ + {1}], { + Repeated[True]}], Identity, + MatchQ[ + + Apply[# == Log[#2]& , + CalculateUtilities`GraphicsUtilities`Private`ticks, {1}], { + Repeated[True]}], Exp, + TrueQ[ + Quiet[ + Apply[Equal, + Apply[Divide, Transpose[ + Rest[CalculateUtilities`GraphicsUtilities`Private`ticks]] - + Part[CalculateUtilities`GraphicsUtilities`Private`ticks, + 1]]]]], + + With[{CalculateUtilities`GraphicsUtilities`Private`slope = + Apply[Divide, + Apply[Subtract, + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, {-1, + 1}]]]}, + SetPrecision[(# - Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, 1, + 1])/CalculateUtilities`GraphicsUtilities`Private`slope + + Part[CalculateUtilities`GraphicsUtilities`Private`ticks, + 1, 2], 3]& ], True, None]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Blank[]] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`type, + Blank[]], + BlankNullSequence[]] := + CalculateUtilities`GraphicsUtilities`Private`type; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[Identity, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Blank[]] := + With[{CalculateUtilities`GraphicsUtilities`Private`nf = + CalculateUtilities`GraphicsUtilities`Private`numberForm, + CalculateUtilities`GraphicsUtilities`Private`acc = + Floor[Max[ + Ceiling[ + FullSimplify[Log[10, + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]] - + Log[10, (CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/100]]], + 3] - RealExponent[ + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]]]}, + CalculateUtilities`GraphicsUtilities`Private`nf[#, + CalculateUtilities`GraphicsUtilities`Private`acc]& ]; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[Exp, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Blank[]] := + With[{CalculateUtilities`GraphicsUtilities`Private`prec = + Max[ + Ceiling[ + FullSimplify[Log[10, + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]] - + Log[10, (CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/100]]], + 3]}, Quiet[ + RawBoxes[ + ToBoxes[ + NumberForm[ + Exp[#], + CalculateUtilities`GraphicsUtilities`Private`prec]]]]& ]; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[DateString, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Pattern[CalculateUtilities`GraphicsUtilities`Private`pts, + Blank[]]] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`dates, + CalculateUtilities`GraphicsUtilities`Private`spec}, + CalculateUtilities`GraphicsUtilities`Private`dates = + Map[DateList, + CalculateUtilities`GraphicsUtilities`Private`pts]; + CalculateUtilities`GraphicsUtilities`Private`spec = Switch[ + Map[Length, + Map[Union, + Transpose[ + CalculateUtilities`GraphicsUtilities`Private`dates]]], { + Blank[], 1, 1, + BlankSequence[]}, {"Year"}, { + Blank[], + Blank[], 1, + BlankSequence[]}, {"MonthNameShort", " ", "Year"}, + Blank[], { + "DayShort", " ", "MonthNameShort", " ", "Year"}]; + If[(CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/ + 31536000 > 25, + CalculateUtilities`GraphicsUtilities`Private`spec = { + "Year"}]; + With[{CalculateUtilities`GraphicsUtilities`Private`s = + CalculateUtilities`GraphicsUtilities`Private`spec}, + DateString[#, + CalculateUtilities`GraphicsUtilities`Private`s]& ]]; + CalculateUtilities`GraphicsUtilities`Private`numberForm = + Function[{ + CalculateUtilities`GraphicsUtilities`Private`a, + CalculateUtilities`GraphicsUtilities`Private`acc}, + Quiet[ + RawBoxes[ + ToBoxes[ + NumberForm[CalculateUtilities`GraphicsUtilities`Private`a, + Max[1, + Ceiling[ + RealExponent[ + CalculateUtilities`GraphicsUtilities`Private`a] + + CalculateUtilities`GraphicsUtilities`Private`acc]], + ExponentFunction -> (Null& ), + NumberFormat -> (StringReplace[#, StringExpression[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`s, + BlankSequence[]], ".", EndOfString] -> + CalculateUtilities`GraphicsUtilities`Private`s]& )]]]]]]], + ReleaseHold[ + Uncompress[ + "6:eJztVm1v0zAQbinv7/\ +APkPiMKCDgCxLQwZg0oCTle734klq4drCdbfDnwWc3SbN2lWI6QFP64VRfmsd3zz13vQcHMkr7vV5P\ +X7Tmg+Q0vYKn+9aM5DyXhaDvjnMFWjMp0gv47Lo1MZgd4OQHUO+7bM17qebE+PMrfJ/\ +wpODEwFfDODMM9HRXkXzGEl17xood2p9MuUwIZz/\ +h4fDl8PmL4WMPg7GMiTGghH7aFjKfKaIh7SHQJWveciK++\ +eO98vip4DyG7wWIBPQd650oQi2MFIRjPsG3nm+\ +mbmJihghKFD1zmpw8R20v0EYxkU1gnuMbp5M1bAtMVKY9N7dKbjYpyId/FR/\ +I2MXkPS5pd3YEhoVxzug7Kat/zt0Az6/bwit5tJ44zO8NR96IYYegV+\ +l81LpOnpGqa130C67Oar5sNcjTp0z9v7TPtFkN40nbMGB+YGu8Xnur8M/\ +awsscu34h7tvWfPaOEnDdcKgE91HSgi+iaKY88BJtn67OrcNj3Kj4jtEZUsEKJ7Jxlv3i+\ +uNuBV5vCjHWbroF6Yh6BkSQg3VRx+\ +0Oy5gZzYgiiQVeXNcvm2wi61AC7mxfeyYoswPME7JpeUKzly7VnZhk9uWPilvJ5USTIe97wkAGaqPo\ +r2F9lCVX0IkMjCTGC5p6DeawSmpMVLDsByVInBPBEJL9sh/\ +3zT9crgRStatQXcqzOHClOQ5Pol8WeB9EZmbNHTtwdAW3LWYTyaNadRFL0+Vpsz2m+\ +02mGzc0B3ooCaElCR/o3abQbQp/dVNY2YO7NaFbE7o1oVsTujXh/10TXMT4r/Qbd364Xg=="]]}; + Typeset`initDone$$ = True), DynamicModuleValues :> {}, + Deinitialization :> None, + UntrackedVariables :> {Typeset`size$$}, + SynchronousInitialization -> True, + UnsavedVariables :> {Typeset`initDone$$}, + UndoTrackedVariables :> { + Typeset`show$$, Typeset`bookmarkMode$$}], "Manipulate", + Deployed -> True, StripOnInput -> False], TraditionalForm], + Manipulate`InterpretManipulate[1]], TraditionalForm]], + "Output", { + Background -> None, + GraphicsBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics"}, + DefaultAxesStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsAxes"], DefaultFrameStyle -> Directive[ + GrayLevel[0, 0.35], FontColor -> GrayLevel[0.25], FontOpacity -> + 1, "GraphicsFrame"], DefaultFrameTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsFrameTicks"], + DefaultTicksStyle -> + Directive[ + FontFamily -> "Times", FontSize -> 10, "GraphicsTicks"]}, + Graphics3DBoxOptions -> { + DefaultBaseStyle -> {FontFamily -> "Times", "Graphics3D"}}}, + NumberPoint -> ".", CellSize -> {550, Automatic}, + AutoStyleOptions -> {"HighlightFormattingErrors" -> False}, + RenderingOptions -> { + "3DRenderingMethod" -> "BSPTreeOrDepthBuffer"}]}], + XMLElement["dataformats", {}, {"minput"}]}], + XMLElement["subpod", {"title" -> ""}, { + XMLElement["minput", {}, {"Plot[Sqrt[x^16 + x^18]/3, {x, -84, 84}]"}], + XMLElement["cell", {"compressed" -> True, "string" -> False}, { + Cell[ + BoxData[ + FormBox[ + TagBox[ + FormBox[ + StyleBox[ + + DynamicModuleBox[{ + CalculateUtilities`GraphicsUtilities`Private`max3089$$ = 0.5, + CalculateUtilities`GraphicsUtilities`Private`min3088$$ = \ +-0.5, CalculateUtilities`GraphicsUtilities`Private`more$$ = False, + Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, + Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, + Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", + Typeset`specs$$ = {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`more$$], { + False, True}}, {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$], \ +-0.5, "min"}, -1, 1}, {{ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`max3089$$], + 0.5, "max"}, -1, 1}, { + Hold[ + Style[ + Overlay[{ + Dynamic[ + RawBoxes[ + FEPrivate`FrontEndResource[ + "WABitmaps", "PodInfoBackground"]]], + Pane[ + Column[{ + Grid[{{ + Manipulate`Place[1], + Manipulate`Place[2]}}]}], + ImageMargins -> {{20, 30}, {10, 10}}]}, {1, 2}, 2, + Alignment -> {Left, Top}]]], + Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = + Automatic, Typeset`update$$ = 0, Typeset`initDone$$ = False, + Typeset`skipInitDone$$ = False, + CalculateUtilities`GraphicsUtilities`Private`more$1816816$$ = + False, CalculateUtilities`GraphicsUtilities`Private`min3088$\ +1816817$$ = 0, CalculateUtilities`GraphicsUtilities`Private`max3089$1816818$$ = + 0}, + DynamicBox[ + Manipulate`ManipulateBoxes[ + 2, TraditionalForm, + "Variables" :> { + CalculateUtilities`GraphicsUtilities`Private`max3089$$ = + 0.5, CalculateUtilities`GraphicsUtilities`Private`min3088$\ +$ = -0.5, CalculateUtilities`GraphicsUtilities`Private`more$$ = False}, + "ControllerVariables" :> { + Hold[ + CalculateUtilities`GraphicsUtilities`Private`more$$, + CalculateUtilities`GraphicsUtilities`Private`more$1816816$\ +$, False], + Hold[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$, + CalculateUtilities`GraphicsUtilities`Private`min3088$\ +1816817$$, 0], + Hold[ + CalculateUtilities`GraphicsUtilities`Private`max3089$$, + CalculateUtilities`GraphicsUtilities`Private`max3089$\ +1816818$$, 0]}, "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, + Typeset`bookmarkMode$$, Typeset`animator$$, + Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, + Typeset`size$$, Typeset`update$$, Typeset`initDone$$, + Typeset`skipInitDone$$}, "Body" :> Quiet[ + Function[Null, + CalculateUtilities`GraphicsUtilities`Private`post$1816795[ + Plot[ + SlotSequence[1], AspectRatio -> If[ + TrueQ[ + CalculateUtilities`GraphicsUtilities`Private`aspect], + Automatic, 1/GoldenRatio]]], HoldAll][ + Rational[1, 3] ($CellContext`x^16 + $CellContext`x^18)^ + Rational[1, 2], {$CellContext`x, + If[ + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$], + ( + Piecewise[{{ + 0. + 89.50044469163267 Tan[1.5040801783846716` #], # < + 0}}, 0. + + 89.50044469163267 Tan[1.5040801783846716` #]]& )[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$], \ +-83.72], + If[ + And[ + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$], + NumericQ[ + CalculateUtilities`GraphicsUtilities`Private`max3089$$]], + ( + Piecewise[{{ + 0. + 89.50044469163267 Tan[1.5040801783846716` #], # < + 0}}, 0. + 89.50044469163267 Tan[1.5040801783846716` #]]& )[ + If[ + CalculateUtilities`GraphicsUtilities`Private`min3088$$ == + CalculateUtilities`GraphicsUtilities`Private`max3089$$, + CalculateUtilities`GraphicsUtilities`Private`min3088$$ + + 0.16744, + CalculateUtilities`GraphicsUtilities`Private`max3089$$]], + 83.72]}, + LabelStyle -> {FontFamily -> "Bitstream Charter"}, + WorkingPrecision -> 69, + PlotRange -> {Automatic, Automatic}, LabelStyle -> {}, + Ticks -> Automatic, ImageSize -> 220., AxesLabel -> { + RawBoxes[ + FormBox["x", TraditionalForm]], + RawBoxes[ + FormBox["y", TraditionalForm]]}, AxesLabel -> { + RawBoxes[ + FormBox["x", TraditionalForm]], None}]], + "Specifications" :> {{ + CalculateUtilities`GraphicsUtilities`Private`more$$, { + False, True}, ControlType -> None}, {{ + CalculateUtilities`GraphicsUtilities`Private`min3088$$, \ +-0.5, "min"}, -1, 1, ImageSize -> Tiny, ControlPlacement -> 1}, {{ + CalculateUtilities`GraphicsUtilities`Private`max3089$$, + 0.5, "max"}, -1, 1, ImageSize -> Tiny, ControlPlacement -> + 2}, + Style[ + Overlay[{ + Dynamic[ + RawBoxes[ + FEPrivate`FrontEndResource[ + "WABitmaps", "PodInfoBackground"]]], + Pane[ + Column[{ + Grid[{{ + Manipulate`Place[1], + Manipulate`Place[2]}}]}], + ImageMargins -> {{20, 30}, {10, 10}}]}, {1, 2}, 2, + Alignment -> {Left, Top}]]}, + "Options" :> { + ControlPlacement -> Bottom, + FrameMargins -> {{0, 0}, {0, 10}}, Paneled -> False, + AppearanceElements -> {}, + LabelStyle -> { + "DialogStyle", FontColor -> GrayLevel[0.25]}}, + "DefaultOptions" :> {}], SingleEvaluation -> True], + Initialization :> ({ + ReleaseHold[ + Hold[ + CalculateUtilities`GraphicsUtilities`Private`WACleanTicks[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`res, + CalculateUtilities`GraphicsUtilities`Private`unitformat}, + CalculateUtilities`GraphicsUtilities`Private`res = + ReplaceAll[ + ReplaceAll[ + Part[ + DeleteCases[ + Replace[ + ReplaceAll[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Alternatives[ + Style, $CellContext`UnitNumberForm, NumberForm] -> (#& )], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, { + PatternTest[ + BlankSequence[], NumberQ]}] :> + Thread[{CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`t}]], { + Blank[], "", + BlankNullSequence[]}], All, + Span[1, 2]], Superscript[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[Integer]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`p, + Blank[Integer]]] :> + CalculateUtilities`GraphicsUtilities`Private`b^ + CalculateUtilities`GraphicsUtilities`Private`p], Row[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + BlankSequence[]]}, "\[Times]"] :> + Times[CalculateUtilities`GraphicsUtilities`Private`a]]; If[ + MatchQ[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 2], + Condition[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`quants, { + Alternatives[ + BlankSequence[$CellContext`ShortQuantity], + BlankSequence[Quantity]]}], Length[ + Union[ + + Map[$CellContext`UnitObjectPart, + CalculateUtilities`GraphicsUtilities`Private`quants]]] == + 1]], CalculateUtilities`GraphicsUtilities`Private`\ +unitformat = $CellContext`ToCDFQuantityFunction[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, 1, 2]]; + CalculateUtilities`GraphicsUtilities`Private`unitformat -> + Thread[{ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 1], + $CellContext`QuantityPart[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, All, 2], + $CellContext`UnitObjectPart[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`res, 1, + 2]]]}], + CalculateUtilities`GraphicsUtilities`Private`res]]; + Options[ + CalculateUtilities`GraphicsUtilities`Private`post$1816795]\ + = {"ReturnInteractiveTypes" -> False, "Nearest" -> Automatic}; + CalculateUtilities`GraphicsUtilities`Private`post$1816795[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`g, + Blank[Graphics]], + OptionsPattern[]] := Check[ + + Module[{ + CalculateUtilities`GraphicsUtilities`Private`lines, + CalculateUtilities`GraphicsUtilities`Private`pts, + CalculateUtilities`GraphicsUtilities`Private`gg, + CalculateUtilities`GraphicsUtilities`Private`type, + CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r, + CalculateUtilities`GraphicsUtilities`Private`oldepilog, + CalculateUtilities`GraphicsUtilities`Private`range, + CalculateUtilities`GraphicsUtilities`Private`gridlines, + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle = OptionValue["Nearest"]}, + CalculateUtilities`GraphicsUtilities`Private`oldepilog = + Replace[ + ReplaceAll[Epilog, + Options[CalculateUtilities`GraphicsUtilities`Private`g]], + Epilog -> Sequence[]]; Switch[ + ReplaceAll[{Frame, Axes}, + Options[ + CalculateUtilities`GraphicsUtilities`Private`g]], {True, + Blank[]}, + CalculateUtilities`GraphicsUtilities`Private`type = + Frame; {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r} = + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + ReplaceAll[FrameTicks, + Options[ + CalculateUtilities`GraphicsUtilities`Private`g]]], { + Blank[], True}, + CalculateUtilities`GraphicsUtilities`Private`type = + Axes; {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l} = + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + ReplaceAll[Ticks, + Options[CalculateUtilities`GraphicsUtilities`Private`g]]], + Blank[], + CalculateUtilities`GraphicsUtilities`Private`type = None]; + If[ + And[ + CalculateUtilities`GraphicsUtilities`Private`type === + Frame, + Or[ + Not[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`t === None, + CalculateUtilities`GraphicsUtilities`Private`b === + CalculateUtilities`GraphicsUtilities`Private`t]], + Not[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`r === None, + CalculateUtilities`GraphicsUtilities`Private`l === + CalculateUtilities`GraphicsUtilities`Private`r]]]], + CalculateUtilities`GraphicsUtilities`Private`type = None]; + If[ + TrueQ[ + OptionValue["ReturnInteractiveTypes"]], + Which[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`type === + None, CalculateUtilities`GraphicsUtilities`Private`b === + None, CalculateUtilities`GraphicsUtilities`Private`l === + None], {}, + FreeQ[CalculateUtilities`GraphicsUtilities`Private`g, + Alternatives[Line, Point]], {}, True, { + "Tooltips", "Coordinates"}], If[ + FreeQ[CalculateUtilities`GraphicsUtilities`Private`g, + Alternatives[Line, Point]], + Return[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`gg = + Normal[CalculateUtilities`GraphicsUtilities`Private`g]; + CalculateUtilities`GraphicsUtilities`Private`pts = + Partition[ + Flatten[ + Cases[ + Part[CalculateUtilities`GraphicsUtilities`Private`gg, 1], + Point[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[]]] :> + CalculateUtilities`GraphicsUtilities`Private`a, + Infinity]], 2]; + If[Length[ + CalculateUtilities`GraphicsUtilities`Private`pts] < 2, + CalculateUtilities`GraphicsUtilities`Private`lines = Cases[ + Part[CalculateUtilities`GraphicsUtilities`Private`gg, 1], + Blank[Line], Infinity]; + If[CalculateUtilities`GraphicsUtilities`Private`lines === \ +{}, + Return[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`pts = Flatten[ + Cases[CalculateUtilities`GraphicsUtilities`Private`lines, + Line[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[]]] :> + CalculateUtilities`GraphicsUtilities`Private`a, Infinity], + 1]; If[ + CalculateUtilities`GraphicsUtilities`Private`neareststyle === + Automatic, If[ + CalculateUtilities`GraphicsUtilities`Private`orderedLines[ + CalculateUtilities`GraphicsUtilities`Private`lines], + CalculateUtilities`GraphicsUtilities`Private`neareststyle = + "1D", CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle = "2D"]; Null], + If[ + CalculateUtilities`GraphicsUtilities`Private`neareststyle === + Automatic, + CalculateUtilities`GraphicsUtilities`Private`neareststyle = + "2D"]]; + CalculateUtilities`GraphicsUtilities`Private`range = + Replace[ + ReplaceAll[PlotRange, + Options[CalculateUtilities`GraphicsUtilities`Private`g]], + Except[{{ + PatternTest[ + Blank[], NumberQ], + PatternTest[ + Blank[], NumberQ]}, { + PatternTest[ + Blank[], NumberQ], + PatternTest[ + Blank[], NumberQ]}}] :> { + Through[ + {Min, Max}[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 1]]], + Through[ + {Min, Max}[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 2]]]}]; CalculateUtilities`GraphicsUtilities`Private`b = + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[CalculateUtilities`GraphicsUtilities`Private`b, + First[CalculateUtilities`GraphicsUtilities`Private`range], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 1]]; CalculateUtilities`GraphicsUtilities`Private`l = + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[CalculateUtilities`GraphicsUtilities`Private`l, + Last[CalculateUtilities`GraphicsUtilities`Private`range], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, + 2]]; CalculateUtilities`GraphicsUtilities`Private`\ +oldgridlines = ReplaceAll[GridLines, + Options[CalculateUtilities`GraphicsUtilities`Private`g]]; + CalculateUtilities`GraphicsUtilities`Private`gridlines = + With[{CalculateUtilities`GraphicsUtilities`Private`gray = + GrayLevel[0.7]}, + Replace[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines,\ + {Pattern[CalculateUtilities`GraphicsUtilities`Private`a, { + Blank[List], + Blank[List]}] :> Dynamic[ + Join[CalculateUtilities`GraphicsUtilities`Private`a, + Replace[ + MousePosition[{"Graphics", Graphics}, None], { + None -> {{}, {}}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`x, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`y, + Blank[]]} :> {{{ + CalculateUtilities`GraphicsUtilities`Private`x, + CalculateUtilities`GraphicsUtilities`Private`gray}}, {{ + CalculateUtilities`GraphicsUtilities`Private`y, + CalculateUtilities`GraphicsUtilities`Private`gray}}}}], + 2]], { + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + Blank[List]], Automatic} :> + With[{CalculateUtilities`GraphicsUtilities`Private`\ +divisions = {CalculateUtilities`GraphicsUtilities`Private`a, + FindDivisions[ + Last[CalculateUtilities`GraphicsUtilities`Private`range], + 7]}}, + Dynamic[ + Join[ + CalculateUtilities`GraphicsUtilities`Private`divisions, + Replace[ + MousePosition[{"Graphics", Graphics}, None], { + None -> {{}, {}}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`x, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`y, + Blank[]]} :> {{{ + CalculateUtilities`GraphicsUtilities`Private`x, + CalculateUtilities`GraphicsUtilities`Private`gray}}, {{ + CalculateUtilities`GraphicsUtilities`Private`y, + CalculateUtilities`GraphicsUtilities`Private`gray}}}}], + 2]]], Blank[] -> Dynamic[ + + Map[{{#, + CalculateUtilities`GraphicsUtilities`Private`gray}}& , + MousePosition[{"Graphics", Graphics}, None]]]}]]; If[ + Or[ + CalculateUtilities`GraphicsUtilities`Private`type === + None, CalculateUtilities`GraphicsUtilities`Private`b === + None, CalculateUtilities`GraphicsUtilities`Private`l === + None], + Show[ + CalculateUtilities`GraphicsUtilities`Private`g, GridLines -> + CalculateUtilities`GraphicsUtilities`Private`gridlines, + If[ + MatchQ[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + Alternatives[None, GridLines]], + Method -> {"GridLinesInFront" -> True}, + Apply[Sequence, {}]]], + + With[{CalculateUtilities`GraphicsUtilities`Private`nf = + If[CalculateUtilities`GraphicsUtilities`Private`\ +neareststyle === "1D", + + With[{CalculateUtilities`GraphicsUtilities`Private`n = + Nearest[Part[ + CalculateUtilities`GraphicsUtilities`Private`pts, All, 1] -> + CalculateUtilities`GraphicsUtilities`Private`pts]}, + CalculateUtilities`GraphicsUtilities`Private`n[ + Part[#, 1]]& ], + + With[{CalculateUtilities`GraphicsUtilities`Private`n = + Nearest[Transpose[ + Transpose[ + CalculateUtilities`GraphicsUtilities`Private`pts]/Abs[ + Apply[ + Subtract, + CalculateUtilities`GraphicsUtilities`Private`range, { + 1}]]] -> + CalculateUtilities`GraphicsUtilities`Private`pts], + CalculateUtilities`GraphicsUtilities`Private`scale = Abs[ + Apply[ + Subtract, + CalculateUtilities`GraphicsUtilities`Private`range, { + 1}]]}, CalculateUtilities`GraphicsUtilities`Private`n[#/ + CalculateUtilities`GraphicsUtilities`Private`scale]& ]], + CalculateUtilities`GraphicsUtilities`Private`left = + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`bottom = + CalculateUtilities`GraphicsUtilities`Private`b}, + Show[ + CalculateUtilities`GraphicsUtilities`Private`g, GridLines -> + CalculateUtilities`GraphicsUtilities`Private`gridlines, + If[ + MatchQ[ + CalculateUtilities`GraphicsUtilities`Private`oldgridlines, + Alternatives[None, GridLines]], + Method -> {"GridLinesInFront" -> True}, + Apply[Sequence, {}]], + Epilog -> { + CalculateUtilities`GraphicsUtilities`Private`oldepilog, + Dynamic[ + + DynamicModule[{ + CalculateUtilities`GraphicsUtilities`Private`pt = + CalculateUtilities`GraphicsUtilities`Private`nf[ + MousePosition[{"Graphics", Graphics}, {0, 0}]], + CalculateUtilities`GraphicsUtilities`Private`scaled = + MousePosition[{"GraphicsScaled", Graphics}, None]}, + If[ + CalculateUtilities`GraphicsUtilities`Private`scaled === + None, {}, { + Text[ + Style[ + Row[{ + CalculateUtilities`GraphicsUtilities`Private`bottom[ + Part[CalculateUtilities`GraphicsUtilities`Private`pt, 1, + 1]], + CalculateUtilities`GraphicsUtilities`Private`left[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`pt, 1, 2]]}, + ","], 12], + Part[ + CalculateUtilities`GraphicsUtilities`Private`pt, 1], { + 1.5 Sign[Part[ + CalculateUtilities`GraphicsUtilities`Private`scaled, 1] - + 0.5], 0}, Background -> White], + AbsolutePointSize[7], + Point[CalculateUtilities`GraphicsUtilities`Private`pt], + White, + AbsolutePointSize[5], + Point[ + CalculateUtilities`GraphicsUtilities`Private`pt]}]]]}]]]]]\ +, CalculateUtilities`GraphicsUtilities`Private`g]; + CalculateUtilities`GraphicsUtilities`Private`post$1816795[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`g, + Blank[]], + BlankNullSequence[]] := + CalculateUtilities`GraphicsUtilities`Private`g; + CalculateUtilities`GraphicsUtilities`Private`orderedLines[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + BlankSequence[Line]]}] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`ordered, + CalculateUtilities`GraphicsUtilities`Private`intervals}, + CalculateUtilities`GraphicsUtilities`Private`ordered = + Apply[And, + Map[OrderedQ[ + Part[#, 1, All, 1]]& , + Hold[CalculateUtilities`GraphicsUtilities`Private`l]]]; If[ + Not[ + TrueQ[ + CalculateUtilities`GraphicsUtilities`Private`ordered]], + Return[False]]; + CalculateUtilities`GraphicsUtilities`Private`intervals = + Part[{CalculateUtilities`GraphicsUtilities`Private`l}, + All, 1, {1, -1}, 1]; Length[ + Apply[ + Interval, + CalculateUtilities`GraphicsUtilities`Private`intervals]] === L\ +ength[CalculateUtilities`GraphicsUtilities`Private`intervals]]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + Alternatives[Automatic, FrameTicks]] = { + Identity, Identity, Identity, Identity}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`r, + Blank[]]}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, {{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`l, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`r, + Blank[]]}, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`t, + Blank[]]}}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`b, + CalculateUtilities`GraphicsUtilities`Private`l, + CalculateUtilities`GraphicsUtilities`Private`t, + CalculateUtilities`GraphicsUtilities`Private`r}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Frame, + Blank[]] = {None, None, None, None}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + Alternatives[Automatic, Ticks]] = {Identity, Identity}; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`h, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`v, + Blank[]]}] := + Map[CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction, {CalculateUtilities`GraphicsUtilities`Private`h, + CalculateUtilities`GraphicsUtilities`Private`v}]; + CalculateUtilities`GraphicsUtilities`Private`\ +ScaleCoordinatesToTicks[Axes, + Blank[]] = {None, None}; + CalculateUtilities`GraphicsUtilities`Private`CDFCleanTicks[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := ReplaceAll[ + ReplaceAll[ + Part[ + DeleteCases[ + ReplaceAll[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Alternatives[Style, NumberForm] -> (#& )], { + Blank[], "", + BlankNullSequence[]}], All, + Span[1, 2]], Superscript[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`b, + Blank[Integer]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`p, + Blank[Integer]]] :> + CalculateUtilities`GraphicsUtilities`Private`b^ + CalculateUtilities`GraphicsUtilities`Private`p], Row[{ + Pattern[CalculateUtilities`GraphicsUtilities`Private`a, + BlankSequence[]]}, "\[Times]"] :> + Times[CalculateUtilities`GraphicsUtilities`Private`a]]; + + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks$, + Blank[]]] := + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + CalculateUtilities`GraphicsUtilities`Private`WACleanTicks[ + CalculateUtilities`GraphicsUtilities`Private`ticks$]]; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[None] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[False] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[True] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[Automatic] = Identity; + CalculateUtilities`GraphicsUtilities`Private`\ +TicksToFunction[All] = Identity; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[Pattern[CalculateUtilities`GraphicsUtilities`Private`func, + Blank[]] -> + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, + Blank[]]] := Replace[ + + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[CalculateUtilities`GraphicsUtilities`Private`ticks], + Pattern[CalculateUtilities`GraphicsUtilities`Private`f, + Except[None]] :> + Composition[ + CalculateUtilities`GraphicsUtilities`Private`func, + CalculateUtilities`GraphicsUtilities`Private`f]]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[{}] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, { + Repeated[{ + Blank[Integer], + Blank[String]}]}]] := Which[ + Quiet[ + MatchQ[ + Apply[SameQ, + Map[Part[ + DateList[#], + Span[2, All]]& , + CalculateUtilities`GraphicsUtilities`Private`ticks, { + 2}], {1}], { + Repeated[True]}]], DateString, + Apply[And, + StringMatchQ[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 2], NumberString]], + + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Transpose[{ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 1], + ToExpression[ + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, All, + 2]]}]], True, None]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Pattern[ + CalculateUtilities`GraphicsUtilities`Private`ticks, { + Repeated[{ + PatternTest[ + Blank[], NumericQ], + PatternTest[ + Blank[], NumericQ]}]}]] := Which[ + MatchQ[ + Apply[ + Equal, CalculateUtilities`GraphicsUtilities`Private`ticks,\ + {1}], { + Repeated[True]}], Identity, + MatchQ[ + + Apply[# == Log[#2]& , + CalculateUtilities`GraphicsUtilities`Private`ticks, {1}], { + Repeated[True]}], Exp, + TrueQ[ + Quiet[ + Apply[Equal, + Apply[Divide, Transpose[ + Rest[CalculateUtilities`GraphicsUtilities`Private`ticks]] - + Part[CalculateUtilities`GraphicsUtilities`Private`ticks, + 1]]]]], + + With[{CalculateUtilities`GraphicsUtilities`Private`slope = + Apply[Divide, + Apply[Subtract, + Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, {-1, + 1}]]]}, + SetPrecision[(# - Part[ + CalculateUtilities`GraphicsUtilities`Private`ticks, 1, + 1])/CalculateUtilities`GraphicsUtilities`Private`slope + + Part[CalculateUtilities`GraphicsUtilities`Private`ticks, + 1, 2], 3]& ], True, None]; + CalculateUtilities`GraphicsUtilities`Private`\ +iTicksToFunction[ + Blank[]] = None; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`type, + Blank[]], + BlankNullSequence[]] := + CalculateUtilities`GraphicsUtilities`Private`type; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[Identity, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Blank[]] := + With[{CalculateUtilities`GraphicsUtilities`Private`nf = + CalculateUtilities`GraphicsUtilities`Private`numberForm, + CalculateUtilities`GraphicsUtilities`Private`acc = + Floor[Max[ + Ceiling[ + FullSimplify[Log[10, + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]] - + Log[10, (CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/100]]], + 3] - RealExponent[ + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]]]}, + CalculateUtilities`GraphicsUtilities`Private`nf[#, + CalculateUtilities`GraphicsUtilities`Private`acc]& ]; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[Exp, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Blank[]] := + With[{CalculateUtilities`GraphicsUtilities`Private`prec = + Max[ + Ceiling[ + FullSimplify[Log[10, + Max[ + + Abs[{CalculateUtilities`GraphicsUtilities`Private`min, + CalculateUtilities`GraphicsUtilities`Private`max}]]] - + Log[10, (CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/100]]], + 3]}, Quiet[ + RawBoxes[ + ToBoxes[ + NumberForm[ + Exp[#], + CalculateUtilities`GraphicsUtilities`Private`prec]]]]& ]; + CalculateUtilities`GraphicsUtilities`Private`\ +RefineCoordinateFunction[DateString, { + Pattern[CalculateUtilities`GraphicsUtilities`Private`min, + Blank[]], + Pattern[CalculateUtilities`GraphicsUtilities`Private`max, + Blank[]]}, + Pattern[CalculateUtilities`GraphicsUtilities`Private`pts, + Blank[]]] := + Module[{ + CalculateUtilities`GraphicsUtilities`Private`dates, + CalculateUtilities`GraphicsUtilities`Private`spec}, + CalculateUtilities`GraphicsUtilities`Private`dates = + Map[DateList, + CalculateUtilities`GraphicsUtilities`Private`pts]; + CalculateUtilities`GraphicsUtilities`Private`spec = Switch[ + Map[Length, + Map[Union, + Transpose[ + CalculateUtilities`GraphicsUtilities`Private`dates]]], { + Blank[], 1, 1, + BlankSequence[]}, {"Year"}, { + Blank[], + Blank[], 1, + BlankSequence[]}, {"MonthNameShort", " ", "Year"}, + Blank[], { + "DayShort", " ", "MonthNameShort", " ", "Year"}]; + If[(CalculateUtilities`GraphicsUtilities`Private`max - + CalculateUtilities`GraphicsUtilities`Private`min)/ + 31536000 > 25, + CalculateUtilities`GraphicsUtilities`Private`spec = { + "Year"}]; + With[{CalculateUtilities`GraphicsUtilities`Private`s = + CalculateUtilities`GraphicsUtilities`Private`spec}, + DateString[#, + CalculateUtilities`GraphicsUtilities`Private`s]& ]]; + CalculateUtilities`GraphicsUtilities`Private`numberForm = + Function[{ + CalculateUtilities`GraphicsUtilities`Private`a, + CalculateUtilities`GraphicsUtilities`Private`acc}, + Quiet[ + RawBoxes[ + ToBoxes[ + NumberForm[CalculateUtilities`GraphicsUtilities`Private`a, + Max[1, + Ceiling[ + RealExponent[ + CalculateUtilities`GraphicsUtilities`Private`a] + + CalculateUtilities`GraphicsUtilities`Private`acc]], + ExponentFunction -> (Null& ), + NumberFormat -> (StringReplace[#, StringExpression[ + Pattern[CalculateUtilities`GraphicsUtilities`Private`s, + BlankSequence[]], ".", EndOfString] -> + CalculateUtilities`GraphicsUtilities`Private`s]& )]]]]]]], + ReleaseHold[ + Uncompress[ + "6:eJztVm1v0zAQbikw3hn8AyQ+\ +I8qb9gVp0MGYNKAk5XtviZNYuHawnW3w58FnN0mzdpViOkBT+uFUX5rHd889d71HRyJI+\ +r1eT1015oNgcbKFp4fGjMQsFwWP353mkihFBU+u4LNbxoRE7xEGP0jsfNeNeS/\ +kDLQ7v8b3gUUFA02+asqopkRN9yXkGY1U7RlLemx+MmUiAkZ/\ +ksfDneGrnacvHQzGMgatieTqeVvIPJOgSNJDoGvGvGXAv7njg/\ +L4qWAsJN8LwiOi7hvvREJsYAQHhvl433q5mbqDiWngMcj4wmmy8hy1vUBpSXk6IbMc3zifrGFbYJCp\ 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--- /dev/null +++ b/Introduction to Computer Science/Website/finance/Dockerfile @@ -0,0 +1,5 @@ +FROM tiangolo/uwsgi-nginx-flask +ENV STATIC_URL /static +ENV STATIC_PATH /mnt/e/Education/Online Computer Sience degree/Introduction to Computer Science/Website/finance +COPY ./requirements.txt /var/www/requirements.txt +RUN pip install -r /var/www/requirements.txt \ No newline at end of file -- 2.51.2