(* Content-type: application/mathematica *)

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              3.5 + $CellContext`v$$}, {-3.5 - $CellContext`v$$, 
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$CellContext`q$$], $CellContext`Nr[$CellContext`u$$, $CellContext`p$$, \
$CellContext`q$$]/$CellContext`Cv[$CellContext`u$$, $CellContext`p$$, \
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             "]]}}}, {
         Axes -> True, AxesOrigin -> {0, 0}, 
          PlotRange -> {{-3.5, 3.5}, {-3.5, 3.5}}, PlotRangeClipping -> True, 
          PlotRangePadding -> {Automatic, Automatic}}], $CellContext`r[
         Pattern[$CellContext`t, 
          Blank[]]] := {
        Cos[$CellContext`t]^3, Sin[$CellContext`t]^3, 0}, $CellContext`r[
         Pattern[$CellContext`s, 
          Blank[]], 
         Pattern[$CellContext`p, 
          Blank[]], 
         Pattern[$CellContext`q, 
          Blank[]]] := {$CellContext`p 
         Sin[(2 Pi) $CellContext`s], $CellContext`q 
         Cos[(2 Pi) $CellContext`s]}, $CellContext`Ev[
         Pattern[$CellContext`s, 
          Blank[]], 
         Pattern[$CellContext`p, 
          Blank[]], 
         Pattern[$CellContext`q, 
          Blank[]]] := {(($CellContext`p^2 - $CellContext`q^2) 
          Sin[(2 Pi) $CellContext`s]^3)/$CellContext`p, ((-$CellContext`p^2 + \
$CellContext`q^2) Cos[(2 Pi) $CellContext`s]^3)/$CellContext`q}, 
       VectorFieldPlots`ListVectorFieldPlot[
         Pattern[VectorFieldPlots`Private`vects, {
           Repeated[{{
              Blank[], 
              Blank[]}, {
              Blank[], 
              Blank[]}}]}], 
         PatternTest[
          Pattern[VectorFieldPlots`Private`opts, 
           BlankNullSequence[]], OptionQ]] := 
       Module[{VectorFieldPlots`Private`maxsize, 
          VectorFieldPlots`Private`scale, VectorFieldPlots`Private`scalefunct,
           VectorFieldPlots`Private`colorfunct, 
          VectorFieldPlots`Private`points, VectorFieldPlots`Private`vectors, 
          VectorFieldPlots`Private`colors, VectorFieldPlots`Private`mags, 
          VectorFieldPlots`Private`scaledmag, 
          VectorFieldPlots`Private`allvecs, VectorFieldPlots`Private`vecs = 
          N[VectorFieldPlots`Private`vects], 
          VectorFieldPlots`Private`arropts}, {
           VectorFieldPlots`Private`maxsize, VectorFieldPlots`Private`scale, 
            VectorFieldPlots`Private`scalefunct, 
            VectorFieldPlots`Private`colorfunct} = 
          ReplaceAll[{
            VectorFieldPlots`MaxArrowLength, VectorFieldPlots`ScaleFactor, 
             VectorFieldPlots`ScaleFunction, ColorFunction}, 
            Flatten[{VectorFieldPlots`Private`opts, 
              Options[VectorFieldPlots`ListVectorFieldPlot]}]]; 
         VectorFieldPlots`Private`vecs = 
          Cases[VectorFieldPlots`Private`vecs, {{
              PatternTest[
               Blank[], VectorFieldPlots`Private`numberQ], 
              PatternTest[
               Blank[], VectorFieldPlots`Private`numberQ]}, {
              PatternTest[
               Blank[], VectorFieldPlots`Private`numberQ], 
              PatternTest[
               Blank[], VectorFieldPlots`Private`numberQ]}}, Infinity]; {
           VectorFieldPlots`Private`points, VectorFieldPlots`Private`vectors} = 
          Transpose[VectorFieldPlots`Private`vecs]; 
         VectorFieldPlots`Private`mags = 
          Map[VectorFieldPlots`Private`magnitude, 
            VectorFieldPlots`Private`vectors]; 
         If[VectorFieldPlots`Private`colorfunct == None, 
           VectorFieldPlots`Private`colorfunct = {}& ]; If[
           Apply[Equal, VectorFieldPlots`Private`mags], 
           VectorFieldPlots`Private`colors = Table[
             Evaluate[
              VectorFieldPlots`Private`colorfunct[0]], {
              Length[VectorFieldPlots`Private`mags]}], 
           VectorFieldPlots`Private`colors = 
           Map[VectorFieldPlots`Private`colorfunct, (
              VectorFieldPlots`Private`mags - Min[
              VectorFieldPlots`Private`mags])/Max[
             VectorFieldPlots`Private`mags - Min[
              VectorFieldPlots`Private`mags]]]]; 
         If[VectorFieldPlots`Private`scalefunct =!= None, 
           VectorFieldPlots`Private`scaledmag = Map[If[# == 0, 0, 
               VectorFieldPlots`Private`scalefunct[#]]& , 
              VectorFieldPlots`Private`mags]; {
             VectorFieldPlots`Private`vectors, VectorFieldPlots`Private`mags} = 
            Transpose[
              MapThread[If[
                Or[#3 == 0, 
                 Not[
                  VectorFieldPlots`Private`numberQ[#2]]], {{0, 0}, 
                 0}, {(# #2)/#3, #2}]& , {
               VectorFieldPlots`Private`vectors, 
                VectorFieldPlots`Private`scaledmag, 
                VectorFieldPlots`Private`mags}]]]; 
         VectorFieldPlots`Private`allvecs = 
          Transpose[{
            VectorFieldPlots`Private`colors, VectorFieldPlots`Private`points, 
             VectorFieldPlots`Private`vectors, 
             VectorFieldPlots`Private`mags}]; If[
           VectorFieldPlots`Private`numberQ[VectorFieldPlots`Private`maxsize],
            VectorFieldPlots`Private`allvecs = 
           Select[VectorFieldPlots`Private`allvecs, Part[#, 4] <= 
             N[VectorFieldPlots`Private`maxsize]& ]]; If[
           VectorFieldPlots`Private`numberQ[VectorFieldPlots`Private`scale], 
           VectorFieldPlots`Private`scale = 
           VectorFieldPlots`Private`scale/Max[VectorFieldPlots`Private`mags], 
           VectorFieldPlots`Private`scale = 1]; 
         VectorFieldPlots`Private`arropts = 
          VectorFieldPlots`Private`getoldarrowopts[
            Flatten[{VectorFieldPlots`Private`opts, 
              Options[VectorFieldPlots`ListVectorFieldPlot]}]]; 
         If[VectorFieldPlots`Private`arropts =!= {}, Needs["Graphics`Arrow`"]; 
           VectorFieldPlots`Private`allvecs = Apply[Flatten[{#, 
                
                Arrow[#2, #2 + VectorFieldPlots`Private`scale #3, 
                 VectorFieldPlots`Private`arropts, Graphics`Arrow`HeadScaling -> 
                 Automatic, Graphics`Arrow`HeadLength -> 0.02]}]& , 
              VectorFieldPlots`Private`allvecs, {1}], 
           VectorFieldPlots`Private`allvecs = Apply[Flatten[{#, 
               If[VectorFieldPlots`Private`scale #3 == {0., 0.}, 
                Point[#2], 
                Arrow[{#2, #2 + VectorFieldPlots`Private`scale #3}]]}]& , 
             VectorFieldPlots`Private`allvecs, {1}]]; Graphics[{
            Thickness[Small], 
            Arrowheads[0.02], VectorFieldPlots`Private`allvecs}, 
           FilterRules[
            Flatten[{VectorFieldPlots`Private`opts, 
              Options[VectorFieldPlots`ListVectorFieldPlot]}], 
            Options[Graphics]]]], VectorFieldPlots`ListVectorFieldPlot[
         PatternTest[
          Pattern[VectorFieldPlots`Private`vects, 
           Blank[List]], TensorRank[#] === 3& ], 
         Pattern[VectorFieldPlots`Private`opts, 
          BlankNullSequence[]]] := VectorFieldPlots`ListVectorFieldPlot[
         Flatten[
          MapIndexed[{
            Reverse[#2], #}& , 
           Reverse[VectorFieldPlots`Private`vects], {2}], 1], 
         VectorFieldPlots`Private`opts], VectorFieldPlots`ListVectorFieldPlot[
         Pattern[VectorFieldPlots`Private`v, 
          Blank[]], 
         BlankNullSequence[]] := Condition[Null, Message[
           MessageName[VectorFieldPlots`ListVectorFieldPlot, "lpvf"]]; False],
        Options[VectorFieldPlots`ListVectorFieldPlot] := {
        AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False, 
         AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, 
         Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, 
         ColorFunction -> None, ColorOutput -> Automatic, ContentSelectable -> 
         Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, 
         FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, 
         GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., 
         ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, 
         VectorFieldPlots`MaxArrowLength -> None, Method -> Automatic, 
         PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> False, 
         PlotRangePadding -> Automatic, PlotRegion -> Automatic, 
         PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True,
          VectorFieldPlots`ScaleFactor -> Automatic, 
         VectorFieldPlots`ScaleFunction -> None, Ticks -> Automatic, 
         TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> 
         TraditionalForm}, 
       TagSet[VectorFieldPlots`ListVectorFieldPlot, 
        MessageName[VectorFieldPlots`ListVectorFieldPlot, "lpvf"], 
        "ListVectorFieldPlot requires a rectangular array of vectors or a \
list of {base, vector} pairs."], 
       TagSet[VectorFieldPlots`ListVectorFieldPlot, 
        MessageName[VectorFieldPlots`ListVectorFieldPlot, "usage"], 
        "\!\(\*RowBox[{\"ListVectorFieldPlot\", \"[\", RowBox[{\"{\", \
RowBox[{RowBox[{\"{\", RowBox[{RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"11\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"y\", \"TI\"], StyleBox[\"11\", \"TR\"]]}], \"}\
\"}], \",\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], \
StyleBox[\"12\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"y\", \"TI\"], \
StyleBox[\"12\", \"TR\"]]}], \"}\"}], \",\", StyleBox[\"\[Ellipsis]\", \
\"TR\"]}], \"}\"}], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \
\"]\"}]\) generates a plot of the vector field corresponding to the array of \
vectors \!\(\*RowBox[{\"{\", RowBox[{RowBox[{\"{\", RowBox[{RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"11\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"y\", \"TI\"], StyleBox[\"11\", \"TR\"]]}], \"}\
\"}], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}], \",\", StyleBox[\"\
\[Ellipsis]\", \"TR\"]}], \"}\"}]\).\n\!\(\*RowBox[{\"ListVectorFieldPlot\", \
\"[\", RowBox[{\"{\", RowBox[{RowBox[{\"{\", \
RowBox[{SubscriptBox[StyleBox[\"pt\", \"TI\"], StyleBox[\"1\", \"TR\"]], \
\",\", SubscriptBox[StyleBox[\"vec\", \"TI\"], StyleBox[\"1\", \"TR\"]]}], \
\"}\"}], \",\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"pt\", \"TI\"], \
StyleBox[\"2\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"vec\", \"TI\"], \
StyleBox[\"2\", \"TR\"]]}], \"}\"}], \",\", StyleBox[\"\[Ellipsis]\", \
\"TR\"]}], \"}\"}], \"]\"}]\) generates a plot of a list of vectors, each \
based at the corresponding point."], 
       TagSet[VectorFieldPlots`MaxArrowLength, 
        MessageName[VectorFieldPlots`MaxArrowLength, "usage"], 
        "MaxArrowLength is an option for the vector field visualization \
functions that determines the longest vector to be drawn."], 
       TagSet[VectorFieldPlots`ScaleFactor, 
        MessageName[VectorFieldPlots`ScaleFactor, "usage"], 
        "ScaleFactor is an option for the vector field visualization \
functions that scales the vectors so that the longest vector displayed is of \
the length specified."], 
       TagSet[VectorFieldPlots`ScaleFunction, 
        MessageName[VectorFieldPlots`ScaleFunction, "usage"], 
        "ScaleFunction is an option for the vector field visualization \
functions that rescales each vector to a length determined by applying a pure \
function to the current length of that vector."], 
       VectorFieldPlots`Private`numberQ[
         Pattern[VectorFieldPlots`Private`n, 
          Blank[]]] := NumberQ[
         N[VectorFieldPlots`Private`n]], VectorFieldPlots`Private`magnitude[
         Pattern[VectorFieldPlots`Private`v, 
          Blank[List]]] := Sqrt[
         Dot[VectorFieldPlots`Private`v, VectorFieldPlots`Private`v]], 
       VectorFieldPlots`Private`getoldarrowopts[
         Pattern[VectorFieldPlots`Private`opts, 
          Blank[]]] := 
       Module[{VectorFieldPlots`Private`selopts}, 
         VectorFieldPlots`Private`selopts = 
          Select[VectorFieldPlots`Private`opts, 
            MemberQ[{
             "HeadScaling", "HeadLength", "HeadCenter", "HeadWidth", 
              "HeadShape", "ZeroShape"}, 
             SymbolName[
              First[#]]]& ]; Map[ReplaceAll[
             SymbolName[
              First[#]], {
             "HeadScaling" -> Graphics`Arrow`HeadScaling, "HeadLength" -> 
              Graphics`Arrow`HeadLength, "HeadCenter" -> 
              Graphics`Arrow`HeadCenter, "HeadWidth" -> 
              Graphics`Arrow`HeadWidth, "HeadShape" -> 
              Graphics`Arrow`HeadShape, "ZeroShape" -> 
              Graphics`Arrow`ZeroShape}] -> Part[#, 2]& , 
           VectorFieldPlots`Private`selopts]], $DisplayFunction = 
       Identity, $CellContext`OscGr = Graphics[{{{}, {}, {
            Hue[0.67, 0.6, 0.6], 
            RGBColor[1, 0, 0], 
            Thickness[Large], 
            Line[CompressedData["
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           Sin[(2 Pi) $CellContext`s] - ($CellContext`q^3 (1 + 
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          Sin[(2 Pi) $CellContext`s]^3 + ($CellContext`p^3 
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           Sin[$CellContext`u] + ((($CellContext`p $CellContext`q^2) 
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         Pattern[$CellContext`q, 
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