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We will vary the coefficients ", StyleBox["a", FontWeight->"Bold"], " and ", StyleBox["b ", FontWeight->"Bold"], "of the polynomial", StyleBox[" p", FontWeight->"Bold"], ":" }], "Text", FontFamily->"Times New Roman"], Cell["\<\ p = x^3 + a x+ b; a = Cos[t]; b = Sin[t]; graph := Plot[p,{x,-2,2},PlotRange->{{-2,2},{-6,6}}];\ \>", "Input", CellLabel->"In[1]:="], Cell[TextData[{ "To create a plot of the graph, we choose a specific value for ", StyleBox["t ", FontWeight->"Bold"], " and call upon ", StyleBox["graph", FontFamily->"Courier", FontWeight->"Bold"], "; for instance:" }], "Text", FormatType->InputForm, FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell["t=2.2; graph;", "Input", CellLabel->"In[5]:=", FormatType->InputForm], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font 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This file is placed in the directory where ", StyleBox["Mathematica", FontSlant->"Italic"], " is running:" }], "Text", FormatType->TextForm, FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[BoxData[ \(Display["\", graph, "\"]\)], "Input", CellLabel->"In[6]:="], Cell[BoxData[ FormBox[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], TraditionalForm]], "Output", CellLabel->"Out[6]="] }, Open ]], Cell[TextData[{ "The following Do-loop creates 20 GIF files with the names pic.11, \ pic.12,...., pic.30. These are the individual frames of the animation. We \ take 20 values for ", StyleBox["t", FontWeight->"Bold"], " within the interval [0,2 pi]. We chose these filenames (instead of \ pic.1, pic.2,..., pic.20 or 1.gif, 2.gif,..., 20.gif) because of the \ lexicographical order unix uses to save files. We DO NOT want to change the \ order in which the frames are shown in the animation! 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It creates an animated GIF file named \"CubicPolys.gif\". The \"delay\" \ flag controls the delay time between frames. The \"loop\" flag tells the \ browser how many times to run the animation loop:" }], "Text", FontFamily->"Times New Roman"], Cell["!convert -delay 20 -loop 10 pic* CubicPolys.gif", "Input", CellLabel->"In[8]:="], Cell[TextData[{ "The animated file \"CubicPolys.gif\" can be incorporated into an HTML \ document. For instance, with the line:\n\t\t\t\t", StyleBox["", FontFamily->"Courier"] }], "Text", FontFamily->"Times New Roman"], Cell["\<\ You can remove (delete) the 20 files pic.* with the \ following:\ \>", "Text", FormatType->InputForm, FontFamily->"Times New Roman"], Cell["!rm -f pic.*", "Input", CellLabel->"In[9]:=", FormatType->InputForm] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1280}, {0, 1024}}, ScreenStyleEnvironment->"Working", WindowSize->{923, 685}, WindowMargins->{{Automatic, 40}, {Automatic, 117}}, PrintingCopies->1, PrintingPageRange->{1, 9999}, PrintingOptions->{"PrintingMargins"->{{54, 54}, {72, 0}}, "PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PrintCellBrackets"->False, "PrintRegistrationMarks"->False, "PrintMultipleHorizontalPages"->False, "Magnification"->1}, StyleDefinitions -> "Textbook.nb" ] (*********************************************************************** Cached data follows. 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