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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 461900, 35619]*) (*NotebookOutlinePosition[ 462761, 35650]*) (* CellTagsIndexPosition[ 462717, 35646]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ PlotE Documentation I: Producing Graphs\ \>", "Title", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["The Plot Window", "Subtitle", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["Variables", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is capable of recognizing the variable or variables you use. It also goes \ to great pains to decide which variables you intend to apply to the \ horizontal and vertical axes, and which you intend to be the independent \ variable. The ingredients that go into these decisions are the expressions \ you supply, standard mathematical conventions, and the ", StyleBox["Variables", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option. ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " attempts to make all this transparent to the user, and you may never need \ to worry about it. But if you do, here are some of the details." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Effects", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ -- The horizontal and vertical variables will be used to label the axes. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "-- If the independent variable of a particular function is in the set \n \ ", StyleBox["$SequenceLetters", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", that function will be treated as a sequence. (See the \n section on \ Plotables.)" }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ -- If the vertical variable is the independent variable of a particular \ function, that function will be plotted \"sideways\". \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ -- If any bounds item(s) do not include a variable, those interpretation of \ those bounds will depend on the horizontal, vertical, and independent \ variables. If the vertical variable is the independent variable, the first Bounds item will \ be assigned to it and the second Bounds item to the horizontal variable. \ Otherwise the first Bounds item will be assigned to the horizontal variable and the \ second Bounds item to the vertical variable. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Variables Option", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The value of the ", StyleBox["Variables", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option must be a list of two items of type ", StyleBox["Symbol", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (default: ", StyleBox["{x,y}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "). These will be taken to be the default horizontal and independent \ variable and the default vertical variable. " }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Bounds", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ A variable (optionally) used in the first Bounds item will be taken to be \ the horizontal variable. A variable (optionally) used in the second Bounds \ item will be taken to be the vertical variable. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Parametric Equations", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " If you give parametric equations in actual equation form, the \ variables on the left side of the parametric equations are taken to be the \ horizontal and vertical variables. The parameter itself is taken to be the \ independent variable.\n Parameter bounds is required, and if there is not \ one inside the list of parametric equations, ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " will choose the first Bounds item. Therefore parameter bounds should \ always precede bounds for the horizontal and vertical axes." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Functions", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " Variables found in the plotable items will be used if there is doubt \ as the horizontal, vertical, or independent variables. \n-- the first element \ of the ", StyleBox["Variables", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option will be used as the horizontal and \n independent variable if \ it occurs in the plotable items, otherwise the first \n alphabetically \ among those occuring.\n-- the second element of the ", StyleBox["Variables", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option will be used as the vertical \n variable if it occurs in the \ plotable items, otherwise the second alphabetically \n among those \ occuring. " }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Problems", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " There is some potential for confusion in complicated situations or if \ you don't make your intentions clear. ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " can usually resolve ambiguities, but when there are problems, here are \ some suggestions:" }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "-- Always include the parameter variable in the parameter bounds; for \ example \n use ", StyleBox["{t,0,Pi}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " instead of ", StyleBox["{0,Pi}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ -- Place parameter bounds inside the list of parametric equations to resolve confusion concerning the parameter variable. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "-- Using explicit variables inside bounds can help eliminate variable \ problems; for \n example use ", StyleBox["{x,-2,2},{y,-1,1}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " instead of ", StyleBox["{-2,2},{-1,1}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["Bounds", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " A \"Bounds\" item is one that specifies the interval for either the \ horizontal or the vertical axis. Bounds items may be of the form ", StyleBox["{min,max}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " or ", StyleBox["{var,min,max}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". In general the first Bounds item will be taken as the plot interval and \ applied to the horizontal axis; however if the function plotted is a function \ of the default vertical variable, this interval will applied to the vertical \ axis. A second bounds item will be applied to the remaining axis, usually the \ vertical axis.\n In most cases there is no need to give the variables, but \ it can't hurt and may repair those rare cases where PlotE becomes confused \ about your choice of variables. There is no need to use an explicit ", StyleBox["PlotRange", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option in PlotE, although it will be accepted." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ In the case of plotting parametric equations, there may be three Bounds \ items, one for the parameter interval, and one for each axis. In this case \ the parameter interval must come first, and must contain the parameter \ variable. For more details see \"Plotables: Parametric Equations\" below.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Note: In previous versions of PlotE, it was permitted to give bounds not \ contained within list brackets. This feature has been removed for \ publication, and bounds now must be given within list brackets. There are two \ reasons for this change. One is that experience shows that novice users \ quickly adapt to the consistent use of list brackets to represent intervals, \ and seldom revert to forgetting them. 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.30902 0 2 Msboxa [(x)] 1.025 .30902 -1 0 Msboxa [(-4)] .01131 .07358 1 0 Msboxa [(-2)] .01131 .1913 1 0 Msboxa [(2)] .01131 .42674 1 0 Msboxa [(4)] .01131 .54446 1 0 Msboxa [(y)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .21429 .30902 m .21429 .31527 L s P [(1)] .21429 .30902 0 2 Mshowa p .002 w .40476 .30902 m .40476 .31527 L s P [(2)] .40476 .30902 0 2 Mshowa p .002 w .59524 .30902 m .59524 .31527 L s P [(3)] .59524 .30902 0 2 Mshowa p .002 w .78571 .30902 m .78571 .31527 L s P [(4)] .78571 .30902 0 2 Mshowa p .002 w .97619 .30902 m .97619 .31527 L s P [(5)] .97619 .30902 0 2 Mshowa p .001 w .0619 .30902 m .0619 .31277 L s P p .001 w .1 .30902 m .1 .31277 L s P p .001 w .1381 .30902 m .1381 .31277 L s P p .001 w .17619 .30902 m .17619 .31277 L s P p .001 w .25238 .30902 m .25238 .31277 L s P p .001 w .29048 .30902 m .29048 .31277 L s P p .001 w .32857 .30902 m 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.02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r [ ] 0 setdash .002 w .97619 .01472 m .89683 .03924 L .81746 .06377 L .7381 .08829 L .65873 .11282 L .57937 .13734 L .5 .16187 L .42063 .18639 L .34127 .21092 L .2619 .23544 L .18254 .25997 L .10317 .28449 L .06349 .29675 L .04365 .30289 L .03373 .30595 L .02877 .30748 L .02629 .30825 L .02381 .30902 L .02877 .31055 L .03373 .31208 L .04365 .31515 L .06349 .32128 L .10317 .33354 L .18254 .35807 L .2619 .38259 L .34127 .40712 L .42063 .43164 L .5 .45617 L .57937 .48069 L .65873 .50522 L .7381 .52974 L .81746 .55427 L .89683 .57879 L .97619 .60332 L s P P % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{314, 194}, ImageMargins->{{69, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]]}, Open]], Cell[CellGroupData[{Cell["AspectRatio, ScaleRatio & PlotRange", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The ", 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The \ keyword ", StyleBox["Same", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["ScaleRatio->1", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (although it is actually implemented via ", StyleBox["AspectRatio->Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ").\n The options ", StyleBox["ScaleRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["PlotRange", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", and ", StyleBox["AspectRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " are not independent; you can specify any two of the three. If specific \ values are assigned to all three options, ", StyleBox["AspectRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is ignored.\n The option ", StyleBox["AspectLimits", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is designed to prevent graphs from becoming too thin horizontally or \ vertically due to unforseen problems with ", StyleBox["ScaleRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["PlotRange", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", and ", StyleBox["AspectRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". It restricts the aspect ratio of the graph to lie within limits \ specified by the value of ", StyleBox["AspectLimits", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". 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", StyleBox["ColorMode", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " can be either ", StyleBox["Color", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (default) or ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", and determines whether ", StyleBox["ColorStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " or ", StyleBox["MonoStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is used as the set of default styles. ", StyleBox["ColorStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["MonoStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " must each be a list of plotstyles. The default value for ", StyleBox["ColorStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is ", StyleBox["{Blue,Red,Green,Black, Cyan,Magenta,Yellow,Gray}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". The default value for ", StyleBox["MonoStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is ", StyleBox["{Black,Gray,{Black,Dotted},{Gray,Dotted}}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". 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{Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell["DefaultBackground & DefaultStyle", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " PlotE introduces two additional default style options.\n ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " has an option ", StyleBox["DefaultBackground", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "; its purpose is to allow ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " to set a preferred background color without corrupting the ", StyleBox["Background", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option of ", StyleBox["Plot", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". When ", StyleBox["Background", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is set to ", StyleBox["Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", the value of ", StyleBox["DefaultBackground", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is used (rather than ", StyleBox["White", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "). ", StyleBox["DefaultBackground", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is initially set to ", StyleBox["Ecru", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " = ", StyleBox["RGBColor[1,1,0.8]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (a pastel yellow). If ", StyleBox["Background", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is anything other than ", StyleBox["Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", it takes precedence over ", StyleBox["DefaultBackground", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ".\n The option ", StyleBox["DefaultStyle", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " provides styles to be used as defaults for graph lines and dots and \ geometric objects in the absence of other information. The initial setting is \ {", StyleBox["Thickness[0.002],Dashing[{}],PointSize[0.01]}.", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "" }], "Text", ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["User Styles", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " Instead of using default styles, style information may be included in \ the ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command. In this case default styles are completely ignored and only the \ given styles are used." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Colors", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ If a only colors are given, they are applied to the functions plotted, \ with cyclic repetition if necessary. 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But if two lists (or a list and a single item) of styles \ are given, one involving only color and the other excluding color, the two \ lists are \.bcthreaded\.bd together. The effect is that colors and other \ styles items are treated separately, each cyclically repeating if \ necessary.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Examples", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " In this example, ", StyleBox["Cyan,Dotted", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " is treated as a single style." }], "SmallText", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ PlotE[Sin[x],Cos[x],{0,Pi},{-1,1}, \tCyan,Dotted ];\ \>", "Input", PageWidth->Infinity, AspectRatioFixed->False, ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 12 scalefont setfont % Background color 1 1 .8 r MFill % Scaling calculations 0.02381 0.303152 0.309017 0.294302 [ [(pi/6)] .18254 .30902 0 2 Msboxa [(pi/3)] .34127 .30902 0 2 Msboxa [(pi/2)] .5 .30902 0 2 Msboxa [(2pi/3)] .65873 .30902 0 2 Msboxa 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You can define a function in advance \ and use it in the PlotE command, or use can use a pure function on the spot. \ Here is an example where the graph is colored by a shade of green whose \ brightness is given by the y-coordinate of the point.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Example", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["\<\ PlotE[x^2,{-1,1}, ColorFunction->(RGBColor[0,Last[#],0]&)];\ \>", "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 12 scalefont setfont % Background color 1 1 .8 r MFill % Scaling calculations 0.5 0.47619 0.014715 0.588604 [ [(-1)] .02381 .01472 0 2 Msboxa [(-0.5)] .2619 .01472 0 2 Msboxa [(0.5)] .7381 .01472 0 2 Msboxa [(1)] .97619 .01472 0 2 Msboxa [(x)] 1.025 .01472 -1 0 Msboxa [(0.2)] .4875 .13244 1 0 Msboxa [(0.4)] .4875 .25016 1 0 Msboxa [(0.6)] .4875 .36788 1 0 Msboxa [(0.8)] .4875 .4856 1 0 Msboxa [(1)] .4875 .60332 1 0 Msboxa [(y)] .5 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 .01472 m .02381 .02097 L s P [(-1)] .02381 .01472 0 2 Mshowa p .002 w .2619 .01472 m .2619 .02097 L s P [(-0.5)] .2619 .01472 0 2 Mshowa p .002 w .7381 .01472 m .7381 .02097 L s P [(0.5)] .7381 .01472 0 2 Mshowa p .002 w .97619 .01472 m .97619 .02097 L s P [(1)] .97619 .01472 0 2 Mshowa p .001 w .07143 .01472 m .07143 .01847 L s P p .001 w .11905 .01472 m .11905 .01847 L s P p .001 w .16667 .01472 m .16667 .01847 L s P p .001 w .21429 .01472 m .21429 .01847 L s P p .001 w .30952 .01472 m .30952 .01847 L s P p .001 w .35714 .01472 m .35714 .01847 L s P p .001 w .40476 .01472 m .40476 .01847 L s P p .001 w .45238 .01472 m .45238 .01847 L s P p .001 w .54762 .01472 m .54762 .01847 L s P p .001 w .59524 .01472 m .59524 .01847 L s P p .001 w .64286 .01472 m .64286 .01847 L s P p .001 w .69048 .01472 m .69048 .01847 L s P p .001 w .78571 .01472 m .78571 .01847 L s P p .001 w .83333 .01472 m .83333 .01847 L s P p .001 w .88095 .01472 m .88095 .01847 L s P p .001 w .92857 .01472 m .92857 .01847 L s P [(x)] 1.025 .01472 -1 0 Mshowa p .002 w 0 .01472 m 1 .01472 L s P p .002 w .5 .13244 m .50625 .13244 L s P [(0.2)] .4875 .13244 1 0 Mshowa p .002 w .5 .25016 m .50625 .25016 L s P [(0.4)] .4875 .25016 1 0 Mshowa p .002 w .5 .36788 m .50625 .36788 L s P [(0.6)] .4875 .36788 1 0 Mshowa p .002 w .5 .4856 m .50625 .4856 L s P [(0.8)] .4875 .4856 1 0 Mshowa p .002 w .5 .60332 m .50625 .60332 L s P [(1)] .4875 .60332 1 0 Mshowa p .001 w .5 .03826 m .50375 .03826 L s P p .001 w .5 .0618 m .50375 .0618 L s P p .001 w .5 .08535 m .50375 .08535 L s P p .001 w .5 .10889 m .50375 .10889 L s P p .001 w .5 .15598 m .50375 .15598 L s P p .001 w .5 .17952 m .50375 .17952 L s P p .001 w .5 .20307 m .50375 .20307 L s P p .001 w .5 .22661 m .50375 .22661 L s P p .001 w 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.004 w .59921 .04026 m .61905 .0515 L s P p 0 .087 0 r .004 w .61905 .0515 m .65873 .08012 L s P p 0 .142 0 r .004 w .65873 .08012 m .69841 .1169 L s P p 0 .212 0 r .004 w .69841 .1169 m .7381 .16187 L s P p 0 .295 0 r .004 w .7381 .16187 m .77778 .215 L s P p 0 .392 0 r .004 w .77778 .215 m .81746 .27632 L s P p 0 .503 0 r .004 w .81746 .27632 m .85714 .3458 L s P p 0 .628 0 r .004 w .85714 .3458 m .89683 .42347 L s P p 0 .767 0 r .004 w .89683 .42347 m .93651 .50931 L s P p 0 .92 0 r .004 w .93651 .50931 m .97619 .60332 L s P P P P % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{314, 194}, ImageMargins->{{69, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]]}, Open]]}, Open]], Cell[CellGroupData[{Cell["Plotables", "Subtitle", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ PlotE recognizes five different types of items to be plotted: formulas, \ equations, parametric equations, sequences, and data sets.\ \>", "Text", 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A function of two variables will \ usually generate an error message. Functions with different independent \ variables may be used, but a function of the default second variable (usually \ y) will be plotted with the independent variable on the vertical axis.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Examples", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["PlotE[x^2 Exp[-x],{0,3}];", "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 12 scalefont setfont % Background color 1 1 .8 r MFill % Scaling calculations 0.02381 0.31746 0.014715 1.087307 [ [(0.5)] .18254 .01472 0 2 Msboxa [(1)] .34127 .01472 0 2 Msboxa [(1.5)] .5 .01472 0 2 Msboxa [(2)] .65873 .01472 0 2 Msboxa [(2.5)] .81746 .01472 0 2 Msboxa [(3)] .97619 .01472 0 2 Msboxa [(x)] 1.025 .01472 -1 0 Msboxa [(0.1)] .01131 .12345 1 0 Msboxa [(0.2)] .01131 .23218 1 0 Msboxa [(0.3)] .01131 .34091 1 0 Msboxa [(0.4)] .01131 .44964 1 0 Msboxa [(0.5)] .01131 .55837 1 0 Msboxa [(y)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .18254 .01472 m .18254 .02097 L s P [(0.5)] .18254 .01472 0 2 Mshowa p .002 w .34127 .01472 m .34127 .02097 L s P [(1)] .34127 .01472 0 2 Mshowa p .002 w .5 .01472 m .5 .02097 L s P [(1.5)] .5 .01472 0 2 Mshowa p .002 w .65873 .01472 m .65873 .02097 L s P [(2)] .65873 .01472 0 2 Mshowa p .002 w .81746 .01472 m .81746 .02097 L s P [(2.5)] .81746 .01472 0 2 Mshowa p .002 w .97619 .01472 m .97619 .02097 L s P [(3)] .97619 .01472 0 2 Mshowa p .001 w .05556 .01472 m .05556 .01847 L s P p .001 w .0873 .01472 m .0873 .01847 L s P p .001 w .11905 .01472 m .11905 .01847 L s P p .001 w .15079 .01472 m .15079 .01847 L s P p .001 w .21429 .01472 m .21429 .01847 L s P p .001 w .24603 .01472 m .24603 .01847 L s P p .001 w .27778 .01472 m .27778 .01847 L s P p .001 w .30952 .01472 m .30952 .01847 L s P p .001 w .37302 .01472 m .37302 .01847 L s P p .001 w .40476 .01472 m .40476 .01847 L s P p .001 w .43651 .01472 m .43651 .01847 L s P p .001 w .46825 .01472 m .46825 .01847 L s P p .001 w .53175 .01472 m .53175 .01847 L s P p .001 w .56349 .01472 m .56349 .01847 L s P p .001 w .59524 .01472 m .59524 .01847 L s P p .001 w .62698 .01472 m .62698 .01847 L s P p .001 w .69048 .01472 m .69048 .01847 L s P p .001 w .72222 .01472 m .72222 .01847 L s P p .001 w .75397 .01472 m .75397 .01847 L s P p .001 w .78571 .01472 m .78571 .01847 L s P p .001 w .84921 .01472 m .84921 .01847 L s P p .001 w .88095 .01472 m .88095 .01847 L s P p .001 w .9127 .01472 m .9127 .01847 L s P p .001 w .94444 .01472 m .94444 .01847 L s P [(x)] 1.025 .01472 -1 0 Mshowa p .002 w 0 .01472 m 1 .01472 L s P p .002 w .02381 .12345 m .03006 .12345 L s P [(0.1)] .01131 .12345 1 0 Mshowa p .002 w .02381 .23218 m .03006 .23218 L s P [(0.2)] .01131 .23218 1 0 Mshowa p .002 w .02381 .34091 m .03006 .34091 L s P [(0.3)] 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The option ", StyleBox["MaxSeqPoints", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (default:200) sets an upper bound on the number of points plotted \ individually in the graph of a sequence. If a larger interval is given, only \ a representative selection of points is plotted, and lines are not drawn \ between points. This can of course give a misleading picture in rare \ circumstances, but it beats plotting 100,000 points. 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The point size can be \ overridden by including a point size primitive or keyword in the command.\n \ The ", StyleBox["Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " value uses the value ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " when plotting functions, equations, and parametric equations, ", StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " when plotting sequences, and ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " when plotting data sets." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The following keyword equivalents are available:\n", StyleBox["PlotJoined->True: Lines,", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " ", StyleBox["Nodots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "\n", StyleBox["PlotJoined->False: Dots, Nolines\nPlotJoined->Both: Both, Join", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "\n", StyleBox["Nodots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Nolines", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " are equivalents for the options ", StyleBox["PlotJoined->True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["PlotJoined->False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " respectively. These keywords are designed for plotting sequences when one \ does not wish both dots and lines, but they could be used in other contexts \ as well." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The ", StyleBox["PlotJoined", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option applies to all items plotted regardless of their type. To apply \ different values of the ", StyleBox["PlotJoined", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option to multiple items, use a list of options values (see the third \ example below)." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Examples", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{Cell["PlotE[x^3,{-1,1},PlotJoined->False];", "Input", ImageRegion->{{0, 1}, {0, 1}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 12 scalefont setfont % Background color 1 1 .8 r MFill % Scaling calculations 0.5 0.47619 0.330518 7.899863 [ [(-1)] .02381 .33052 0 2 Msboxa [(-0.5)] .2619 .33052 0 2 Msboxa [(0.5)] .7381 .33052 0 2 Msboxa [(1)] .97619 .33052 0 2 Msboxa [(x)] 1.025 .33052 -1 0 Msboxa [(-0.04)] .4875 .01452 1 0 Msboxa [(-0.03)] .4875 .09352 1 0 Msboxa [(-0.02)] .4875 .17252 1 0 Msboxa [(-0.01)] .4875 .25152 1 0 Msboxa [(0.01)] .4875 .40952 1 0 Msboxa 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.33051 Mdot .5 .33052 Mdot .50124 .33052 Mdot .50248 .33052 Mdot .50372 .33052 Mdot .50496 .33053 Mdot .5062 .33054 Mdot .50744 .33055 Mdot .50868 .33057 Mdot .50992 .33059 Mdot .5124 .33066 Mdot .51364 .3307 Mdot .51488 .33076 Mdot .51736 .3309 Mdot .51984 .33109 Mdot .52232 .33133 Mdot .5248 .33163 Mdot .52976 .33245 Mdot .53472 .33358 Mdot .53968 .33509 Mdot .54464 .33703 Mdot .5496 .33945 Mdot .55952 .34595 Mdot .56944 .35502 Mdot .57937 .36709 Mdot .58929 .38259 Mdot .59921 .40195 Mdot .61905 .45395 Mdot .63889 .52653 Mdot .65873 .62311 Mdot .67857 .74711 Mdot .69841 .90198 Mdot .7381 1.318 Mdot .77778 1.8986 Mdot .81746 2.67122 Mdot .85714 3.66327 Mdot .89683 4.9022 Mdot .93651 6.41542 Mdot .97619 8.23038 Mdot P P % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{314, 194}, ImageMargins->{{69, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]], Cell[CellGroupData[{Cell["PlotE[Sin[x],{0,Pi},PlotJoined->Both];", 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Mdot .7381 .10091 Mdot .77778 .07553 Mdot .81746 .05414 Mdot .85714 .03712 Mdot .87698 .03033 Mdot .89683 .02474 Mdot .91667 .02037 Mdot .92659 .01865 Mdot .93651 .01723 Mdot .94643 .01613 Mdot .95139 .0157 Mdot .95635 .01535 Mdot .96131 .01507 Mdot .96379 .01496 Mdot .96627 .01487 Mdot .96875 .0148 Mdot .96999 .01478 Mdot .97123 .01475 Mdot .97247 .01474 Mdot .97371 .01472 Mdot .97495 .01472 Mdot .97619 .01472 Mdot P P % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{314, 194}, ImageMargins->{{69, Inherited}, {Inherited, Inherited}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCacheValid->False]}, Open]]}, Open]], Cell[CellGroupData[{Cell["SubPlots", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " Any item of the form ", StyleBox["SubPlot[...]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " inside a ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command will be treated as a complete ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command to be combined into the resulting graph. This is a powerful \ construction that can be used in a variety of ways. 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StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command. This could also be done using Piece functions. (See the chapter \ on Extras.) 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Notice that \ the segment of sin(12x) is much cruder than with SubPlots. This is because \ the Piece function is graphed over the entire interval, so only one-third of \ the points plotted were actually used. If the function were plotted over a \ smaller interval or oscillated more rapidly, the graph could be completely \ wrong. With SubPlots each function is plotted only over its designated \ interval, so all points calculated are used in drawing its graph.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " SubPlots give you complete freedom in using the features of PlotE in \ any combination, even if the features cannot be combined in a single plot. In \ particular SubPlots make it unnecessary to do several plots and then use the \ ", StyleBox["Show", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command. " }], "Text", ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["Zoom", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["Zoom", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is a command that can occur only inside a ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command. The syntax is ", StyleBox["Zoom[point,factor:5,times:1]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". ", StyleBox["point", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " can be an ordered pair or just an x-coordinate, in which case the first \ function plotted is used to calculate the y-coordinate. ", StyleBox["factor", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (default:5) is the magnification factor used when zooming in. ", StyleBox["times", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (default:5) is the number of times zooming at the given magnification \ factor is performed.\n By using a magnification factor of less than 1, you \ can zoom out instead of zooming in.\n In order to use ", StyleBox["Zoom", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", there must be an explicit y-interval (or the keyword ", StyleBox["Square", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ") given in the ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Examples", "Subsubsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Zoom[{2,0}]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " zooms in on the point {2,0} with the default magnification factor of 5.\n\ ", StyleBox["Zoom[1]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " zooms in on the point on the graph with x-coordinate of 1.\n", StyleBox["Zoom[1,10]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " zooms in with a magnification factor of 10.\n", StyleBox["Zoom[{2,0},3,4]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " zooms in 4 times with a magnification factor of 3.\n", StyleBox["Zoom[1,1/5]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " zooms out with a magnification factor of 1/5." }], "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotE[x(x-2)^2,{0,3},{0,3},Zoom[{2,0}]];", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotE[x(x-2)^2,{0,3},{0,3},Zoom[1]];", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotE[x(x-2)^2,{0,3},{0,3},Zoom[1,10]];", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotE[x(x-2)^2,{0,3},{0,3},Zoom[{2,0},3,4]];", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotE[x(x-2)^2,{0,3},{0,3},Zoom[1,1/5]];", "Input", Evaluatable->False, ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["Fills", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The region between a graph and the x-axis, or between multiple graphs, \ can be filled in using the keyword ", StyleBox["Fill", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". 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The keyword ", StyleBox["Concavity", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " will show the concave up and concave down portions of each function in \ different colors. Both keywords can be used, in which case all four \ combinations of direction and concavity will be shown in different colors. 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The idea was that if MaxSlope were set to say, 1000, all \ segments of slope greater than 1000 were deleted from the graph. This option \ has been removed from PlotE since the methods listed above seem to be \ superior and to make MaxSlope obsolete. If you feel otherwise, MaxSlope could \ be reinstated.\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["Graphics", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " An item or items with head ", StyleBox["Graphics", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["ContourGraphics", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", or ", StyleBox["DensityGraphics", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " may be included in a PlotE command, and will be combined with the results \ of the remainder of the command. This is done very simplistically and the \ results may or may not be as desired. 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Keywords are \ shortcuts to doing common things that otherwise are a lot more bother. Most \ are divided into two types: Geometric keywords which replace unwieldy \ geometric style primitives, and Option Substitutes, which replace wordy \ options. 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Unnecessary unless the ", StyleBox["ColorMode", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option has been set to ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Frame", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Frame-> (Frame->True)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Frame", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " places a box around the graph and axes on the outside of the box." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Fill", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Fill-> (GraphFill->True)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Fill", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " fills in the regions between graphs." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Grid", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Grid-> (Grids->Automatic)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Grid", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is the easiest way to place a grid in the plot. For more details on \ grids, see the chapter on Geometric Objects." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Hide", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Hide-> (DisplayFunction->Identity)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Hide", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " suppresses the generation of a graphics cell. This is useful if \ generating a ", StyleBox["Graphics", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " object you don't want to display immediately." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Invert", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Invert-> (Invert->True)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Invert", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " causes the coordinates of all plotted points to be reversed. This applies \ to all items plotted; use a ", StyleBox["SubPlot", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " to apply it to only some items." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Mono", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Mono-> (ColorMode->Mono)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " uses white background and grayscale graphs. Useful for monochrome \ monitors and printers. ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " does not prevent color due to ", StyleBox["DefaultColor", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["ColorFunction", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", or geometric objects." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Lines & Nodots", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Lines-> \t(PlotJoined->True) Nodots-> (PlotJoined->True)\ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Lines", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Nodots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " suppress the drawing of dots at points used in plotting a graph. This is \ only necessarily when they would otherwise be drawn, as in the graphing of a \ sequence. As a side effect, lines are drawn even when they would not \ ordinarily be drawn, as with a data set." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Dots & Nolines", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[StyleBox["Dots->\t\t\t\t(PlotJoined->False)\nNolines->\t\ (PlotJoined->False)", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"]], "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Dots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Nolines", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " suppress the drawing of lines between points used in plotting a graph. \ This might be useful in the graphing of a sequence, when they would \ ordinarily be drawn. As a side effect, dots are drawn even when they would \ not ordinarily be drawn, as with an ordinary function." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Both & Join", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[StyleBox["Both->\t\t\t\t(PlotJoined->Both)\nJoin->\t\t\t\t\ (PlotJoined->Both)", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"]], "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Join", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " ask for the drawing of of both dots at plotted points and lines between \ those points." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Origin", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Origin-> (AxesOrigin->{0,0})", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Origin", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " guarantees that the axes intersect at (0,0)." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Para", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Para-> (Parametrics->True)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Para", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " guarantees any list of two functions be treated as parametric equations." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Rainbow", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Rainbow->(ColorFunction->Automatic)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Rainbow", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " draws a graph whose color varies through the cycle Red-Yellow- \ Green-Cyan-Blue-Magenta-Red. This is useful when plotting parametric \ equations to see where the graph begins and the actual motion following." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Same", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Same-> (AspectRatio->Automatic)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Same", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " guarantees the same scale is used on both axes." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Square", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["Square-> ({hmin,hmax},AspectRatio->Automatic)", "Text", PageWidth->Infinity, ImageRegion->{{0, 1}, {0, 1}}, FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], Cell[TextData[{ StyleBox["Square", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["Same", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and using the same bounds for each axis. For example, ", StyleBox["{0,4},Square", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is an exact equivalent for ", StyleBox["{0,4},{0,4},Same", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Other", "Section", ImageRegion->{{0, 1}, {0, 1}}], Cell["Direction", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Direction", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " causes the increasing and decreasing portions of formula graphs to be \ plotted in different colors." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Concavity", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ StyleBox["Concavity", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " causes the concave up and concave down portions of formula graphs to be \ plotted in different colors." }], "Text", ImageRegion->{{0, 1}, {0, 1}}]}, Open]], Cell[CellGroupData[{Cell["Option List", "Subtitle", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ Additional options for PlotE concerning geometric objects are discussed \ in the second part of the PlotE documentation. Among those listed here, you \ will seldom want to use any of them directly in a PlotE command -- there are \ usually an easier way. Those with asterisks are ones you are encouraged to \ modify to suit your own tastes. \ \>", "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Options", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell["*AspectLimits->{1/6,3}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The value can be a list of two positive real numbers, which are the \ smallest and largest values of AspectRatio permitted in a graph. A value of \ ", StyleBox["None", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is interpreted as ", StyleBox["{0,Infinity}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ".\";" }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*Asymptotes->True", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " A value of ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " means that asymptotes and removable disconinuities will be searched for \ and drawn. A value of ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " means this will not be done, and can result in improved performance on \ slower computers.\t" }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*AsymptoteStyle->{GrayLevel[0.5],Dotted}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["AsymptoteStyle", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives a style appropriate for lines which isused to draw asymptotes." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["ColorFunction->None", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["ColorFunction", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " allows graph segments to be drawn in different colors. The value can be a \ function of a point ", StyleBox["{x,y}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " with output of the form ", StyleBox["RGBColor[a,b,c]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". The value ", StyleBox["Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " produces a full range of color. The keyword ", StyleBox["Rainbow", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is interpreted as ", StyleBox["ColorFunction->Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*ColorMode->Color", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The possible values are ", StyleBox["Color", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", each of which can be used as a keyword to change the setting. ", StyleBox["Color", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " invokes the use of ColorStyles for automatic graph coloring, and ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " invokes the use of MonoStyles." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ *ColorStyles->{Blue,Red,Green,Black,Cyan,Magenta,Yellow,Gray}\ \>", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["ColorStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives a list of graph colors or styles appropriate for a color monitor or \ printer. They will be used sequentially, with repetition if necessary, when \ no graph styles are specified in a ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command and ", StyleBox["ColorMode", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is set to ", StyleBox["Color", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*Dashes->{0.02,0.01}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["Dashes", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the values for ", StyleBox["Dashing[{a,b}]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " to be substituted for the keyword ", StyleBox["Dotted", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*DefaultBackground->Ecru", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["DefaultBackground", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " specifies a background color to be used in all plots when no ", StyleBox["Background", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " option is used. (This may seem redundant, but I wanted to provide a way \ to change the default background color without making a permanent change to \ the Background option of Plot.)" }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["\<\ *DefaultStyle->{Thickness[0.002],Dashing[{}], \tPointSize[0.01]}\ \>", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["DefaultStyle", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " sets general defaults for style primitives such as ", StyleBox["Thickness", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " or ", StyleBox["PointSize", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " which are used when no other specification is available. The only \ practical use of this option is to change the default thickness of graphs. \ Point sizes are usually controlled by other options." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["GraphFill->False", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " If the value is ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", regions between graphs of functions are filled with the colors given by \ ", StyleBox["GraphFillColors", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". If the value is a list of colors, those colors are used for the fills. \ The keyword ", StyleBox["Fill", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["GraphFill->True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", and ", StyleBox["Fill[colors]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["GraphFill->{colors}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*GraphFillColors->{Cyan,Magenta,Yellow,Gray}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["GraphFillColors", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives a list of colors to be used by ", StyleBox["GraphFill", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Indicators->None", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["Indicators", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is an option for PlotE intended for internal use. The value can be ", StyleBox["None", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " or any subset of ", StyleBox["{Direction,Concavity}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". The user can directly include as keywords any indicators desired." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Invert->False", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " If the value is ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", the x- and y-coordinates of all points plotted are reversed. If the \ value is ", StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", both the original and inverted graphs are plotted. A value of ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " leaves the graph unchanged. For use with more than one function, a list \ of these values can be given, applying to each function in turn." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*InvertStyle->Automatic", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["InvertStyle", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the style to apply to a graph generated by ", StyleBox["Invert", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". There is currently no good alternative to this option for altering the \ style of the inverted graph." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*MaxSeqPoints->200", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["MaxSeqPoints", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the maximum number of points plotted for a sequence. If the domain \ of the plot exceeds this number, only a selection of points will be plotted. \ This allows you to plot sequences over very large intervals without worrying \ about the number of points generated. To always plot all points for \ sequences, use a value of ", StyleBox["Infinity", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*MonoStyles->{Black,Gray,{Black,Dotted},{Gray,Dotted}}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["MonoStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives a list of graph styles appropriate for a monochrome monitor or \ printer. They will be used sequentially, with repetition if necessary, when \ no graph styles are specified in a ", StyleBox["PlotE", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " command and ", StyleBox["ColorStyles", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is set to ", StyleBox["Mono", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*Parametrics->False", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " If the value is ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", pairs of functions in list braces are treated as ordinary functions. If \ the value is ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", pairs of functions in list braces are treated as parametric equations. \ The keyword ", StyleBox["Para", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["Parametrics->True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["PlotJoined->Automatic", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " If the value is ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", dots are not drawn at the locations of plotted points, but lines \ connecting those points are drawn. If the value is ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", dots are drawn but not connecting lines. If the value is ", StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", both dots and lines are drawn. If the value is ", StyleBox["Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is used for data sets of points, ", StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is used for sequences, and ", StyleBox["True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is used for all other graphs. For use with more than one function, a list \ of these values can be given, applying to each function in turn. ", StyleBox["Dots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Nolines", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " are keywords equivalent to ", StyleBox["PlotJoined->True", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", ", StyleBox["Lines", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Nodots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " are keywords equivalent to ", StyleBox["PlotJoined->False", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ", and ", StyleBox["Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " and ", StyleBox["Join", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " are keywords equivalent to ", StyleBox["PlotJoined->Both", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["*PlotInterval->{-5,5}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["PlotInterval", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the default plot interval for the independent variable." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["ScaleRatio->Automatic", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["ScaleRatio", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the ratio of the length of one unit on the vertical axis to the \ length of one unit on the horizontal axis. The keyword ", StyleBox["Same", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["ScaleRatio->1", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " (or ", StyleBox["AspectRatio->Automatic", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ") and results in the same scale being used on both axes." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["SeqInterval->{0,10}", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["SeqInterval", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " gives the default plot interval for sequences." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["Splits-> None", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " ", StyleBox["Splits", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " removes the graph segments containing the points listed. The keyword ", StyleBox["Split[values]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is equivalent to ", StyleBox["Splits->{values}", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], "." }], "Text", ImageRegion->{{0, 1}, {0, 1}}], Cell["SubPlots->None", "Subsection", ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ " The value must be ", StyleBox["None", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " or a list of subplots, each of which will be interpreted as a PlotE \ command to be executed. ", StyleBox["SubPlots", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], " is intended for internal use; the user can directly include subplots in \ the form ", StyleBox["SubPlot[items]", FontFamily->"Courier", FontSize->12, FontWeight->"Bold"], ". 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