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(*^ ::[paletteColors = 128; currentKernel; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, cellOutline, groupLikeTitle, center, M36, N36, O486, bold, R65535, L3, r58981, g58981, b58981, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, cellOutline, groupLikeTitle, center, M36, N36, O486, bold, R8100, G6950, B56548, r58981, g58981, b58981, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, cellOutline, groupLikeTitle, center, M36, N36, O486, bold, R32767, B32767, r58981, g58981, b58981, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M18, O486, bold, R65535, a8, 14, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M19, O486, bold, B65535, a6, 12, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteDot, O486, R2709, G36863, B4225, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, O487, a2, e2, 14, "Times"; ; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M19, N18, O487, 12; fontset = input, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeInput, M18, N5, O487, bold, a2, e2, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N5, O487, L-4, a2, e2, 12, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, 12, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l33, w385, h266, 12, "Courier"; ; fontset = name, inactive, nowordwrap, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, B65535, 10, "Times"; ; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; ; fontset = Left Header, inactive, 10, "Times"; ; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12; fontset = Left Footer, inactive, center, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; ; fontset = clipboard, inactive, noKeepOnOnePage, preserveAspect, M7, 12; fontset = completions, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12; fontset = special1, nowordwrap, noKeepOnOnePage, preserveAspect, cellOutline, center, M36, N36, O486, b49152, a2, e2, 14, "Times"; ; fontset = special2, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, center, M7, 12; fontset = special3, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, right, M7, 12; fontset = special4, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12; fontset = special5, inactive, nowordwrap, noKeepOnOnePage, preserveAspect, M7, 12;] :[font = title; inactive; preserveAspect; ] Welcome to GUM ------------------ Graphics Utilities for Mathematica :[font = subsubtitle; inactive; Cclosed; preserveAspect; startGroup; ] Introduction :[font = text; inactive; preserveAspect; ] The package demonstrated here is the result of a continuing project begun in December 1990 to make Mathematica graphics more powerful and easier to use. It is specifically aimed toward use by students and instructors in computer laboratories, but should be of interest to anyone using Mathematica graphics on a regular basis. Steps are being taken to make the full package available commercially at a reasonable price. If you like what you see here, you can help this process by letting your favorite publisher of academic texts and software know you are interested! ;[s] 5:0,0;103,1;114,2;291,3;302,4;577,-1; 5:1,13,10,Times,0,14,0,0,0;1,13,10,Times,2,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,13,10,Times,2,14,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subsection; inactive; preserveAspect; ] A Brief Description of GUM :[font = text; inactive; preserveAspect; endGroup; ] The centerpiece of GUM is the PlotE (for “PlotExtended”) command, a major enhancement of the built-in Plot command which provides flexible syntax, automatic convenience features, and over 40 new options. There are several other graphics utility commands, primarily useful in Calculus instruction: Zoom, Newton, Riemann, Trapezoidal, Simpson, PlotDirection, PlotConcavity, InterP, and Cobweb. Most of these are based on PlotE so that options and keywords for PlotE can be used with these as well. One example of each of these is given below. There are also a number of miscellaneous features not directly graphical in nature. ;[s] 29:0,0;34,1;39,2;106,3;110,4;305,5;309,6;311,7;317,8;319,9;326,10;328,11;339,12;341,13;348,14;350,15;363,16;365,17;378,18;380,19;386,20;388,21;391,22;392,23;398,24;427,25;432,26;466,27;471,28;632,-1; 29:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,10,8,Courier,0,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,0,12,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subtitle; inactive; Cclosed; preserveAspect; startGroup; ] PlotE :[font = text; inactive; preserveAspect; ] Note: In laboratory use the PlotE function is accessed via the command Plot. In this demonstration we will use PlotE explicitly, and Plot will give the standard Mathematica command, allowing comparison with PlotE. ;[s] 13:0,0;28,1;33,2;71,3;75,4;111,5;116,6;133,7;137,8;161,9;172,10;208,11;213,12;214,-1; 13:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,13,10,Times,2,14,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] PlotE Sampler :[font = subsubsection; inactive; preserveAspect; ] #1 - Points :[font = input; Cclosed; dontPreserveAspect; startGroup; ] PlotE[10 Sin[x],{0,Pi}, Points->{{Pi/2,Red,Open}, {Pi/2,5,Red,"f(b)",Above,Right,Coords}, {2.5,Open}, {1,Blue,XLine,YLine,Dotted,"f(a)",Above}}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.303152 0.014715 0.05886 [ [(pi/6)] 0.18254 0.01472 0 2 Msboxa [(pi/3)] 0.34127 0.01472 0 2 Msboxa [(pi/2)] 0.5 0.01472 0 2 Msboxa [(2pi/3)] 0.65873 0.01472 0 2 Msboxa [(5pi/6)] 0.81746 0.01472 0 2 Msboxa [(pi)] 0.97619 0.01472 0 2 Msboxa [(x)] 1.025 0.01472 -1 0 Msboxa [(2)] 0.01131 0.13244 1 0 Msboxa [(4)] 0.01131 0.25016 1 0 Msboxa [(6)] 0.01131 0.36788 1 0 Msboxa [(8)] 0.01131 0.4856 1 0 Msboxa [(10)] 0.01131 0.60332 1 0 Msboxa [(y)] 0.02381 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.18254 0.01472 moveto 0.18254 0.02097 lineto stroke grestore [(pi/6)] 0.18254 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.34127 0.01472 moveto 0.34127 0.02097 lineto stroke grestore [(pi/3)] 0.34127 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.5 0.01472 moveto 0.5 0.02097 lineto stroke grestore [(pi/2)] 0.5 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.65873 0.01472 moveto 0.65873 0.02097 lineto stroke grestore [(2pi/3)] 0.65873 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.81746 0.01472 moveto 0.81746 0.02097 lineto stroke grestore [(5pi/6)] 0.81746 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.97619 0.01472 moveto 0.97619 0.02097 lineto stroke grestore [(pi)] 0.97619 0.01472 0 2 Mshowa [(x)] 1.025 0.01472 -1 0 Mshowa gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke grestore gsave 0.002 setlinewidth 0.02381 0.13244 moveto 0.03006 0.13244 lineto stroke grestore [(2)] 0.01131 0.13244 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.25016 moveto 0.03006 0.25016 lineto stroke grestore [(4)] 0.01131 0.25016 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.36788 moveto 0.03006 0.36788 lineto stroke 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grestore grestore gsave 0 0 1 setrgbcolor [ ] 0 setdash 6 Mabswid 0.78169 0.36698 Mdot 1 1 1 setrgbcolor 4 Mabswid 0.78169 0.36698 Mdot grestore gsave 0 0 1 setrgbcolor [ ] 0 setdash 6 Mabswid 0.32696 0.51001 Mdot gsave [(f\(a\))] 0.32696 0.51001 0 -3 Mshowa grestore grestore % End of Graphics MathPictureEnd :[font = subsubsection; inactive; preserveAspect; ] #2 - Regions & Polygons :[font = input; Cclosed; dontPreserveAspect; startGroup; ] PlotE[{0,Pi},{0,1}, Regions-> {{Pi/3,2Pi/3,Sin[x]/3,Sin[x]/2,Fill,Blue}, {0,1,Sin[y]/2,Sin[y],Fill,Green}}, Polygons->{{Pi/3,0.6},{2Pi/3,0.6},{Pi/2,1}, Fill,Yellow,Edges,Blue,Dotted,Dots,Red}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.303152 0.014715 0.588604 [ [(pi/6)] 0.18254 0.01472 0 2 Msboxa 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0.50569 lineto 0.61905 0.52778 lineto 0.65873 0.54346 lineto 0.69841 0.55562 lineto 0.7381 0.56555 lineto 0.77778 0.57395 lineto 0.81746 0.58123 lineto 0.85714 0.58764 lineto 0.89683 0.59338 lineto 0.93651 0.59858 lineto 0.97619 0.60332 lineto stroke grestore grestore % End of Graphics MathPictureEnd :[font = subsubsection; inactive; preserveAspect; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 0; ] Example #2: x1/3 ;[s] 2:0,0;13,1;16,-1; 2:1,10,8,Times,2,12,0,0,0;1,8,6,Times,33,9,0,0,0; :[font = input; Cclosed; preserveAspect; startGroup; ] Plot[x^(1/3),{x,-5,5}]; :[font = message; inactive; Cclosed; preserveAspect; startGroup; ] 1/3 Plot::plnr: CompiledFunction[{x}, x , -CompiledCode-][x] is not a machine-size real number at x = -5.. :[font = message; inactive; preserveAspect; ] 1/3 Plot::plnr: CompiledFunction[{x}, x , -CompiledCode-][x] is not a machine-size real number at x = -4.58333. :[font = message; inactive; preserveAspect; ] 1/3 Plot::plnr: CompiledFunction[{x}, x , -CompiledCode-][x] is not a machine-size real number at x = -4.16667. :[font = message; inactive; preserveAspect; ] General::stop: Further output of Plot::plnr will be suppressed during this calculation. :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 132; endGroup; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.342 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.190476 0.008143 0.190476 [ [(1)] 0.21429 0.00814 0 2 Msboxa [(2)] 0.40476 0.00814 0 2 Msboxa [(3)] 0.59524 0.00814 0 2 Msboxa [(4)] 0.78571 0.00814 0 2 Msboxa [(5)] 0.97619 0.00814 0 2 Msboxa [(0.25)] 0.01131 0.05576 1 0 Msboxa [(0.5)] 0.01131 0.10338 1 0 Msboxa [(0.75)] 0.01131 0.151 1 0 Msboxa [(1)] 0.01131 0.19862 1 0 Msboxa [(1.25)] 0.01131 0.24624 1 0 Msboxa [(1.5)] 0.01131 0.29386 1 0 Msboxa [(1.75)] 0.01131 0.34148 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.343 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.21429 0.00814 moveto 0.21429 0.01439 lineto stroke grestore [(1)] 0.21429 0.00814 0 2 Mshowa gsave 0.002 setlinewidth 0.40476 0.00814 moveto 0.40476 0.01439 lineto stroke grestore [(2)] 0.40476 0.00814 0 2 Mshowa gsave 0.002 setlinewidth 0.59524 0.00814 moveto 0.59524 0.01439 lineto stroke grestore [(3)] 0.59524 0.00814 0 2 Mshowa gsave 0.002 setlinewidth 0.78571 0.00814 moveto 0.78571 0.01439 lineto stroke grestore [(4)] 0.78571 0.00814 0 2 Mshowa gsave 0.002 setlinewidth 0.97619 0.00814 moveto 0.97619 0.01439 lineto stroke grestore [(5)] 0.97619 0.00814 0 2 Mshowa gsave 0.001 setlinewidth 0.0619 0.00814 moveto 0.0619 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.1 0.00814 moveto 0.1 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.1381 0.00814 moveto 0.1381 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.17619 0.00814 moveto 0.17619 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.25238 0.00814 moveto 0.25238 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.29048 0.00814 moveto 0.29048 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.32857 0.00814 moveto 0.32857 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.36667 0.00814 moveto 0.36667 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.44286 0.00814 moveto 0.44286 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.48095 0.00814 moveto 0.48095 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.51905 0.00814 moveto 0.51905 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.55714 0.00814 moveto 0.55714 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.63333 0.00814 moveto 0.63333 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.67143 0.00814 moveto 0.67143 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.70952 0.00814 moveto 0.70952 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.74762 0.00814 moveto 0.74762 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.82381 0.00814 moveto 0.82381 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.8619 0.00814 moveto 0.8619 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.9 0.00814 moveto 0.9 0.01189 lineto stroke grestore gsave 0.001 setlinewidth 0.9381 0.00814 moveto 0.9381 0.01189 lineto stroke grestore gsave 0.002 setlinewidth 0 0.00814 moveto 1 0.00814 lineto stroke grestore gsave 0.002 setlinewidth 0.02381 0.05576 moveto 0.03006 0.05576 lineto stroke grestore [(0.25)] 0.01131 0.05576 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.10338 moveto 0.03006 0.10338 lineto stroke grestore [(0.5)] 0.01131 0.10338 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.151 moveto 0.03006 0.151 lineto stroke grestore [(0.75)] 0.01131 0.151 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.19862 moveto 0.03006 0.19862 lineto stroke grestore [(1)] 0.01131 0.19862 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.24624 moveto 0.03006 0.24624 lineto stroke grestore [(1.25)] 0.01131 0.24624 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.29386 moveto 0.03006 0.29386 lineto stroke grestore [(1.5)] 0.01131 0.29386 1 0 Mshowa gsave 0.002 setlinewidth 0.02381 0.34148 moveto 0.03006 0.34148 lineto stroke grestore [(1.75)] 0.01131 0.34148 1 0 Mshowa gsave 0.001 setlinewidth 0.02381 0.01767 moveto 0.02756 0.01767 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.02719 moveto 0.02756 0.02719 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.03671 moveto 0.02756 0.03671 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.04624 moveto 0.02756 0.04624 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.06529 moveto 0.02756 0.06529 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.07481 moveto 0.02756 0.07481 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.08433 moveto 0.02756 0.08433 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.09386 moveto 0.02756 0.09386 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.1129 moveto 0.02756 0.1129 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.12243 moveto 0.02756 0.12243 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.13195 moveto 0.02756 0.13195 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.14148 moveto 0.02756 0.14148 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.16052 moveto 0.02756 0.16052 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.17005 moveto 0.02756 0.17005 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.17957 moveto 0.02756 0.17957 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.1891 moveto 0.02756 0.1891 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.20814 moveto 0.02756 0.20814 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.21767 moveto 0.02756 0.21767 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.22719 moveto 0.02756 0.22719 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.23671 moveto 0.02756 0.23671 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.25576 moveto 0.02756 0.25576 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.26529 moveto 0.02756 0.26529 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.27481 moveto 0.02756 0.27481 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.28433 moveto 0.02756 0.28433 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.30338 moveto 0.02756 0.30338 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.3129 moveto 0.02756 0.3129 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.32243 moveto 0.02756 0.32243 lineto stroke grestore gsave 0.001 setlinewidth 0.02381 0.33195 moveto 0.02756 0.33195 lineto stroke grestore gsave 0.002 setlinewidth 0.02381 0 moveto 0.02381 0.342 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.342 lineto 0 0.342 lineto closepath clip newpath gsave gsave 0.004 setlinewidth 0.02381 0.00814 moveto 0.02629 0.05295 lineto 0.02877 0.0646 lineto 0.03125 0.07277 lineto 0.03373 0.07928 lineto 0.03869 0.08957 lineto 0.04365 0.09777 lineto 0.05357 0.11073 lineto 0.06349 0.12106 lineto 0.08333 0.1374 lineto 0.10317 0.15041 lineto 0.14286 0.171 lineto 0.18254 0.18739 lineto 0.2619 0.21333 lineto 0.34127 0.23398 lineto 0.42063 0.25142 lineto 0.5 0.26666 lineto 0.57937 0.28029 lineto 0.65873 0.29268 lineto 0.7381 0.30407 lineto 0.81746 0.31465 lineto 0.89683 0.32454 lineto 0.97619 0.33385 lineto stroke grestore grestore % End of Graphics MathPictureEnd :[font = input; Cclosed; preserveAspect; startGroup; ] PlotE[x^(1/3),{x,-5,5}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.095238 0.309017 0.172109 [ [(-4)] 0.11905 0.30902 0 2 Msboxa [(-2)] 0.30952 0.30902 0 2 Msboxa [(2)] 0.69048 0.30902 0 2 Msboxa [(4)] 0.88095 0.30902 0 2 Msboxa [(x)] 1.025 0.30902 -1 0 Msboxa [(-1.5)] 0.4875 0.05085 1 0 Msboxa [(-1)] 0.4875 0.13691 1 0 Msboxa [(-0.5)] 0.4875 0.22296 1 0 Msboxa [(0.5)] 0.4875 0.39507 1 0 Msboxa [(1)] 0.4875 0.48113 1 0 Msboxa [(1.5)] 0.4875 0.56718 1 0 Msboxa [(y)] 0.5 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.11905 0.30902 moveto 0.11905 0.31527 lineto stroke grestore [(-4)] 0.11905 0.30902 0 2 Mshowa gsave 0.002 setlinewidth 0.30952 0.30902 moveto 0.30952 0.31527 lineto stroke grestore [(-2)] 0.30952 0.30902 0 2 Mshowa gsave 0.002 setlinewidth 0.69048 0.30902 moveto 0.69048 0.31527 lineto stroke grestore [(2)] 0.69048 0.30902 0 2 Mshowa gsave 0.002 setlinewidth 0.88095 0.30902 moveto 0.88095 0.31527 lineto stroke grestore [(4)] 0.88095 0.30902 0 2 Mshowa gsave 0.001 setlinewidth 0.15714 0.30902 moveto 0.15714 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.19524 0.30902 moveto 0.19524 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.23333 0.30902 moveto 0.23333 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.27143 0.30902 moveto 0.27143 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.34762 0.30902 moveto 0.34762 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.38571 0.30902 moveto 0.38571 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.42381 0.30902 moveto 0.42381 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.4619 0.30902 moveto 0.4619 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.5381 0.30902 moveto 0.5381 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.57619 0.30902 moveto 0.57619 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.61429 0.30902 moveto 0.61429 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.65238 0.30902 moveto 0.65238 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.72857 0.30902 moveto 0.72857 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.76667 0.30902 moveto 0.76667 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.80476 0.30902 moveto 0.80476 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.84286 0.30902 moveto 0.84286 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.08095 0.30902 moveto 0.08095 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.04286 0.30902 moveto 0.04286 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.00476 0.30902 moveto 0.00476 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.91905 0.30902 moveto 0.91905 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.95714 0.30902 moveto 0.95714 0.31277 lineto stroke grestore gsave 0.001 setlinewidth 0.99524 0.30902 moveto 0.99524 0.31277 lineto stroke grestore [(x)] 1.025 0.30902 -1 0 Mshowa gsave 0.002 setlinewidth 0 0.30902 moveto 1 0.30902 lineto stroke grestore gsave 0.002 setlinewidth 0.5 0.05085 moveto 0.50625 0.05085 lineto stroke grestore [(-1.5)] 0.4875 0.05085 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.13691 moveto 0.50625 0.13691 lineto stroke grestore [(-1)] 0.4875 0.13691 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.22296 moveto 0.50625 0.22296 lineto stroke grestore [(-0.5)] 0.4875 0.22296 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.39507 moveto 0.50625 0.39507 lineto stroke grestore [(0.5)] 0.4875 0.39507 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.48113 moveto 0.50625 0.48113 lineto stroke grestore [(1)] 0.4875 0.48113 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.56718 moveto 0.50625 0.56718 lineto stroke grestore [(1.5)] 0.4875 0.56718 1 0 Mshowa gsave 0.001 setlinewidth 0.5 0.06806 moveto 0.50375 0.06806 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.08528 moveto 0.50375 0.08528 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.10249 moveto 0.50375 0.10249 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.1197 moveto 0.50375 0.1197 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.15412 moveto 0.50375 0.15412 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.17133 moveto 0.50375 0.17133 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.18854 moveto 0.50375 0.18854 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.20575 moveto 0.50375 0.20575 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.24017 moveto 0.50375 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.25738 moveto 0.50375 0.25738 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.2746 moveto 0.50375 0.2746 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.29181 moveto 0.50375 0.29181 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.32623 moveto 0.50375 0.32623 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.34344 moveto 0.50375 0.34344 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.36065 moveto 0.50375 0.36065 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.37786 moveto 0.50375 0.37786 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.41228 moveto 0.50375 0.41228 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.42949 moveto 0.50375 0.42949 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.4467 moveto 0.50375 0.4467 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.46391 moveto 0.50375 0.46391 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.49834 moveto 0.50375 0.49834 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.51555 moveto 0.50375 0.51555 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.53276 moveto 0.50375 0.53276 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.54997 moveto 0.50375 0.54997 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.03364 moveto 0.50375 0.03364 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.01643 moveto 0.50375 0.01643 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.58439 moveto 0.50375 0.58439 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.6016 moveto 0.50375 0.6016 lineto stroke grestore [(y)] 0.5 0.61803 0 -4 Mshowa gsave 0.002 setlinewidth 0.5 0 moveto 0.5 0.61803 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave gsave 0 0 1 setrgbcolor [ ] 0 setdash 1 Mabswid 0.02381 0.01472 moveto 0.06349 0.02313 lineto 0.10317 0.03207 lineto 0.14286 0.04163 lineto 0.18254 0.05192 lineto 0.22222 0.06311 lineto 0.2619 0.07543 lineto 0.30159 0.0892 lineto 0.34127 0.10496 lineto 0.38095 0.12362 lineto 0.42063 0.14706 lineto 0.44048 0.16187 lineto 0.46032 0.18047 lineto 0.47024 0.19222 lineto 0.48016 0.20699 lineto 0.48512 0.21632 lineto 0.49008 0.22804 lineto 0.49256 0.23544 lineto 0.49504 0.24474 lineto 0.49628 0.25062 lineto 0.49752 0.258 lineto 0.5 0.30902 lineto 0.50124 0.34951 lineto 0.50248 0.36003 lineto 0.50372 0.36741 lineto 0.50496 0.37329 lineto 0.50744 0.38259 lineto 0.50992 0.39 lineto 0.51488 0.40172 lineto 0.51984 0.41105 lineto 0.52976 0.42581 lineto 0.53968 0.43757 lineto 0.55952 0.45617 lineto 0.57937 0.47098 lineto 0.61905 0.49442 lineto 0.65873 0.51307 lineto 0.69841 0.52883 lineto 0.7381 0.5426 lineto 0.77778 0.55492 lineto 0.81746 0.56611 lineto 0.85714 0.57641 lineto 0.89683 0.58597 lineto 0.93651 0.59491 lineto 0.97619 0.60332 lineto stroke grestore grestore % End of Graphics MathPictureEnd :[font = subsubsection; inactive; preserveAspect; ] Example #3: cos(x) & sec(x) :[font = input; Cclosed; preserveAspect; startGroup; ] Plot[{Cos[x],Sec[x]},{x,-Pi,Pi},PlotRange->{-3,3}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 292; pictureHeight = 266; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.90946 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.151576 0.454728 0.151576 [ [(-3)] 0.04527 0.45473 0 2 Msboxa [(-2)] 0.19685 0.45473 0 2 Msboxa [(-1)] 0.34842 0.45473 0 2 Msboxa [(1)] 0.65158 0.45473 0 2 Msboxa [(2)] 0.80315 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0.5248 0.60305 lineto 0.52976 0.60294 lineto 0.53968 0.60264 lineto 0.5496 0.60226 lineto 0.55952 0.60179 lineto 0.57937 0.6006 lineto 0.59921 0.59907 lineto 0.61905 0.59721 lineto 0.65873 0.59248 lineto 0.69841 0.58643 lineto 0.7381 0.5791 lineto 0.77778 0.5705 lineto Mistroke 0.81746 0.56068 lineto 0.85714 0.54967 lineto 0.89683 0.53752 lineto 0.93651 0.52428 lineto 0.97619 0.51001 lineto Mfstroke grestore grestore gsave gsave 0 0 1 setrgbcolor [ ] 0 setdash 5 Mabswid 0.5 0.60332 Mdot 1 1 1 setrgbcolor 3 Mabswid 0.5 0.60332 Mdot grestore grestore % End of Graphics MathPictureEnd :[font = section; inactive; Cclosed; preserveAspect; startGroup; ] A Short Guide to PlotE :[font = subsection; inactive; Cclosed; preserveAspect; startGroup; ] PlotE Basics :[font = subsubsection; inactive; preserveAspect; ] A Simple Plot :[font = input; Cclosed; preserveAspect; startGroup; ] PlotE[t^2,{-3,3}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.15873 0.014715 0.0654 [ [(-3)] 0.02381 0.01472 0 2 Msboxa [(-2)] 0.18254 0.01472 0 2 Msboxa [(-1)] 0.34127 0.01472 0 2 Msboxa [(1)] 0.65873 0.01472 0 2 Msboxa [(2)] 0.81746 0.01472 0 2 Msboxa [(3)] 0.97619 0.01472 0 2 Msboxa [(t)] 1.025 0.01472 -1 0 Msboxa [(2)] 0.4875 0.14552 1 0 Msboxa [(4)] 0.4875 0.27632 1 0 Msboxa [(6)] 0.4875 0.40712 1 0 Msboxa [(8)] 0.4875 0.53792 1 0 Msboxa [(y)] 0.5 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.02381 0.01472 moveto 0.02381 0.02097 lineto stroke grestore [(-3)] 0.02381 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.18254 0.01472 moveto 0.18254 0.02097 lineto stroke grestore [(-2)] 0.18254 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.34127 0.01472 moveto 0.34127 0.02097 lineto stroke grestore [(-1)] 0.34127 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.65873 0.01472 moveto 0.65873 0.02097 lineto stroke grestore [(1)] 0.65873 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.81746 0.01472 moveto 0.81746 0.02097 lineto stroke grestore [(2)] 0.81746 0.01472 0 2 Mshowa gsave 0.002 setlinewidth 0.97619 0.01472 moveto 0.97619 0.02097 lineto stroke grestore [(3)] 0.97619 0.01472 0 2 Mshowa gsave 0.001 setlinewidth 0.05556 0.01472 moveto 0.05556 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.0873 0.01472 moveto 0.0873 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.11905 0.01472 moveto 0.11905 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.15079 0.01472 moveto 0.15079 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.21429 0.01472 moveto 0.21429 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.24603 0.01472 moveto 0.24603 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.27778 0.01472 moveto 0.27778 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.30952 0.01472 moveto 0.30952 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.37302 0.01472 moveto 0.37302 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.40476 0.01472 moveto 0.40476 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.43651 0.01472 moveto 0.43651 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.46825 0.01472 moveto 0.46825 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.53175 0.01472 moveto 0.53175 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.56349 0.01472 moveto 0.56349 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.59524 0.01472 moveto 0.59524 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.62698 0.01472 moveto 0.62698 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.69048 0.01472 moveto 0.69048 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.72222 0.01472 moveto 0.72222 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.75397 0.01472 moveto 0.75397 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.78571 0.01472 moveto 0.78571 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.84921 0.01472 moveto 0.84921 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.88095 0.01472 moveto 0.88095 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.9127 0.01472 moveto 0.9127 0.01847 lineto stroke grestore gsave 0.001 setlinewidth 0.94444 0.01472 moveto 0.94444 0.01847 lineto stroke grestore [(t)] 1.025 0.01472 -1 0 Mshowa gsave 0.002 setlinewidth 0 0.01472 moveto 1 0.01472 lineto stroke grestore gsave 0.002 setlinewidth 0.5 0.14552 moveto 0.50625 0.14552 lineto stroke grestore [(2)] 0.4875 0.14552 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.27632 moveto 0.50625 0.27632 lineto stroke grestore [(4)] 0.4875 0.27632 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.40712 moveto 0.50625 0.40712 lineto stroke grestore [(6)] 0.4875 0.40712 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.53792 moveto 0.50625 0.53792 lineto stroke grestore [(8)] 0.4875 0.53792 1 0 Mshowa gsave 0.001 setlinewidth 0.5 0.04088 moveto 0.50375 0.04088 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.06704 moveto 0.50375 0.06704 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.0932 moveto 0.50375 0.0932 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.11936 moveto 0.50375 0.11936 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.17168 moveto 0.50375 0.17168 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.19784 moveto 0.50375 0.19784 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.224 moveto 0.50375 0.224 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.25016 moveto 0.50375 0.25016 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.30248 moveto 0.50375 0.30248 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.32864 moveto 0.50375 0.32864 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.3548 moveto 0.50375 0.3548 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.38096 moveto 0.50375 0.38096 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.43328 moveto 0.50375 0.43328 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.45944 moveto 0.50375 0.45944 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.4856 moveto 0.50375 0.4856 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.51176 moveto 0.50375 0.51176 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.56408 moveto 0.50375 0.56408 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.59024 moveto 0.50375 0.59024 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.6164 moveto 0.50375 0.6164 lineto stroke grestore [(y)] 0.5 0.61803 0 -4 Mshowa gsave 0.002 setlinewidth 0.5 0 moveto 0.5 0.61803 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave gsave 0 0 1 setrgbcolor [ ] 0 setdash 1 Mabswid 0.02381 0.60332 moveto 0.06349 0.50931 lineto 0.10317 0.42347 lineto 0.14286 0.3458 lineto 0.18254 0.27632 lineto 0.22222 0.215 lineto 0.2619 0.16187 lineto 0.30159 0.1169 lineto 0.34127 0.08012 lineto 0.38095 0.0515 lineto 0.40079 0.04026 lineto 0.42063 0.03107 lineto 0.44048 0.02391 lineto 0.4504 0.0211 lineto 0.46032 0.0188 lineto 0.47024 0.01701 lineto 0.4752 0.01631 lineto 0.48016 0.01574 lineto 0.48512 0.01529 lineto 0.4876 0.01511 lineto 0.49008 0.01497 lineto 0.49256 0.01486 lineto 0.4938 0.01481 lineto 0.49504 0.01478 lineto 0.49628 0.01475 lineto 0.49752 0.01473 lineto 0.49876 0.01472 lineto 0.5 0.01472 lineto 0.50124 0.01472 lineto 0.50248 0.01473 lineto 0.50372 0.01475 lineto 0.50496 0.01478 lineto 0.50744 0.01486 lineto 0.50992 0.01497 lineto 0.5124 0.01511 lineto 0.51488 0.01529 lineto 0.51984 0.01574 lineto 0.5248 0.01631 lineto 0.52976 0.01701 lineto 0.53968 0.0188 lineto 0.5496 0.0211 lineto 0.55952 0.02391 lineto 0.57937 0.03107 lineto 0.59921 0.04026 lineto 0.61905 0.0515 lineto 0.65873 0.08012 lineto 0.69841 0.1169 lineto 0.7381 0.16187 lineto 0.77778 0.215 lineto 0.81746 0.27632 lineto Mistroke 0.85714 0.3458 lineto 0.89683 0.42347 lineto 0.93651 0.50931 lineto 0.97619 0.60332 lineto Mfstroke grestore grestore % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; ] The graph is automatically in Blue instead of boring Black. PlotE recognizes t as the independent variable and labels the axes accordingly. Equivalent Form: PlotE[t^2,{t,-3,3}]; ;[s] 5:0,0;60,1;65,2;157,3;176,4;178,-1; 5:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subsubsection; inactive; preserveAspect; ] Two Functions :[font = input; Cclosed; preserveAspect; startGroup; ] PlotE[x^2,x^3,-3,3]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.15873 0.236421 0.09355 [ [(-3)] 0.02381 0.23642 0 2 Msboxa [(-2)] 0.18254 0.23642 0 2 Msboxa [(-1)] 0.34127 0.23642 0 2 Msboxa [(1)] 0.65873 0.23642 0 2 Msboxa [(2)] 0.81746 0.23642 0 2 Msboxa [(3)] 0.97619 0.23642 0 2 Msboxa [(x)] 1.025 0.23642 -1 0 Msboxa [(-2)] 0.4875 0.04932 1 0 Msboxa [(-1)] 0.4875 0.14287 1 0 Msboxa [(1)] 0.4875 0.32997 1 0 Msboxa [(2)] 0.4875 0.42352 1 0 Msboxa [(3)] 0.4875 0.51707 1 0 Msboxa [(4)] 0.4875 0.61062 1 0 Msboxa [(y)] 0.5 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0.02381 0.23642 moveto 0.02381 0.24267 lineto stroke grestore [(-3)] 0.02381 0.23642 0 2 Mshowa gsave 0.002 setlinewidth 0.18254 0.23642 moveto 0.18254 0.24267 lineto stroke grestore [(-2)] 0.18254 0.23642 0 2 Mshowa gsave 0.002 setlinewidth 0.34127 0.23642 moveto 0.34127 0.24267 lineto stroke grestore [(-1)] 0.34127 0.23642 0 2 Mshowa gsave 0.002 setlinewidth 0.65873 0.23642 moveto 0.65873 0.24267 lineto stroke grestore [(1)] 0.65873 0.23642 0 2 Mshowa gsave 0.002 setlinewidth 0.81746 0.23642 moveto 0.81746 0.24267 lineto stroke grestore [(2)] 0.81746 0.23642 0 2 Mshowa gsave 0.002 setlinewidth 0.97619 0.23642 moveto 0.97619 0.24267 lineto stroke grestore [(3)] 0.97619 0.23642 0 2 Mshowa gsave 0.001 setlinewidth 0.05556 0.23642 moveto 0.05556 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.0873 0.23642 moveto 0.0873 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.11905 0.23642 moveto 0.11905 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.15079 0.23642 moveto 0.15079 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.21429 0.23642 moveto 0.21429 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.24603 0.23642 moveto 0.24603 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.27778 0.23642 moveto 0.27778 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.30952 0.23642 moveto 0.30952 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.37302 0.23642 moveto 0.37302 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.40476 0.23642 moveto 0.40476 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.43651 0.23642 moveto 0.43651 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.46825 0.23642 moveto 0.46825 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.53175 0.23642 moveto 0.53175 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.56349 0.23642 moveto 0.56349 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.59524 0.23642 moveto 0.59524 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.62698 0.23642 moveto 0.62698 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.69048 0.23642 moveto 0.69048 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.72222 0.23642 moveto 0.72222 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.75397 0.23642 moveto 0.75397 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.78571 0.23642 moveto 0.78571 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.84921 0.23642 moveto 0.84921 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.88095 0.23642 moveto 0.88095 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.9127 0.23642 moveto 0.9127 0.24017 lineto stroke grestore gsave 0.001 setlinewidth 0.94444 0.23642 moveto 0.94444 0.24017 lineto stroke grestore [(x)] 1.025 0.23642 -1 0 Mshowa gsave 0.002 setlinewidth 0 0.23642 moveto 1 0.23642 lineto stroke grestore gsave 0.002 setlinewidth 0.5 0.04932 moveto 0.50625 0.04932 lineto stroke grestore [(-2)] 0.4875 0.04932 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.14287 moveto 0.50625 0.14287 lineto stroke grestore [(-1)] 0.4875 0.14287 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.32997 moveto 0.50625 0.32997 lineto stroke grestore [(1)] 0.4875 0.32997 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.42352 moveto 0.50625 0.42352 lineto stroke grestore [(2)] 0.4875 0.42352 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.51707 moveto 0.50625 0.51707 lineto stroke grestore [(3)] 0.4875 0.51707 1 0 Mshowa gsave 0.002 setlinewidth 0.5 0.61062 moveto 0.50625 0.61062 lineto stroke grestore [(4)] 0.4875 0.61062 1 0 Mshowa gsave 0.001 setlinewidth 0.5 0.06803 moveto 0.50375 0.06803 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.08674 moveto 0.50375 0.08674 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.10545 moveto 0.50375 0.10545 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.12416 moveto 0.50375 0.12416 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.16158 moveto 0.50375 0.16158 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.18029 moveto 0.50375 0.18029 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.199 moveto 0.50375 0.199 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.21771 moveto 0.50375 0.21771 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.25513 moveto 0.50375 0.25513 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.27384 moveto 0.50375 0.27384 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.29255 moveto 0.50375 0.29255 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.31126 moveto 0.50375 0.31126 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.34868 moveto 0.50375 0.34868 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.36739 moveto 0.50375 0.36739 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.3861 moveto 0.50375 0.3861 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.40481 moveto 0.50375 0.40481 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.44223 moveto 0.50375 0.44223 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.46094 moveto 0.50375 0.46094 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.47965 moveto 0.50375 0.47965 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.49836 moveto 0.50375 0.49836 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.53578 moveto 0.50375 0.53578 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.55449 moveto 0.50375 0.55449 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.5732 moveto 0.50375 0.5732 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.59191 moveto 0.50375 0.59191 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.03061 moveto 0.50375 0.03061 lineto stroke grestore gsave 0.001 setlinewidth 0.5 0.0119 moveto 0.50375 0.0119 lineto stroke grestore [(y)] 0.5 0.61803 0 -4 Mshowa gsave 0.002 setlinewidth 0.5 0 moveto 0.5 0.61803 lineto stroke grestore grestore 0 0 moveto 1 0 lineto 1 0.61803 lineto 0 0.61803 lineto closepath clip newpath gsave gsave 0 0 1 setrgbcolor [ ] 0 setdash 1 Mabswid stroke stroke stroke stroke 0.17958 0.61803 moveto 0.18254 0.61062 lineto stroke 0.18254 0.61062 moveto 0.22222 0.52292 lineto 0.2619 0.44691 lineto 0.30159 0.38259 lineto 0.34127 0.32997 lineto 0.38095 0.28904 lineto 0.40079 0.27296 lineto 0.42063 0.25981 lineto 0.44048 0.24958 lineto 0.4504 0.24556 lineto 0.46032 0.24227 lineto 0.47024 0.23971 lineto 0.4752 0.2387 lineto 0.48016 0.23788 lineto 0.48512 0.23724 lineto 0.4876 0.23699 lineto 0.49008 0.23679 lineto 0.49256 0.23663 lineto 0.4938 0.23656 lineto 0.49504 0.23651 lineto 0.49628 0.23647 lineto 0.49752 0.23644 lineto 0.49876 0.23643 lineto 0.5 0.23642 lineto 0.50124 0.23643 lineto 0.50248 0.23644 lineto 0.50372 0.23647 lineto 0.50496 0.23651 lineto 0.50744 0.23663 lineto 0.50992 0.23679 lineto 0.5124 0.23699 lineto 0.51488 0.23724 lineto 0.51984 0.23788 lineto 0.5248 0.2387 lineto 0.52976 0.23971 lineto 0.53968 0.24227 lineto 0.5496 0.24556 lineto 0.55952 0.24958 lineto 0.57937 0.25981 lineto 0.59921 0.27296 lineto 0.61905 0.28904 lineto 0.65873 0.32997 lineto 0.69841 0.38259 lineto 0.7381 0.44691 lineto 0.77778 0.52292 lineto 0.81746 0.61062 lineto stroke 0.82042 0.61803 moveto 0.81746 0.61062 lineto stroke stroke stroke stroke stroke grestore gsave 1 0 0 setrgbcolor [ ] 0 setdash 1 Mabswid stroke stroke stroke stroke stroke stroke stroke stroke 0.28397 0 moveto 0.30159 0.05371 lineto stroke 0.30159 0.05371 moveto 0.32143 0.10322 lineto 0.34127 0.14287 lineto 0.36111 0.17375 lineto 0.38095 0.19695 lineto 0.39087 0.20602 lineto 0.40079 0.21358 lineto 0.41071 0.21977 lineto 0.42063 0.22473 lineto 0.43056 0.22859 lineto 0.44048 0.23149 lineto 0.44544 0.23262 lineto 0.4504 0.23357 lineto 0.45536 0.23434 lineto 0.46032 0.23496 lineto 0.46528 0.23544 lineto 0.47024 0.2358 lineto 0.47272 0.23595 lineto 0.4752 0.23606 lineto 0.47768 0.23616 lineto 0.48016 0.23624 lineto 0.48264 0.2363 lineto 0.48512 0.23634 lineto 0.48636 0.23636 lineto 0.4876 0.23638 lineto 0.48884 0.23639 lineto 0.49008 0.2364 lineto 0.49132 0.23641 lineto 0.49256 0.23641 lineto 0.4938 0.23642 lineto 0.49504 0.23642 lineto 0.49628 0.23642 lineto 0.49752 0.23642 lineto 0.5 0.23642 lineto 0.50124 0.23642 lineto 0.50248 0.23642 lineto 0.50372 0.23642 lineto 0.50496 0.23642 lineto 0.5062 0.23643 lineto 0.50744 0.23643 lineto 0.50868 0.23644 lineto 0.50992 0.23644 lineto 0.51116 0.23645 lineto 0.5124 0.23647 lineto 0.51488 0.2365 lineto 0.51736 0.23654 lineto 0.51984 0.2366 lineto 0.52232 0.23668 lineto 0.5248 0.23678 lineto 0.52976 0.23704 lineto Mistroke 0.53472 0.2374 lineto 0.53968 0.23788 lineto 0.54464 0.2385 lineto 0.5496 0.23928 lineto 0.55952 0.24135 lineto 0.56944 0.24425 lineto 0.57937 0.24811 lineto 0.58929 0.25307 lineto 0.59921 0.25926 lineto 0.61905 0.27589 lineto 0.63889 0.29909 lineto 0.65873 0.32997 lineto 0.67857 0.36962 lineto 0.69841 0.41914 lineto 0.7381 0.55215 lineto Mfstroke 0.75218 0.61803 moveto 0.7381 0.55215 lineto stroke stroke stroke stroke stroke stroke stroke grestore grestore % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; ] The functions are automatically plotted in different colors. Equivalent Form: PlotE[{x^2,x^3},{-3,3}]; ;[s] 3:0,0;78,1;101,2;103,-1; 3:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subsubsection; inactive; preserveAspect; ] Range Interval :[font = input; Cclosed; preserveAspect; startGroup; ] PlotE[x^2,x^3,-1,1,-1,1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.309017 0.294302 [ [(-1)] 0.02381 0.30902 0 2 Msboxa [(-0.5)] 0.2619 0.30902 0 2 Msboxa [(0.5)] 0.7381 0.30902 0 2 Msboxa [(1)] 0.97619 0.30902 0 2 Msboxa [(x)] 1.025 0.30902 -1 0 Msboxa [(-1)] 0.4875 0.01472 1 0 Msboxa [(-0.5)] 0.4875 0.16187 1 0 Msboxa [(0.5)] 0.4875 0.45617 1 0 Msboxa [(1)] 0.4875 0.60332 1 0 Msboxa [(y)] 0.5 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] 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The style keywords Dotted and Thick are available in addition to the usual style primitives. ;[s] 5:0,0;71,1;77,2;82,3;87,4;146,-1; 5:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = input; Cclosed; dontPreserveAspect; startGroup; ] PlotE[Sin[x],Cos[x],0,Pi,-1,1,SameScale, {Cyan,Dotted},{Magenta,Thick}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 245; endGroup; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.63662 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.02381 0.303152 0.31831 0.303152 [ [(pi/6)] 0.18254 0.31831 0 2 Msboxa [(pi/3)] 0.34127 0.31831 0 2 Msboxa [(pi/2)] 0.5 0.31831 0 2 Msboxa [(2pi/3)] 0.65873 0.31831 0 2 Msboxa [(5pi/6)] 0.81746 0.31831 0 2 Msboxa [(pi)] 0.97619 0.31831 0 2 Msboxa [(x)] 1.025 0.31831 -1 0 Msboxa [(-1)] 0.01131 0.01516 1 0 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functions; it can graph sequences, data sets, equations, and parametric equations, all at the same time. In fact, PlotE doesn't have to do anything at all! It can also create a variety of geometric objects. But first, let's show how to do nothing at all! ;[s] 4:0,0;5,1;154,2;159,3;295,-1; 4:1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = subsubsection; inactive; preserveAspect; ] Thin Air :[font = input; Cclosed; preserveAspect; startGroup; ] PlotE[]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 33; pictureWidth = 385; pictureHeight = 238; endGroup; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.095238 0.309017 0.05886 [ [(-4)] 0.11905 0.30902 0 2 Msboxa [(-2)] 0.30952 0.30902 0 2 Msboxa [(2)] 0.69048 0.30902 0 2 Msboxa [(4)] 0.88095 0.30902 0 2 Msboxa [(x)] 1.025 0.30902 -1 0 Msboxa [(-4)] 0.4875 0.07358 1 0 Msboxa [(-2)] 0.4875 0.1913 1 0 Msboxa [(2)] 0.4875 0.42674 1 0 Msboxa [(4)] 0.4875 0.54446 1 0 Msboxa [(y)] 0.5 0.61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] 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Max[{12, 168^(1/2), e^Pi}] ;[o] Pi Max[{12, Sqrt[168], e }] :[font = output; output; inactive; preserveAspect; endGroup; endGroup; ] Min[{12, 168^(1/2), e^Pi}] ;[o] Pi Min[{12, Sqrt[168], e }] :[font = input; Cclosed; preserveAspect; startGroup; ] NMax[{20, e^Pi, Sqrt[168],fred}] NMin[{20, e^Pi, Sqrt[168],fred}] :[font = output; output; inactive; Cclosed; preserveAspect; startGroup; ] E^Pi ;[o] Pi e :[font = output; output; inactive; preserveAspect; endGroup; endGroup; ] 168^(1/2) ;[o] Sqrt[168] :[font = subsubsection; inactive; preserveAspect; ] MakeTable :[font = input; Cclosed; nowordwrap; preserveAspect; startGroup; ] MakeTable[{Sin[x],Sin[x]/x},{1,0.5,0.2,0.1,0.01,0.001,0.0001,0.00001}, {"x","sin(x)","sin(x)/x"},15] :[font = output; output; inactive; preserveAspect; fontLeading = 0; endGroup; ] TableForm[{{1, 0.84147098480789700000, 0.84147098480789700000}, {0.5, 0.479425538604203000000, 0.95885107720840600000}, {0.2, 0.198669330795061000000, 0.99334665397530600000}, {0.1, 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preserveAspect; fontLeading = 0; endGroup; ] TableForm[{{1, "(1,1)", "(2,4)", 3.}, {-1, "(1,1)", "(0,0)", 1.}, {0.5, "(1,1)", "(1.5,2.25)", 2.5}, {-0.5, "(1,1)", "(0.5,0.25)", 1.5}, {0.2, "(1,1)", "(1.2,1.44)", 2.2}, {-0.2, "(1,1)", "(0.8,0.64)", 1.8}, {0.1, "(1,1)", "(1.1,1.21)", 2.1}, {-0.1, "(1,1)", "(0.9,0.81)", 1.9}, {0.05, "(1,1)", "(1.05,1.1025)", 2.05}, {-0.05, "(1,1)", "(0.95,0.9025)", 1.95}, {0.02, "(1,1)", "(1.02,1.0404)", 2.02}, {-0.02, "(1,1)", "(0.98,0.9604)", 1.98}, {0.01, "(1,1)", "(1.01,1.0201)", 2.01}, {-0.01, "(1,1)", "(0.99,0.9801)", 1.99}}, TableHeadings -> {None, {"h", "(a,f[a])", "(a+h,f[a+h])", "slope"}}] ;[o] h (a,f[a]) (a+h,f[a+h]) slope 1 (1,1) (2,4) 3. -1 (1,1) (0,0) 1. 0.5 (1,1) (1.5,2.25) 2.5 -0.5 (1,1) (0.5,0.25) 1.5 0.2 (1,1) (1.2,1.44) 2.2 -0.2 (1,1) (0.8,0.64) 1.8 0.1 (1,1) (1.1,1.21) 2.1 -0.1 (1,1) (0.9,0.81) 1.9 0.05 (1,1) (1.05,1.1025) 2.05 -0.05 (1,1) (0.95,0.9025) 1.95 0.02 (1,1) (1.02,1.0404) 2.02 -0.02 (1,1) (0.98,0.9604) 1.98 0.01 (1,1) 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It has the advantage that you donàt have to remember what comes first, the functions or the intervals: ;[s] 5:0,0;16,1;21,2;47,3;52,4;157,-1; 5:1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0;1,10,8,Courier,1,12,0,0,0;1,13,10,Times,0,14,0,0,0; :[font = input; Cclosed; nowordwrap; preserveAspect; startGroup; ] Clear[g,x]; g[x_]:= Piece[x^2,0 <= x <= 1,2 - x,1 <= x <= 2,Exp[2-x],2 <= x <= 4]; g[x] :[font = output; output; inactive; preserveAspect; endGroup; ] Which[0 <= x <= 1, x^2, 1 <= x <= 2, 2 - x, 2 <= x <= 4, E^(2 - x)] ;[o] 2 2 - x Which[0 <= x <= 1, x , 1 <= x <= 2, 2 - x, 2 <= x <= 4, e ] :[font = text; inactive; preserveAspect; ] Also you can specify a default condition by ¼else½ or ¼otherwise½. :[font = input; Cclosed; nowordwrap; preserveAspect; startGroup; ] Clear[h,x]; h[x_]:= Piece[1,-2 <= x <= -1,-1,1 <= x <= 2,0,otherwise]; PlotE[h[x],{-3,3},SameScale]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; 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