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# 12. Plotting

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## 12.1 Introduction to Plotting

Maxima uses an external plotting package to make the plots (see the section on Plotting formats). The plotting functions calculate a set of points and pass them to the plotting package together with a set of commands. That information can be passed to the external program either through a pipe or by calling the program with the name of a file where the data has been saved. The data file is given the name `maxout.interface`, where `interface` is the name of the plotting interface being used (gnuplot, xmaxima, mgnuplot or gnuplot_pipes).

The `maxout.interface` file, in the cases when it is used, is created in the directory specified by the system variable `maxima_tempdir`. That location can be changed; by assigning to that variable a string that represents a valid directory where Maxima can create new files.

After a plot has been created, the file `maxout.interface` can be executed again with the appropriate external program. If a Maxima plotting command fails to show anything, that file can be inspected to look for possible sources of problems.

Together with the plotting functions described in this chapter, package draw adds other functionalities. Note that some plotting options are named equal in both plotting contexts, but with different syntax; if you want to access the draw information related to these options, you have to type `?? opt`, where `opt` is the name of the option.

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@ref{Category: Plotting}

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## 12.2 Plotting Formats

There are currently two external plotting programs that Maxima use: Gnuplot and Xmaxima. There are various different formats for those programs, which can be selected with the option `plot_format` (see the Plotting Options section).

The plotting formats are the following:

- gnuplot (default on Windows)

  Used to launch the external program gnuplot, which must be installed in your system. All plotting commands and data are saved into the file `maxout.gnuplot`.

- gnuplot_pipes (default on non-Windows platforms)

  This format is not available in Windows platforms. It is similar to the `gnuplot` format except that the commands are sent to gnuplot through a pipe, while the data are saved into the file `maxout.gnuplot_pipes`. A single gnuplot process is kept open and subsequent plot commands will be sent to the same process, replacing previous plots, unless the gnuplot pipe is closed with the function `gnuplot_close`. When this format is used, the function `gnuplot_replot` can be used to modify a plot that has already displayed on the screen.

  This format should only be used to plot to the screen; for plotting to files it is better to use the `gnuplot` format.

- mgnuplot

  Mgnuplot is a Tk-based wrapper around gnuplot. It is included in the Maxima distribution. Mgnuplot offers a rudimentary GUI for gnuplot, but has fewer overall features than the plain gnuplot interface. Mgnuplot requires an external gnuplot installation and, in Unix systems, the Tcl/Tk system.

- xmaxima

  Xmaxima is a Tcl/Tk graphical interface for Maxima that can also be used to display plots created when Maxima is run from the console or from other graphical interfaces. To use this format, the xmaxima program, which is distributed together with Maxima, should be installed. If Maxima is being run from xmaxima itself, this format will make the plot functions send the data and commands through the same socket used for the communication between Maxima and Xmaxima. When used from the console or from other interface, the commands and data will be saved in the file `maxout.xmaxima`, and the xmaxima program will be launched with the name of the location of that file as argument.

  In previous versions this format used to be called `openmath`; that old name will still be accepted as a synonym for `xmaxima`.

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@ref{Category: Plotting}

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## 12.3 Functions and Variables for Plotting

Function: contour_plot (expr, x_range, y_range, options, …)

  It plots the contours (curves of equal value) of expr over the region x_range by y_range. Any additional arguments are treated the same as in `plot3d`.

  This function only works when the plot format is either `gnuplot` or `gnuplot_pipes`. The additional package `implicit_plot` can also be used to plot contours and it works for any format. See `implicit_plot`.

  Examples:

      (%i1) contour_plot (x^2 + y^2, [x, -4, 4], [y, -4, 4])$

      (%i1) F(x, y) := x^3 + y^2;
                                         3    2
      (%o1)                  F(x, y) := x  + y
      (%i2) contour_plot (F, [u, -4, 4], [v, -4, 4])$

  You can add any options accepted by `plot3d`; for instance, the option `legend` with a value of false, to remove the legend. Gnuplot chooses, by default, 3 contours to show. To increase the number of levels, it is necessary to specify a custom gnuplot preamble:

      (%i1) contour_plot (u^3 + v^2, [u, -4, 4], [v, -4, 4],
                          [legend,false],
                          [gnuplot_preamble, "set cntrparam levels 12"])$

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  @ref{Category: Plotting}

Function: get_plot_option (keyword, index)

  Returns a value of the option with name keyword, stored in the global variable `plot_options`. A value of 1 for the index will return the keyword itself; a value of 2 turn returns the first parameter following the keyword, and so on.

  See also `plot_options`, `set_plot_option` and the section on Plotting Options.

Function: implicit_plot (expr, x_range, y_range)
Function: implicit_plot ([expr_1, …, expr_n], x_range, y_range)

  Displays a plot of one or more expressions in implicit form. expr is the expression to be plotted, x_range the range of the horizontal axis and y_range the range of vertical axis. `implicit_plot` respects global setting for the Gnuplot driver set by the set_plot_option function. Options can also be passed to `implicit_plot` function as optional arguments.

  `implicit_plot` works by tracking sign changes on the area given by x_range and y_range and can fail for complicated expressions.

  `load(implicit_plot)` loads this function.

  Example:

      (%i1) implicit_plot (x^2 = y^3 - 3*y + 1, [x, -4, 4], [y, -4, 4],
       [gnuplot_preamble, "set zeroaxis"]);

  ·

  @ref{Category: Plotting} · @ref{Category: Share packages} · @ref{Category: Package implicit_plot}

Function: make_transform ([var1, var2, var3], fx, fy, fz)

  Returns a function suitable to be used in the option `transform_xy` of plot3d. The three variables var1, var2, var3 are three dummy variable names, which represent the 3 variables given by the plot3d command (first the two independent variables and then the function that depends on those two variables). The three functions fx, fy, fz must depend only on those 3 variables, and will give the corresponding x, y and z coordinates that should be plotted. There are two transformations defined by default: `polar_to_xy` and `spherical_to_xyz`. See the documentation for those two transformations.

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System function: polar_to_xy

  It can be given as value for the `transform_xy` option of plot3d. Its effect will be to interpret the two independent variables in plot3d as the distance from the z axis and the azimuthal angle (polar coordinates), and transform them into x and y coordinates.

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  @ref{Category: Plotting}

Function: plot2d (plot, x_range, …, options, …)
Function: plot2d ([plot_1, …, plot_n], …, options, …)
Function: plot2d ([plot_1, …, plot_n], x_range, …, options, …)

  Where plot, plot_1, …, plot_n can be either expressions, function names or a list with the any of the forms: `[discrete, [x1, ..., xn], [y1, ..., yn]]`, `[discrete, [[x1, y1], ..., [xn, ..., yn]]` or `[parametric, x_expr, y_expr, t_range]`.

  Displays a plot of one or more expressions as a function of one variable or parameter.

  `plot2d` displays one or several plots in two dimensions. When expressions or function name are used to define the plots, they should all depend on only one variable var and the use of x_range will be mandatory, to provide the name of the variable and its minimum and maximum values; the syntax for x_range is: `[variable, min, max]`.

  A plot can also be defined in the discrete or parametric forms. The discrete form is used to plot a set of points with given coordinates. A discrete plot is defined by a list starting with the keyword discrete, followed by one or two lists of values. If two lists are given, they must have the same length; the first list will be interpreted as the x coordinates of the points to be plotted and the second list as the y coordinates. If only one list is given after the discrete keyword, each element on the list should also be a list with two values that correspond to the x and y coordinates of a point.

  A parametric plot is defined by a list starting with the keyword parametric, followed by two expressions or function names and a range for the parameter. The range for the parameter must be a list with the name of the parameter followed by its minimum and maximum values: `[param, min, max]`. The plot will show the path traced out by the point with coordinates given by the two expressions or functions, as param increases from min to max.

  A range for the vertical axis is an optional argument with the form: `[y, min, max]` (the keyword y is always used for the vertical axis). If that option is used, the plot will show that exact vertical range, independently of the values reached by the plot. If the vertical range is not specified, it will be set up according to the minimum and maximum values of the second coordinate of the plot points.

  All other options should also be lists, starting with a keyword and followed by one or more values. See `plot_options`.

  If there are several plots to be plotted, a legend will be written to identity each of the expressions. The labels that should be used in that legend can be given with the option `legend`. If that option is not used, Maxima will create labels from the expressions or function names.

  Examples:

  Plot of a common function:

      (%i1) plot2d (sin(x), [x, -%pi, %pi])$

  If the functions grows too fast, it might be necessary to limit the values in the vertical axis using the y option:

      (%i1) plot2d (sec(x), [x, -2, 2], [y, -20, 20])$
      plot2d: some values were clipped.

  The aspect of the plot might be different depending on the plotting program used. For instance, when the plot box is disable, Xmaxima will plot the axes using arrows:

      (%i1) plot2d ( x^2-1, [x, -3, 3], [y, -2, 10],
                            [box, false], [plot_format, xmaxima])$

  A plot with a logarithmic scale:

      (%i1) plot2d (exp(3*s), [s, -2, 2], [logy])$

  Plotting functions by name:

      (%i1) F(x) := x^2 $
      (%i2) :lisp (defun |$g| (x) (m* x x x))
      $g
      (%i2) H(x) := if x < 0 then x^4 - 1 else 1 - x^5 $
      (%i3) plot2d ([F, G, H], [u, -1, 1], [y, -1.5, 1.5])$

  A plot of the butterfly curve, defined parametrically:

      (%i1) r: (exp(cos(t))-2*cos(4*t)-sin(t/12)^5)$
      (%i2) plot2d([parametric, r*sin(t), r*cos(t),
                   [t, -8*%pi, 8*%pi], [nticks, 2000]])$

  A "circle" with two turns, when plotted with only 7 points:

      (%i1) plot2d ([parametric, cos(t), sin(t),
                    [t, -2*%pi, 2*%pi], [nticks, 8]])$

  Plot of a common function together with the parametric representation of a circle. The size of the plot has been adjusted with the x and y options, to make the circle look round and not deformed as an ellipse. These values work well for the Postscript terminal used to produce this plot; you might have to adjust the values for your screen.

      (%i1) plot2d([[parametric, cos(t), sin(t),
                    [t,0,2*%pi], [nticks, 80]],
              abs(x)], [x,-2,2], [y, -1.5, 1.5])$
      plot2d: some values were clipped.

  A plot of a discrete set of points, defining x and y coordinates separately:

      (%i1) plot2d ([discrete, [10, 20, 30, 40, 50],
                               [.6, .9, 1.1, 1.3, 1.4]])$

  The same points shown in the previous example, defining each point separately and without any lines joining the points:

      (%i1) plot2d([discrete, [[10, .6], [20, .9], [30, 1.1],
                               [40, 1.3], [50, 1.4]]],
                              [style, points])$

  In this example, a table with three columns is saved in a file "data.txt" which is then read and the second and third column are plotted on the two axes:

      (%i1) with_stdout ("data.txt", for x:0 thru 10 do
                                         print (x, x^2, x^3))$
      (%i2) data: read_matrix ("data.txt")$
      (%i3) plot2d ([discrete, transpose(data)[2], transpose(data)[3]],
        [style,points], [point_type,diamond], [color,red])$

  A plot of experimental data points together with the theoretical function that predicts the data:

      (%i1) xy: [[10, .6], [20, .9], [30, 1.1], [40, 1.3], [50, 1.4]]$
      (%i2) plot2d([[discrete, xy], 2*%pi*sqrt(l/980)], [l,0,50],
              [style, points, lines], [color, red, blue],
              [point_type, asterisk],
              [legend, "experiment", "theory"],
              [xlabel, "pendulum's length (cm)"],
              [ylabel, "period (s)"])$

  See also the section about Plotting Options.

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  @ref{Category: Plotting}

Function: plot3d (expr, x_range, y_range, …, options, …)
Function: plot3d ([expr_1, …, expr_n], x_range, y_range, …, options, …)

  Displays a plot of one or more surfaces defined as functions of two variables or in parametric form.

  The functions to be plotted may be specified as expressions or function names. The mouse can be used to rotate the plot looking at the surface from different sides.

  Examples:

  Plot of a common function:

      (%i1) plot3d (2^(-u^2 + v^2), [u, -3, 3], [v, -2, 2])$

  Use of the z option to limit a function that goes to infinity (in this case the function is minus infinity on the x and y axes); this also shows how to plot with only lines and no shading:

      (%i1) plot3d ( log ( x^2*y^2 ), [x, -2, 2], [y, -2, 2], [z, -8, 4],
                     [palette, false], [color, magenta, blue])$

  The infinite values of z can also be avoided by choosing a grid that does not fall on any asymptotes; this example also shows how to select one of the predefined palettes, in this case the fourth one:

      (%i1) plot3d (log (x^2*y^2), [x, -2, 2], [y, -2, 2],
               [grid, 29, 29],
               [palette, get_plot_option(palette,5)])$

  Two surfaces in the same plot, sharing the same domain; in gnuplot the two surfaces will use the same palette:

      (%i1) plot3d ([2^(-x^2 + y^2), 4*sin(3*(x^2+y^2))/(x^2+y^2),
                    [x, -3, 3], [y, -2, 2]])$

  The same two surfaces, but now with different domains; in xmaxima each surface will use a different palette, chosen from the list defined by the option palette:

      (%i1) plot3d ([[2^(-x^2 + y^2),[x,-2,2],[y,-2,2]],
               4*sin(3*(x^2+y^2))/(x^2+y^2),
               [x, -3, 3], [y, -2, 2]], [plot_format,xmaxima])$

  Plot of a Klein bottle, defined parametrically:

      (%i1) expr_1:5*cos(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3.0)-10.0$
      (%i2) expr_2:-5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y) + 3.0)$
      (%i3) expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))$
      (%i4) plot3d ([expr_1, expr_2, expr_3], [x, -%pi, %pi],
              [y, -%pi, %pi], [grid, 40, 40])$

  Plot of a spherical harmonic, using of the predefined transformations, `spherical_to_xyz`, to transform from spherical to rectangular coordinates. See the documentation for `spherical_to_xyz`.

      (%i1) plot3d (sin(2*theta)*cos(phi), [theta, 0, %pi],
                    [phi, 0, 2*%pi],
                    [transform_xy, spherical_to_xyz], [grid,30,60])$

  Use of the predefined function `polar_to_xy` to transform from cylindrical to rectangular coordinates. See the documentation for `polar_to_xy`. This example also shows how to eliminate the bounding box and the legend.

      (%i1) plot3d (r^.33*cos(th/3), [r, 0, 1], [th, 0, 6*%pi],
               [grid, 12, 80],
               [transform_xy, polar_to_xy], [box, false],
               [legend,false])$

  Plot of a sphere using the transformation from spherical to rectangular coordinates. In xmaxima the three axes are scaled in the same proportion, maintaining the symmetric shape of the sphere. A palette with different shades of a single color is used:

      (%i1) plot3d ( 5, [theta, 0, %pi], [phi, 0, 2*%pi],
               [plot_format,xmaxima],
               [transform_xy, spherical_to_xyz],
               [palette,[value,0.65,0.7,0.1,0.9]])$

  Definition of a function of two-variables using a matrix. Notice the single quote in the definition of the function, to prevent plot3d from failing when it realizes that the matrix will require integer indices.

      (%i1) M: matrix([1, 2, 3, 4], [1, 2, 3, 2], [1, 2, 3, 4],
                      [1, 2, 3, 3])$
      (%i2) f(x, y) := float('M [round(x), round(y)])$
      (%i3) plot3d (f(x,y), [x, 1, 4], [y, 1, 4], [grid, 4, 4])$
      apply: subscript must be an integer; found: round(x)

  By setting the elevation equal to zero, a surface can be seen as a map in which each color represents a different level. The option `colorbox` is used to show the correspondence among colors and levels, and the mesh lines are disabled to make the colors easier to see.

      (%i1) plot3d (cos (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4],
              [mesh_lines_color, false], [elevation, 0], [azimuth, 0],
              [colorbox, true], [grid, 150, 150])$

  See also the section about Plotting Options.

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  @ref{Category: Plotting}

System variable: plot_options

  Elements of this list state the default options for plotting. If an option is present in a `plot2d` or `plot3d` call, that value takes precedence over the default option. Otherwise, the value in `plot_options` is used. Default options are assigned by `set_plot_option`. There are other local options specific to each plotting command, and not included in this list of global options.

  Each element of `plot_options` is a list of two or more items. The first item is the name of the option, and the remainder comprises the value or values assigned to the option. In some cases, the assigned value is a list, which may include several items.

  See also `set_plot_option`, `get_plot_option` and the section on Plotting Options.

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Function: set_plot_option (option)

  Accepts most of the options listed in the section Plotting Options, and saves them into the global variable `plot_options`.

  `set_plot_option` evaluates its argument and returns the complete list `plot_options` (after modifying the option given).

  See also `plot_options`, `get_plot_option` and the section on Plotting Options.

  Example:

  Modification of the `grid` values.

      (%i1) set_plot_option ([grid, 30, 40]);
      (%o1) [[t, - 3, 3], [grid, 30, 40], [transform_xy, false],
      [run_viewer, true], [axes, true], [plot_format, gnuplot_pipes],
      [color, blue, red, green, magenta, black, cyan],
      [point_type, bullet, circle, plus, times, asterisk, box, square,
      triangle, delta, wedge, nabla, diamond, lozenge],
      [palette, [hue, 0.25, 0.7, 0.8, 0.5],
      [hue, 0.65, 0.8, 0.9, 0.55], [hue, 0.55, 0.8, 0.9, 0.4],
      [hue, 0.95, 0.7, 0.8, 0.5]], [gnuplot_term, default],
      [gnuplot_out_file, false], [nticks, 29], [adapt_depth, 5],
      [gnuplot_preamble, ], [gnuplot_default_term_command,
      set term pop], [gnuplot_dumb_term_command, set term dumb 79 22],
      [gnuplot_ps_term_command, set size 1.5, 1.5;set term postscript \
      eps enhanced color solid 24], [plot_realpart, false]]

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System function: spherical_to_xyz

  It can be given as value for the `transform_xy` option of `plot3d`. Its effect will be to interpret the two independent variables and the function in `plot3d` as the spherical coordinates of a point (first, the angle with the z axis, then the angle of the xy projection with the x axis and finally the distance from the origin) and transform them into x, y and z coordinates.

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  @ref{Category: Plotting}

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## 12.4 Plotting Options

All options consist of a list starting with one of the keywords in this section, followed by one or more values. Most of the options can be used in any of the plotting commands (`plot2d`, `plot3d`, `contour_plot`, `implicit_plot`) or in the function `set_plot_option`. The exceptions will be specified in the following list.

Plot option: adapt_depth [adapt_depth, integer]

  Default value: `5`

  The maximum number of splittings used by the adaptive plotting routine.

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  @ref{Category: Plotting}

Plot option: axes [axes, symbol]

  Default value: `true`

  Where symbol can be either `true`, `false`, `x` or `y`. If `false`, no axes will be shown; if equal to `x` or `y` only the x or y axis will be shown, and if it is equal to `true`, both axes will be shown. This option is used only by plot2d and implicit_plot.

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Plot option: azimuth [azimuth, number]

  Default value: `30`

  A plot3d plot can be thought of as starting with its x and y axis in the horizontal and vertical axis, as in plot2d, and the z axis coming out of the paper perpendicularly. The z axis is then rotated around the x axis an angle equals to `elevation` and then the xy plane is rotated around the new z axis an angle `azimuth`. This option sets the value for the azimuth, in degrees.

  See also `elevation`.

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Plot option: box [box, symbol]

  Default value: `true`

  If set to `true`, a bounding box will be drawn for the plot; if set to `false`, no box will be drawn.

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Plot option: color [color, color_1, …, color_n]

  Default value: `blue`, `red`, `green`, `magenta`, `black`, `cyan`

  In `plot2d` and `implicit_plot`, it defines the color (or colors) for the various curves. In `plot3d`, it defines the colors used for the mesh lines of the surfaces, when no palette is being used; one side of the surface will have color color_1 and the other color_2 (or the same color if there is only one color).

  If there are more curves or surfaces than colors, the colors will be repeated in sequence. When using gnuplot, the colors could be: `blue`, `red`, `green`, `magenta`, `black`, or `cyan`; in xmaxima the colors can be those or a string starting with the character # and followed by six hexadecimal digits: two for the red component, two for green component and two for the blue component. If given the name of an unknown color, black will be used instead.

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Plot option: colorbox [colorbox, symbol]

  Default value: `false`

  Where symbol can be either `true` or `false`. If `true`, whenever `plot3d` uses a palette of different colors to represent the different values of z, a box will be shown on the right, indicating the colors used according to the scale of values of z. This option does not work in xmaxima.

  ·

  @ref{Category: Plotting}

Plot option: elevation [elevation, number]

  Default value: `60`

  A `plot3d` plot can be thought of as starting with its x and y axis in the horizontal and vertical axis, as in `plot2d`, and the z axis coming out of the paper perpendicularly. The z axis is then rotated around the x axis an angle equals to `elevation` and then the xy plane is rotated around the new z axis an angle `azimuth`. This option sets the value for the elevation, in degrees.

  See also `azimuth`.

  ·

  @ref{Category: Plotting}

Plot option: grid [grid, integer, integer]

  Default value: `30`, `30`

  Sets the number of grid points to use in the x- and y-directions for three-dimensional plotting.

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Plot option: legend [legend, string_1, …, string_n]
Plot option: legend [legend, false]

  It specifies the labels for the plots when various plots are shown. If there are more plots than the number of labels given, they will be repeated. If given the value `false`, no legends will be shown. By default, the names of the expressions or functions will be used, or the words discrete1, discrete2, …, for discrete sets of points. This option can not be set with `set_plot_option`.

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Plot option: logx [logx]

  Makes the horizontal axes to be scaled logarithmically. It can not be used with `set_plot_option`.

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  @ref{Category: Plotting}

Plot option: logy [logy]

  Makes the vertical axes to be scaled logarithmically. It can not be used with `set_plot_option`.

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  @ref{Category: Plotting}

Plot option: mesh_lines_color [mesh_lines_color, color]

  Default value: `black`

  It sets the color used by plot3d to draw the mesh lines, when a palette is being used. It accepts the same colors as for the option `color` (see the list of allowed colors in `color`). It can also be given a value `false` to eliminate completely the mesh lines.

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  @ref{Category: Plotting}

Plot option: nticks [nticks, integer]

  Default value: `29`

  When plotting functions with `plot2d`, it is gives the initial number of points used by the adaptive plotting routine for plotting functions. When plotting parametric functions with plot2d or `plot3d`, it sets the number of points that will be shown for the plot.

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  @ref{Category: Plotting}

Plot option: palette [palette, [palette_1], …, [palette_n]]
Plot option: palette [palette, false]

  Default value: `[hue, 0.25, 0.7, 0.8, 0.5]`, `[hue, 0.65, 0.8, 0.9, 0.55]`, `[hue, 0.55, 0.8, 0.9, 0.4]`, `[hue, 0.95, 0.7, 0.8, 0.5]`

  It can consist of one palette or a list of several palettes. Each palette is a list with a keyword followed by four numbers. The first three numbers, which must be between 0 and 1, define the hue, saturation and value of a basic color to be assigned to the minimum value of z. The keyword specifies which of the three attributes (hue, saturation or value) will be increased according to the values of z. The last number indicates the increase corresponding to the maximum value of z. That last number can be bigger than 1 or negative; the corresponding values of the modified attribute will be rounded modulo 1.

  Gnuplot only uses the first palette in the list; xmaxima will use the palettes in the list sequentially, when several surfaces are plotted together; if the number of palettes is exhausted, they will be repeated sequentially.

  The color of the mesh lines will be given by the option `mesh_lines_color`. If `palette` is given the value `false`, the surfaces will not be shaded but represented with a mesh of curves only. In that case, the colors of the lines will be determined by the option `color`.

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Plot option: plot_format [plot_format, format]

  Default value: `gnuplot`, in Windows systems, or `gnuplot_pipes` in other systems.

  Where format is one of the following: gnuplot, xmaxima, mgnuplot or gnuplot_pipes.

  It sets the format to be used for plotting.

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Plot option: plot_realpart [plot_realpart, symbol]

  Default value: `false`

  If set to `true`, the functions to be plotted will be considered as complex functions whose real value should be plotted; this is equivalent to plotting `realpart(function)`. If set to `false`, nothing will be plotted when the function does not give a real value. For instance, when `x` is negative, `log(x)` gives a complex value, with real value equal to `log(abs(x))`; if `plot_realpart` were `true`, `log(-5)` would be plotted as `log(5)`, while nothing would be plotted if `plot_realpart` were `false`.

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Plot option: point_type [point_type, type_1, …, type_n]

  Default value: `bullet`, `circle`, `plus`, `times`, `asterisk`, `box`, `square`, `triangle`, `delta`, `wedge`, `nabla`, `diamond`, `lozenge`

  In gnuplot, each set of points to be plotted with the style "points" or "linespoints" will be represented with objects taken from this list, in sequential order. If there are more sets of points than objects in this list, they will be repeated sequentially. The possible objects that can be used are: `bullet`, `circle`, `plus`, `times`, `asterisk`, `box`, `square`, `triangle`, `delta`, `wedge`, `nabla`, `diamond`, `lozenge`

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Plot option: psfile [psfile, string]

  Saves the plot into a Postscript file with name equal to string, rather than showing it in the screen. By default, the file will be created in the directory defined by the variable `maxima_tempdir`. The value of that variable can be changed to save the file in a different directory.

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Plot option: run_viewer [run_viewer, symbol]

  Default value: `true`

  Controls whether or not the appropriate viewer for the plot format should be run.

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Plot option: style [style, type_1, …, type1_n]
Plot option: style [style, [style_1], …, [style_n]]

  Default value: `lines` (will plot all sets of points joined with lines of thickness 1 and the first color given by the option `color` ).

  The styles that will be used for the various functions or sets of data in a 2d plot. The word style must be followed by one or more styles. If there are more functions and data sets than the styles given, the styles will be repeated. Each style can be either lines for line segments, points for isolated points, linespoints for segments and points, or dots for small isolated dots. Gnuplot accepts also an impulses style.

  Each of the styles can be enclosed inside a list with some additional parameters. lines accepts one or two numbers: the width of the line and an integer that identifies a color. The default color codes are: 1: blue, 2: red, 3: magenta, 4: orange, 5: brown, 6: lime and 7: aqua. If you use Gnuplot with a terminal different than X11, those colors might be different; for example, if you use the option [gnuplot_term, ps], color index 4 will correspond to black, instead of orange.

  points accepts one two or three parameters; the first parameter is the radius of the points, the second parameter is an integer that selects the color, using the same code used for lines and the third parameter is currently used only by Gnuplot and it corresponds to several objects instead of points. The default types of objects are: 1: filled circles, 2: open circles, 3: plus signs, 4: x, 5: *, 6: filled squares, 7: open squares, 8: filled triangles, 9: open triangles, 10: filled inverted triangles, 11: open inverted triangles, 12: filled lozenges and 13: open lozenges.

  linesdots accepts up to four parameters: line width, points radius, color and type of object to replace the points.

  See also `color` and `point_type`.

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Plot option: t [t, min, max]

  Default value: `-3`, `3`

  Default range for parametric plots.

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Plot option: transform_xy [transform_xy, symbol]

  Default value: `false`

  Where symbol is either `false` or the result obtained by using the function `transform_xy`. If different from `false`, it will be used to transform the 3 coordinates in plot3d.

  See `make_transform`, `polar_to_xy` and `spherical_to_xyz`.

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Plot option: x [x, min, max]

  When used as the first option in a `plot2d` command (or any of the first two in `plot3d` ), it indicates that the first independent variable is x and it sets its range. It can also be used again after the first option (or after the second option in plot3d) to define the effective horizontal domain that will be shown in the plot.

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Plot option: xlabel [xlabel, string]

  Specifies the string that will label the first axis; if this option is not used, that label will be the name of the independent variable, when plotting functions with `plot2d` or `implicit_plot`, or the name of the first variable, when plotting surfaces with `plot3d` or contours with `contour_plot`, or the first expression in the case of a parametric plot. It can not be used with `set_plot_option`.

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Plot option: y [y, min, max]

  When used as one of the first two options in `plot3d`, it indicates that one of the independent variables is y and it sets its range. Otherwise, it defines the effective domain of the second variable that will be shown in the plot.

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Plot option: ylabel [ylabel, string]

  Specifies the string that will label the second axis; if this option is not used, that label will be "y", when plotting functions with `plot2d` or `implicit_plot`, or the name of the second variable, when plotting surfaces with `plot3d` or contours with `contour_plot`, or the second expression in the case of a parametric plot. It can not be used with `set_plot_option`.

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Plot option: z [z, min, max]

  Used in `plot3d` to set the effective range of values of z that will be shown in the plot.

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Plot option: zlabel [zlabel, string]

  Specifies the string that will label the third axis, when using `plot3d`. If this option is not used, that label will be "z", when plotting surfaces, or the third expression in the case of a parametric plot. It can not be used with `set_plot_option` and it will be ignored by `plot2d` and `implicit_plot`.

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## 12.5 Gnuplot Options

There are several plot options specific to gnuplot. All of them consist of a keyword (the name of the option), followed by a string that should be a valid gnuplot command, to be passed directly to gnuplot. In most cases, there exist a corresponding plotting option that will produce a similar result and whose use is more recommended than the gnuplot specific option.

Plot option: gnuplot_term

  Sets the output terminal type for gnuplot.

  - default (default value)

    Gnuplot output is displayed in a separate graphical window.

  - dumb

    Gnuplot output is displayed in the Maxima console by an "ASCII art" approximation to graphics.

  - ps

    Gnuplot generates commands in the PostScript page description language. If the option `gnuplot_out_file` is set to filename, gnuplot writes the PostScript commands to filename. Otherwise, it is saved as `maxplot.ps` file.

  - any other valid gnuplot term specification

    Gnuplot can generate output in many other graphical formats such as png, jpeg, svg etc. To create plot in all these formats the `gnuplot_term` can be set to any supported gnuplot term name (symbol) or even full gnuplot term specification with any valid options (string). For example `[gnuplot_term, png]` creates output in PNG (Portable Network Graphics) format while `[gnuplot_term, "png size 1000,1000"]` creates PNG of 1000 x 1000 pixels size. If the option `gnuplot_out_file` is set to filename, gnuplot writes the output to filename. Otherwise, it is saved as `maxplot.term` file, where term is gnuplot terminal name.

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Plot option: gnuplot_out_file

  When used in conjunction with the `gnuplot_term` option, it can be used to save the plot in a file, in one of the graphic formats supported by Gnuplot. If you want to create a Postscript file, you can use the option `psfile` instead, which will also work in Openmath, and does the same thing with just one option.

      [gnuplot_term, png], [gnuplot_out_file, "graph3.png"]

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Plot option: gnuplot_pm3d

  With a value of `false`, it can be used to prevent the usage of PM3D mode, which is enabled by default.

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Plot option: gnuplot_preamble

  Inserts gnuplot commands before the plot is drawn. Any valid gnuplot commands may be used. Multiple commands should be separated with a semi-colon. The example shown produces a log scale plot. The default value for `gnuplot_preamble` is the empty string `""`.

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Plot option: gnuplot_curve_titles

  This is an old option that has been replaced by `legend` described above.

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Plot option: gnuplot_curve_styles

  This is an obsolete option that has been replaced by `style`.

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Plot option: gnuplot_default_term_command

  The gnuplot command to set the terminal type for the default terminal. The default value is `"set term pop"`.

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Plot option: gnuplot_dumb_term_command

  The gnuplot command to set the terminal type for the dumb terminal. The default value is `"set term dumb 79 22"`, which makes the text output 79 characters by 22 characters.

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Plot option: gnuplot_ps_term_command

  The gnuplot command to set the terminal type for the PostScript terminal. The default value is `"set size 1.5, 1.5; set term postscript eps enhanced color solid 24"`, which sets the size to 1.5 times gnuplot's default, and the font size to 24, among other things. See the gnuplot documentation for `set term postscript` for more information.

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## 12.6 Gnuplot_pipes Format Functions

Function: gnuplot_start ()

  Opens the pipe to gnuplot used for plotting with the `gnuplot_pipes` format. Is not necessary to manually open the pipe before plotting.

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Function: gnuplot_close ()

  Closes the pipe to gnuplot which is used with the `gnuplot_pipes` format.

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Function: gnuplot_restart ()

  Closes the pipe to gnuplot which is used with the `gnuplot_pipes` format and opens a new pipe.

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Function: gnuplot_replot ()
Function: gnuplot_replot (s)

  Updates the gnuplot window. If `gnuplot_replot` is called with a gnuplot command in a string s, then `s` is sent to gnuplot before reploting the window.

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Function: gnuplot_reset ()

  Resets the state of gnuplot used with the `gnuplot_pipes` format To update the gnuplot window call `gnuplot_replot` after `gnuplot_reset`.

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