Rename specvar integer-info to *integer-info*

[maxima.git] / doc / info / Plotting.texi

@c Time-stamp: "2024-03-07 12:17:14 villate"
@menu
* Introduction to Plotting::
* Plotting Formats::
* Functions and Variables for Plotting::
* Plotting Options::
* Gnuplot Options::
* Gnuplot_pipes Format Functions::
@end menu

@c -----------------------------------------------------------------------------
@node Introduction to Plotting, Plotting Formats, Plotting, Plotting
@section Introduction to Plotting
@c -----------------------------------------------------------------------------

To make the plots, Maxima can use an external plotting package or its
own graphical interface Xmaxima (see the section on @mref{Plotting
Formats}). The plotting functions calculate a set of points and pass
them to the plotting package together with a set of commands specific to
that graphic program. In some cases those commands and data are saved in
a file and the graphic program is executed giving it the name of that
file to be parsed.

When a file is created, it will begiven the name
@code{maxout_xxx.format}, where @code{xxx} is a number that is unique to
every concurrently-running instance of Maxima and @code{format} is the
name of the plotting format being used (@code{gnuplot}, @code{xmaxima},
@code{mgnuplot} or @code{geomview}).

There are commands to save the plot in a graphic format file, rather
than showing it in the screen. The default name for that graphic file is
@code{maxplot.extension}, where @code{extension} is the extension
normally used for the kind of graphic file selected, but that name can
also be specified by the user.

The @code{maxout_xxx.format} and @code{maxplot.extension} files are created
in the directory specified by the system variable
@mrefdot{maxima_tempdir} That location can be changed by assigning to
that variable (or to the environment variable @env{MAXIMA_TEMPDIR}) a string
that represents a valid directory where Maxima can create new files. The
output of the Maxima plotting command will be a list with the names of
the file(s) created, including their complete path, or empty if no files
are created. Those files should be deleted after the maxima session ends.

If the format used is either @code{gnuplot} or @code{xmaxima}, and the
@code{maxout_xxx.gnuplot} or @code{maxout_xxx.xmaxima} was saved,
@code{gnuplot} or @code{xmaxima} can be run, giving it the name of that
file as argument, in order to view again a plot previously created in
Maxima. Thus, when a Maxima plotting command fails, the format can be
set to @code{gnuplot} or @code{xmaxima} and the plain-text file
@code{maxout_xxx.gnuplot} (or @code{maxout_xxx.xmaxima}) can be
inspected to look for the source of the problem.

The additional package @ref{draw} provides functions similar to the ones
described in this section with some extra features, but it only works
with @code{gnuplot}. Note that some plotting options have the same name
in both plotting packages, but their syntax and behavior is
different. To view the documentation for a graphic option @code{opt},
type @code{?? opt} in order to choose the information for either of
those two packages.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox

@c -----------------------------------------------------------------------------
@node Plotting Formats, Functions and Variables for Plotting, Introduction to Plotting, Plotting
@section Plotting Formats
@c -----------------------------------------------------------------------------

Maxima can use either Gnuplot, Xmaxima or Geomview as graphics
program. Gnuplot and Geomview are external programs which must be
installed separately, while Xmaxima is distributed with Maxima. To see
which plotting format you are currently using, use the command
@code{get_plot_option(plot_format);} and to change to another format,
you can use @code{set_plot_option([plot_format, <format>])}, where
@code{<format>} is the name of one of the formats described below. Those
two commands show and change the global plot format, while each
individual plotting command can use its own format, if it includes an
option @code{[plot_format, <format>]} (see @mref{get_plot_option} and
@mref{set_plot_option}).

The plotting formats are the following:

@itemize @bullet
@item
@strong{gnuplot}

Used to launch the external program gnuplot, which must be installed in
your system.  All plotting commands and data are saved into the file
@code{maxout_xxx.gnuplot}.

@item
@strong{gnuplot_pipes} (default value)

It is similar to the @code{gnuplot} format except that the commands and
plot data are sent directly to @code{gnuplot} without creating any
files.  A single gnuplot process is kept open, with a single graphic
window, and subsequent plot commands will be sent to the same process,
replacing previous plots in that same window. Even if the graphic window
is closed, the @code{gnuplot} process is still running until the end of
the session or until it is killed with @mrefdot{gnuplot_close}. The
function @mref{gnuplot_replot} can be used to modify a plot that has
already been displayed on the screen or to open again the graphic window
after it was closed.

This format does not work with some versions of Lisp under Windows and
it is only used to plot to the screen; whenever graphic files are to be
created, the format is silently switched to @code{gnuplot} and the
commands needed to create the graphic file are saved with the data in
file @code{maxout_xxx.gnuplot}.

@item
@strong{mgnuplot}

Mgnuplot is a Tk-based wrapper around gnuplot. It is an old interface
still included in the Maxima distribution, but it is currently disabled
because it does not have most of the features introduced by the newer
versions of the plotting commands. Mgnuplot requires an external gnuplot
installation and, in Unix systems, the Tcl/Tk system.

@item
@strong{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, must be installed; in some
Linux distributions Xmaxima is distributed in a package separate from
other parts of Maxima. If Maxima is being run from the Xmaxima console,
the data and commands are passed to xmaxima through the same socket used
for the communication between Maxima and the Xmaxima console. When used
from a terminal or from graphical interfaces different from Xmaxima, the
commands and data are saved in the file @code{maxout_xxx.xmaxima} and
xmaxima is run with the name of that file as argument.

@item
@strong{geomview}

Geomview, a Motif based interactive 3D viewing program for Unix. It can
only be used to display plots created with @code{plot3d}. To use this
format, the geomview program must be installed.

@end itemize

@opencatbox{Categories:}
@category{Plotting}
@closecatbox

@c -----------------------------------------------------------------------------
@node Functions and Variables for Plotting, Plotting Options, Plotting Formats, Plotting
@section Functions and Variables for Plotting
@c -----------------------------------------------------------------------------

@c -----------------------------------------------------------------------------
@anchor{geomview_command}
@defvr {System variable} geomview_command

This variable stores the name of the command used to run the geomview
program when the plot format is @code{geomview}. Its default value is
"geomview".  If the geomview program is not found unless you give
its complete path or if you want to try a different version of it,
you may change the value of this variable. For instance,

@c ===beg===
@c geomview_command: "/usr/local/bin/my_geomview"$
@c ===end===
@example
(%i1) geomview_command: "/usr/local/bin/my_geomview"$
@end example

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{get_plot_option}
@deffn {Function} get_plot_option (@var{keyword}, @var{index})

Returns the current default value of the option named @var{keyword},
which is a list. The optional argument @var{index} must be a positive
integer which can be used to extract only one element from the list
(element 1 is the name of the option).

See also @mrefcomma{set_plot_option} @mref{remove_plot_option} and the
section on @mrefdot{Plotting Options}
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_command}
@defvr {System variable} gnuplot_command

This variable stores the name of the command used to run the gnuplot
program when the plot format is @code{gnuplot} or
@code{gnuplot_pipes}. Its default value is "gnuplot". If the gnuplot
program is not found unless you give its complete path or if you want to
try a different version of it, you may change the value of this
variable. For instance,

@c ===beg===
@c gnuplot_command: "/usr/local/bin/my_gnuplot"$
@c ===end===
@example
(%i1) gnuplot_command: "/usr/local/bin/my_gnuplot"$
@end example

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_file_args}
@defvr {System variable} gnuplot_file_args

When a graphic file is going to be created using @code{gnuplot}, this
variable is used to specify the format used to print the file name given
to gnuplot. Its default value is "~a" in SBCL and Openmcl, and "~s" in
other lisp versions, which means that the name of the file will be
passed without quotes if SBCL or Openmcl are used and within quotes if
other Lisp versions are used. The contents of this variable can be
changed in order to add options for the gnuplot program, adding those
options before the format directive "~s".

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_view_args}
@defvr {System variable} gnuplot_view_args

This variable is the format used to parse the argument that will be
passed to the gnuplot program when the plot format is
@code{gnuplot}. Its default value is "-persist ~a" when SBCL or Openmcl
are used, and "-persist ~s" with other Lisp variants, where "~a" or "~s"
will be replaced with the name of the file where the gnuplot commands
have been written (usually "maxout_xxx.gnuplot"). The option
@code{-persist} tells gnuplot to exit after the commands in the file
have been executed, without closing the window that displays the plot.

Those familiar with gnuplot, might want to change the value of this
variable. For example, by changing it to:

@c ===beg===
@c gnuplot_view_args: "~s -"$
@c ===end===
@example
(%i1) gnuplot_view_args: "~s -"$
@end example

gnuplot will not be closed after the commands in the file have been
executed; thus, the window with the plot will remain, as well as the
gnuplot interactive shell where other commands can be issued in order to
modify the plot.

In Windows versions of Gnuplot older than 4.6.3 the behavior of "~s -"
and "-persist ~s" were the opposite; namely, "-persist ~s" made the plot
window and the gnuplot interactive shell remain, while "~s -" closed the
gnuplot shell keeping the plot window. Therefore, when older gnuplot
versions are used in Windows, it might be necessary to adjust the value
of @code{gnuplot_view_args}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{julia}
@deffn {Function} julia (@var{x}, @var{y}, ...@var{options}...)

Creates a graphic representation of the Julia set for the complex number
(@var{x} + i @var{y}). The two mandatory parameters @var{x} and @var{y}
must be real. This program is part of the additional package
@code{dynamics}, but that package does not have to be loaded; the first
time julia is used, it will be loaded automatically.

Each pixel in the grid is given a color corresponding to the number of
iterations it takes the sequence that starts at that point to move out
of the convergence circle of radius 2 centered at the origin. The number
of pixels in the grid is controlled by the @mref{grid} plot option
(default 30 by 30). The maximum number of iterations is set with the
option @mrefdot{iterations} The program sets its own default palette:
magenta, violet, blue, cyan, green, yellow, orange, red, brown and black,
but it can be changed by adding an explicit @mref{palette} option in the
command.

The default domain used goes from -2 to 2 in both axes and can be
changed with the @code{x} and @code{y} options. By default, the two axes
are shown with the same scale, unless the option @mref{yx_ratio} is used
or the option @mref{same_xy} is disabled. Other general plot options are
also accepted.

The following example shows a region of the Julia set for the number
-0.55 + i0.6. The option @mref{color_bar_tics} is used to prevent
Gnuplot from adjusting the color box up to 40, in which case the points
corresponding the maximum 36 iterations would not be black.

@c ===beg===
@c julia (-0.55, 0.6, [iterations, 36], [x, -0.3, 0.2],
@c   [y, 0.3, 0.9], [grid, 400, 400], [color_bar_tics, 0, 6, 36])$
@c ===end===
@example
@group
(%i1) julia (-0.55, 0.6, [iterations, 36], [x, -0.3, 0.2],
      [y, 0.3, 0.9], [grid, 400, 400], [color_bar_tics, 0, 6, 36])$
@end group
@end example

@ifnotinfo
@image{figures/plotting4,8cm}
@end ifnotinfo

@opencatbox{Categories:}
@category{Package dynamics}
@category{Plotting}
@closecatbox

@end deffn

@c -----------------------------------------------------------------------------
@anchor{make_transform}
@deffn {Function} make_transform ([@var{var1}, @var{var2}, @var{var3}], @var{fx}, @var{fy}, @var{fz})

Returns a function suitable to be used in the option @mref{transform_xy}@w{}
of plot3d.  The three variables @var{var1}, @var{var2}, @var{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
@var{fx}, @var{fy}, @var{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:
@mref{polar_to_xy} and @mrefdot{spherical_to_xyz} See the documentation
for those two transformations.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{mandelbrot}
@deffn {Function} mandelbrot (@var{options})

Creates a graphic representation of the Mandelbrot set. This program is
part of the additional package @code{dynamics}, but that package does
not have to be loaded; the first time mandelbrot is used, the package
will be loaded automatically.

This program can be called without any arguments, in which case it will
use a default value of 9 iterations per point, a grid with dimensions
set by the @mref{grid} plot option (default 30 by 30) and a region
that extends from -2 to 2 in both axes. The options are all the same
that plot2d accepts, plus an option @mref{iterations} to change the
number of iterations.

Each pixel in the grid is given a color corresponding to the number of
iterations it takes the sequence starting at zero to move out
of the convergence circle of radius 2, centered at the origin. The
maximum number of iterations is set by the option @mrefdot{iterations}
The program uses its own default palette: magenta,violet, blue, cyan,
green, yellow, orange, red, brown and black, but it can be changed by
adding an explicit @mref{palette} option in the command. By default, the
two axes are shown with the same scale, unless the option @mref{yx_ratio}
is used or the option @mref{same_xy} is disabled.

Example:

@c ===beg===
@c mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2],
            [grid,400,400])$
@c ===end===
@example
(%i1) mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2],
            [grid,400,400])$
@end example

@ifnotinfo
@image{figures/plotting5,8cm}
@end ifnotinfo

@opencatbox{Categories:}
@category{Package dynamics}
@category{Plotting}
@closecatbox

@end deffn

@c -----------------------------------------------------------------------------
@anchor{polar_to_xy}
@deffn {System function} polar_to_xy

It can be given as value for the @mref{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.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{plot2d}
@deffn  {Function} plot2d @
@fname{plot2d} (@var{expr}, @var{range_x}, @var{options}) @
@fname{plot2d} (@var{expr_1}=@var{expr_2}, @var{range_x}, @var{range_y}, @var{options}) @
@fname{plot2d} ([parametric, @var{expr_x}, @var{expr}_y, @var{range}], @var{options}) @
@fname{plot2d} ([discrete, @var{points}], @var{options}) @
@fname{plot2d} ([contour, @var{expr}], @var{range_x}, @var{range_y}, @var{options}) @
@fname{plot2d} ([@var{type_1}, @dots{}, @var{type_n}], @var{options})

There are 5 types of plots that can be plotted by @code{plot2d}:

@enumerate
@item @b{Explicit functions}. @code{plot2d} (@var{expr}, @var{range_x},
@var{options}), where @var{expr} is an expression that depends on only
one variable, or the name of a function with one input parameter and
numerical results. @var{range_x} is a list with three elements, the
first one being the name of the variable that will be shown on the
horizontal axis of the plot, and the other two elements should be two
numbers, the first one smaller than the second, that define the minimum
and maximum values to be shown on the horizontal axis. The name of the
variable used in @var{range_x} must be the same variable on which
@var{expr} depends. The result will show in the vertical axis the
corresponding values of the expression or function for each value of the
variable in the horizontal axis.

@item @b{Implicit functions}. @code{plot2d} (@var{expr_1}=@var{expr_2},
@var{range_x}, @var{range_y}, @var{options}), where @var{expr_1} and
@var{expr_2} are two expressions that can depend on one or two
variables. @var{range_x} and @var{range_y} must be two lists of three
elements that define the ranges for the variables in the two axes of the
plot; the first element of each list is the name of the corresponding
variable, and the other two elements are the minimum and maximum values
for that variable. The two variables on which @var{expr_1} and
@var{expr_2} can depend are those specified by @var{range_x} and
@var{range_y}. The result will be a curve or a set of curves where the
equation @var{expr_1}=@var{expr_2} is true.

@item @b{Parametric functions}. @code{plot2d} ([parametric,
@var{expr_x}, @var{expr}_y, @var{range}], @var{options}), where
@var{expr_x} and @var{expr}_y are two expressions that depend on a
single parameter. @var{range} must be a three-element list; the first
element must be the name of the parameter on which @var{expr_x} and
@var{expr}_y depend, and the other two elements must be the minimum and
maximum values for that parameter. The result will be a curve in which
the horizontal and vertical coordinates of each point are the values of
@var{expr_x} and @var{expr}_y for a value of the parameter within the
range given.

@item @b{Set of points}. @code{plot2d} ([discrete, @var{points}],
@var{options}), displays a list of points, joined by segments by
default. The horizontal and vertical coordinates of each of those points
can be specified in three different ways: With two lists of the same
length, in which the elements of the first list are the horizontal
coordinates of the points and the second list are the vertical
coordinates, or with a list of two-element lists, each one corresponding
to the two coordinates of one of the points, or with a single list that
defines the vertical coordinates of the points; in this last case, the
horizontal coordinates of the n points will be assumed to be the first n
natural numbers.

@item @b{Contour lines}. @code{plot2d} ([contour, @var{expr}],
@var{range_x}, @var{range_y}, @var{options}), where @var{expr} is an
expression that depends on two variables. @var{range_x} and
@var{range_y} will be lists whose first elements are the names of those
two variables, followed by two numbers that set the minimum and maximum
values for them. The first variable will be represented along the
horizontal axis and the second along the vertical axis. The result will
be a set of curves along which the given expression has certain
values. If those values are not specified with the option @code{levels},
plotd2d will try to choose, at the most, 8 values of the form d*10^n, where d is
either 1, 2 or 5, all of them within the minimum and maximum values of
@var{expr} within the given ranges.
@end enumerate

At the end of a plot2d command several of the options described in
@mref{Plotting Options} can be used. Many instances of the 5 types
described above can be combined into a single plot, by putting them
inside a list: @code{plot2d} ([@var{type_1}, @dots{}, @var{type_n}],
@var{options}). If one of the types included in the list require
@var{range_x} or @var{range_y}, those ranges should come immediately
after the list.

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 @mrefdot{legend}  If that
option is not used, Maxima will create labels from the expressions or
function names.

@c PUT EXAMPLES FOR PRECEDING SIMPLE FORMS OF plot2d HERE
@strong{Examples:}

@enumerate
@item Explicit function.

@c ===beg===
@c plot2d (sin(x), [x, -%pi, %pi])$
@c ===end===
@example
(%i1) plot2d (sin(x), [x, -%pi, %pi])$
@end example

@ifnotinfo
@image{figures/plotting6,8cm}
@end ifnotinfo

@item Implicit function.

@c ===beg===
@c plot2d (x^2-y^3+3*y=2, [x,-2.5,2.5], [y,-2.5,2.5])$
@c ===end===
@example
(%i1) plot2d (x^2-y^3+3*y=2, [x,-2.5,2.5], [y,-2.5,2.5])$
@end example

@ifnotinfo
@image{figures/plotting3,8cm}
@end ifnotinfo

@item Parametric function.

@c ===beg===
@c r: (exp(cos(t))-2*cos(4*t)-sin(t/12)^5)$
@c plot2d([parametric, r*sin(t), r*cos(t), [t,-8*%pi,8*%pi]])$
@c ===end===
@example
(%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]])$
@end example

@ifnotinfo
@image{figures/plotting11,8cm}
@end ifnotinfo

@item Set of points.

@c ===beg===
@c plot2d ([discrete, makelist(i*%pi, i, 1, 5),
@c                            [0.6, 0.9, 0.2, 1.3, 1]])$
@c ===end===
@example
(%i1) plot2d ([discrete, makelist(i*%pi, i, 1, 5),
                            [0.6, 0.9, 0.2, 1.3, 1]])$
@end example

@ifnotinfo
@image{figures/plotting14,8cm}
@end ifnotinfo

@item Contour lines.

@c ===beg===
@c plot2d ([contour, u^3 + v^2], [u, -4, 4], [v, -4, 4])$
@c ===end===
@example
(%i1) plot2d ([contour, u^3 + v^2], [u, -4, 4], [v, -4, 4])$
@end example

@ifnotinfo
@image{figures/plotting2,8cm}
@end ifnotinfo

@end enumerate

@strong{Examples using options}.

If an explicit function grows too fast, the @mref{y} option can be used
to limit the values in the vertical axis:

@c ===beg===
@c plot2d (sec(x), [x, -2, 2], [y, -20, 20])$
@c ===end===
@example
(%i1) plot2d (sec(x), [x, -2, 2], [y, -20, 20])$
@end example

@ifnotinfo
@image{figures/plotting7,8cm}
@end ifnotinfo

When the plot box is disabled, no labels are created for the axes. In
that case, instead of using @mref{xlabel} and @mref{ylabel} to set the
names of the axes, it is better to use option @mrefcomma{label} which
allows more flexibility. Option @mref{yx_ratio} is used to change the
default rectangular shape of the plot; in this example the plot will
fill a square.

@c ===beg===
@c plot2d ( x^2 - 1, [x, -3, 3], nobox, grid2d,
@c      [yx_ratio, 1], [axes, solid], [xtics, -2, 4, 2],
@c      [ytics, 2, 2, 6], [label, ["x", 2.9, -0.3],
@c      ["x^2-1", 0.1, 8]], [title, "A parabola"])$
@c ===end===
@example
(%i1) plot2d ( x^2 - 1, [x, -3, 3], nobox, grid2d,
      [yx_ratio, 1], [axes, solid], [xtics, -2, 4, 2],
      [ytics, 2, 2, 6], [label, ["x", 2.9, -0.3],
      ["x^2-1", 0.1, 8]], [title, "A parabola"])$
@end example

@ifnotinfo
@image{figures/plotting8,8cm}
@end ifnotinfo

A plot with a logarithmic scale in the vertical axis:

@c ===beg===
@c plot2d (exp(3*s), [s, -2, 2], logy)$
@c ===end===
@example
(%i1) plot2d (exp(3*s), [s, -2, 2], logy)$
@end example

@ifnotinfo
@image{figures/plotting9,8cm}
@end ifnotinfo

Plotting functions by name:

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

@ifnotinfo
@image{figures/plotting10,8cm}
@end ifnotinfo

Plot of a circle, using its parametric representation, together with the
function -@code{|@var{x}|}. The circle will only look like a circle if
the scale in the two axes is the same, which is done with the option
@mrefdot{same_xy}

@c ===beg===
@c plot2d([[parametric, cos(t), sin(t), [t,0,2*%pi]], -abs(x)],
@c          [x, -sqrt(2), sqrt(2)], same_xy)$
@c ===end===
@example
@group
(%i1) plot2d([[parametric, cos(t), sin(t), [t,0,2*%pi]], -abs(x)],
         [x, -sqrt(2), sqrt(2)], same_xy)$
@end group
@end example

@ifnotinfo
@image{figures/plotting12,8cm}
@end ifnotinfo

A plot of 200 random numbers between 0 and 9:

@c ===beg===
@c plot2d ([discrete, makelist ( random(10), 200)])$
@c ===end===
@example
@group
(%i1) plot2d ([discrete, makelist ( random(10), 200)])$
@end group
@end example

@ifnotinfo
@image{figures/plotting13,8cm}
@end ifnotinfo

In the next 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:

@c ===beg===
@c display2d:false$
@c with_stdout ("data.txt", for x:0 thru 10 do
@c                              print (x, x^2, x^3))$
@c data: read_matrix ("data.txt")$
@c plot2d ([discrete, transpose(data)[2], transpose(data)[3]],
@c   [style,points], [point_type,diamond], [color,red])$
@c ===end===
@example
(%i1) display2d:false$
(%i2) with_stdout ("data.txt", for x:0 thru 10 do
                             print (x, x^2, x^3))$
(%i3) data: read_matrix ("data.txt")$
(%i4) plot2d ([discrete, transpose(data)[2], transpose(data)[3]],
  [style,points], [point_type,diamond], [color,red])$
@end example

@ifnotinfo
@image{figures/plotting15,8cm}
@end ifnotinfo

A plot of discrete data points together with a continuous function:

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

@ifnotinfo
@image{figures/plotting16,8cm}
@end ifnotinfo

See also the section about Plotting Options.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{plot3d}
@deffn {Function} plot3d @
@fname{plot3d} (@var{expr}, @var{x_range}, @var{y_range}, @dots{}, @var{options}, @dots{}) @
@fname{plot3d} ([@var{expr_1}, @dots{}, @var{expr_n}], @var{x_range}, @var{y_range}, @dots{}, @var{options}, @dots{})

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.

@strong{Examples}.

Plot of a function of two variables:

@c ===beg===
@c plot3d (u^2 - v^2, [u, -2, 2], [v, -3, 3], [grid, 100, 100],
@c         nomesh_lines)$
@c ===end===
@example
@group
(%i1) plot3d (u^2 - v^2, [u, -2, 2], [v, -3, 3], [grid, 100, 100],
        nomesh_lines)$
@end group
@end example

@ifnotinfo
@image{figures/plotting17,8cm}
@end ifnotinfo

Use of the @mref{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:

@c ===beg===
@c plot3d ( log ( x^2*y^2 ), [x, -2, 2], [y, -2, 2], [z, -8, 4],
@c          nopalette, [color, magenta])$
@c ===end===
@example
@group
(%i1) plot3d ( log ( x^2*y^2 ), [x, -2, 2], [y, -2, 2], [z, -8, 4],
         nopalette, [color, magenta])$
@end group
@end example

@ifnotinfo
@image{figures/plotting18,8cm}
@end ifnotinfo

The infinite values of z can also be avoided by choosing a grid that
does not fall on any points where the function is undefined, as in the
next example, which also shows how to change the palette and how to
include a color bar that relates colors to values of the z variable:

@c ===beg===
@c plot3d (log (x^2*y^2), [x, -2, 2], [y, -2, 2],[grid, 29, 29],
@c       [palette, [gradient, red, orange, yellow, green]],
@c       color_bar, [xtics, 1], [ytics, 1], [ztics, 4],
@c       [color_bar_tics, 4])$
@c ===end===
@example
@group
(%i1) plot3d (log (x^2*y^2), [x, -2, 2], [y, -2, 2],[grid, 29, 29],
       [palette, [gradient, red, orange, yellow, green]],
       color_bar, [xtics, 1], [ytics, 1], [ztics, 4],
       [color_bar_tics, 4])$
@end group
@end example

@ifnotinfo
@image{figures/plotting19,8cm}
@end ifnotinfo

Two surfaces in the same plot. Ranges specific to one of the surfaces can
be given by placing each expression and its ranges in a separate list;
global ranges for the complete plot are also given after the function
definitions.

@c ===beg===
@c plot3d ([[-3*x - y, [x, -2, 2], [y, -2, 2]],
@c    4*sin(3*(x^2 + y^2))/(x^2 + y^2), [x, -3, 3], [y, -3, 3]],
@c    [x, -4, 4], [y, -4, 4])$
@c ===end===
@example
(%i1) plot3d ([[-3*x - y, [x, -2, 2], [y, -2, 2]],
   4*sin(3*(x^2 + y^2))/(x^2 + y^2), [x, -3, 3], [y, -3, 3]],
   [x, -4, 4], [y, -4, 4])$
@end example

@ifnotinfo
@image{figures/plotting20,8cm}
@end ifnotinfo

Plot of a Klein bottle, defined parametrically:

@c ===beg===
@c expr_1: 5*cos(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3)-10$
@c expr_2: -5*sin(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3)$
@c expr_3: 5*(-sin(x/2)*cos(y)+cos(x/2)*sin(2*y))$
@c plot3d ([expr_1, expr_2, expr_3], [x, -%pi, %pi],
@c         [y, -%pi, %pi], [grid, 50, 50])$
@c ===end===
@example
(%i1) expr_1: 5*cos(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3)-10$
(%i2) expr_2: -5*sin(x)*(cos(x/2)*cos(y)+sin(x/2)*sin(2*y)+3)$
(%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, 50, 50])$
@end example

@ifnotinfo
@image{figures/plotting21,8cm}
@end ifnotinfo

Plot of a ``spherical harmonic'' function, using the predefined
transformation, @code{spherical_to_xyz} to transform from spherical
coordinates to rectangular coordinates. See the documentation for
@mrefdot{spherical_to_xyz}

@c ===beg===
@c plot3d (sin(2*theta)*cos(phi), [theta,0,%pi], [phi,0,2*%pi],
@c    [transform_xy, spherical_to_xyz], [grid, 30, 60], nolegend)$
@c ===end===
@example
(%i1) plot3d (sin(2*theta)*cos(phi), [theta,0,%pi], [phi,0,2*%pi],
      [transform_xy, spherical_to_xyz], [grid, 30, 60], nolegend)$
@end example

@ifnotinfo
@image{figures/plotting22,8cm}
@end ifnotinfo

Use of the pre-defined function @code{polar_to_xy} to transform from
cylindrical to rectangular coordinates.  See the documentation for
@mrefdot{polar_to_xy}

@c ===beg===
@c plot3d (r^.33*cos(th/3), [r,0,1], [th,0,6*%pi], nobox,
@c     nolegend, [grid, 12, 80], [transform_xy, polar_to_xy])$
@c ===end===
@example
@group
(%i1) plot3d (r^.33*cos(th/3), [r,0,1], [th,0,6*%pi], nobox,
    nolegend, [grid, 12, 80], [transform_xy, polar_to_xy])$
@end group
@end example

@ifnotinfo
@image{figures/plotting23,8cm}
@end ifnotinfo

Plot of a sphere using the transformation from spherical to rectangular
coordinates. Option @mref{same_xyz} is used to get the three axes
scaled in the same proportion. When transformations are used, it is not
convenient to eliminate the mesh lines, because Gnuplot will not show the
surface correctly.

@c ===beg===
@c plot3d ( 5, [theta,0,%pi], [phi,0,2*%pi], same_xyz, nolegend,
@c   [transform_xy, spherical_to_xyz], [mesh_lines_color,blue],
@c   [palette,[gradient,"#1b1b4e", "#8c8cf8"]])$
@c ===end===
@example
@group
(%i1) plot3d ( 5, [theta,0,%pi], [phi,0,2*%pi], same_xyz, nolegend,
  [transform_xy, spherical_to_xyz], [mesh_lines_color,blue],
  [palette,[gradient,"#1b1b4e", "#8c8cf8"]])$
@end group
@end example

@ifnotinfo
@image{figures/plotting24,8cm}
@end ifnotinfo

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

@c ===beg===
@c M: matrix([1,2,3,4], [1,2,3,2], [1,2,3,4], [1,2,3,3])$
@c f(x, y) := float('M [round(x), round(y)])$
@c plot3d (f(x,y), [x,1,4], [y,1,4], [grid,3,3], nolegend)$
@c ===end===
@example
(%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,3,3], nolegend)$
@end example

@ifnotinfo
@image{figures/plotting25,8cm}
@end ifnotinfo

By setting the elevation equal to zero, a surface can be seen as a map
in which each color represents a different level.

@c ===beg===
@c plot3d (cos (-x^2 + y^3/4), [x,-4,4], [y,-4,4], [zlabel,""],
@c        [mesh_lines_color,false], [elevation,0], [azimuth,0],
@c        color_bar, [grid,80,80], noztics, [color_bar_tics,1])$
@c ===end===
@example
@group
(%i1) plot3d (cos (-x^2 + y^3/4), [x,-4,4], [y,-4,4], [zlabel,""],
       [mesh_lines_color,false], [elevation,0], [azimuth,0],
       color_bar, [grid,80,80], noztics, [color_bar_tics,1])$
@end group
@end example

@ifnotinfo
@image{figures/plotting26,8cm}
@end ifnotinfo

See also @mrefdot{Plotting Options}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{plot_options}
@defvr {System variable} plot_options

This option is being kept for compatibility with older versions, but its
use is deprecated. To set global plotting options, see their current
values or remove options, use @mrefcomma{set_plot_option}
@mref{get_plot_option} and @mrefdot{remove_plot_option}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{remove_plot_option}
@deffn {Function} remove_plot_option (@var{name})

Removes the default value of an option. The name of the option must be given.

See also @mrefcomma{set_plot_option} @mref{get_plot_option} and
@mref{Plotting Options}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn
@c -----------------------------------------------------------------------------
@anchor{set_plot_option}
@deffn {Function} set_plot_option (@var{option})

Accepts any of the options listed in the section Plotting Options, and
saves them for use in plotting commands. The values of the options set
in each plotting command will have precedence, but if those options are
not given, the default values set with this function will be used.

@code{set_plot_option} evaluates its argument and returns the complete
list of options (after modifying the option given). If called without
any arguments, it will simply show the list of current default options.

See also @mrefcomma{remove_plot_option} @mref{get_plot_option} and the section
on Plotting Options.

Example:

Modification of the @mref{grid} values.

@c ===beg===
@c set_plot_option ([grid, 30, 40]);
@c ===end===
@example
(%i1) set_plot_option ([grid, 30, 40]);
(%o1) [[plot_format, gnuplot_pipes], [grid, 30, 40], 
[run_viewer, true], [axes, true], [nticks, 29], [adapt_depth, 5], 
[color, blue, red, green, magenta, black, cyan], 
[point_type, bullet, box, triangle, plus, times, asterisk], 
[palette, [gradient, green, cyan, blue, violet], 
[gradient, magenta, violet, blue, cyan, green, yellow, orange, 
red, brown, black]], [gnuplot_preamble, ], [gnuplot_term, default]]
@end example

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{spherical_to_xyz}
@deffn {System function} spherical_to_xyz

It can be given as value for the @mref{transform_xy} option of
@mrefdot{plot3d} Its effect will be to interpret the two independent
variables and the function in @code{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.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@node Plotting Options, Gnuplot Options, Functions and Variables for Plotting, Plotting
@section Plotting Options
@c -----------------------------------------------------------------------------

All options consist of a list starting with one of the keywords in this
section, followed by one or more values. If the option appears inside
one of the plotting commands, its value will be local for that
command. It the option is given as argument to
@mrefcomma{set_plot_option} its value will be global and used in all
plots, unless it is overridden by a local value.

Some of the options may have different effects in different plotting
commands as it will be pointed out in the following list. The options
that accept among their possible values true or false, can also be set
to true by simply writing their names, and false by writing their names
with the prefix no. For instance, typing @code{logx} as an option is
equivalent to writing @code{[logx, true]} and @code{nobox} is equivalent
to @code{[box, false]}. When just the name of the option is used for an
option which cannot have a value @code{true}, it means that any value
previously assigned to that option will be removed, leaving it to the
graphic program to decide what to do.

@c -----------------------------------------------------------------------------
@anchor{adapt_depth}
@defvr {Plot option} adapt_depth [adapt_depth, @var{integer}]
Default value: @code{5}

The maximum number of splittings used by the adaptive plotting routine
of @mref{plot2d}; @var{integer} must be a non-negative integer. A value
of zero means that adaptive plotting will not be used and the resulting
plot will have 1+4*@var{nticks} points (see option @mref{nticks}). To
have more control on the number of points and their positions, a list of
points can be created and then plotted using the @code{discrete} method
of @code{plot2d}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{axes}
@defvr {Plot option} axes @
[axes, @var{symbol}], axes, noaxes

Default value: @code{true}

Where @var{symbol} can be either @code{true}, @code{false}, @code{x},
@code{y} or @code{solid}. If @code{false}, no axes are shown; if equal
to @code{x} or @code{y} only the x or y axis will be shown; if it is
equal to @code{true}, both axes will be shown and @code{solid} will show
the two axes with a solid line, rather than the default broken
line. This option does not have any effect in the 3 dimensional plots.
The single keywords @code{axes} and @code{noaxes} can be used as
synonyms for @code{[axes, true]} and @code{[axes, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{azimuth}
@defvr {Plot option} azimuth [azimuth, @var{number}]

Default value: @code{30}

A plot3d plot can be thought of as starting with the x and y axis in the
horizontal and vertical axis, as in plot2d, and the z axis coming out of
the screen.  The z axis is then rotated around the x axis through an
angle equal to @mref{elevation} and then the new xy plane is rotated
around the new z axis through an angle @mrefdot{azimuth} This option sets
the value for the azimuth, in degrees.

See also @mrefdot{elevation}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{option_box}
@defvr {Plot option} box [box, @var{symbol}], box, nobox

Default value: @code{true}

If set to @code{true}, a bounding box will be drawn for the plot; if set
to @code{false}, no box will be drawn.
The single keywords @code{box} and @code{nobox} can be used as
synonyms for @code{[box, true]} and @code{[box, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{color}
@defvr {Plot option} color [color, @var{color_1}, @dots{}, @var{color_n}]

In 2d plots it defines the color (or colors) for the various curves.  In
@mrefcomma{plot3d} it defines the colors used for the mesh lines of the
surfaces, when no palette is being used.

If there are more curves or surfaces than colors, the colors will be
repeated in sequence. The valid colors are @code{red}, @code{green},
@code{blue}, @code{magenta}, @code{cyan}, @code{yellow}, @code{orange},
@code{violet}, @code{brown}, @code{gray}, @code{black}, @code{white}, 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 the name of a given color is unknown color, black
will be used instead.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{color_bar}
@defvr {Plot option} color_bar [color_bar, @var{symbol}], color_bar, @
nocolor_bar

Default value: @code{false} in plot3d, @code{true} in mandelbrot and julia

Where @var{symbol} can be either @code{true} or @code{false}.  If
@code{true}, whenever @mrefcomma{plot3d} @mref{mandelbrot} or
@mref{julia} use a palette to represent different values, a box will be
shown on the right, showing the corresponding between colors and values.
The single keywords @code{color_bar} and @code{nocolor_bar} can be used
as synonyms for @code{[color_bar, true]} and @code{[color_bar, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{color_bar_tics}
@defvr {Plot option} color_bar_tics [color_bar_tics, @var{x1}, @var{x2}, @
@var{x3}], color_bar_tics, nocolor_bar_tics

Defines the values at which a mark and a number will be placed in the
color bar. The first number is the initial value, the second the
increments and the third is the last value where a mark is placed. The
second and third numbers can be omitted. When only one number is given,
it will be used as the increment from an initial value that will be
chosen automatically. The single keyword @code{color_bar_tics} removes a
value given previously, making the graphic program use its default for
the values of the tics and @code{nocolor_bar_tics} will not show any
tics on the color bar.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{elevation}
@defvr {Plot option} elevation [elevation, @var{number}]

Default value: @code{60}

A plot3d plot can be thought of as starting with the x and y axis in the
horizontal and vertical axis, as in plot2d, and the z axis coming out of
the screen.  The z axis is then rotated around the x axis through an
angle equal to @mref{elevation} and then the new xy plane is rotated
around the new z axis through an angle @mrefdot{azimuth} This option sets
the value for the elevation, in degrees.

See also @mrefdot{azimuth}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{grid}
@defvr {Plot option} grid [grid, @var{integer}, @var{integer}]
Default value: @code{30}, @code{30}

Sets the number of grid points to use in the x- and y-directions for
three-dimensional plotting or for the @mref{julia} and @mref{mandelbrot}
programs.

For a way to actually draw a grid See @mrefdot{grid2d}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{grid2d}
@defvr {Plot option} grid2d [grid2d, @var{value}], grid2d, nogrid2d

Default value: @code{false}

Shows a grid of lines on the xy plane. The points where the grid lines
are placed are the same points where tics are marked in the x and y
axes, which can be controlled with the @mref{xtics} and @mref{ytics}
options.  The single keywords @code{grid2d} and @code{nogrid2d} can be
used as synonyms for @code{[grid2d, true]} and @code{[grid2d, false]}.

See also @mrefdot{grid}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{iterations}
@defvr {Plot option} iterations [iterations, @var{value}]

Default value: @code{9}

Number of iterations made by the programs mandelbrot and julia.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{label}
@defvr  {Plot option} label [label, [@var{string}, @var{x}, @var{y}], @dots{}]

Writes one or several labels in the points with @var{x}, @var{y}
coordinates indicated after each label.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{legend}
@defvr {Plot option} legend [legend, @var{string_1}, @dots{}, @
@var{string_n}], legend, nolegend

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 @code{false}, no legends will be shown.
By default, the names of the expressions or functions will be used, or
the words discrete1, discrete2, @dots{}, for discrete sets of points.
The single keyword @code{legend} removes any previously defined legends,
leaving it to the plotting program to set up a legend. The keyword
@code{nolegend} is a synonym for @code{[legend, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{levels}
@defvr {Plot option} levels [levels, @var{number}, @dots{}] 

This option is used by @mref{plot2d} to do contour plots. If only one
number is given after the keyword @code{levels}, it must be a natural
number; @code{plot2d} will try to plot that number of contours with
values between the minimum and maximum value of the expression given,
with the form d*10^n, where d is either 1, 2 or 5. Since not always it will
be possible to find that number of levels in that interval, the number of
contour lines show will be smaller than the number specified by this
option.

If more than one number are given after the keyword @code{levels},
@mrefdot{plot2d} will show the contour lines corresponding to those
values of the expression plotted, if they exist within the domain used.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{logx}
@defvr {Plot option} logx [logx, @var{value}], logx, nologx

Default value: @code{false}

Makes the horizontal axes to be scaled logarithmically. It can be either
true or false. The single keywords @code{logx} and @code{nologx} can be
used as synonyms for @code{[logx, true]} and @code{[logx, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{logy}
@defvr {Plot option} logy [logy, @var{value}], logy, nology

Default value: @code{false}

Makes the vertical axes to be scaled logarithmically. It can be either
true or false.
The single keywords @code{logy} and @code{nology} can be used as
synonyms for @code{[logy, true]} and @code{[logy, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{mesh_lines_color}
@defvr {Plot option} mesh_lines_color [mesh_lines_color, @var{color}], @
mesh_lines_color, no_mesh_lines

Default value: @code{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
@mref{color}@w{} (see the list of allowed colors in @mref{color}).  It
can also be given a value @code{false} to eliminate completely the mesh
lines. The single keyword @code{mesh_lines_color} removes any previously
defined colors, leaving it to the graphic program to decide what color
to use. The keyword @code{no_mesh_lines} is a synonym for
@code{[mesh_lines_color, false]}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{nticks}
@defvr {Plot option} nticks [nticks, @var{integer}]

Default value: @code{29}

When plotting functions with @mrefcomma{plot2d} it is gives the initial
number of points used by the adaptive plotting routine for plotting
functions. When plotting parametric functions with @mrefcomma{plot3d}
it sets the number of points that will be shown for the plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{palette}
@defvr  {Plot option} palette @
[palette, [@var{palette_1}], @dots{}, [@var{palette_n}]], palette, nopalette

It can consist of one palette or a list of several palettes.  Each
palette is a list with a keyword followed by values. If the keyword is
gradient, it should be followed by a list of valid colors.

If the keyword is hue, saturation or value, it must be followed by 4
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
@mrefdot{mesh_lines_color} If @code{palette} is given the value
@code{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 @mrefdot{color}

The single keyword @code{palette} removes any palette previously
defined, leaving it to the graphic program to decide the palette to use
and @code{nopalette} is a synonym for @code{[palette, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{plotepsilon}
@defvr {Plot option} plotepsilon [plotepsilon, @var{value}]

Default value: 1e-6

This value is used by @mref{plot2d} when plotting implicit functions or
contour lines. When plotting an explicit function @code{expr_1=expr_2},
it is converted into @code{expr_1-expr_2} and the points where that equals
zero are searched. When a contour line for @code{expr} equal to some value
is going to be plotted, the points where @code{expr} minus that value
are equal to zero are searched. The search is done by computing those
expressions at a grid of points (see @mref{sample}). If at one of the
points in that grid the absolute value of the expression is less than
the value of @code{plotepsilon}, it will be assumed to be zero, and
therefore, as being part of the curve to be plotted.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{plot_format}
@defvr {Plot option} plot_format [plot_format, @var{format}]

Default value: @code{gnuplot}, in Windows systems, or @code{gnuplot_pipes} in
other systems.

Where @var{format} is one of the following: gnuplot, xmaxima, mgnuplot,
gnuplot_pipes or geomview.

It sets the format to be used for plotting as explained in
@mrefdot{Plotting Formats}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{plot_real_part}
@defvr {Plot option} plot_realpart [plot_realpart, @var{symbol}], @
plot_realpart, noplot_realpart

Default value: @code{false}

If set to @code{true}, the functions to be plotted will be considered as
complex functions whose real value should be plotted; this is equivalent
to plotting @code{realpart(@var{function})}.  If set to @code{false},
nothing will be plotted when the function does not give a real value.
For instance, when @code{x} is negative, @code{log(x)} gives a complex
value, with real value equal to @code{log(abs(x))}; if
@code{plot_realpart} were @code{true}, @code{log(-5)} would be plotted
as @code{log(5)}, while nothing would be plotted if @code{plot_realpart}
were @code{false}. The single keyword @code{plot_realpart} can be used
as a synonym for @code{[plot_realpart, true]} and @code{noplot_realpart}
is a synonym for @code{[plot_realpart, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{point_type}
@defvr {Plot option} point_type [point_type, @var{type_1}, @dots{}, @
@var{type_n}]

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: @code{bullet}, @code{circle},
@code{plus}, @code{times}, @code{asterisk}, @code{box}, @code{square},
@code{triangle}, @code{delta}, @code{wedge}, @code{nabla}, @code{diamond},
@code{lozenge}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{pdf_file}
@defvr {Plot option} pdf_file [pdf_file, @var{file_name}]

Saves the plot into a PDF file with name equal to @var{file_name},
rather than showing it in the screen.  By default, the file will be
created in the directory defined by the variable
@mrefcomma{maxima_tempdir} unless @var{file_name} contains the character
``/'', in which case it will be assumed to contain the complete path where
the file should be created. The value of @mref{maxima_tempdir} can be changed
to save the file in a different directory. When the option
@mref{gnuplot_pdf_term_command} is also given, it will be used to set up
Gnuplot's PDF terminal; otherwise, Gnuplot's pdfcairo terminal
will be used with solid colored lines of width 3, plot
size of 17.2 cm by 12.9 cm and font of 18 points.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{png_file}
@defvr {Plot option} png_file [png_file, @var{file_name}]

Saves the plot into a PNG graphics file with name equal to @var{file_name},
rather than showing it in the screen. By default, the file will be
created in the directory defined by the variable
@mrefcomma{maxima_tempdir} unless @var{file_name} contains the character
``/'', in which case it will be assumed to contain the complete path where
the file should be created. The value of @mref{maxima_tempdir} can be changed
to save the file in a different directory. When the option
@mref{gnuplot_png_term_command} is also given, it will be used to set up
Gnuplot's PNG terminal; otherwise, Gnuplot's pngcairo terminal
will be used, with a font of size 12. 

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{ps_file}
@defvr {Plot option} ps_file [ps_file, @var{file_name}]

Saves the plot into a Postscript file with name equal to @var{file_name},
rather than showing it in the screen.  By default, the file will be
created in the directory defined by the variable
@mrefcomma{maxima_tempdir} unless @var{file_name} contains the character
``/'', in which case it will be assumed to contain the complete path where
the file should be created. The value of @mref{maxima_tempdir} can be changed
to save the file in a different directory. When the option
@mref{gnuplot_ps_term_command} is also given, it will be used to set up
Gnuplot's Postscript terminal; otherwise, Gnuplot's postscript terminal
will be used with the EPS option, solid colored lines of width 2, plot
size of 16.4 cm by 12.3 cm and font of 24 points.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{run_viewer}
@defvr {Plot option} run_viewer [run_viewer, @var{symbol}], run_viewer, @
norun_viewer

Default value: @code{true}

This option is only used when the plot format is @code{gnuplot} and the
terminal is @code{default} or when the Gnuplot terminal is set to
@code{dumb} (see @mref{gnuplot_term}) and can have a true or false
value.

If the terminal is @code{default}, a file @code{maxout_xxx.gnuplot} (or
other name specified with @mref{gnuplot_out_file}) is created with the
gnuplot commands necessary to generate the plot. Option @code{run_viewer}
controls whether or not Gnuplot will be launched to execute those
commands and show the plot.

If the terminal is @code{default}, gnuplot is run to execute the
commands in @code{maxout_xxx.gnuplot}, producing another file
@code{maxplot.txt} (or other name specified with
@mref{gnuplot_out_file}). Option @code{run_viewer} controls whether or
not that file, with an ASCII representation of the plot, will be shown
in the Maxima or Xmaxima console.

Its default value, true, makes the plots appear in either the console or
a separate graphics window. @code{run_viewer} and @code{norun_viewer}
are synonyms for @code{[run_viewer, true]} and @code{[run_viewer,
false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{same_xy}
@defvr {Plot option} same_xy [same_xy , @var{value}], same_xy, nosame_xy

It can be either true or false. If true, the scales used in the x and y
axes will be the same, in either 2d or 3d plots. See also
@mrefdot{yx_ratio} @code{same_xy} and @code{nosame_xy} are synonyms for
@code{[same_xy, true]} and @code{[same_xy, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{same_xyz}
@defvr {Plot option} same_xyz [same_xyz , @var{value}], same_xyz, nosame_xyz

It can be either true or false. If true, the scales used in the 3 axes
of a 3d plot will be the same. @code{same_xyz} and @code{nosame_xyz} are
synonyms for @code{[same_xyz, true]} and @code{[same_xyz, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{sample}
@defvr {Plot option} sample [sample, @var{nx}, @var{ny}]

Default value: @code{[sample, 47, 47]}

@var{nx} and @var{ny} must be two natural numbers that will be used by
@mref{plot2d} to look for the points that make part of the plot of an
implicit function or a contour line. The domain is divided into @var{nx}
intervals in the horizontal axis and @var{ny} intervals in the vertical
axis and the numerical value of the expression is computed at the
borders of those intervals. Higher values of @var{nx} and @var{ny} will
give smoother curves, but will increase the time needed to trace the
plot. When there are critical points in the plot where the curve changes
direction, to get better results it is more important to try to make
those points to be at the border of the intervals, rather than
increasing @var{nx} and @var{ny}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{style}
@defvr  {Plot option} style @
[style, @var{type_1}, @dots{}, @var{type_n}], @
[style, [@var{style_1}], @dots{}, [@var{style_n}]]

The styles that will be used for the various functions or sets of data
in a 2d plot.  The word @var{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
@var{lines} for line segments, @var{points} for isolated points,
@var{linespoints} for segments and points, or @var{dots} for small
isolated dots.  Gnuplot accepts also an @var{impulses} style.

Each of the styles can be enclosed inside a list with some additional
parameters.  @var{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
[@var{gnuplot_term}, @var{ps}], color index 4 will correspond to black,
instead of orange.

@var{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 @var{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.

@var{linespoints} accepts up to four parameters: line width, points
radius, color and type of object to replace the points.

See also @mref{color} and @mrefdot{point_type}
 
@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{svg_file}
@defvr {Plot option} svg_file [svg_file, @var{file_name}]

Saves the plot into an SVG file with name equal to @var{file_name},
rather than showing it in the screen.  By default, the file will be
created in the directory defined by the variable
@mrefcomma{maxima_tempdir} unless @var{file_name} contains the character
``/'', in which case it will be assumed to contain the complete path where
the file should be created. The value of @mref{maxima_tempdir} can be changed
to save the file in a different directory. When the option
@mref{gnuplot_svg_term_command} is also given, it will be used to set up
Gnuplot's SVG terminal; otherwise, Gnuplot's svg terminal
will be used with font of 14 points.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{t}
@defvr {Plot option} t [t, @var{min}, @var{max}]

Default range for parametric plots.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{title}
@defvr {Plot option} title [title, @var{text}]

Defines a title that will be written at the top of the plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{transform_xy}
@defvr {Plot option} transform_xy [transform_xy, @var{symbol}], notransform_xy

Where @var{symbol} is either @code{false} or the result obtained by
using the function @code{transform_xy}.  If different from @code{false},
it will be used to transform the 3 coordinates in
plot3d. @code{notransform_xy} removes any transformation function
previously defined.

See @mrefcomma{make_transform} @mref{polar_to_xy} and
@mrefdot{spherical_to_xyz}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{window}
@defvr {Plot option} window [window, @var{n}]

Opens the plot in window number @var{n}, instead of the default window
0. If window number @var{n} is already opened, the plot in that window
will be replaced by the current plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr


@c -----------------------------------------------------------------------------
@anchor{x}
@defvr {Plot option} x [x, @var{min}, @var{max}]

When used as the first option in a @mref{plot2d} command (or any of the
first two in @mref{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.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{xlabel}
@defvr {Plot option} xlabel [xlabel, @var{string}]

Specifies the @var{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 @mref{plot2d} the name of the
first variable, when plotting surfaces with @mref{plot3d}, or the first
expression in the case of a parametric plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{xtics}
@defvr {Plot option} xtics [xtics, @var{x1}, @var{x2}, @var{x3}], @
[xtics, @code{false}], xtics, noxtics

Defines the values at which a mark and a number will be placed in the x
axis. The first number is the initial value, the second the increments
and the third is the last value where a mark is placed. The second and
third numbers can be omitted, in which case the first number is the
increment from an initial value that will be chosen by the graphic
program. If @code{[xtics, false]} is used, no marks or numbers will be
shown along the x axis.

The single keyword @code{xtics} removes any values previously
defined, leaving it to the graphic program to decide the values to use
and @code{noxtics} is a synonym for @code{[xtics, false]}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{xy_scale}
@defvr {Plot option} xy_scale [xy_scale, @var{sx}, @var{sy}]

In a 2d plot, it defines the ratio of the total size of the Window to
the size that will be used for the plot. The two numbers given as
arguments are the scale factors for the x and y axes.

This option does not change the size of the graphic window or the placement
of the graph in the window. If you want to change the aspect ratio of the
plot, it is better to use option @mrefdot{yx_ratio} For instance,
@code{[yx_ratio, 10]} instead of @code{[xy_scale, 0.1, 1]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{y}
@defvr {Plot option} y [y, @var{min}, @var{max}]

When used as one of the first two options in @mrefcomma{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.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{ylabel}
@defvr {Plot option} ylabel [ylabel, @var{string}]

Specifies the @var{string} that will label the second axis; if this
option is not used, that label will be ``y'', when plotting explicit
functions with @mref{plot2d}, or the name of the second variable, when
plotting surfaces with @mref{plot3d}, or the second expression in the
case of a parametric plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{ytics}
@defvr {Plot option} ytics [ytics, @var{y1}, @var{y2}, @var{y3}], @
[ytics, @code{false}], ytics, noytics

Defines the values at which a mark and a number will be placed in the y
axis. The first number is the initial value, the second the increments
and the third is the last value where a mark is placed. The second and
third numbers can be omitted, in which case the first number is the
increment from an initial value that will be chosen by the graphic
program. If @code{[ytics, false]} is used, no marks or numbers will be
shown along the y axis.

The single keyword @code{ytics} removes any values previously
defined, leaving it to the graphic program to decide the values to use
and @code{noytics} is a synonym for @code{[ytics, false]}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{yx_ratio}
@defvr {Plot option} yx_ratio [yx_ratio, @var{r}]

In a 2d plot, the ratio between the vertical and the horizontal sides of
the rectangle used to make the plot. See also @mrefdot{same_xy}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{z}
@defvr {Plot option} z [z, @var{min}, @var{max}]

Used in @mref{plot3d} to set the effective range of values of z that will be
shown in the plot.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{zlabel}
@defvr {Plot option} zlabel [zlabel, @var{string}]

Specifies the @var{string} that will label the third axis, when using
@mrefdot{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 @mref{set_plot_option} and it will be
ignored by @mrefdot{plot2d}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{zmin}
@defvr {Plot option} zmin [zmin, @var{z}], zmin

In 3d plots, the value of z that will be at the bottom of the plot box.

The single keyword @code{zmin} removes any value previously
defined, leaving it to the graphic program to decide the value to use.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{ztics}
@defvr {Plot option} ztics [ztics, @var{z1}, @var{z2}, @var{z3}], @
[ztics, @code{false}], ztics, noztics

Defines the values at which a mark and a number will be placed in the z
axis. The first number is the initial value, the second the increments
and the third is the last value where a mark is placed. The second and
third numbers can be omitted, in which case the first number is the
increment from an initial value that will be chosen by the graphic
program. If @code{[ztics, false]} is used, no marks or numbers will be
shown along the z axis. 

The single keyword @code{ztics} removes any values previously
defined, leaving it to the graphic program to decide the values to use
and @code{noztics} is a synonym for @code{[ztics, false]}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@node Gnuplot Options, Gnuplot_pipes Format Functions, Plotting Options, Plotting
@section Gnuplot Options
@c -----------------------------------------------------------------------------

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.

@c -----------------------------------------------------------------------------
@anchor{gnuplot_term}
@defvr {Plot option} gnuplot_term [gnuplot_term, @var{terminal_name}]

Sets the output terminal type for gnuplot. The argument @var{terminal_name}
can be a string or one of the following 3 special symbols
@itemize @bullet
@item
@strong{default} (default value)

Gnuplot output is displayed in a separate graphical window and the
gnuplot terminal used will be specified by the value of the option
@mrefdot{gnuplot_default_term_command}

@item
@strong{dumb}

Gnuplot output is saved to a file @code{maxout_xxx.gnuplot} using "ASCII
art" approximation to graphics. If the option @mref{gnuplot_out_file} is
set to @var{filename}, the plot will be saved there, instead of the
default @code{maxout_xxx.gnuplot}. The settings for the ``dumb'' terminal of
Gnuplot are given by the value of option
@mrefdot{gnuplot_dumb_term_command} If option @mref{run_viewer} is set
to true and the plot_format is @code{gnuplot} that ASCII representation
will also be shown in the Maxima or Xmaxima console.

@item
@strong{ps}

Gnuplot generates commands in the PostScript page description language.
If the option @mref{gnuplot_out_file} is set to @var{filename}, gnuplot
writes the PostScript commands to @var{filename}.  Otherwise, it is
saved as @code{maxplot.ps} file. The settings for this terminal are given by the value of the option @mrefdot{gnuplot_dumb_term_command}

@item
A string representing any valid gnuplot term specification

Gnuplot can generate output in many other graphical formats such as png,
jpeg, svg etc. To use those formats, option @code{gnuplot_term} can be
set to any supported gnuplot term name (which must be a symbol) or even a
full gnuplot term specification with any valid options (which must be a string).  For
example @code{[gnuplot_term, png]} creates output in PNG (Portable
Network Graphics) format while @code{[gnuplot_term, "png size
1000,1000"]} creates PNG of 1000 x 1000 pixels size.  If the option
@mref{gnuplot_out_file} is set to @var{filename}, gnuplot writes the
output to @var{filename}.  Otherwise, it is saved as
@code{maxplot.@var{term}} file, where @var{term} is gnuplot terminal
name.
@end itemize

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_out_file}
@defvr {Plot option} gnuplot_out_file [gnuplot_out_file, @var{file_name}]

It can be used to replace the default name for the file that contains
the commands that will interpreted by gnuplot, when the terminal is set
to @code{default}, or to replace the default name of the graphic file
that gnuplot creates, when the terminal is different from
@code{default}. If it contains one or more slashes, ``/'', the name of
the file will be left as it is; otherwise, it will be appended to the
path of the temporary directory. The complete name of the files created
by the plotting commands is always sent as output of those commands so
they can be seen if the command is ended by semi-colon.

When used in conjunction with the @mref{gnuplot_term} option, it can be
used to save the plot in a file, in one of the graphic formats supported
by Gnuplot. To create PNG, PDF, Postscript or SVG, it is easier to use
options @mrefcomma{png_file} @mrefcomma{pdf_file} @mrefcomma{ps_file}
or @mrefdot{svg_file}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

     @c -----------------------------------------------------------------------------
@anchor{gnuplot_script_file}
@defvr {Plot option} gnuplot_script_file [gnuplot_script_file, @var{file_name_or_function}]

Creates a plot with @code{plot2d}, @code{plot3d}, @code{mandelbrot} or
@code{julia} using the @code{gnuplot} @mref{plot_format} and saving
the script sent to Gnuplot in the file specified by @var{file_name_or_function}.
The value @var{file_name_or_function} can be a string or a Maxima function of
one variable that returns a string. If that string corresponds to a
complete file path (directory and file name), the script will be created in
that file and will not be deleted after Maxima is closed; otherwise, the
string will give the name of a file to be created in the temporary directory
and deleted when Maxima is closed.

In this example, the script file name is set to ``sin.gnuplot'', in the
current directory.

@example
(%i1) plot2d( sin(x), [x,0,2*%pi], [gnuplot_script_file, "./sin.gnuplot"]);

(%o1) ["./sin.gnuplot"]
@end example

In this example, @code{gnuplot_maxout_prt(@var{file})} is a function
that takes the default file name, @var{file}. It constructs a full file
name for the data file by interpolating a random 8-digit integer with a
pad of zeros into the default file name (``maxout'' followed by the id
number of the Maxima process, followed by ``.gnuplot''). The temporary
directory is determined by @mref{maxima_tempdir} (it is ``/tmp'' in this
example).

@example
(%i1) gnuplot_maxout_prt(file) := block([beg,end],
        [beg,end] : split(file,"."),
        printf(false,"~a_~8,'0d.~a",beg,random(10^8-1),end)) $

(%i2) plot2d( sin(x), [x,0,2*%pi], [gnuplot_script_file, gnuplot_maxout_prt]);

(%o2) ["/tmp/maxout68715_09606909.gnuplot"]
@end example

By default, the script would have been saved in a file named
@code{maxoutXXXXX.gnuplot} (XXXXX=68715 in this example) in the temporary
directory. If the print statement in function @code{gnuplot_maxout_prt}
above included a directory path, the file would have been saved in that
directory rather than in the temporary directory.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_pm3d}
@defvr {Plot option} gnuplot_pm3d [gnuplot_pm3d, @var{value}]

With a value of @code{false}, it can be used to disable the use of PM3D
mode, which is enabled by default.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_preamble}
@defvr {Plot option} gnuplot_preamble [gnuplot_preamble, @var{string}]

This option inserts gnuplot commands before any other commands sent to
Gnuplot. Any valid gnuplot commands may be used. Multiple commands should
be separated with a semi-colon. See also @mrefdot{gnuplot_postamble}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_postamble}
@defvr {Plot option} gnuplot_postamble [gnuplot_postamble, @var{string}]

This option inserts gnuplot commands after other commands sent to
Gnuplot and right before the plot command is sent. Any valid gnuplot
commands may be used. Multiple commands should be separated with a
semi-colon. See also @mrefdot{gnuplot_preamble}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_default_term_command}
@defvr {Plot option} gnuplot_default_term_command
[gnuplot_default_term_command, @var{command}]

The gnuplot command to set the terminal type for the default
terminal. It this option is not set, the command used will be: @code{"set term wxt size 640,480 font \",12\"; set term pop"}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_dumb_term_command}
@defvr {Plot option} gnuplot_dumb_term_command
[gnuplot_dumb_term_command, @var{command}]

The gnuplot command to set the terminal type for the dumb terminal.  It
this option is not set, the command used will be: @code{"set term dumb
79 22"}, which makes the text output 79 characters by 22 characters.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_pdf_term_command}
@defvr {Plot option} gnuplot_pdf_term_command [gnuplot_pdf_term_command, @var{command}]

The gnuplot command to set the terminal type for the PDF
terminal.  If this option is not set, the command used will be: @code{"set term pdfcairo color solid lw 3 size 17.2 cm, 12.9 cm font \",18\""}. See the gnuplot documentation for more information.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_png_term_command}
@defvr {Plot option} gnuplot_png_term_command [gnuplot_png_term_command, @var{command}]

The gnuplot command to set the terminal type for the PNG terminal.  If
this option is not set, the command used will be:
@code{"set term pngcairo font \",12\""}. See the gnuplot documentation
for more information.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_ps_term_command}
@defvr {Plot option} gnuplot_ps_term_command [gnuplot_ps_term_command, @var{command}]

The gnuplot command to set the terminal type for the PostScript
terminal.  If this option is not set, the command used will be: @code{"set term postscript eps color solid lw 2 size 16.4 cm, 12.3 cm font \",24\""}. See the gnuplot documentation for @code{set term postscript} for
more information.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_strings}
@defvr {Plot option} gnuplot_strings [gnuplot_strings, @var{value}]

With a value of @code{true}, all strings used in labels and titles will
be interpreted by gnuplot as ``enhanced'' text, if the terminal being used
supports it. In enhanced mode, some characters such as ^ and _ are not
printed, but interpreted as formatting characters. For a list of the
formatting characters and their meaning, see the documentation for enhanced
in Gnuplot. The default value for this option is @code{false}, which will
not treat any characters as formatting characters.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_svg_background}
@defvr {Plot option} gnuplot_svg_background @*

    [gnuplot_svg_background, @var{color}] @*
    nognuplot_svg_background

Specify the background color for SVG image output.
@var{color} must be a string which specifies a color name recognized by Gnuplot,
or an RGB triple of the form @code{"#xxxxxx"} where @code{x} is a hexadecimal digit.
The default value is @code{"white"}.

When the value of @code{gnuplot_svg_background} is @code{false},
the background is the default determined by Gnuplot.
At present (April 2023),
the Gnuplot default is to specify the background in SVG output as @code{"none"}.

@code{nognuplot_svg_background}, specified by itself without a value,
is equivalent to @code{[gnuplot_svg_background, false]}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_svg_term_command}
@defvr {Plot option} gnuplot_svg_term_command [gnuplot_svg_term_command, @var{command}]

The gnuplot command to set the terminal type for the SVG
terminal.  If this option is not set, the command used will be:
@code{"set term svg font \",14\""}. See the gnuplot documentation for
more information.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_curve_titles}
@defvr {Plot option} gnuplot_curve_titles

This is an obsolete option that has been replaced by @mref{legend} described
above.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@anchor{gnuplot_curve_styles}
@defvr {Plot option} gnuplot_curve_styles

This is an obsolete option that has been replaced by @mrefdot{style}

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end defvr

@c -----------------------------------------------------------------------------
@node Gnuplot_pipes Format Functions,  , Gnuplot Options, Plotting
@section Gnuplot_pipes Format Functions
@c -----------------------------------------------------------------------------

@c -----------------------------------------------------------------------------
@anchor{gnuplot_start}
@deffn {Function} gnuplot_start ()

Opens the pipe to gnuplot used for plotting with the @code{gnuplot_pipes}
format.  Is not necessary to manually open the pipe before plotting.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_close}
@deffn {Function} gnuplot_close ()

Closes the pipe to gnuplot which is used with the @code{gnuplot_pipes} format.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_send}
@deffn {Function} gnuplot_send (@var{s})

Sends the command @var{s} to the gnuplot pipe. If that pipe is not currently
opened, it will be opened before sending the command. @var{s} must be a
string.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_restart}
@deffn {Function} gnuplot_restart ()

Closes the pipe to gnuplot which is used with the @code{gnuplot_pipes}
format and opens a new pipe.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_replot}
@deffn  {Function} gnuplot_replot @
@fname{gnuplot_replot} () @
@fname{gnuplot_replot} (@var{s})

Updates the gnuplot window.  If @code{gnuplot_replot} is called with a
gnuplot command in a string @var{s}, then @code{s} is sent to gnuplot
before reploting the window.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn

@c -----------------------------------------------------------------------------
@anchor{gnuplot_reset}
@deffn {Function} gnuplot_reset ()

Resets the state of gnuplot used with the @code{gnuplot_pipes} format.  To
update the gnuplot window call @mref{gnuplot_replot} after @code{gnuplot_reset}.

@opencatbox{Categories:}
@category{Plotting}
@closecatbox
@end deffn