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12.1 Introduction to Plotting | ||
12.2 Plotting Formats | ||
12.3 Functions and Variables for Plotting | ||
12.4 Plotting Options | ||
12.5 Gnuplot Options | ||
12.6 Gnuplot_pipes Format Functions |
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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_xxx.format
, where xxx
is a number that is unique
to every concurrently-running instance of Maxima and format
is
the name of the plotting format being used (gnuplot
,
xmaxima
, mgnuplot
, gnuplot_pipes
or geomview
).
There are to save the plot in a graphic format file. In those cases, the
file maxout_xxx.format
created by Maxima includes commands that will
make the external plotting program save the result in a graphic
file. The default name for that graphic file is
maxplot.extension
, where extension
is the extension
normally used for the kind of graphic file selected.
The maxout_xxx.format
and maxplot.extension
files are created
in the directory specified by the system variable
maxima_tempdir
. That location can be changed by assigning to
that variable (or to the environment variable 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.
If the format used is either gnuplot
or xmaxima
, the
external programs gnuplot
or xmaxima
can be run, giving it
the file maxout_xxx.format
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 gnuplot
or xmaxima
and the
plain-text file maxout_xxx.gnuplot
(or maxout_xxx.xmaxima
) can be
inspected to look for the source of the problem.
The additional package draw provides functions similar to the ones
described in this section with some extra features. 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 opt
, type ?? opt
in order to choose the
information for either of those two packages.
Categories: Plotting
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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. There are various different formats for
those programs, which can be selected with the option plot_format
(see also the Plotting Options
section).
The plotting formats are the following:
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_xxx.gnuplot
.
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_xxx.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 is only used to plot to the screen; whenever graphic files are
created, the format is silently switched to gnuplot
and
the commands needed to create the graphic file are saved with the data
in file maxout_xxx.gnuplot
.
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 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. 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 maxout_xxx.xmaxima
and xmaxima is run with the
name of that file as argument.
In previous versions this format used to be called openmath
; that
old name still works as a synonym for xmaxima
.
Geomview, a Motif based interactive 3D viewing program for Unix, can also be used to display plots created by Maxima. To use this format, the geomview program must be installed.
Categories: Plotting
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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
, which works in any graphic format, can also be
used to plot contours but a separate expression must be given for each
contour.
Examples:
(%i1) contour_plot (x^2 + y^2, [x, -4, 4], [y, -4, 4])$
You can add any options accepted by plot3d
; for instance, the
option legend
with a value of false, to remove the
legend. By default, Gnuplot chooses and displays 3 contours. To increase the
number of contours, it is necessary to use a custom
gnuplot_preamble
, as in the next example:
(%i1) contour_plot (u^3 + v^2, [u, -4, 4], [v, -4, 4], [legend,false], [gnuplot_preamble, "set cntrparam levels 12"])$
Categories: Plotting
This variable stores the name of the command used to run the geomview
program when the plot format is 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,
(%i1) geomview_command: "/usr/local/bin/my_geomview"$
Categories: Plotting
Returns the current default value of the option named keyword, which is a list. The optional argument 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 set_plot_option
, remove_plot_option
and the
section on Plotting Options.
This variable stores the name of the command used to run the gnuplot
program when the plot format is gnuplot
. 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,
(%i1) gnuplot_command: "/usr/local/bin/my_gnuplot"$
Categories: Plotting
When a graphic file is going to be created using gnuplot
, this
variable is used to specify the way the file name should be passed to
gnuplot. Its default value is "~s", which means that the name of the
file will be passed directly. 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".
Categories: Plotting
This variable is used to parse the argument that will be passed to the
gnuplot program when the plot format is gnuplot
. Its default
value is "-persist ~s", where "~s" will be replaced with the name of the
file where the gnuplot commands have been written (usually
"maxout_xxx.gnuplot"). The option -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:
(%i1) gnuplot_view_args: "~s -"$
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 gnuplot_view_args
.
Categories: Plotting
Displays a plot of a function on the real plane, defined implicitly by
the expression expr. The domain in the plane is defined by
x_range and y_range. Several functions can be represented on
the same plot, giving a list [expr_1, …, expr_n] of
expressions that define them. This function uses the global format
options set up with the set_plot_option
. Additional options can
also be given as extra arguments for the implicit_plot
command.
The method used by implicit_plot
consists of tracking sign
changes on the domain given and it can fail for complicated expressions.
load(implicit_plot)
loads this function.
Example:
(%i1) load(implicit_plot)$ (%i2) implicit_plot (x^2 = y^3 - 3*y + 1, [x, -4, 4], [y, -4, 4])$
Categories: Plotting · Share packages · Package implicit_plot
Creates a graphic representation of the Julia set for the complex number
(x + i y). The two mandatory parameters x and y
must be real. This program is part of the additional package
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 grid
plot option
(default 30 by 30). The maximum number of iterations is set with the
option 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 palette
option in the
command.
The default domain used goes from -2 to 2 in both axes and can be
changed with the x
and y
options. By default, the two axes
are shown with the same scale, unless the option yx_ratio
is used
or the option 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 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.
(%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])$
Categories: Package dynamics · Plotting
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.
Categories: Plotting
Creates a graphic representation of the Mandelbrot set. This program is
part of the additional package 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 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 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 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 palette
option in the command. By default, the
two axes are shown with the same scale, unless the option yx_ratio
is used or the option same_xy
is disabled.
Example:
[grid,400,400])$
(%i1) mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2], [grid,400,400])$
Categories: Package dynamics · Plotting
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.
Categories: Plotting
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 could also be a list with two values that correspond to the x and y coordinates of a point, or it could be a sequence of numerical values which will be plotted at consecutive integer values (1,2,3,...) on the x axis.
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 function 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])$
When the plot box is disabled, no labels are created for the axes. In
that case, instead of using xlabel
and ylabel
to set the
names of the axes, it is better to use option label
, which
allows more flexibility. Option yx_ratio
is used to change the
default rectangular shape of the plot; in this example the plot will
fill a square.
(%i1) plot2d ( x^2 - 1, [x, -3, 3], [box, false], 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"])$
A plot with a logarithmic scale in the vertical axis:
(%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]])$
Plot of a circle, using its parametric representation, together with the
function -|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 same_xy
.
(%i1) plot2d([[parametric, cos(t), sin(t), [t,0,2*%pi]], -abs(x)], [x, -sqrt(2), sqrt(2)], same_xy)$
A plot of 200 random numbers between 0 and 9:
(%i1) plot2d ([discrete, makelist ( random(10), 200)])$
A plot of a discrete set of points, defining x and y coordinates separately:
(%i1) plot2d ([discrete, makelist(i*%pi, i, 1, 5), [0.6, 0.9, 0.2, 1.3, 1]])$
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:
(%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 discrete data points together with a continuous function:
(%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.
Categories: Plotting
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 function of two variables:
(%i1) plot3d (u^2 - v^2, [u, -2, 2], [v, -3, 3], [grid, 100, 100], [mesh_lines_color,false])$
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])$
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:
(%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])$
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 functions definitions.
(%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])$
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)-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])$
Plot of a "spherical harmonic" function, using the predefined
transformation, spherical_to_xyz
to transform from spherical
coordinates 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], [legend,false])$
Use of the pre-defined function polar_to_xy
to transform from
cylindrical to rectangular coordinates. See the documentation for
polar_to_xy
.
(%i1) plot3d (r^.33*cos(th/3), [r,0,1], [th,0,6*%pi], [box, false], [grid, 12, 80], [transform_xy, polar_to_xy], [legend, false])$
Plot of a sphere using the transformation from spherical to rectangular
coordinates. Option 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.
(%i1) plot3d ( 5, [theta, 0, %pi], [phi, 0, 2*%pi], same_xyz, [transform_xy, spherical_to_xyz], [mesh_lines_color,blue], [palette,[gradient,"#1b1b4e", "#8c8cf8"]], [legend, false])$
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,3,3],[legend,false])$
By setting the elevation equal to zero, a surface can be seen as a map in which each color represents a different level.
(%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], [ztics,false], [color_bar_tics,1])$
See also the section about Plotting Options.
Categories: Plotting
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 set_plot_option
,
get_plot_option
and remove_plot_option
.
Categories: Plotting
Removes the default value of an option. The name of the option must be given.
See also set_plot_option
, get_plot_option
and the section
on Plotting Options.
Categories: Plotting
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.
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 remove_plot_option
, get_plot_option
and the section
on Plotting Options.
Example:
Modification of the grid
values.
(%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]]
Categories: Plotting
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.
Categories: Plotting
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All options consist of a list starting with one of the keywords in this section, followed by one or more values. 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. For instance, typing logx as an option is equivalent to writing [logx, true].
Default value: 5
The maximum number of splittings used by the adaptive plotting routine.
Categories: Plotting
Default value: true
Where symbol can be either true
, false
, x
,
y
or solid
. If false
, no axes are shown; if equal
to x
or y
only the x or y axis will be shown; if it is
equal to true
, both axes will be shown and 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.
Categories: Plotting
Default value: 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 elevation
and then the new xy plane is rotated
around the new z axis through an angle azimuth
. This option sets
the value for the azimuth, in degrees.
See also elevation
.
Categories: Plotting
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.
Categories: Plotting
In 2d plots 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.
If there are more curves or surfaces than colors, the colors will be
repeated in sequence. The valid colors are red
, green
,
blue
, magenta
, cyan
, yellow
, orange
,
violet
, brown
, gray
, black
, 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.
Categories: Plotting
Default value: false
in plot3d, true
in mandelbrot and julia
Where symbol can be either true
or false
. If
true
, whenever plot3d
, mandelbrot
or
julia
use a palette to represent different values, a box will be
shown on the right, showing the corresponding between colors and values.
Categories: Plotting
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.
Categories: Plotting
Default value: 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 elevation
and then the new xy plane is rotated
around the new z axis through an angle azimuth
. This option sets
the value for the azimuth, in degrees.
See also azimuth
.
Categories: Plotting
Default value: 30
, 30
Sets the number of grid points to use in the x- and y-directions for
three-dimensional plotting or for the julia
and mandelbrot
programs.
Categories: Plotting
Default value: 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 xtics
and ytics
options.
Categories: Plotting
Default value: 9
Number of iterations made by the programs mandelbrot and julia.
Categories: Plotting
Writes one or several labels in the points with x, y coordinates indicated after each label.
Categories: Plotting
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.
Categories: Plotting
Makes the horizontal axes to be scaled logarithmically. It can be either true or false.
Categories: Plotting
Makes the vertical axes to be scaled logarithmically. It can be either true or false.
Categories: Plotting
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.
Categories: Plotting
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 plot3d
,
it sets the number of points that will be shown for the plot.
Categories: Plotting
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
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
.
Categories: Plotting
Default value: gnuplot
, in Windows systems, or gnuplot_pipes
in
other systems.
Where format is one of the following: gnuplot, xmaxima, mgnuplot, gnuplot_pipes or geomview.
It sets the format to be used for plotting.
Categories: Plotting
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
.
Categories: Plotting
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
.
Categories: Plotting
Saves the plot into a PDF file with name equal to file_name,
rather than showing it in the screen. By default, the file will be
created in the directory defined by the variable
maxima_tempdir
, unless 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 maxima_tempdir
can be changed
to save the file in a different directory. When the option
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.
Categories: Plotting
Saves the plot into a PNG graphics file with name equal to file_name,
rather than showing it in the screen. By default, the file will be
created in the directory defined by the variable
maxima_tempdir
, unless 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 maxima_tempdir
can be changed
to save the file in a different directory. When the option
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.
Categories: Plotting
Saves the plot into a Postscript file with name equal to file_name,
rather than showing it in the screen. By default, the file will be
created in the directory defined by the variable
maxima_tempdir
, unless 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 maxima_tempdir
can be changed
to save the file in a different directory. When the option
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.
Categories: Plotting
This option is only used when the plot format is gnuplot
and the
terminal is default
or when the Gnuplot terminal is set to
dumb
(see gnuplot_term
) and can have a true or false
value.
If the terminal is default
, a file maxout_xxx.gnuplot
(or
other name specified with gnuplot_out_file
) is created with the
gnuplot commands necessary to generate the plot. Option run_viewer
controls whether or not Gnuplot will be launched to execute those
commands and show the plot.
If the terminal is default
, gnuplot is run to execute the
commands in maxout_xxx.gnuplot
, producing another file
maxplot.txt
(or other name specified with
gnuplot_out_file
). Option run_viewer
controls whether or
not that file, with an ASCII representation of the plot, will be shown
in the Maxima or Xmaxima console.
The default value for this option is true, making the plots to be shown in either the console or a separate graphics window.
Categories: Plotting
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 yx_ratio
.
Categories: Plotting
It can be either true or false. If true, the scales used in the 3 axes of a 3d plot will be the same.
Categories: Plotting
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.
linespoints accepts up to four parameters: line width, points radius, color and type of object to replace the points.
See also color
and point_type
.
Categories: Plotting
Saves the plot into an SVG file with name equal to file_name,
rather than showing it in the screen. By default, the file will be
created in the directory defined by the variable
maxima_tempdir
, unless 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 maxima_tempdir
can be changed
to save the file in a different directory. When the option
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.
Categories: Plotting
Default range for parametric plots.
Categories: Plotting
Defines a title that will be written at the top of the plot.
Categories: Plotting
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
.
Categories: Plotting
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.
Categories: Plotting
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
.
Categories: Plotting
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. When only one number is given, it will be used as the increment from an initial value that will be chosen automatically.
Categories: Plotting
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.
Categories: Plotting
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.
Categories: Plotting
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
.
Categories: Plotting
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. When only one number is given, it will be used as the increment from an initial value that will be chosen automatically
Categories: Plotting
In a 2d plot, the ratio between the vertical and the horizontal sides of
the rectangle used to make the plot. See also same_xy
.
Categories: Plotting
Used in plot3d
to set the effective range of values of z that will be
shown in the plot.
Categories: Plotting
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
.
Categories: Plotting
In 3d plots, the value of z that will be at the bottom of the plot box.
Categories: Plotting
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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.
Sets the output terminal type for gnuplot. The argument terminal_name can be a string or one of the following 3 special symbols
Gnuplot output is displayed in a separate graphical window and the
gnuplot terminal used will be specified by the value of the option
gnuplot_default_term_command
.
Gnuplot output is saved to a file maxout_xxx.gnuplot
using "ASCII
art" approximation to graphics. If the option gnuplot_out_file
is
set to filename, the plot will be saved there, instead of the
default maxout_xxx.gnuplot
. The settings for the "dumb" terminal of
Gnuplot are given by the value of option
gnuplot_dumb_term_command
. If option run_viewer
is set
to true and the plot_format is gnuplot
that ASCII representation
will also be shown in the Maxima or Xmaxima console.
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. The settings for this terminal are given by the value of the option gnuplot_dumb_term_command
.
Gnuplot can generate output in many other graphical formats such as png,
jpeg, svg etc. To use those formats, option 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 [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.
Categories: Plotting
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 default
, or to replace the default name of the graphic file
that gnuplot creates, when the terminal is different from
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 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 png_file
, pdf_file
, ps_file
,
or svg_file
.
Categories: Plotting
With a value of false
, it can be used to disable the use of PM3D
mode, which is enabled by default.
Categories: Plotting
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 gnuplot_postamble
.
Categories: Plotting
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 gnuplot_preamble
.
Categories: Plotting
[gnuplot_default_term_command, command]
The gnuplot command to set the terminal type for the default
terminal. It this option is not set, the command used will be: "set term wxt size 640,480 font \",12\"; set term pop"
.
Categories: Plotting
[gnuplot_dumb_term_command, command]
The gnuplot command to set the terminal type for the dumb terminal. It
this option is not set, the command used will be: "set term dumb
79 22"
, which makes the text output 79 characters by 22 characters.
Categories: Plotting
The gnuplot command to set the terminal type for the PDF
terminal. If this option is not set, the command used will be: "set term pdfcairo color solid lw 3 size 17.2 cm, 12.9 cm font \",18\""
. See the gnuplot documentation for more information.
Categories: Plotting
The gnuplot command to set the terminal type for the PNG terminal. If
this option is not set, the command used will be:
"set term pngcairo font \",12\""
. See the gnuplot documentation
for more information.
Categories: Plotting
The gnuplot command to set the terminal type for the PostScript
terminal. If this option is not set, the command used will be: "set term postscript eps color solid lw 2 size 16.4 cm, 12.3 cm font \",24\""
. See the gnuplot documentation for set term postscript
for
more information.
Categories: Plotting
The gnuplot command to set the terminal type for the SVG
terminal. If this option is not set, the command used will be:
"set term svg font \",14\""
. See the gnuplot documentation for
more information.
Categories: Plotting
This is an obsolete option that has been replaced legend
described
above.
Categories: Plotting
This is an obsolete option that has been replaced by style
.
Categories: Plotting
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Opens the pipe to gnuplot used for plotting with the gnuplot_pipes
format. Is not necessary to manually open the pipe before plotting.
Categories: Plotting
Closes the pipe to gnuplot which is used with the gnuplot_pipes
format.
Categories: Plotting
Closes the pipe to gnuplot which is used with the gnuplot_pipes
format and opens a new pipe.
Categories: Plotting
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.
Categories: Plotting
Resets the state of gnuplot used with the gnuplot_pipes
format. To
update the gnuplot window call gnuplot_replot
after gnuplot_reset
.
Categories: Plotting
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