wxMaxima is a graphical user interface (GUI) for the Maxima computer algebra system (CAS). wxMaxima allows to use all of Maxima's functions. In addition, it provides convenient wizards for accessing the most commonly used features. This manual describes some of the features that make wxMaxima one of the most popular GUIs for Maxima.
In the open-source domain big systems are normally split into smaller projects that are easier to handle for small groups of developers. For example a CD burner program will consist of a command-line tool that actually burns the CD and a graphical user interface that allows users to use it without having to learn about all the command line switches and in fact without using the commandline at all. One advantage of this approach is that the developing work that was invested into the command-line program can be shared by many programs without having to re-invent the wheel: The same CD-burner command-line program can be used as a “send-to-CD”-plug-in for a file manager application, for the “burn to CD” function of a music player and as the CD writer for a DVD backup tool. Another advantage is that splitting one big task into smaller parts allows the developers to provide several user interfaces for the same program.
Computer algebra systems like Maxima fit into this framework. A CAS can provide the logic behind a arbitrary precision calculator application or it can do automatic transforms of formulas in the background of a bigger system (e.g., Sage). Alternatively, it can be a actually used as a free-standing system. Maxima can be accessed via a command line. Often, however, an interface like wxMaxima proves a more efficient way to access the software, especially for newcomers. computer algebra system.
Maxima is a full-featured computer algebra system (CAS). In other words it is a program that can solve mathematical problems by rearranging formulas and finding a formula that solves the problem as opposed to just outputting the numeric value of the result. In other words, Maxima can serve as a calculator that gives numerical representations of variables, but it can also provide analytical solutions. Furthermore, it offers a range of numerical methods of analysis for equations or systems of equations that cannot be solved analytically.
Extensive documentation for Maxima is available on the internet,
There is extensive documentation for maxima available in the internet
part of this documentation is also available in wxMaxima's help menu: Pressing the <Help> key (on most systems that would be the <F1> key) wxmaxima's context-sensitive help feature will automatically jump to maxima's manual page for the command at the cursor.
wxMaxima is a graphical user interface that provides the full functionality and flexibility of Maxima. wxMaxima offers users a graphical display and many features that make working with Maxima easier. For example wxMaxima allows one to export any cell's contents (or, if that is needed, any part of a formula, as well) as text, as LaTeX or as MathML specification at a simple right-click. Indeed, an entire workbook can be exported, either as an HTML file or as a LaTeX file.
The calculations are performed by the Maxima command-line tool in the background.
Much of wxMaxima is self-explaining, but some details require attention. This site contains a number of workbooks that address various aspects of Maxima. Working through some of these (particularly the "10 minute (wx)Maxima tutorial") will increase one's familiarity with both the content of Maxima and the use of wxMaxima to interact with Maxima. This manual concentrates on describing aspects of wxMaxima that are not likely to be self-evident and that might not be covered in the online material.
One of the very few things that aren't standard is that wxMaxima organizes the data for Maxima into cells that are only evaluated (which means: sent to Maxima) when the user requests this. When a cell is evaluated, all commands in that cell, and only that cell, are evaluated as a batch. (One can select a set of adjacent cells and evaluate them together. Also, one can instruct Maxima to evaluate all cells in a workbook in one pass.) This approach might feel unfamiliar at the first sight. It does, however drastically ease work with big documents (where the user certainly does not want every small change to automatically to trigger a full re-evaluation of the whole document). Also, this approach is very handy for debugging.
The cells wxMaxima automatically creates on typing some text are Maxima input cells that will eventually be sent to Maxima.
On evaluation of an input cell's contents the input cell maxima
assigns a label to the input (by default shown in red and recognizable
by the %i) by which it can be referenced later n the wxMaxima
session. The output that Maxima generates will be shown in a different
style (which can be
user-selected) and preceded by a Maxima label that begins beginning
with %o. The output item can be accessed later with a reference
to this code. By default wxMaxima will also attempt to replace this
dynamically-generated label by a more descriptive name if the user
provides one. The %o-style label Maxima auto-generates will
still be accessible, though.
Besides the input cells wxMaxima allows for text cells for documentation, image cells, title cells, chapter cells and section cells. Every cell has it's own undo buffer so debugging by changing the values of several cells and then gradually reverting the unneeded changes is rather easy. Furthermore the worksheet itself has a global undo buffer that can undo cell edits, adds and deletes.
The figure below shows a title cell, a section cell, a text cell, and part of an input/output cell.
The worksheet is organized in cells that work like very much like the styles word processors offer. Each cell can contain one of the following types of content:
It sometimes is desirable to allow selecting multiple cells or only part of a cell for export or Drag-and-Drop. However, beginning such an action in the middle of one cell and ending it in the middle of another will almost certainly lead to unexpected results. wxMaxima will therefore extend the selection to full cells in this case.
wxMaxima works around this by defining two types of cursors wxMaxima will switch between automatically when needed:
wxMaxima contains an autocompletion feature that is triggered via the menu (Cell/Complete Word) or alternatively by pressing the key combination <Ctrl>+<k>. The autocompletion is context-sensitive and if activated within an unit specification for ezUnits it will offer a list of applicable units.
Besides completing the current command's or variable's name the autocompletion is able to show a template for most of the commands indicating the type (and meaning) of the parameters this program expects. To activate this feature press <Shift>+<Ctrl>+<k> or select the respective menu item (Cell/Show Template).
Computers traditionally store characters in 8-bit values. This allows for a maximum of 256 different characters. All letters, numbers, and control symbols (end of transmission, end of string, lines and edges for drawing rectangles for menus etc.) of nearly any given language can fit within that limit.
For most countries the codepage of 256 characters that has been chosen does not include Greek letters, though. To overcome this limitation unicode has been invented: This is a method of including characters that are not normally used in the English language in a text that (as long as only the basic form of Latin characters is used) looks like plain 8-bit ASCII.
Maxima allows for unicode characters if it runs on a lisp that supports them. If the wxWidgets library that wxMaxima is built on supports unicode characters, too, then wxMaxima can be built with unicode support. In this case it (besides a Greek Characters Sidebar) provides a method of entering Greek characters using the keyboard:
The lowercase greek letters actually can be entered both by enter a lating letter or the whole latin name of the greek letter followed and preceded by a press of the escape key:
a alpha i iota r rho
b beta k kappa s sigma
g gamma l lambda t tau
d delta m mu u upsilon
e epsilon n nu f phi
z zeta x xi c chi
h eta om omicron y psi
q theta p pi o omega
The same is true for the uppercase greek letters:
A Alpha I Iota R Rho
B Beta K Kappa S Sigma
G Gamma L Lambda T Tau
D Delta M Mu U Upsilon
E Epsilon N Nu P Phi
Z Zeta X Xi C Chi
H Eta Om Omicron Y Psi
T Theta P Pi O Omega
This mechanism also allows to enter some miscellaneous mathematical symbols:
hbar planck's constant: a h with a vertical bar above it
Hbar a H with a vertical bar above it
This mechanism also allows to enter some miscellaneous mathematical symbols:
2 squared
3 to the power of three
/2 1/2
partial partial sign (the d of dx/dt)
integral integral sign
sq root
ii imaginary
ee element
hb or hbar h barred
Hbar H barred
in in
impl,implies implies
inf infinity
empty empty
TB Big triangle right
tb small triangle right
and and
or or
xor xor
nand nand
nor nor
equiv equivalent
not not
union union
inter intersection
subseteq subset or equal
subset subset
notsubseteq not subset or equal
notsubset not subset
approx approximately
propto proportional to
neq,!=,/=
or # not equal to
+/- or pm a plus/minus sign
<= or leq equal or less than
>= or geq equal or greater than
<< or ll much less than
>> or gg much greater than
equiv equivalent to
qed end of proof
sum sum sign
prod product sign
exists "there exists" sign
nexists "there is no" sign
parallel a "parallel" sign
perp a "perpendicular" sign
leadsto a "leads to" sign
-> a right arrow
If a special symbol isn't in the list it is possible to input arbitrary
unicode characters by pressing <ESC>number of the character<ESC>.
<ESC>61<ESC> therefore results in an a.
Be aware that a maxima running on a lisp without unicode support might not be able to deal with files that contain special unicode characters.
Please note that most of these symbols (notable exceptions are the logic symbols) don't have a special meaning in maxima and therefore will be interpreted as ordinary characters - or might provoke unexpected results in case that the maxima is being run by a lisp that doesn't support dealing with special unicode characters.
Shortcuts to the most important Maxima commands and a history of the last issued commands can be accessed using the side panes. They can be enabled using the "Panes" entry in the "Maxima" menu. The shortcuts can be moved to where the location is most convenient, inside or outside the wxMaxima window. The same commands can be accessed via the menus.
It seems that several word processors and similar programs either recognize MathML input and automatically insert it as an editable 2D equation - or (like libreOffice 5.1) have an equation editor that offers an “import MathML from clipboard” feature. In order to address this wxMaxima offers a “copy to word processor” right-click menu entry that outputs the selected part of an equation in a format the external program (hopefully) understands.
A wxMaxima workbook can be exported as either an HTML file or a LaTeX file. The program uses a set of standard markdown conventions. Markdown in many cases collides with the notations that are frequently used for mathematics. wxMaxima will recognize bullet lists, though, for the HTML and TeX export when the items are marked with stars.
Ordinary text
* One item, indentation level 1
* Another item at indentation level 1
* An item at a second indentation level
* A second item at the second indentation level
* A third item at the first indentation level
Ordinary text
wxMaxima will also recognize => and replace it by a
cogito => sum.
Other symbols the markdown parser will recognize are <= and
>= for comparisons, a double-pointed double arrow (<=>),
single- headed arrows (<->, -> and <-) and
+/- as the respective sign. For TeX output also << and
>> are recognized.
Most hotkeys can be found in the text of the respective menus. Since they are actually taken from the menu text and thus can be customized by the translations of wxMaxima to match the needs of users of the local keyboard, we do not document them here. A few hotkeys or hotkey aliases, though, are not documented in the menus:
Ctrl+Shift+Delete deletes a complete cell.
Ctrl+Tab or Ctrl+Shift triggers the auto-completion mechanism.
Ctrl+I or Ctrl+O Zoom in or out.
If a text cell begins with TeX: the TeX export contains the literal text
that follows the TeX: marker.
The material that is developed in a wxMaxima session can be stored for later use in any of three ways:
.mac files are ordinary text files that can be read using maxima's read command or wxMaxima's File/Batch File menu entry.
One Example:
A .mac file named Quadratic.mac was created. It
consists of two commands: f(x) := (x - 5)^2; and
wxdraw2d( explicit(f(x),x,-5,15)).
The result of entering that batch file appears below. (Some directory
path information is deleted.)
%i1 read("test.mac");
You can be use .mac files for writing own library of
macros. But since they don't contain enough structural information
they cannot be read back as a wxMaxima session.
.wxm files contain the input for maxima, as well as any text cells, title cells and chapter or section cells the user has typed in. Pictures and Maxima's output are not saved along with the .wxm file, though.
This xml-based file format saves all text and images the work sheet contains. It is the preferred file format now and comes in two flavors:
For some common configuration variables wxMaxima offers two ways of configuring:
The animation framerate that is used for new animations is kept in the variable wxanimate_framerate. The initial value this variable will contain in a new worksheet can be changed using the configuration dialogue.
After the next start plots embedded into the worksheet will be created with this size if the value of wxplot_size isn't changed by maxima.
In order to set the plot size of a single graph only use the following notation can be used that sets a variable's value for one command only:
wxdraw2d( explicit(x^2,x,-5,5)), wxplot_size=[480,480]$.
The style menu allows customization that pertains to the appearance of your notebook as you work.
It also contains the option to use jsMath fonts. It is a good idea to install these fonts since they were especially designed for maths and tend to resolve issues that can be caused by broken fonts. If they are not installed on your computer, the option to activate them will not be highlighted. The jsMath fonts can be found on this site.
This option enables two things:
If this value is set to a value bigger than zero maxima will work in a more mobile-device-like fashion:
wxMaxima is predominantly a graphical user interface for Maxima. That is, it primarily passes along commands to Maxima and reports the results of executing those commands. In some cases, however, it adds functionality to Maxima. wxMaxima's ability to generate reports by exporting a workbook's contents to HTML and LaTeX files has been mentioned. This section considers some ways that wxMaxima enhances the inclusion of graphics into a session. described here.
if wxsubscripts is set to true variable names of the format x_y are
displayed using a subscript if
y is a single letter
y is an integer
If the variable name doesn't match these requirements it can still be declared as
"to be subscripted" using the command
wxdeclare_subscript(variable_name); or wxdeclare_subscript([variable_name1,variable_name2,...]);
Declaring a variable as subscripted can be reverted using the following command:
wxdeclare_subscript(variable_name,false);
Plotting (having fundamentally to do with graphics) is a place where a graphical user interface will have to provide some extensions to the original program.
Maxima normally instructs the external program gnuplot to open a separate window for every diagram it creates. Since many times it is convenient to embed graphs into the work sheet instead wxMaxima provides its own set of plot functions that don't differ from the corresponding maxima functions save in their name: They are all prefixed by a “wx”. For example wxplot corresponds to plot, wxdraw corresponds to draw and wxhistogram corresponds to histogram.
As noted above, the configure dialog provides a way to change the default size plots are created with which sets the starting value of wxplot_size. The plotting routines of wxMaxima respect this variable that specifies the size of a plot in pixels. It can always be queried or used to set the size of the following plots:
%i1 wxplot_size:[1200,800];
%o1 [1200,800];
%i2 wxdraw2d(
explicit(
sin(x),
x,1,10
)
)$
If the size of only one plot is to be changed maxima provides a canonical way to change an attribute only for the current cell.
%i1 wxplot_size:[1200,800];
%o1 [1200,800];
%i1 wxdraw2d(
explicit(
sin(x),
x,1,10
)
),wxplot_size=[1600,800]$
%i1 wxdraw2d(
explicit(
sin(x),
x,1,10
)
),wxplot_size=[1600,800]$
Gnuplot doesn't seem to provide a portable way of determining whether it
supports the high-quality bitmap output the cairo library provides.
On systems where gnuplot is compiled to use this library the
pngcairo option from the configuration menu (that can be overridden
by the variable wxplot_pngcairo) enables support for
antialiasing and additional line styles.
The with_slider_draw command is a version of wxdraw2d
that does prepare multiple plots and allows to switch between them
by moving the slider on top of the screen. If ImageMagick is installed
wxMaxima even allows to export this animation as an animated gif.
The first two arguments for with_slider_draw are the name of
the variable that is stepped between the plots and a list of the
values of these variable. The arguments that follow are the ordinary
arguments for wxdraw2d:
with_slider_draw(
f,[1,2,3,4,5,6,7,10],
title=concat("f=",f,"Hz"),
explicit(
sin(2*%pi*f*x),
x,0,1
),grid=true
);
The same functionality for 3d plots is accessible as with_slider_draw3d.
There is a second set of functions making use of the slider
wxanimate_draw and
wxanimate_draw3d:
wxanimate_draw(
a, 3,
explicit(sin(a*x), x, -4, 4),
title=printf(false, "a=~a", a));
Normally the animations are played back or exported with the frame rate chosen in the configuration of wxMaxima. To set the speed an individual animation is played back the variable wxanimate_framerate can be used:
wxanimate(a, 10,
sin(a*x), [x,-5,5]), wxanimate_framerate=6$
The animation functions have a pitfall that one has to be aware of when using them: The slider variable's value are substituted into the expression that is to be plotted - which will fail, if the variable isn't directly visible in the expression. Therefore the following example will fail:
f:sin(a*x);
with_slider_draw(
a,makelist(i/2,i,1,10),
title=concat("a=",float(a)),
grid=true,
explicit(f,x,0,10)
)$
If Maxima is forced to first evaluate the expression and then asked to substitute the slider's value plotting works fine instead:
f:sin(a*x);
with_slider_draw(
a,makelist(i/2,i,1,10),
title=concat("a=",float(a)),
grid=true,
explicit(''f,x,0,10)
)$
While not being a provided by wxMaxima this feature of Maxima (on setups that support it) sometimes comes in handily. The following example comes from a post from Mario Rodriguez to the Maxima mailing list:
load(draw);
/* Parabola in window #1 */
draw2d(terminal=[wxt,1],explicit(x^2,x,-1,1));
/* Parabola in window #2 */
draw2d(terminal=[wxt,2],explicit(x^2,x,-1,1));
/* Paraboloid in window #3 */
draw3d(terminal=[wxt,3],explicit(x^2+y^2,x,-1,1,y,-1,1));
if the .wxmx file format is being used embedding files in a wxMaxima project can be done as easily as per drag-and-drop. But sometimes (for example if an image's contents might change later on in a session) it is better to tell the file to load the image on evaluation:
show_image("Mann.png");
If the Maxima user directory there is a text file named wxmaxima-init.mac the contents of the file is passed to Maxima automatically every time a new worksheet has been started.
To find out which directory Maxima uses as the user directory just type in the following line:
maxima_userdir;
The answer from Maxima will specify the name of the directory that the startup file can be placed in.
%o1 /home/username/.maxima
R_150) or the like into
subscripted variables. See wxdeclare_subscript for details
which variable names are automatically converted.
Maxima/maxima's pwd is path to document is checked.
read_matrix) to work without specifying the whole path to the
file that has to be read or written. On Windows this is
deactivated, though: The Lisp Standard doesn't contain a concept of
the current working directory. Therefore there is no standard
way of setting it and changing to a directory that isn't on
the drive Maxima has been installed to might cause Maxima to
try to read is own package files from this drive, too, instead
of from the drive Maxima has been installed to. Setting
wxchangedir to true tells wxMmaxima that it has to
risk that and to set Maxima's working directory.
The function (table_form) displays a 2D list in a form that is
more readable than the output Maxima's default output routine.
table_form(
[
[1,2],
[3,4]
]
)$
wxMaxima provides a few functions that gather bug reporting information about the current system:
wxbuild_info() gathers information about the currently
running version of wxMaxima
wxbug_report() tells how and where to file bugs
Since Maxima (the program that does the actual mathematics) and wxMaxima (providing the easy-to-use user interface) are separate programs that communicate by the means of a local network connection. Therefore the most probable cause is that this connection is somehow not working. For example a firewall could be set up in a way that it doesn't just prevent against unauthorized connections from the internet (and perhaps to intercept some connections to the internet, too), but it also to blocks inter-process-communication inside the same computer. Note that since Maxima is being run by a lisp processor the process communication that is blocked from does not necessarily have to be named "maxima". Common names of the program that opens the network connection would be sbcl, gcl, ccl, lisp.exe or similar names.
On Un*x computers another possible reason would be that the loopback network that provides network connections between two programs in the same computer isn't properly configured.
Internally most modern xml-based formats are ordinary zip-files with one special characteristic: the first file in the archive is stored uncompressed and provides information about what type of program can open this file.
If the zip signature at the end of the file is still intact after renaming a broken .wxmx file to .zip most operating systems will provide a way to extract any portion of information that is stored inside it. The can be done when there is the need of recovering the original image files from a text processor document. If the zip signature isn't intact that does not need to be the end of the world: If wxMaxima during saving detected that something went wrong there will be a wxmx~ file whose contents might help and even if there isn't such a file: If the configuration option is set that .wxmx files have to be optimized for version control it is possible to rename the .wxmx file to a .txt file and to use a text editor to recover the file's contents.
In old versions of Maxima this might be caused by the fact that a closing brace, bracket, parenthesis or hyphenation mark is missing: In this case Maxima waits until it gets the rest of its input (which it never does).
In order to find out if this is the issue the operating system normally provides a way to determine if Maxima is actually really working forever trying to solve the current problem.
Normally wxMaxima waits for the whole 2D formula to be transferred before
it begins to typeset. This saves time for making many attempts to typeset a
only partially completed equation. There is a disp command, though, that
will provide debug output immediately and without waiting for the current
Maxima command to finish, though:
for i:1 thru 10 do (
disp(i),
t:makelist(i,i,1000000),
length(t)
)$
The jsMath fonts allow for excellent 2D-display of equations. But there are of broken versions of this package that crash wxMaxima. A working version can be downloaded from http://www.math.union.edu/~dpvc/jsmath/download/jsMath-fonts.html math.union.edu. To make wxMaxima actually use these fonts the according checkbox has to be enabled in the Styles tab of wxMaxima's configuration dialogue.
wxMaxima relies on a third-party tool (ImageMagick) to convert animations to the animated gif format. This will obviously only work if this package is installed and known to the system (on windows the path to ImageMagick's convert.exe has to be part of the PATH system variable to make the system find it).
Another possible reason of not getting an animated gif is that this image would exceed the format's (or ImageMagick's) capabilities:
This means that wxMaxima was unable to read the file Maxima was supposed to instruct gnuplot to create.
Possible reasons that might cause this are:
implicit_plot but this package wasn't loaded by Maxima's
load() command before trying to plot.
The value of the slider variable by default is only substituted into the
expression that is to be plotted if it is visible there. Putting an
ev() around this expression should resolve this problem.
There are separate undo functions for cell operations and for changes inside of cells so chances are low that this ever happens. If it does there are several methods to recover data:
%i1 playback();
One possible reason is that Maxima cannot be found in the location that is set in the “Maxima” tab of wxMaxima's configuration dialog and therefore won't run at all. Setting the path to a working Maxima binary should fix this problem.
It is theoretically possible that wxMaxima doesn't realize that Maxima has finished calculating and therefore never gets informed it can send new data to Maxima. If this is the case “Trigger evaluation” might resynchronize the two programs.
On windows File I/O isn't relative to the directory of the current
file by default. If you store the Maxima file on the drive wxMaxima is
installed to setting wxchangedir to true will fix
that for load, read_list, batch,
read_matrix, save and all similar commands.
Setting this variable to true might have a drawback, though:
Maxima knows which directory it is installed in and will search for
any additional package that is requested by a load command in
this directory, too. But it might not know which drive it is installed
on. If wxchangedir is true and the current file is saved
on a different drive than the one Maxima is installed on Maxima
therefore might fail to load the additional packages it was bundled
with.
SBCL by default comes with a memory limit that allows it to run even on
low-end computers. When compiling a big software package like lapack
or dealing with extremely big lists or equations this limit might be
too low. In order to extend the limits sbcl can be provided with the
command line parameter
--dynamic-space-size that tells sbcl how many megabytes it
should reserve. A 32bit-windows-sbcl can reserve up to 999 Megabytes,
1800. A 64-bit sbcl version running on windows can be instructed to use
more than the about 1280 Megabytes compiling lapack needs.
One way to provide maxima (and thus sbcl) with command line parameters is
the additional parameters field of wxMaxima's configuration
dialogue.
Installing the package ibus-gtk should resolve this issue. See
(https://bugs.launchpad.net/ubuntu/+source/wxwidgets3.0/+bug/1421558) for details.
If your Maxima is based on sbcl the following lines have to be added to your .sblrc:
(setf sb-impl::*default-external-format* :utf-8)
The folder this file has to be placed in is system- and installation-specific. But any sbcl-based Maxima that already has evaluated a cell in the current session will happily tell where it can be found after getting the following command:
:lisp (sb-impl::userinit-pathname)
It is easier to make it first generate the images and then import them again as the following two functions will do:
load("draw");
pngdraw(name,[contents]):=
(
draw(
append(
[
terminal=pngcairo,
dimensions=wxplot_size,
file_name=name
],
contents
)
),
show_image(printf(false,"~a.png",name))
);
pngdraw2d(name,[contents]):=
pngdraw(name,gr2d(contents));
pngdraw2d("Test",
explicit(sin(x),x,1,10)
);
Not directly using Maxima. But there are gnuplot commands for it:
wxdraw2d(
user_preamble="set size ratio 1;set tmargin 3;set bmargin 3;set lmargin 3;set rmargin 3",
explicit(sin(x),x,1,10)
),wxplot_size=[1000,1000];
There is: Just add the following lines to the LaTeX preamble (for example by using the respective field in the config dialog):
\usepackage[a4paper,landscape,left=1cm,right=1cm,top=1cm,bottom=1cm]{geometry}
Most operating systems provide less complicated ways of starting programs than the command line so this possibility is only rarely used. wxMaxima still provides some command line switches, though.
-v or --version: Output the version information
-h or --help: Output a short help text
-o or --open: Open the filename given as argument to this
command-line switch
-b or --batch: If the command-line opens a file all cells in this file are
evaluated and the file is saved afterwards. This is for example useful if
the sesson described in the file makes Maxima generate output files.
Batch-processing will be stopped if wxMaxima detects that Maxima has output
an error and will pause if Maxima has a question: Mathematics is somewhat
interactive by nature so a completely interaction-free batch processing
cannot always be guaranteed.
-f or --ini: Use the init file that was
given as argument to this command-line switch