The wxMaxima user manual

WxMaxima is a graphical user interface (GUI) for the Maxima computer algebra system (CAS). WxMaxima allows one 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.

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Introduction to wxMaxima

<em>Maxima</em> and wxMaxima

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 implement it without having to learn about all the command line switches and in fact without using the command line 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: 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.

A computer algebra system (CAS) like Maxima fits into this framework. A CAS can provide the logic behind an 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 used directly 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.

<em>Maxima</em>

Maxima is a full-featured computer algebra system (CAS). A CAS 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, and 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 in the internet. Part of this documentation is also available in wxMaxima’s help menu. Pressing the Help key (on most systems the F1 key) causes _wxMaxima_’s context-sensitive help feature to automatically jump to _Maxima_’s manual page for the command at the cursor.

WxMaxima

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 a HTML file or as a LaTeX file. Documentation for wxMaxima, including workbooks to illustrate aspects of its use, is online at the wxMaxima help site, as well as via the help menu.

The calculations that are entered in wxMaxima are performed by the Maxima command-line tool in the background.

Workbook basics

Much of wxMaxima is self-explaining, but some details require attention. This site contains a number of workbooks that address various aspects of wxMaxima. 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.

The workbook approach

One of the very few things that are not standard in wxMaxima is that it organizes the data for Maxima into cells that are evaluated (which means: sent to Maxima) only when the user requests this. When a cell is evaluated, all commands in that cell, and only that cell, are evaluated as a batch. (The preceding statement is not quite accurate: 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.) _WxMaxima_’s approach to submitting commands for execution might feel unfamiliar at the first sight. It does, however, drastically ease work with big documents (where the user does not want every change to automatically trigger a full re-evaluation of the whole document). Also, this approach is very handy for debugging.

If text is typed into wxMaxima it automatically creates a new worksheet cell. The type of this cell can be selected in the toolbar. If a code cell is created the cell can be sent to Maxima, which causes the result of the calculation to be displayed below the code. A pair of such commands is shown below.

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 in the wxMaxima session. The output that Maxima generates also gets a label that begins with o and by default is hidden, except if the user assigns the output a name. In this case by default the user-defined label is displayed. The o-style label Maxima auto-generates will also 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 its 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 different cell types (title cells, section cells, subsection cells, text cells, input/output cells and image cells).

Cells

The worksheet is organized in cells. WxMaxima knows the following cell types:

• Math cells, containing one or more lines of Maxima input.
• Output of, or a question from, Maxima.
• Image cells.
• Text cells, that can for example be used for documentation.
• A title, section or a subsection. 6 levels of different headings are possible.
• Page breaks.

The default behavior of wxMaxima when text is entered is to automatically create a math cell. Cells of other types can be created using the Cell menu, using the hot keys shown in the menu or using the drop-down list in the toolbar. Once the non-math cell is created, whatever is typed into the file is interpreted as text.

A (C-style) comment text can be part of a math cell as follows: /* This comment will be ignored by Maxima */

"`/*`" marks the start of the comment, "`*/`" the end.

Horizontal and vertical cursors

If the user tries to select a complete sentence, a word processor will try to extend the selection to automatically begin and end with a word boundary. Likewise, if more than one cell is selected, wxMaxima will extend the selection to whole cells.

What isn’t standard is that wxMaxima provides drag-and-drop flexibility by defining two types of cursors. WxMaxima will switch between them automatically when needed:

• The cursor is drawn horizontally if it is moved in the space between two cells or by clicking there.
• A vertical cursor that works inside a cell. This cursor is activated by moving the cursor inside a cell using the mouse pointer or the cursor keys and works much like the cursor in a text editor.

When you start wxMaxima, you will only see the blinking horizontal cursor. If you start typing, a math cell will be automatically created and the cursor will change to a regular vertical one (you will see a right arrow as "prompt", after the Math cell is evaluated (CTRL+ENTER), you will see the labels, e.g. (i1), (o1)).

You might want to create a different cell type (using the "Cell" menu), maybe a title cell or text cell, which describes, what will be done, when you start creating your worksheet.

If you navigate between the different cells, you will also see the (blinking) horizontal cursor, where you can insert a cell into your worksheet (either a math cell, by just start typing your formula - or a different cell type using the menu).

Sending cells to Maxima

The command in a code cell is executed once by pressing CTRL+ENTER, SHIFT+ENTER or the ENTER key on the keypad. The wxMaxima default is to enter commands when either CTRL+ENTER or SHIFT+ENTER is entered, but wxMaxima can be configured to execute commands in response to ENTER.

Command autocompletion

WxMaxima contains an autocompletion feature that is triggered via the menu (Cell/Complete Word) or alternatively by pressing the key combination CTRL+SPACE. The autocompletion is context-sensitive. For example, if activated within a unit specification for ezUnits it will offer a list of applicable units.

Besides completing a file name, a unit name, or the current command or variable 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+SPACE or select the respective menu item (Cell/Show Template).

Greek characters

Computers traditionally stored 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 things like Greek letters, though, that are frequently used in mathematics. To overcome this type of limitation Unicode has been invented: An encoding that makes English text work like normal, but to use much more than 256 characters.

Maxima allows Unicode if it was compiled using a Lisp compiler that either supports Unicode or that doesn’t care about the font encoding. As at least one of this pair of conditions is likely to be true. WxMaxima provides a method of entering Greek characters using the keyboard:

• A Greek letter can be entered by pressing the ESC key and then starting to type the Greek character’s name.
• Alternatively it can be entered by pressing ESC, one letter (or two for the Greek letter omicron) and ESC again. In this case the following letters are supported:

key	Greek letter	key	Greek letter	key	Greek letter
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
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

You can also use the "Greek letters"-sidebar to enter the Greek letters.

Attention: Lookalike characters

Several Latin letters look like the Greek letters, e.g. the Latin letter "A" and the Greek letter "Alpha". Although they look identical, they are two different Unicode characters, represented by different Unicode code points (numbers).

This might be problematic, if you assign a value to the variable A and later use the Greek letter Alpha to do something with this variable, especially on printouts. For the Greek letter my (which is also used as prefix for micro) there are also two different Unicode code points.

The "Greek letters"-sidebar therefore has the option, that lookalike characters are not available (which can be changed using a right-click menu).

The same mechanism also allows to enter some miscellaneous mathematical symbols:

keys to enter	mathematical symbol
hbar	Planck’s constant: a h with a horizontal bar above it
Hbar	a H with a horizontal bar above it
2	squared
3	to the power of three
/2	1/2
partial	partial sign (the d of dx/dt)
integral	integral sign
sq	square root
ii	imaginary
ee	element
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 to
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
qed	end of proof
nabla	a nabla operator
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
-->	a long right arrow

You can also use the "Symbols"-sidebar to enter these Mathematical symbols.

If a special symbol isn’t in the list, it is possible to input arbitrary Unicode characters by pressing ESC [number of the character (hexadecimal)] ESC. Additionally the "symbols" sidebar has a right-click menu that allow to display a list of all available Unicode symbols one can add to this toolbar or to the worksheet.

ESC61ESC therefore results in an a.

Please note that most of these symbols (notable exceptions are the logic symbols) do not have a special meaning in Maxima and therefore will be interpreted as ordinary characters. If Maxima is compiled using a Lisp that doesn’t support Unicode characters they might cause an error message.

It may be the case that e.g. Greek characters or mathematical symbols are not included in the selected font, then they can not be displayed. To solve that problem, select other fonts (using: Edit -> Configure -> Style).

Unicode replacement

wxMaxima will replace several Unicode characters with their respective Maxima expressions, e.g. "²" with "^2", "³" with "^3", the square root sign with the function sqrt(), the (mathematical) Sigma sign (which is not the same Unicode character as the corresponding Greek letter) with sum(), etc.

Side Panes

Shortcuts to the most important Maxima commands, things like a table of contents, windows with debug messages or a history of the last issued commands can be accessed using the side panes. They can be enabled using the "View" menu. They all can be moved to other locations inside or outside the wxMaxima window. Other useful panes is the one that allows to input Greek letters using the mouse.

In the "table of contents" side pane, one can increase or decrease a heading by just clicking on the heading with the right mouse button and select the next higher or lower heading type.

MathML output

Several word processors and similar programs either recognize MathML input and automatically insert it as an editable 2D equation - or (like LibreOffice) have an equation editor that offers an “import MathML from clipboard” feature. Others support RTF maths. WxMaxima, therefore, offers several entries in the right-click menu.

Markdown support

WxMaxima offers a set of standard Markdown conventions that don’t collide with mathematical notation. One of these elements is bullet lists.

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 recognize text starting with > chars as block quotes:

Ordinary text
> quote quote quote quote
> quote quote quote quote
> quote quote quote quote
Ordinary text

_WxMaxima_’s TeX and HTML output will also recognize => and replace it by the corresponding Unicode sign:

cogito => sum.

Other symbols the HTML and TeX export 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.

Hotkeys

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+TAB triggers the auto-completion mechanism.
• SHIFT+SPACE inserts a non-breaking space.

Raw TeX in the TeX export

If a text cell begins with TeX: the TeX export contains the literal text that follows the TeX: marker. Using this feature allows the entry of TeX markup within the wxMaxima workbook.

File Formats

The material that is developed in a wxMaxima session can be stored for later use in any of three ways:

.mac

.mac files are ordinary text files that contain Maxima commands. They can be read using _Maxima_’s batch() or load() command or _wxMaxima_’s File/Batch File menu entry.

One example is shown below. Quadratic.mac defines a function and afterward generates a plot with wxdraw2d(). Afterward the contents of the file Quadratic.mac are printed and newly defined function f() is evaluated.

Attention: Although the file Quadratic.mac has a usual Maxima extension (.mac), it can only be read by wxMaxima, since the command wxdraw2d() is a wxMaxima-extension to Maxima. (Command line) Maxima will ignore the unknown command wxdraw2d() and print it as output again.

You can be use .mac files for writing your own library of macros. But since they don’t contain enough structural information they cannot be read back as a wxMaxima session.

.wxm

.wxm files contain the worksheet except for Maxima_’s output. On Maxima versions >5.38 they can be read using _Maxima_’s load() function just as .mac files can be. With this plain-text format, it sometimes is unavoidable that worksheets that use new features are not downwards-compatible with older versions of _wxMaxima.

File format of wxm files

This is just a plain text file (you can open it with a text editor), containing the cell contents as some special Maxima comments.

It starts with the following comment:

/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 24.02.2_DevelopmentSnapshot ] */

And then the cells follow, encoded as Maxima comments, e.g. a section cell:

/* [wxMaxima: section start ]
Title of the section
   [wxMaxima: section end   ] */

or (in a Math cell the input is of course not commented out (the output is not saved in a wxm file)):

/* [wxMaxima: input   start ] */
f(x):=x^2+1$
f(2);
/* [wxMaxima: input   end   ] */

Images are Base64 encoded with the image type as first line):

/* [wxMaxima: image   start ]
jpg
[very chaotic looking character sequence]
   [wxMaxima: image   end   ] */

A page break is just one line containing:

/* [wxMaxima: page break    ] */

And folded cells marked by:

/* [wxMaxima: fold    start ] */
...
/* [wxMaxima: fold    end   ] */

.wxmx

This XML-based file format saves the complete worksheet including things like the zoom factor and the watchlist. It is the preferred file format.

File format of wxmx files

A wxmx-file seems to be a binary format, but one can handle it with tools, which are included in your OS. It is a zip file, one can decompress it with unzip (maybe rename it before, so that is recognized by the unzip program of your OS). We do not use the compression function, just the possibility to merge several files into one file - images are already compressed and the rest is simple text (probably much smaller, than huge images, which are included).

It does contain the following files:

• mimetype: this file does contain the mimetype of wxMaxima files: text/x-wxmathml
• format.txt: a short description about wxMaxima and the wxmx file format
• Images (e.g. png, jpeg): inline plots which were produced in the wxMaxima session and included images.
• content.xml: a XML document, which contains the various cells of your document in XML format.

So, if something goes wrong, you can unzip a wxMaxima document (maybe rename it before to a zip-file), maybe make changes in the content.xml file with a text editor, or replace an broken image, zip the files again, probably rename the zip to a wxmx-file - and you get another modified wxmx-file.

Configuration options

For some common configuration variables wxMaxima offers two ways of configuring:

• The configuration dialog box below lets you change their default values for the current and subsequent sessions.
• Also, the values for most configuration variables can be changed for the current session only by overwriting their values from the worksheet, as shown below.

Default animation framerate

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.

Default plot size for new <em>maxima</em> sessions

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]$

Match parenthesis in text controls

This option enables two things:

• If an opening parenthesis, bracket, or double quote is entered wxMaxima will insert a closing one after it.
• If text is selected if any of these keys is pressed the selected text will be put between the matched signs.

Don’t save the worksheet automatically

If this option is set, the file where the worksheet is will be overwritten only the request of the user. In case of a crash/power loss/... a recent backup copy is still made available in the temp directory, though.

If this option isn’t set wxMaxima behaves more like a modern cellphone app:

• Files are saved automatically on exit
• And the file will automatically be saved every 3 minutes.

Where is the configuration saved?

If you are using Unix/Linux, the configuration information will be saved in a file .wxMaxima in your home directory (if you are using wxWidgets < 3.1.1), or .config/wxMaxima.conf ((XDG-Standard) if wxWidgets >= 3.1.1 is used). You can retrieve the wxWidgets version from the command wxbuild_info(); or by using the menu option Help->About. wxWidgets is the cross-platform GUI library, which is the base for wxMaxima (therefore the wx in the name). (Since the filename starts with a dot, .wxMaxima or .config will be hidden).

If you are using Windows, the configuration will be stored in the registry. You will find the entries for wxMaxima at the following position in the registry: HKEY_CURRENT_USER\Software\wxMaxima

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Extensions to <em>Maxima</em>

WxMaxima is primarily a graphical user interface for Maxima. As such, its main purpose is to pass along commands to Maxima and to report the results of executing those commands. In some cases, however, wxMaxima 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 in a session.

Subscripted variables

wxsubscripts specifies, if (and how) wxMaxima will autosubscript variable names:

If it is false, the functionality is off, wxMaxima will not autosubscript part of variable names after an underscore.

If it is set to 'all, everything after an underscore will be subscripted.

If it is set to true variable names of the format x_y are displayed using a subscript if

• Either x or y is a single letter or
• y is an integer (can include more than one character).

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);

You can use the menu "View->Autosubscript" to set these values.

User feedback in the status bar

Long-running commands can provide user feedback in the status bar. This user feedback is replaced by any new feedback that is placed there (allowing to use it as a progress indicator) and is deleted as soon as the current command sent to Maxima is finished. It is safe to use wxstatusbar() even in libraries that might be used with plain Maxima (as opposed to wxMaxima): If wxMaxima isn’t present the wxstatusbar() command will just be left unevaluated.

for i:1 thru 10 do (
    /* Tell the user how far we got */
    wxstatusbar(concat("Pass ",i)),
    /* (sleep n) is a Lisp function, which can be used */
    /* with the character "?" before. It delays the */
    /* program execution (here: for 3 seconds) */
    ?sleep(3)
)$

Plotting

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.

Embedding a plot into the worksheet

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 worksheet 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”.

The following plotting functions have wx-counterparts:

wxMaxima’s plot function	Maxima’s plot function
wxplot2d()	plot2d
wxplot3d()	plot3d
wxdraw2d()	draw2d
wxdraw3d()	draw2d
wxdraw()	draw
wximplicit_plot()	implicit_plot
wxhistogram()	histogram
wxscatterplot()	scatterplot
wxbarsplot()	barsplot
wxpiechart()	piechart
wxboxplot()	boxplot

If a wxm-file is read by (console) Maxima, these functions are ignored (and printed as output, as other unknown functions in Maxima).

If you got problems with one of these functions, please check, if the problem exists in the the Maxima function too (e.g. you got an error with wxplot2d(), check the same plot in the Maxima command plot2d() (which opens the plot in a separate Window)). If the problem does not disappear, it is most likely a Maxima issue and should be reported in the Maxima bugtracker. Or maybe a Gnuplot issue.

Making embedded plots bigger or smaller

As noted above, the configure dialog provides a way to change the default size plots created 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:

wxplot_size:[1200,800]$
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. In this usage the specification wxplot_size = [value1, value2] is appended to the wxdraw2d( ) command, and is not part of the wxdraw2d command.

wxdraw2d(
    explicit(
        sin(x),
        x,1,10
    )
),wxplot_size=[1600,800]$

Setting the size of embedded plot with wxplot_size works for embedded plots using e.g. wxplot, wxdraw, wxcontour_plot and wximplicit_plot commands and for embedded animations with with_slider_draw and wxanimate commands.

Better quality plots

Gnuplot doesn’t seem to provide a portable way of determining whether it supports the high-quality bitmap output that 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. If wxplot_pngCairo is set without Gnuplot supporting this the result will be error messages instead of graphics.

Opening embedded plots in interactive <em>Gnuplot</em> windows

If a plot was generated using the wxdraw-type commands (wxplot2d and wxplot3d isn’t supported by this feature) and the file size of the underlying Gnuplot project isn’t way too high wxMaxima offers a right-click menu that allows to open the plot in an interactive Gnuplot window.

Opening Gnuplot’s command console in <tt>plot</tt> windows

On MS Windows, there are two Gnuplot programs, gnuplot.exe and wgnuplot.exe. You can configure, which command should be used using the configuration menu. wgnuplot.exe offers the possibility to open a console window, where gnuplot commands can be entered into, gnuplot.exe does not offer this possibility. Unfortunately, wgnuplot.exe causes Gnuplot to "steal" the keyboard focus for a short time every time a plot is prepared.

Embedding animations into the spreadsheet

3D diagrams tend to make it hard to read quantitative data. A viable alternative might be to assign the 3rd parameter to the mouse wheel. 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. WxMaxima 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, which allows for rotating 3d plots:

wxanimate_autoplay:true;
wxanimate_framerate:20;
with_slider_draw3d(
    α,makelist(i,i,1,360,3),
    title=sconcat("α=",α),
    surface_hide=true,
    contour=both,
    view=[60,α],
    explicit(
        sin(x)*sin(y),
        x,-π,π,
        y,-π,π
    )
)$

If the general shape of the plot is what matters it might suffice to move the plot just a little bit in order to make its 3D nature available to the intuition:

wxanimate_autoplay:true;
wxanimate_framerate:20;
with_slider_draw3d(
    t,makelist(i,i,0,2*π,.05*π),
    title=sconcat("α=",α),
    surface_hide=true,
    contour=both,
    view=[60,30+5*sin(t)],
    explicit(
        sin(x)*y^2,
        x,-2*π,2*π,
        y,-2*π,2*π
    )
)$

For those more familiar with plot than with draw, there is a second set of functions:

• with_slider and
• wxanimate.

Normally the animations are played back or exported with the frame rate chosen in the configuration of wxMaxima. To set the speed at 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 use _Maxima_’s makelist command and therefore share the pitfall that the slider variable’s value is substituted into the expression only if the variable is 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 explicitly asked to substitute the slider’s value plotting works fine instead:

f:sin(a*x);
with_slider_draw(
    b,makelist(i/2,i,1,10),
    title=concat("a=",float(b)),
    grid=true,
    explicit(
        subst(a=b,f),
        x,0,10
    )
)$

Opening multiple plots in contemporaneous windows

While not being 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));

Plotting multiple plots in the same window is possible, too (the same is possible in command line Maxima with the standard draw() command):

wxdraw(
  gr2d(
    key="sin (x)",grid=[2,2],
    explicit(sin(x),x,0,2*%pi)),
  gr2d(
    key="cos (x)",grid=[2,2],
    explicit(cos(x),x,0,2*%pi))
);

The "Plot using draw" side pane

The "Plot using draw" sidebar hides a simple code generator that allows generating scenes that make use of some of the flexibility of the draw package maxima comes with.

2D

Generates the skeleton of a draw() command that draws a 2D scene. This scene later has to be filled with commands that generate the scene’s contents, for example by using the buttons in the rows below the "2D" button.

One helpful feature of the 2D button is that it allows to set up the scene as an animation in which a variable (by default it is t) has a different value in each frame: Often a moving 2D plot allows easier interpretation than the same data in a non-moving 3D one.

3D

Generates the skeleton of a draw() command that draws a 3D scene. If neither a 2D nor a 3D scene is set up, all of the other buttons set up a 2D scene that contains the command the button generates.

Expression

Appends a standard plot of an expression like sin(x), x*sin(x) or x^2+2*x-4 to the draw() command the cursor currently is in. If there is no draw command a 2D scene with the plot is generated. Each scene can be filled with any number of plots.

Implicit plot

Tries to find all points an expression like y=sin(x), y*sin(x)=3 or x^2+y^2=4 is true at and plots the resulting curve in the draw() command the cursor currently is in. If there is no draw command a 2D scene with the plot is generated.

Parametric plot

Steps a variable from a lower limit to an upper limit and uses two expressions like t*sin(t) and t*cos(t) for generating the x, y (and in 3D plots also z) coordinates of a curve that is put into the current draw command.

Points

Draws many points that can optionally be joined. The coordinates of the points are taken from a list of lists, a 2D array or one list or array for each axis.

Diagram title

Draws a title on the upper end of the diagram,

Axis

Sets up the axis.

Contour

(Only for 3D plots): Adds contour lines similar to the ones one can find in a map of a mountain to the plot commands that follow in the current draw() command and/or to the ground plane of the diagram. Alternatively, this wizard allows skipping drawing the curves entirely only showing the contour plot.

Plot name

Adds a legend entry showing the next plot’s name to the legend of the diagram. An empty name disables generating legend entries for the following plots.

Line colour

Sets the line colour for the following plots the current draw command contains.

Fill colour

Sets the fill colour for the following plots the current draw command contains.

Grid

Pops up a wizard that allows to set up grid lines.

Accuracy

Allows to select an adequate point in the speed vs. accuracy tradeoff that is part of any plot program.

Modify font and font size for plots

Especially when you use a high resolution display, the default font size might be very small. For the draw-based commands, you can set the font / font size using options like font=..., font_size=..., e.g.:

wxdraw2d(
     font="Helvetica",
     font_size=30,
     explicit(sin(x),x,1,10));

For the plot-commands (e.g. wxplot2d, wxplot3d) font sizes and fonts can be set using the gnuplot_preamble command, e.g.:

wxplot2d(sin(x),[x,1,10],
         [gnuplot_preamble, "set tics font \"Arial, 30\"; set xlabel font \",20\"; set ylabel font \",20\";"]);

This sets the font for the numbers to Arial with size 30, the size for the xlabel and ylabel font to 20 (with the default font).

Read the Maxima and Gnuplot documentation for further information. Note: Gnuplot seems to have issues with larger font sizes, see wxMaxima issue 1966.

Embedding graphics

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("man.png");

Startup files

The config dialogue of wxMaxima offers to edit two files with commands that are executed on startup:

• A file that contains commands that are executed on starting up Maxima: maxima-init.mac
• one file of additional commands that are executed if wxMaxima is starting Maxima: wxmaxima-init.mac

For example, if Gnuplot is installed in /opt (maybe on MacOS), you can add gnuplot_command:"/opt/local/bin/gnuplot"$ (or /opt/gnuplot/bin/gnuplot or any other path) to these files.

These files are in the Maxima user directory (usually USERPROFILE%/maxima in Windows, $HOME/.maxima otherwise). The location can be found out with the command: maxima_userdir;

Special variables wx...

• wxsubscripts tells Maxima if it should convert variable names that contain an underscore (R_150 or the like) into subscripted variables. See wxdeclare_subscript for details which variable names are automatically converted.
• wxfilename: This variable contains the name of the file currently opened in wxMaxima.
• wxdirname: This variable contains the name the directory, in which the file currently opened in wxMaxima is.
• wxplot_pngcairo tells whether wxMaxima tries to use Gnuplot_’s pngcairo terminal that provides more line styles and a better overall graphics quality.
• wxplot_size defines the resolution of embedded plots.
• wxchangedir: On most operating systems _wxMaxima automatically sets Maxima_’s working directory to the directory of the current file. This allows file I/O (e.g. by read_matrix) to work without specifying the whole path to the file that has to be read or written. On Windows this feature sometimes causes error messages and therefore can be set to false from the config dialogue.
• wxanimate_framerate: The number of frames per second the following animations have to be played back with.
• wxanimate_autoplay: Automatically play animations by default?
• wxmaximaversion: Returns the version number of _wxMaxima.
• wxwidgetsversion: Returns the wxWidgets version wxMaxima is using.

Pretty-printing 2D output

The function table_form() displays a 2D list in a form that is more readable than the output from _Maxima_’s default output routine. The input is a list of one or more lists. Like the "print" command, this command displays output even when ended with a dollar sign. Ending the command with a semicolon results in the same table along with a "done" statement.

table_form(
    [
        [1,2],
        [3,4]
    ]
)$

As the next example shows, the lists that are assembled by the table_form command can be created before the command is executed.

Also, because a matrix is a list of lists, matrices can be converted to tables in a similar fashion.

Bug reporting

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

Marking output being drawn in red

Maxima_’s box() command causes _wxMaxima to print its argument with a red foreground, if the second argument to the command is the text highlight.

Output rendering.

With set_display() one can set, how wxMaxima will render the output.

set_display('xml) is the default value. Here Maxima speaks to wxMaxima using an (machine readable) XML-dialect (can be seen in the "Raw XML sidebar") and outputs the resulting formulas nicely rendered, e.g. pretty Matrices, Square root signs, fractions, etc.

set_display('ascii) causes wxMaxima to output formulas as in command line Maxima - as ASCII-Art.

set_display('none) causes 'one-line' ASCII results - the same as the command line Maxima command display2d:false; does.

Help menu

WxMaxima’s help menu provides access to the Maxima and wxMaxima manual, tips, some example worksheets and in command line Maxima included demos (the demo() command).

Please notice, that the demos write:

At the ’_’ prompt, type ’;’ and <enter> to proceed with the demonstration.

That is valid for command-line Maxima, however in wxMaxima by default it is necessary to continue the demonstration with: CTRL+ENTER

(That can be configured in the Configure->Worksheet->"Hotkeys for sending commands to Maxima" menu.)

---

Troubleshooting

Cannot connect to <em>Maxima</em>

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 unauthorized connections from the internet (and perhaps intercept some connections to the internet, too), but also 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 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 Unix 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.

How to save data from a broken .wxmx file

Internally most modern XML-based formats are ordinary zip files. WxMaxima doesn’t turn on compression, so the contents of .wxmx files can be viewed in any text editor.

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 the information that is stored inside it. This can be done when there is a 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: The .wxmx file is a container format and the XML portion is stored uncompressed. It it is possible to rename the .wxmx file to a .txt file and to use a text editor to recover the XML portion of the file’s contents (it starts with <?xml version="1.0" encoding="UTF-8"?> and ends with </wxMaximaDocument>. Before and after that text you will see some unreadable binary contents in the text editor).

If a text file containing only these contents (e.g. copy and paste this text into a new file) is saved as a file ending in .xml, wxMaxima will know how to recover the text from the document.

I want some debug info to be displayed on the screen before my command has finished

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:

for i:1 thru 10 do (
   disp(i),
   /* (sleep n) is a Lisp function, which can be used */
   /* with the character "?" before. It delays the */
   /* program execution (here: for 3 seconds) */
   ?sleep(3)
)$

Alternatively one can look for the wxstatusbar() command above.

Plotting only shows a closed empty envelope with an error message

This means that wxMaxima could not read the file Maxima that was supposed to instruct Gnuplot to create.

Possible reasons for this error are:

• The plotting command is part of a third-party package like implicit_plot but this package was not loaded by Maxima_’s load() command before trying to plot.
• _Maxima tried to do something the currently installed version of Gnuplot isn’t able to understand. In this case, a file ending in .gnuplot located in the directory, which Maxima_’s variable maxima_userdir is pointing, contains the instructions from _Maxima to Gnuplot. Most of the time, this file’s contents therefore are helpful when debugging the problem.
• Gnuplot was instructed to use the pngCairo library that provides antialiasing and additional line styles, but it was not compiled to support this possibility. Solution: Uncheck the "Use the Cairo terminal for the plot" checkbox in the configuration dialog and don’t set wxplot_pngcairo to true from Maxima.
• Gnuplot didn’t output a valid .png file.

Plotting an animation results in “error: undefined variable”

The value of the slider variable by default is only substituted into the expression that is to be plotted if it is visible there. Using a subst command that substitutes the slider variable into the equation to plot resolves this problem. At the end of section Embedding animations into the spreadsheet, you can see an example.

I lost cell content and undo doesn’t remember

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:

• WxMaxima actually has two undo features: The global undo buffer that is active if no cell is selected and a per-cell undo buffer that is active if the cursor is inside a cell. It is worth trying to use both undo options in order to see if an old value can still be accessed.
• If you still have a way to find out what label Maxima has assigned to the cell just type in the cell’s label and its contents will reappear.
• If you don’t: Don’t panic. In the “View” menu there is a way to show a history pane that shows all Maxima commands that have been issued recently.
• If nothing else helps Maxima contains a replay feature:

playback();

<em>WxMaxima</em> starts up with the message “Maxima process terminated.”

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.

Maxima is forever calculating and not responding to input

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.

My SBCL-based <em>Maxima</em> runs out of memory

The Lisp compiler 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 of 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. 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 for Maxima" field of _wxMaxima_’s configuration dialogue.

Input sometimes is sluggish/ignoring keys on Ubuntu

Installing the package ibus-gtk should resolve this issue. See (https://bugs.launchpad.net/ubuntu/+source/wxwidgets3.0/+bug/1421558) for details.

<em>WxMaxima</em> halts when <em>Maxima</em> processes Greek characters or Umlauts

If your Maxima is based on SBCL the following lines have to be added to your .sbclrc:

(setf sb-impl::*default-external-format* :utf-8)

The folder where this file has to be placed 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)

Note concerning Wayland (recent Linux/BSD distributions)

There seem to be issues with the Wayland Display Server and wxWidgets. WxMaxima may be affected, e.g. that sidebars are not moveable.

You can either disable Wayland and use X11 instead (globally) or just tell, that wxMaxima should use the X Window System by setting: GDK_BACKEND=x11

E.g. start wxMaxima with:

GDK_BACKEND=x11 wxmaxima

Why is the integrated manual browser not offered on my Windows PC?

Either wxWidgets wasn’t compiled with support for Microsoft’s webview2 or Microsoft’s webview2 isn’t installed.

Why is the external manual browser not working on my Linux box?

The HTML browser might be a snap, flatpack or appimage version. All of these typically cannot access files that are installed on your local system. Another reason might be that maxima or wxMaxima is installed as a snap, flatpack or something else that doesn’t give the host system access to its contents. A third reason might be that the maxima HTML manual isn’t installed and the online one cannot be accessed.

Can I make <em>wxMaxima</em> output both image files and embedded plots at once?

The worksheet embeds `.png files. WxMaxima allows the user to specify where they should be generated:

wxdraw2d(
    file_name="test",  /* extension .png automatically added */
    explicit(sin(x),x,1,10)
);

If a different format is to be used, it is easier to generate the images and then import them into the worksheet again:

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)
);

Can I set the aspect ratio of an embedded plot?

Use the variable wxplot_size:

wxdraw2d(
    explicit(sin(x),x,1,10)
),wxplot_size=[1000,1000];

After upgrading to MacOS 13.1 plot and/or draw commands output error messages like

1 HIToolbox 0x00007ff80cd91726 _ZN15MenuBarInstance22EnsureAutoShowObserverEv + 102
2 HIToolbox 0x00007ff80cd912b8 _ZN15MenuBarInstance14EnableAutoShowEv + 52
3 HIToolbox 0x00007ff80cd35908 SetMenuBarObscured + 408
...

This might be an issue with the operating system. Disable the hiding of the menu bar (SystemSettings => Desktop & Dock => Menu Bar) might solve the issue. See wxMaxima issue #1746 for more information.

Logging

Log messages might be helpful to debug problems. WxMaxima can log many events. Most log entries will be helpful for developers, especially in case of problems or bugs. If you run a "Release"-Build, the log windows is not shown by default, if you run a development version, it is shown by default as a second window. You can enable and disable this window using the "View->Toggle log window" menu entry.

Messages are not 'lost', if the log window is not shown, if you select to show the log window later, you will see past log messages (if you did not clear the messages).

Such messages may be helpful, when you create bug reports (or trying to find a bug by yourself).

Log messages can (additionally) be printed to STDERR, when using the command line option "--logtostderr". On Windows a separate text console will be opened, as a Windows GUI application does not have the standard IO connected.

---

FAQ

Is there a way to make more text fit on a LaTeX page?

Yes. Use the LaTeX package "geometry" to specify the size of the borders.

You can add the following line to the LaTeX preamble (for example by using the respective field in the config dialogue ("Export"->"Additional lines for the TeX preamble"), to set borders of 1cm):

\usepackage[left=1cm,right=1cm,top=1cm,bottom=1cm]{geometry}

Is there a dark mode?

If wxWidgets is new enough, wxMaxima will automatically be in dark mode if the rest of the operating system is. The worksheet itself is by default equipped with a bright background. But it can be configured otherwise. Alternatively, there is a View/Invert worksheet brightness menu entry that allows to quickly convert the worksheet from dark to bright and vice versa.

<em>WxMaxima</em> sometimes hangs for several seconds once in the first minute

WxMaxima delegates some big tasks like parsing Maxima_’s >1000-page-manual to background tasks, which normally goes totally unnoticed. At the moment the result of such a task is needed, though, it is possible that _wxMaxima needs to wait a couple of seconds before it can continue its work.

Especially when testing new locale settings, a message box "locale ’xx_YY’ can not be set" occurs

(The same problem can occur with other applications too). The translations seem okay after you click on ’OK’. WxMaxima does not only use its own translations but the translations of the wxWidgets framework too.

These locales maybe not present in the system. On Ubuntu/Debian systems they can be generated using: dpkg-reconfigure locales

How can I use symbols for real numbers, natural numbers (ℝ, ℕ), etc.?

You can find these symbols in the Unicode sidebar (search for ’double-struck capital’). But the selected font must also support these symbols. If they do not display properly, select another font.

How can a Maxima script determine, if it is running under wxMaxima or command line Maxima?

If wxMaxima is used, the Maxima variable maxima_frontend is set to wxmaxima. The Maxima variable maxima_frontend_version contains the wxMaxima version in this case.

If no frontend is used (you are using command line Maxima), these variables are false.

---

Command-line arguments

Usually you can start programs with a graphical user interface just by clicking on a desktop icon or desktop menu entry. WxMaxima - if started from the command line - 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=<str>: Open the filename given as an argument to this command-line switch
• -e or --eval: Evaluate the file after opening it.
• -b or --batch: If the command-line opens a file all cells in this file are evaluated and the file is saved afterward. This is for example useful if the session 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.
• --logtostderr: Log all "debug messages" sidebar messages to stderr, too.
• --pipe: Pipe messages from Maxima to stdout.
• --exit-on-error: Close the program on any maxima error.
• -f or --ini=<str>: Use the init file that was given as an argument to this command-line switch
• -u, --use-version=<str>: Use maxima version <str>.
• -l, --lisp=<str>: Use a Maxima compiled with Lisp compiler <str>.
• -X, --extra-args=<str>: Allows to specify extra Maxima arguments
• -m or --maxima=<str>: allows specifying the location of the maxima binary
• --enableipc: Lets Maxima control wxMaxima via interprocess communications. Use this option with care.
• --wxmathml-lisp=<str>: Location of wxMathML.lisp (if not the built-in should be used, mainly for developers).

Instead of a minus, some operating systems might use a dash in front of the command-line switches.

---

About the program, contributing to wxMaxima

wxMaxima is mainly developed using the programming language C++ using the wxWidgets framework, as build system we use CMake, a small part is written in Lisp. You can contribute to wxMaxima, join the wxMaxima project at https://github.com/wxMaxima-developers/wxmaxima, if you have knowledge of these programming languages and want to help and contribute to the open source project wxMaxima.

But not only programmers are necessary! You can also contribute to wxMaxima, if you help to improve the documentation, find and report bugs (and maybe bugfixes), suggest new features, help to translate wxMaxima or the manual to your language (read the README.md in the locale subdirectory how wxMaxima and the manual can be translated).

Or answer questions of other users in the discussion forum.

The source code of wxMaxima is documented using Doxygen here.

The program is nearly self-contained, so except for system libraries (and the wxWidgets library), no external dependencies (like graphic files or the Lisp part (the wxmathML.lisp-file) is needed, these files are included in the executable.

If you are a developer, you might want to try out a modified wxmathML.lisp-file without recompiling everything, one can use the command line option --wxmathml-lisp=<str> to use another Lisp file, not the included one.