WxMaxima

1 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.

Prima di esaminare i contenuti della guida, è meglio evidenziare alcuni punti relativi alla sua consultazione. Immediatamente di seguito c’è un breve sommario. Facendo clic su uno degli elementi elencati si sposta il cursore nella parte superiore della sezione indicata del manuale. Facendo clic su Sommario si sposta il cursore su un sommario esteso. Questa tabella estesa può essere usata per arrivare direttamente a parti specifiche del manuale. Il collegamento Contenuti viene visualizzato lungo il testo a scopo di orientamento nella navigazione.

WxMaxima basics

I comandi che wxMaxima aggiunge a Maxima

What to do if wxMaxima does not work as expected?

Domande ricorrenti

The command-line arguments wxMaxima supports.

How can you contribute to the development of wxMaxima?


2 Introduzione a wxMaxima

2.1 Maxima e wxMaxima

Nel dominio open source, i grandi sistemi sono normalmente suddivisi in progetti più piccoli che sono più facili da gestire per piccoli gruppi di sviluppatori. Ad esempio, un programma di masterizzazione di CD sarà costituito da uno strumento a riga di comando che effettivamente masterizza il CD e da un’interfaccia utente grafica che consente agli utenti di utilizzarlo senza dover conoscere tutte le opzioni della riga di comando, e di fatto senza utilizzare affatto la riga di comando. Un vantaggio di questo approccio è che il lavoro di sviluppo che è stato investito nel programma a riga di comando può essere condiviso da molti programmi: lo stesso programma a riga di comando del masterizzatore CD può essere utilizzato come plug-in “invia-al-CD” per un’applicazione di gestione file, per la funzione “masterizza su CD” di un lettore musicale e come masterizzatore di CD per uno strumento di backup su DVD. Un altro vantaggio è che suddividere una grande attività in parti più piccole consente agli sviluppatori di fornire diverse interfacce utente per lo stesso programma.

Un sistema di algebra computazionale (CAS) come Maxima si inserisce in questo quadro. Un CAS può fornire la logica dietro un’applicazione di calcolatrice di precisione arbitraria o può fare trasformazioni automatiche di formule sullo sfondo di un sistema più grande (ad esempio, [Sage] (https://www.sagemath.org/)). In alternativa, può essere utilizzato direttamente come sistema indipendente. Maxima è utilizzabile tramite riga di comando. Spesso, tuttavia, un’interfaccia come wxMaxima si rivela un modo più efficiente per accedere al software, in particolare per i nuovi utenti.

2.1.1 Maxima

Maxima è un sistema di algebra computazionale (CAS) completo. Un CAS è un programma in grado di risolvere problemi matematici riorganizzando le formule e trovando una formula che risolve il problema invece di emettere semplicemente il valore numerico del risultato. In altre parole, Maxima può fungere da calcolatrice che fornisce rappresentazioni numeriche di variabili e può anche fornire soluzioni analitiche. Inoltre, offre una gamma di metodi numerici di analisi per equazioni o sistemi di equazioni che non possono essere risolti analiticamente.

schermata di Maxima, riga di comando

Ampia documentazione per Maxima è [disponibile su Internet] (https://maxima.sourceforge.io/documentation.html). Parte di questa documentazione è disponibile anche nel menu di aiuto di wxMaxima. Premendo il tasto Guida (sulla maggior parte dei sistemi il tasto F1), la funzione di guida sensibile al contesto di wxMaxima passa automaticamente alla pagina di manuale di Maxima per il comando sotto il cursore.

2.1.2 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.

wxMaxima window

I calcoli immessi in wxMaxima vengono eseguiti dallo strumento della riga di comando Maxima in background.

2.2 Nozioni di base sulle cartelle di lavoro

Gran parte di wxMaxima si spiega da sé, ma alcuni dettagli richiedono attenzione. Questo sito contiene una serie di cartelle di lavoro che affrontano vari aspetti di wxMaxima. Lavorare attraverso alcuni di questi (in particolare il “tutorial (wx)Maxima di 10 minuti”) può essere utile ad aumentare la propria familiarità sia con il contenuto di Maxima sia con l’uso di wxMaxima per interagire con Maxima. Questo manuale si concentra sulla descrizione degli aspetti di wxMaxima che probabilmente non sono evidenti e che potrebbero non essere trattati nel materiale online.

2.2.1 L’approccio della cartella di lavoro

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.

Se il testo viene digitato in wxMaxima, si crea automaticamente una nuova cella del foglio di lavoro. Il tipo di questa cella può essere selezionato nella barra degli strumenti. Se viene creata una cella di codice, la cella può essere inviata a Maxima, il che fa sì che il risultato del calcolo venga visualizzato sotto il codice. Di seguito viene mostrata una coppia di tali comandi.

Input/output cell

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.

Oltre alle celle di ingresso, wxMaxima consente l’uso di celle di testo per la documentazione, celle immagine, celle titolo, celle capitolo e celle sezione. Ogni cella ha una propria memoria degli annullamenti, quindi eseguire la correzione modificando i valori di più celle e quindi ripristinare gradualmente le modifiche non necessarie, è piuttosto semplice. Inoltre, il foglio di lavoro stesso ha una memoria degli annullamenti globale che può annullare le modifiche, le aggiunte e le eliminazioni delle celle.

La figura seguente mostra diversi tipi di celle (celle titolo, celle sezione, celle sottosezione, celle testo, celle ingresso/uscita e celle immagine).

Esempio di celle wxMaxima diverse

2.2.2 Celle

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

Il comportamento predefinito di wxMaxima quando viene inserito del testo è creare automaticamente una cella matematica. È possibile creare celle di altro tipo utilizzando il menu Cella, utilizzando i tasti di scelta rapida visualizzati nel menu o utilizzando l’elenco a discesa nella barra degli strumenti. Una volta creata la cella non-matematica, tutto ciò che viene digitato nel file viene interpretato come testo.

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

/*” marca l’inizio del commento, mentre “*/” la sua fine.

2.2.3 Cursori orizzontali e verticali

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:

Quando si avvia wxMaxima, è visibile solo un cursore orizzontale lampeggiante. Se si inizia a digitare, viene creata automaticamente una cella matematica e il cursore diventa verticale (si vedrà una freccia destra come “prompt”, dopo l’elaborazione della cella matematica (CTRL+INVIO), si noteranno, ad esempio, le etichette (%i1) e (%o1)).

(blinking) cursore orizzontale dopo l’avvio di wxMaxima

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).

(blinking) cursore orizzontale tra celle

2.2.4 Invio delle celle a 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.

2.2.5 Autocompletamento comandi

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.

ezUnits

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).

2.2.5.1 Caratteri greci

I computer tradizionalmente memorizzavano i caratteri in valori a 8 bit. Ciò consente un massimo di 256 caratteri diversi. Tutte le lettere, i numeri e i simboli di controllo (fine trasmissione, fine stringa, linee e bordi per disegnare rettangoli per i menu, ecc. .) di quasi tutte le lingue possono essere compresi in tale limitazione.

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:

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).

Lo stesso meccanismo permette anche di inserire alcuni simboli matematici vari:

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.

ESC 61 ESC diventa quindi una 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).

2.2.6 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.

2.2.7 Pannelli laterali

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.

Esempio di diversi pannelli laterali

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.

Eleva o abbassa le intestazioni nel riquadro laterale del sommario

2.2.8 Uscita MathML

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.

2.2.9 Supporto Markdown

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

Testo normale
 * Un elemento, livello indentazione 1
 * Un altro elemento a livello indentazione 1
   * Un elemento al secondo livello di indentazione
   * Un secondo elemento al secondo livello di indentazione
 * Un terzo elemento al primo livello di indentazione
Testo normale

WxMaxima will recognize text starting with > chars as block quotes:

Testo normale
> citazione citazione citazione
> citazione citazione citazione
> citazione citazione citazione
Testo normale

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.

2.2.10 Scorciatoie da tastiera

La maggior parte dei tasti di scelta rapida si trova nel testo dei rispettivi menu. Dal momento che sono effettivamente presi dal testo del menu e quindi possono essere personalizzati dalle traduzioni di wxMaxima per soddisfare le esigenze degli utenti della tastiera locale, non vengono documentati quì. Alcuni tasti di scelta rapida o alias di tasti di scelta rapida, tuttavia, non sono documentati neanche nei menu:

2.2.11 TeX grezzo nell’esportazione TeX

Se una cella di testo inizia con TeX:, l’esportazione TeX contiene il testo letterale che segue l’indicatore TeX:. L’utilizzo di questa funzione consente l’inserimento del marcatore TeX all’interno della cartella di lavoro wxMaxima.

2.3 Formati di file

Il materiale sviluppato in una sessione wxMaxima può essere archiviato per un uso successivo in uno dei seguenti tre modi:

2.3.1 .mac

I file .mac sono normali file di testo che contengono comandi Maxima. Possono essere letti usando il comando batch() o load() di Maxima o la voce di menu File/File batch di wxMaxima.

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.

Loading a file with batch()

Attenzione: Sebbene il file Quadratic.mac abbia una normale estensione Maxima (.mac), può essere letto solo da wxMaxima, poiché il comando wxdraw2d() è un’estensione wxMaxima di Maxima.

Si può usare i file .mac per scrivere la propria libreria di macro. Ma dal momento che non contengono informazioni strutturali sufficienti, non possono essere rilette come sessioni wxMaxima.

2.3.2 .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.

2.3.3 .wxmx

Questo formato di file basato su XML salva il foglio di lavoro completo, inclusi elementi come il fattore di zoom e la watchlist. È il formato di file preferito.

2.4 Opzioni di configurazione

Per alcune variabili di configurazione comuni wxMaxima offre due modalità di configurazione:

Configurazione wxMaxima 1

2.4.1 Frequenza di quadro animazioni predefinita

La frequenza di quadro dell’animazione usata per le nuove animazioni è conservata nella variabile wxanimate_framerate. Il valore iniziale che questa variabile conterrà in un nuovo foglio di lavoro può essere modificato utilizzando la finestra di configurazione.

2.4.2 Dimensione predefinita dei grafici per le nuove sessioni maxima

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.

Per impostare la dimensione del grafico di un singolo grafico è possibile utilizzare solo la seguente notazione che imposta il valore di una variabile per un solo comando:

wxdraw2d(
   explicit(
       x^2,
       x,-5,5
   )
), wxplot_size=[480,480]$

2.4.3 Abbina parentesi nei controlli di testo

Questa opzione abilita due cose:

2.4.4 Non salvare il foglio di lavoro automaticamente

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.

Se questa opzione non è impostata, wxMaxima si comporta più come una moderna app per cellulari:

2.4.5 Dove viene salvata la configurazione?

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).

Se si sta usando Windows, la configurazione verrà memorizzata nel registro di sistema. Le voci per wxMaxima sono nella seguente posizione nel registro: HKEY_CURRENT_USER\Software\wxMaxima


3 Estensioni a Maxima

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.

3.1 Variabili pedice

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

How variables are autosubscripted using wxsubscripts

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.

3.2 Feedback utente nella barra di stato

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 (
    /* Dice all'utente a che punto è l'esecuzione */
    wxstatusbar(concat("Pass ",i)),
    /* (sleep n) è una funzione Lisp, che può essere usata */
    /* con prima il carattere "?". Ritarda */
    /* l'esecuzione del programma (qui per 3 secondi) */
    ?sleep(3)
)$

3.3 Diagrammi

Fare diagrammi (che ha fondamentalmente a che fare con la grafica) è un luogo in cui un’interfaccia utente grafica dovrà fornire alcune estensioni al programma originale.

3.3.1 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).

3.3.2 Rendere i diagrammi incorporati più grandi o più piccoli

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
    )
)$

Se è necessario modificare la dimensione di un solo grafico, Maxima fornisce un modo canonico per modificare un attributo solo per la cella corrente. Con questo metodo di utilizzo la specifica wxplot_size = [value1, value2] viene aggiunta al comando wxdraw2d() e non fa parte del comando wxdraw2d.

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.

3.3.3 Grafici di qualità superiore

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.

3.3.4 Aprire grafici incorporati in finestre interattive gnuplot

Se un grafico è stato generato utilizzando i comandi di tipo wxdraw (wxplot2d e wxplot3d non sono supportati da questa funzione) e la dimensione del file del progetto gnuplot sottostante non è troppo alta wxMaxima offre un menu accessibile tramite clic con il pulsante destro del mouse che permette di aprire il grafico in una finestra gnuplot interattiva.

3.3.5 Apertura della console dei comandi di gnuplot in finestra plot

Su MS Windows, se nella variabile gnuplot_command di Maxima “gnuplot” viene sostituito da “wgnuplot”, gnuplot offre la possibilità di aprire una finestra della console, dove è possibile inserire i comandi gnuplot. Sfortunatamente, l’abilitazione di questa funzione fa sì che gnuplot “rubi” il focus della tastiera per un breve periodo ogni volta che viene preparato un grafico.

3.3.6 Incorporamento di animazioni nel foglio di calcolo

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.

I primi due argomenti per with_slider_draw sono il nome della variabile che si trova tra i grafici e un elenco dei valori di queste variabili. Gli argomenti che seguono sono gli argomenti ordinari per 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
);

La stessa funzionalità per i grafici 3D è accessibile come with_slider_draw3d, che consente di ruotare i grafici 3D:

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
    )
)$

Se ciò che conta è la forma generale del grafico, potrebbe bastare spostare leggermente il grafico per rendere intuibile la sua natura 3D:

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
    )
)$

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

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)
)$

Se a Maxima viene chiesto esplicitamente di sostituire il valore del dispositivo di scorrimento, il tracciato funziona invece correttamente:

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
    )
)$

3.3.7 Apertura di più grafici in più finestre contemporaneamente

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));

È anche possibile tracciare più grafici nella stessa finestra:

    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))
     );

3.3.8 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.

3.3.8.1 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.

3.3.8.2 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.

3.3.8.3 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.

3.3.8.4 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.

3.3.8.5 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.

3.3.8.6 Punti

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.

3.3.8.7 Diagram title

Draws a title on the upper end of the diagram,

3.3.8.8 Assi

Sets up the axis.

3.3.8.9 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.

3.3.8.10 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.

3.3.8.11 Line colour

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

3.3.8.12 Colore riempimento

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

3.3.8.13 Griglia

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

3.3.8.14 Accuracy

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

3.4 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");

3.5 Startup files

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

These files are in the Maxima user directory (usually maxima in Windows, .maxima otherwise) in the user’s home directory / user profile directory. The location can be found out with the command: maxima_userdir;

3.6 Special variables wx…

3.7 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.

A third table example

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

Another table_form example

3.8 Bug reporting

WxMaxima provides a few functions that gather bug reporting information about the current system:

3.9 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.


4 Risoluzione dei problemi

4.1 Cannot connect to Maxima

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.

4.2 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.

4.3 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)
)$

4.4 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:

4.5 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.

4.6 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:

playback();

4.7 WxMaxima 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.

4.8 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.

4.9 My SBCL-based Maxima 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.

sbcl memory

4.10 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.

4.11 WxMaxima halts when Maxima 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)

4.12 Diagrammi

4.12.1 Can I make wxMaxima 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",
    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)
);

4.12.2 Can I set the aspect ratio of a plot?

Not directly using Maxima. But there are Gnuplot commands for it:

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

4.12.3 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.


5 FAQ

5.1 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}

5.2 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.

5.3 WxMaxima 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.

5.4 Especially when testing new locale settings, a message box “locale ‘xx_YY’ can not be set” occurs

Locale warning

(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

5.5 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.


6 Argomenti della riga di comando

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.

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


7 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 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.