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?
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.
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.
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.
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.
I calcoli immessi in wxMaxima vengono eseguiti dallo strumento della riga di comando Maxima in background.
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.
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.
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).
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.
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)
).
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).
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.
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).
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).
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.
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.
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.
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.
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:
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.
Il materiale sviluppato in una sessione wxMaxima può essere archiviato per un uso successivo in uno dei seguenti tre modi:
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.
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.
.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.
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.
Per alcune variabili di configurazione comuni wxMaxima offre due modalità di configurazione:
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.
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]$ ),
Questa opzione abilita due cose:
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:
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
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.
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
x
or y
is a single letter ory
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.
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)
? )$
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.
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).
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.
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.
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.
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.
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(
makelist(i,i,1,360,3),
α,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*π
) )$
For those more familiar with plot
than with
draw
, there is a second set of functions:
with_slider
ewxanimate
.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
) )$
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))
);
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.
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.
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.
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.
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.
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.
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.
Draws a title on the upper end of the diagram,
Sets up the axis.
(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.
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.
Sets the line colour for the following plots the current draw command contains.
Sets the fill colour for the following plots the current draw command contains.
Pops up a wizard that allows to set up grid lines.
Allows to select an adequate point in the speed vs. accuracy tradeoff that is part of any plot program.
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");
The config dialogue of wxMaxima offers to edit two files with commands that are executed on startup:
maxima-init.mac
wxmaxima-init.mac
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;
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.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.
WxMaxima provides a few functions that gather bug reporting information about the current system:
wxbuild_info()
gathers information about the currently
running version of wxMaximawxbug_report()
tells how and where to file bugsMaxima’s box()
command causes wxMaxima
to print its argument with a red foreground, if the second argument to
the command is the text highlight
.
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.
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.
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)
? )$
This means that wxMaxima could not read the file Maxima that was supposed to instruct gnuplot to create.
Possible reasons for this error are:
implicit_plot
but this package was not loaded by
Maxima’s load()
command before trying to
plot..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.wxplot_pngCairo
to true from Maxima..png
file.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.
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();
One possible reason is that Maxima cannot be found in the location that is set in the “Maxima” tab of wxMaxima’s configuration dialog and therefore won’t run at all. Setting the path to a working Maxima binary should fix this problem.
It is theoretically possible that wxMaxima doesn’t realize that Maxima has finished calculating and therefore never gets informed it can send new data to Maxima. If this is the case “Trigger evaluation” might resynchronize the two programs.
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.
Installing the package ibus-gtk
should resolve this
issue. See (https://bugs.launchpad.net/ubuntu/+source/wxwidgets3.0/+bug/1421558)
for details.
If your Maxima is based on SBCL the following lines have to
be added to your .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)
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)
);
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]; ),
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.
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}
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.
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.
(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
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.
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.
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.