$\chi$CAS for Numworks calculatorsBernard.Parisse@univgrenoblealpes.fr2024 
Abstract: This document explains how to run efficiently $\chi$CAS on Numworks calculators (N0110, N0115, N0120). $\chi$CAS is a port of the Giac/Xcas computer algebra system (CAS) for these calculators. Main features are: CAS, spreadsheet, 2d/3d interactive/analytic geometry, like on highend CAS calculators, and more in some areas.This document is interactive, you can modify and run commands by clicking in the ok button or by hitting Enter.
Contents
 1 Introduction and installation
 2 First steps
 3 Common CAS commands
 4 Probabilities and statistics
 5 Graphics
 6 Programs
 7 The 2d editor.
 8 Managing sessions
 9 Keyboard shortcuts.
 10 Remarks
 11 $\chi$CAS applications
 12 Copyright and Thanks to.
 13 Developer infos.
1 Introduction and installation
$\chi$CAS is a port of the Giac/Xcas computer algebra system (CAS) for the following Numworks calculators (N0110, N0115, N0120).
 In some countries, CAS calculators are not allowed during exams, it is the user responsability to check the rules before running $\chi$CAS in an exam. The authors shall not be held responsible for misuse of $\chi$CAS in exam conditions.
 $\chi$CAS is not compatible with exam mode except on old “unlocked” N0110. In countries where CAS calculators are allowed, there is no reason to forbid $\chi$CAS. If many teachers send a mail to Numworks asking for $\chi$CAS compatibility, we increase the chances that Numworks sign the addin and make it compatible with exam mode.
The following versions of $\chi$CAS are available for the Numworks :
 The initial port, for old Numworks N0110 with Epsilon version at most 15.5 (or unlocked N0110 with Omega or Upsilon). This version is compatible with exam mode.
 An N0110/N0115 external app running on Epsilon 22 or 23. This app is not compatible with exam mode. It is available in short and long version. The long version has full online Xcas documentation and additional support for help in German, Spanish and Greek.
 An N0120 external app running on Epsilon 22 or 23. This app is not compatible with exam mode. It is available in short and long version. The long version has full online Xcas documentation and additional support for help in German, Spanish and Greek.
Refer to the developer section 13 for technical information.
1.1 Calculator
If you have a “locked” Numworks with Epsilon version 16 or above, it is most probably required that you update your Epsilon version. To do that, press the 6 button, hold it down, press RESET, release the 6 button and go on Numworks site to update, then close the Numworks site tab/window.
To install or update $\chi$CAS, connect the USB cable of the calculator, and open a webusb compatible browser on this link click on Install on the top bar and follow instructions.
1.2 Simulator
$\chi$CAS can be installed inside the Numworks simulator, but the current Epsilon license ("All rights reserved”) does currently not allow redistribution of binaries. You can either run Upsilon (based on Epsilon 15.5)+Xcas or compile the simulator yourself. Run Upsilon+Xcas:

Version without installation,
runs inside a browser like Firefox, Chrome,....
Shortcut to run Xcas from Numworks main menu: press the Back key.
With this version, you can share a session by displaying a QR code: press Power (on a real calculator, you can display the QR code by saving the session: press shift EXE then 2 or 3). Press Back to return to the shell.  Windows: download upsilon.zip, open the archive and run upsilon.exe
 Mac, stable version (checked on OS 12.7.1 and 14.4): download
Upsilon.dmg,
open the disk image Upsilon.dmg
Many thanks to Adrien Bertrand who helped me doing the port and build the signed package.  Linux or compile from sources :
wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/upsilon.tar.bz2 tar xfj upsilon.tar.bz2 cd Upsilon wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/ext.tar.bz2 tar xfj ext.tar.bz2 wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/upsilon_cas_full.tgz tar xfz upsilon_cas_full.tgz
then runmksimu
(Linux) ormkmac
(Mac) ormkwin
(Windows). Target javascript can be compiled with emscripten 1.40 and scriptmkw
, it requires versions of GMP, MPFR and MPFI libraries compiled withfPIC
, these libraries can be found in emgiac3, this directory contains a copy of an install of emscripten 1.40.1 on Ubuntu 20x86_64
architecture.
Short procedure to compile Epsilon 22+Xcas, for more details, refer to 13)

Windows
 Install msys2/mingw64
 Open a terminal mingw64 from Windows main menu, submenu msys2. In the option menu of the windows (up left corner) select Keys, then check Ctrlshiftletter shortcut, this enables paste with CtrlshiftV.
 copypaste the following commands (ctrlc then ctrlshiftv)
pacman S wget
wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/nwwin
./nwwin
Wait some time. If everything went well, the simulatorepsilon.exe
will open. The simulator executable isc:\msys64\home\username\epsilon\epsilon.exe
whereusername
is your Windows username. You can move it to another folder or copy it on another PC.
Beware that software licenses do not allow public redistribution.
 Mac :
 From launchpad, type Terminal in the research field, then Enter, this will open a Terminal.
 Download nwmac, check that it is in your Downloads folder.
 Copypaste (commandc and commandv) the command
~/Downloads/nwmac
Wait some time. If everything went well, the simulator will open. It has been copied to/Applications
and may be opened like any other application.  Optionnal, if you want to copy the simulator on another Mac
A packageKhicasnw.pkg
has been created in your Download directory. Open the Mac disk utility, in the File menu select New image, create a disk image. Copy the package to the disk image, eject the disk image from Finder. Now you can copy the disk image (by net or USB key) on another Mac. On the other Mac, open the disk image from Finder then click on the package while pushing the Control key and install.
Beware that software licenses do not allow public redistribution.
 Linux : see 13
Simulator info
Run upsilon.exe
(Windows),
or upsilon.app
in Applications
(Mac),
or ./simu
from epsilon
directory (Linux).
Press Esc to run KhiCAS (or move to KhiCAS at the end of
the Numworks main menu and press Enter).
Note that the shift calculator key does not link to the shift
key of the calculator, so that you can enter a shifted keystroke
from the PC keyboard. Click on the shift key of the simulator
or type the PC left alt key (or Mac left opt key) to simulate a shift key.
Type CtrlP to save a screenshot, note that Linux screenshot is saved in
/tmp/epsilon.png
, rename it before doing another screenshot.
ShiftCtrlP will copy the screen to the clipboard on Mac only.
The simulator can emulate user flash with a tar file named
scripts.tar
. You can create this file with the standard tar
program, archiving several Python scripts and/or Xcas sessions
(saved with Xcas in the File, Export, HP Prime/Casio).
The file khi92.tar may be used as an example, it is proposed when
installing KhiCAS on the Numworks hardware calculator, just
rename it as scripts.tar
and copy to
Documents
folder on a Mac or in the current
directory.
The files in the tarfile will be listed in the file menu and may be modified
from inside KhiCAS in the simulator.
If you want to have debug support, edit build/defaults.mak
and exchange the #
at line 22 and 23, and recompile.
Note that Python support will not work on x86 if compiled with
debug enabled, the nlr*
object files should be compiled
without g
, this can be achieved by compiling everything
in debug mode, then modify defaults.mak
, then
touch python/port/mpconfigport.h
, recompile.
2 First steps
From the main menu (HOME), move the cursor to the $\chi$CAS icon and hit EXE. This opens the “shell” (or history) where you can write most Xcas commands. The Toolbox key will open a menu of important CAS commands, the most commonly CAS commands may be retrieved with fast menus obtained by pressing shift followed by a key of the lower part of the Numworks keyboard (keys without a yellow legend). The application menu (save/restore sessions, ...) is assigned to shift EXE.
For example, type
1/2+1/6
then EXE, you should see the result 2/3
displayed below.
Hint : If you can not find a character on the calculator keyboard, press
shift *
.
You can copy a level from the history of commands by hitting the
up and down arrow keys (once or more) and EXE. Then you can
modify the command and run it with EXE. For example, up arrow twice,
EXE, replace 1/6
by 1/3
and hit EXE.
The last result is stored in ans()
, hit the Ans
calculator key to get it.
It is recommended to store the result in a variable if you want
to reuse it later. There are two ways to store a value in a
variable

rightstore with
=>
using the $\rightarrow$ key (shifted $x^y$ key, labelled F in alpha mode), for example2=>A
stores 2 in variable A. Now, every time you writeA
in a computation, it will be replaced by 2.  leftstore with
:=
(alpha $x,n,t$ keys then shift $\pi$ keys), for exampleA:=2
does the same as2=>A
. Since it requires 4 keystrokes,=
(2 keystrokes) is accepted as a synonym for most simple commands.
The most popular Xcas commands are available from shift1 (algebra)
shift2 (calculus) and shift3 (plot), from various shortcuts (cf. section
9),
or from the cmds (Toolbox), where
they is a short online help with an example.
Hit Toolbox (cmds), choose a submenu,
for example Algebra
, hit EXE,
move the selection to a command, for example factor
.
Now Toolbox will display a short help with an example. Hit EXE or Ans
to copy the example in the commandline.
You can run it as is (EXE) or modify it and run it (EXE) if
you want to factor another polynomial.
When a command returns an expression, it is displayed in 2d mode. You can move with the pad if the expression is larger than the display. Type shift5 to modify the fontsize. Type Back to go back to the shell. The 2d view is in fact a 2d editor that will be explained later.
Now, try to type the command plot(sin(x))
.
Hint: type shift3 (plot), then EXE.
When a command returns a graph, it will be displayed in a 2d frame.
You can modify the displayed area with +
or 
(zoom in or out, /
(orthonormalisation of the frame),
*
(autoscale).
Type Toolbox to modify the graphic window settings Xmin, Xmax, Ymin, Ymax.
Type Back to go back to the shell.
The KhiCAS File menu (shiftEXE) has an item Clear
that will erase
the display. This will not clear the variables, to achieve that
type VARS
, select the last item (restart
)
and confirm with EXE.
Hit HOME to leave $\chi$CAS. Variables and history are saved each time you run a command with EXE, they will be restored if you come back to $\chi$CAS.
3 Common CAS commands
3.1 Expand and factor
From Toolbox commands catalog, select Algebra
, or type shift1.

factor
: factorization. Shortcut=>*
($\rightarrow$ key then *), for example
. Runcfactor
to factor over $\C$. partfrac
: expands a polynomial or performs partial fraction expansion over a fraction. Shortcut=>+
($\rightarrow$ then + key), for example
or
.simplify
: tries to simplify an expression. Shortcut=>/
($\rightarrow$ key then /), for example
ratnormal
: rewrite as an irreducible fraction.
3.2 Calculus
From Toolbox commands catalog, select Calculus
, or type shift2

diff
: derivative. Shortcut'
for derivative with respect to $x$, example
and
are equivalent. For $n$thderivative, add $n$, for example 3rd derivative
. integrate
: antiderivative (1 or 2 or 4 arguments) for example
or
for $\int \frac{1}{t^41} \ dt$
Defined integration with 4 arguments, for example
computes $\int_0^\pi \sin(x)^4 \ dx$. For an approximate computation, enter one boundary as an approx number, for example
limit
: limit of an expression. Example
tabvar
: table of variations of an expression. for example
one can check with the graph
taylor
andseries
: Taylor expansion or asymptotic serie expansion, for example
Addpolynomial
if you do not want to have the remainder term.sum
: discrete summation, for example
computes $\sum_{k=1}^n k^2$,
computes the sum and rewrites it factored.
3.3 Solvers
From Toolbox commands catalog, select Solve
.

solve
solves an equation exactly. Takes the variable to solve for as second argument, unless it isx
, for example
.
If exact solving fails, runfsolve
for approx solving, either with an iterative method starting with a guess
or by dichotomy
For complex solutions, runcsolve
.
It is possible to restrict solutions using assumptions on the variable, for example
then
. solve
can also solve (simple) polynomial systems, enter a list of equations as 1st argument and a list of variables as 2nd argument, for example intersection of a circle and a line:
 Run
linsolve
to solve linear systems. enter a list of equations as 1st argument and a list of variables as 2nd argument, example:
 Run
desolve
to solve exactly a differential equation. for example, to solve $y'=2y$, typedesolve(y'=2y)
.
Another example with an initial condition:
desolve([y'=2y,y(0)=1],x,y)
Runodesolve
for approx solving orplotode
for a graphic representation of the approx. solution. rsolve
solves some recurrence relations $u_{n+1}=f(u_n,...)$, for example to solve the arithmeticogeometric recurrence $u_{n+1}=2u_n+3, u_0=1$, type:
3.4 Arithmetic
When required, the distinction between integer arithmetic
and polynomial arithmetic is done by a prefix i
for
integer commands. For example ifactor
for integer factorization
and factor
for polynomial factorization
(or cfactor
for polynomial factorization over $\C$).
Some commands work for integers and polynomials, like
gcd
and lcm
.
3.4.1 Integers
From Toolbox catalog, select Arithmetic, Crypto
. Shortcut
shift S$\leftrightarrow$D

iquo(a,b)
,irem(a,b)
quotient and remainder of euclidean division of two integers.
isprime(n)
checks whether $n$ is prime. This is a probabilisitic test for large values of $n$.
ifactor(n)
factorizes an integer (not too large, since algorithms used are trial division and Pollard$\rho$, there is not enough RAM for quadratic sieve), for example
Shortcut $\rightarrow$ then * (=>*
)gcd(a,b)
,lcm(a,b)
GCD and LCM of two integers or polynomials.
iegcd(a,b)
(integer extended GCD) returns 3 integers $u,v,d$ such that $au+bv=d$ where $d$ is the GCD of $a$ et $b$, $u<b$ and $v<a$.
ichinrem([a,m],[b,n])
returns (if possible) $c$ such that $c=a \pmod m$ and $c=b \pmod n$ (if $m$ are $n$ coprime, $c$ exists).
powmod(a,n,m)
returns $a^n \pmod m$ computed by the fast modular powering algorithm
asc
converts a string to a list of ASCII code,char
converts back a list to a string. These commands may be used to easily write cryptographic algorithms with string messages.
3.4.2 Polynomials
From Toolbox catalog, select Polynomials
.
The default variable is $x$, otherwise you can specify it as last
optional argument. For example degree(x^2*y)
or degree(x^2*y,x)
return 2,
degree(x^2*y,y)
returns 1.
Polynomials may have
coefficients in the rationals (example 2/3*x+1
), or floats
(example 0.5*x+1
),
or in $\mathbb{Z}/p\mathbb{Z}$
(example 3*x+5 mod 7
)
or in a Galois fields (example, call once GF(2,4)
to define the finite field with 16 elements with generator
g
by default, then
g^2*x+g+1
)

coeff(P,n)
coefficient of $x^n$ in $P$,lcoeff(P)
leading coefficient of $P$, for example
degre(P)
degree of polynomial $P$
quo(P,Q)
,rem(P,Q)
quotient and remainder of euclidean division ofP
byQ
proot(P)
: approx. roots of $P$ (all roots, real and complex)
Graphic representation
interp(X,Y)
: for two lists of the same size, returns the interpolating polynomial $P$ such that $P(X_i)=Y_i$.
Graphic representation
resultant(P,Q)
: resultant of polynomials $P$ and $Q$
hermite(x,n)
: $n$th Hermite polynomial (orthogonal for the density $e^{x^2}dx$ on $\R$)laguerre(x,n,a)
: $n$th Laguerre polynomiallegendre(x,n)
: $n$th Legendre polynomial (orthogonal for the density $dx$ on $[1,1]$)tchebyshev1(n)
andtchebyshev2(n)
Tchebyshev polynomials of 1st and 2nd kind defined by : $T_n(\cos(x))=\cos(nx), \quad U_n(\cos(x))\sin(x)=\sin((n+1)x)$
3.5 Linear algebra, vectors, matrices
Xcas does not make distinction between vectors and lists. For example,
v:=[1,2]; w:=[3,4]
onload
defines 2 vectors $v$ and $w$, then dot
will compute
the scalar product of $v$ and $w$:
A matrix is a list of lists of the same size.
You can enter a matrix element by element using the
matrix editor (shift7 EXE or shiftEXE i). Enter a new variable
name to create a new matrix
or the name of an existing variable to edit a matrix.
The ,
key may be used to insert a line or column, and
the Del
key erases the line or column of the selection.
Type shift3
if you want to undo one edition step.
For small matrices, it is also convenient to enter them directly in the
commandline, for example to define
$A=\left(\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}\right)$
type
A:=[[1,2],[3,4]]
onload
or
It is recommended to store matrices in variables!
If a matrix is defined by a formula, then it’s better to use the
matrix
command (shift7 EXE Back), for example:
returns the matrix where coefficient line $j$ and column $k$
is $\frac{1}{j+k+1}$ (beware, indices begin at 0).
Run idn(n)
to get the identity matrix of order $n$
and ranm(n,m,law,[parameter])
to
get a matrix with random coefficients with dimensions $n,m$.
for example
For basic arithmetic on matrices, use keyboard operators
(+  *
, inverse). Otherwise, open catalog and
select Matrices

eigenvalues and eigenvectors of matrix $A$.
finds the Jordan normal form of matrix $A$, returns matrices $P$ and $D$ such that $P^{1}AP=D$, with $D$ upper triangular (diagonal if $A$ is diagonalizable)
computes matrix $A$ to the $k$th power, where $k$ is symbolic.rref
: row reduction to echelon formlu
: $LU$ factorization of matrix $A$, returns a permutation $P$ and two matrices $L$ (lower) and $U$ (upper) such that $PA=LU$. The result of
may be passed as an argument to the command
to solve a system $Ax=b$ by solving two triangular systems (in $O(n^2)$ instead of $O(n^3)$).qr
$QR$ factorization of matrix $A$, $Q$ is orthogonal and $R$ upper triangular, $A=QR$.svd(A)
singular value decomposition of matrix $A$ returns $U$ orthogonal, $S$ vector of singular values, $Q$ orthogonal such thatA=U*diag(S)*tran(Q)
.
The ratio of the largest and the smallest singular value of $S$ is the condition number of $A$ relative to the Euclidean norm.
4 Probabilities and statistics
4.1 Random numbers
From Toolbox catalog, select Probabilities
then
(real in $[0,1)$) or
(integer between 1 and $n$).
Other commands with prefix rand
are available, followed
by the name of the law, for example randbinomial(n,p)
returns a random integer according to binomial law of parameters $n,p$.
For a random vector or matrix, run
ranv
or ranm
(from Alglin, Matrice
submenu),
for example for a vector with 10 random
reals according to normal law (mean 0, stddev 1), type
4.2 Probabilities
From Toolbox catalog, select Probabilities
(8).
There you will find a few distribution laws:
binomial
, normald
, exponentiald
and uniformd
. Other distribution must be keyed in
or entered with the
help of the main catalog (Toolbox EXE):
chisquared
, geometric
, multinomial
,
studentd
, fisherd
, poisson
.
To get the cumulated distribution function, enter the law name then
the _cdf
suffix (shortcut: select
cdf
in the catalog at the end and press shift1).
Inverse cumulated distribution function follows the same principle
with _icdf
suffix (shortcut:
select cdf
in the catalog and press shift2).
Example : find the centered interval $I$ for the normal law of
mean 5000, standard deviation 200, such that the probability
to be outside $I$ is 5%
4.3 1d statistics
The statistic functions are taking lists as arguments, for example
l:=[9,11,6,13,17,10]
onload
From Toolbox catalog, select Statistics
:

: arithmetic mean of a list 
: standard deviation of a list.
Run
to get an unbiaised estimate of the standard deviation of a population from a samplel

,
,
returns respectivly the median, first and third quartile of a list.
For 1d statistics with frequencies, replace l
by two lists of the same length, the first list being the
values of the serie, the second list the frequencies.
For graphic representations, open catalog, Graphic
and select histogram
or barplot
.
4.4 2d statistics
From Toolbox catalog, select Statistics
:

correlation(X,Y)
: correlation of two lists $X$ and $Y$ of the same length. covariance(X,Y)
:: covariance of two lists $X$ and $Y$ of the same length. regression computations:
run commands with suffix
_regression(X,Y)
, for examplelinear_regression(X,Y)
returns coefficients $m,p$ of the linear regression line $y=mx+p$. linear_regression_plot(X,Y)
and all commands of suffix_regression_plot
will display the line (or curve) of the regression. These commands will also print the $R^2$ coefficient that give information on the quality of adjustment ($R^2$ near 1 is good).
5 Graphics
From Toolbox catalog, select Graphics
(or type the plot fast menu shortcut shift3)
and choose a graphic command. If you want to have more than one curve
on the same graphic, enter several commands with ;
as separator.

plot(f(x),x=a..b)
plot expression $f(x)$ for $x\in [a,b]$. Discretization option:xstep=
, for example
Default is 384 evaluations per plot (one per horizontal pixel). plotseq(f(x),x=[u0,a,b])
webplot for a recurrent sequence $u_{n+1}=f(u_n)$ of first term $u_0$, for example if $u_{n+1}=\sqrt{2+u_n}, u_0=6$, with a plot on $[0,7]$
plotparam([x(t),y(t)],t=tm..tM)
parametric plot $(x(t),y(t))$ for $t\in [t_m,t_M]$. Discretization option:tstep=
. Example
plotpolar(r(theta),theta=a..b)
polar plot of $r(\theta)$ for $\theta \in [a,b]$, for example
plotlist(l)
: plot a listl
, i.e. draws a polygonal line with vertices $(i,l_i)$ (index $i$ starts at 0).
plotlist([X1,Y1],[X2,Y2],...)
polygonal line with vertices the points of coordinates $(X_i,Y_i)$scatterplot(X,Y)
,polygonscatterplot(X,Y)
for two listsX,Y
of the same size, draws the points or a polygonal line of vertices $(X_i,Y_i)$histogram(l,class_min,class_size)
plots the histogram of data inl
, class sizeclass_size
, first class starts atclass_min
. Example: check the random generator quality
plotcontour(f(x,y),[x=xmin..xmax,y=ymin..ymax],[l0,l1,...])
plot implicit curves $f(x,y)=l_0, f(x,y)=l_1,...$.plotfield(f(t,y),[t=tmin..tmax,y=ymin..ymax])
plot the field of tangents for the differential equation $y'=f(t,y)$. Add the optional last parameter,plotode=[t0,y0]
to plot simultaneously the solution with initial condition $y(t_0)=y_0$. Example $y'=\sin(ty)$ for $t \in [3,3]$ and $y \in [2,2]$
N.B.:plotode
may be used outside ofplotfield
. For simultaneous plots, write commands separated by
;
If a command returns an arc of curve, the trace mode is active by default. In this mode, typing the left or right key will move a pointer on the active arc of curve, and display the pointer coordinates (and the parameter value for parametric curves), and a tangent vector (speed). If there are several curves, press up or down to change active curve. Type shift2 to get info on the active curve, then EXE to see a table of value.
Press Toolbox to get the curve study menu. From the curve study menu, you can move the pointer to a location, or to a remarkable point: root, horizontal or vertical tangent, inflexion point, intersection with another curve arc. You can also compute an arc length or the area under the curve between pointer and mark.
When a curve is active, the variables x0,x1,x2,y0,y1,y2
are set with the expressions of position, speed and acceleration
of $x(t)$ and $y(t)$ (for a function curve $x=t$). When
you search a root, horizontal tangent, inflexion, arc length or area
under curve, variables are set with the last value.
Press shift1 for short help on the plotter. There you will learn that you can add/remove a normal vector pointing to the center of curvature (shift4), and/or the osculating circle and radius of curvature (shift5) or get the curve study menu by pressing the $x,n,\theta$ key.
For display options, you can enter an optional argument at the end of the plot command,

display=color
color option: for example to get
typeshift3 EXE sin x
then cursor right,, Toolbox EXE d i s p EXE shift = Toolbox , r e d
display=line_width_2
todisplay=line_width_8
: change segments width (including inside polygonal line used to plot a curve). Simultaneous display options should be added with+
. For exampledisplay=red+line_width_2
 Circles and rectangles with edges parallel to the coordinate
axis may be filled with
display=filled
(this attribute might be added to other attributes)  If you want to define the display window (overwriting
the autoscale computation), select
gl_x
or/andgl_y
and add an $x$ or $y$ interval, for example
Note thatgl_
commands must preced the plotting command.  If you want to remove axes, select
axes
and press shift2 (axes=0
). Likegl_
commands,axes=0
must preced the plotting command. Axes can be removed interactively when the graph screen is displayed by pressing thesin
key.
6 Programs
You can program either with Xcaslike syntax (English or French) or with Pythonlike syntax.
Example : function defined by an algebraic expression
nom_fonction(parametres):=expression
for example simple confidence interval for a frequency $p$ in a sample
of size $N$, type from the shell commandline
Test with
Second example : more precise confidence interval for a frequency $p$
in a sample of size $N$:
To avoid computing twice the same quantity, one can insert
a local variable.
The commandline is not well adapted to write these kinds
of functions. For non algebraic functions, it is best to run the
program editor. Press Toolbox, select Script Editor, clear the editor if it
is not empty (shiftEXE Clear) and
type with the help of test (shift1), loop (shift2)
for programming structures
the following program, in Xcas syntax:
or in Python syntax:
def f(P,N): D=1.96*sqrt(P*(1P)/N) return [PD,P+D]
Type OK to check the syntax. Once
the program is correct, save it (shiftEXE 2), then type Back. Now you
can call your program from the commandline like this
f(0.5,30)
Third example : a loop printing integer squares
from 1 to $n$ in Python syntax.
Enable Python syntax with shiftEXE 8.
Open the Script Editor (shift EXE or Esc from the shell),
if there is some old script source,
clear it (shiftEXE Clear).
Select f(x):=
from shift2 (or from Toolbox, Program, function def),
you should get def f(x):
.
Replace x
by n
move to the end of the line and press EXE to input a newline.
Type Shift2 then EXE, then j space, then
Shift2 then 3. Type 1,n+1)
then shift4 select :
. Type EXE to insert a newline
then Alpha SPACE,
Toolbox, EXE (1 All
), P, R select print
with the cursor
then type EXE, type j,j^2)
then EXE.
def f(n): for j in range(1,n+1): print(j,j^2)
Inside Xcas ^
means power, **
is also accepted like in
Python.
Now, type OK. If syntax is correct,
you will see Success
in the status line. Otherwise, the
first error line number and token will be displayed and cursor will
be positionned at the line where the error was detected. Note that
the error may be before this line but it was only detected later. Note
also that if you are using Python syntax compatibility, programming
structures are translated into Xcas, errors are displayed after
translation, therefore you might see token errors like end
that were added by the translator.
If the program is correct, you can save it with the shiftEXE menu
(save or save as).
You can run it from the commandline by pressing Back then for
example f(10)
should display all squares from 1 to 10.
The turtle is a nice way to learn programming. The turtle is a small
robot that you can move, it handles a pen that marks its path.
Type shiftEXE, Script Editor, then shiftEXE Clear. Type shift6 select
efface
which means clear the screen. You can
access to the turtle commands using shift6 or Toolbox )
.
For example try avance
(forward). Checking the syntax (OK)
will display the turtle window moves.
You can enter several moves in your script, and organize them
inside tests, loops and functions.
For example:
function square(n) repete(4,avance n,tourne_gauche); ffunction:; efface; for n from 1 to 10 do square(10*n); od;
Another example of non algebraic function: the euclidean algorithm
to compute the GCD of two integers.
Press EXE to insert a newline. !
is in the
submenu Programmation_cmds
(11, shortcut $X,\theta,T$)
or in the test shift4 menu.
Xcas syntax
function pgcd(a,b) while b!=0 do a,b:=b,irem(a,b); od; return a; ffunction
Python syntax
def pgcd(a,b): while b!=0: a,b=b,a % b return a
Check with
If your program has runtime errors or if you want
to see it run step by step, run debug
on it,
for example
debug(pgcd(12345,3425))
Unlike adaptations of MicroPython by calculator manufacturers (including
Numworks), the Python syntax in Xcas is fully integrated.
You can therefore use all Xcas commands and data types in your programs.
This corresponds approximatively to importing Python modules
math
, cmath
, random
,
scipy
, numpy
, turtle
, giacpy
.
There is also a small
pixelised graphic commands set
(set_pixel(x,y,c)
, set_pixel()
to synchronize
display, clearscreen()
, draw_line(x1,y1,x2,y2,c)
,
draw_polygon([[x1,y1],[x2,y2],...],c)
,
draw_rectangle(x,y,w,h,c)
, draw_circle(x,y,r,c)
,
the color+width+filled c
parameter is optional,
draw_arc(x,y,rx,ry,t1,t2,c)
draws an ellipsis arc).
And you can somewhat replace matplotlib
with graphic commands of $\chi$CAS
(point
, line
, segment
, circle
,
barplot
, histogram
and all ...plot...
commands). Plus you have natural access to data types
like rationnals or expressions, and you can run CAS commands on them.
The complete list of commands available on the calculator
is given in appendix. For documentation on commands not listed
in the catalog categories, please refer to Xcas documentation.
7 The 2d editor.
If a computation returns an expression, it will be displayed in the 2d expression editor. This also happens if you press shift5 or left arrow key when the selected level is an expression, or if you press shift5 from the commandline if the line is empty or contains a syntaxically correct expression.
Once the 2d editor is open, the expression is displayed in full screen and all or part of the expression is selected. One can run a command on the selection (from the menus or from the keyboard), or edit (in 1d mode) the selection. This is an efficient way to rewrite expressions or edit them.
Example 1 : enter
$\lim_{x \rightarrow 0} \frac{\sin(x)}{x}$
From an empty commandline, type shift5 (view), you should see 0 selected.
Type x then EXE, this will replace 0 by x selected. Type sin
, now
$\sin(x)$ should be selected. Type the division key (above ), you
should see $\frac{\sin(x)}{0}$ with 0 selected, type x then EXE,
you should now see $\frac{\sin(x)}{x}$ with x (below the fraction)
selected. Type the up arrow key, now $\frac{\sin(x)}{x}$
should be selected. Now type shift2 4 (for limit). The expression
is ready to eval, type EXE to copy it to the commandline and EXE
again to eval it. For the same limit at $+\infty$, before leaving
the 2d editor with EXE,
move the selection with the right arrow key, then type shift1 8 (oo) EXE.
Example 2 :
$\int_0^{+\infty} \frac{1}{x^4+1} \ dx$
From an empty commandline, type shift5 (view), then shift2 3 (integrate),
you should see:
$\int_0^1 0 \ dx$
with $x$ selected. We must modify the 1 (upper bound) and
the 0 (integrand). Press left arrow key, this will select the
integrand 0, type 1/(x^4+1)
EXE, then left arrow key shift1 8 EXE.
Type again EXE to copy to commandline, EXE again to run the computation,
the result will be displayed in the 2d editor, EXE will leave the 2d
editor, with the integral and its value in the history.
Example 3 : compute and simplify
$\int \frac{1}{x^4+1} \ dx$
From an empty commandline, type shift5 (view), then shift2 3 (integrate),
you should see
$\int_0^1 0 \ dx$
Move the selection to the lower bound 0 (right arrow key),
type Del, you should see
$\int 0 \ dx$
selected. With the down arrow key, select 0, type 1/(x^4+1)
EXE,
EXE copy to the commandline, EXE to run the compuation, the result
is now displayed in the 2d editor.
With the arrow key, select one of the arctangent, type shift1 EXE (simplify),
this will make a partial simplification, do the same on the second
arctangent.
For a more complete simplification, we will collect the logarithms.
The first step is to exchange two terms of the main sum so that the
logarithms are grouped. Select one of the logarithm with the arrow keys,
then type shiftleft or right arrow key
this will exchange the selection with the right or left sibling.
Now type ALPHA right or left arrow key to extend the selection adding
the right or left sibling. Once the two logarithm terms are selected,
press shift1 2 EXE (factor), decrease the selection to the numerator,
type Toolbox EXE (All), type the letters l, n, c, this moves in the
catalog to the first command beginning with lnc
, select
lncollect
, EXE and shift6 (eval).
8 Managing sessions
8.1 Modifying a session
With the up/down cursor keys, you can move in the history, the current level is printed with reverse colors.
You can move one level in another position with ALPHAup and ALPHAdown. You can delete a level with the Del key (the level is copied into the clipboad).
You can modify an existing level with left shift or right shift.
With left shift, the 2d
editor is called if the level is an expression, with right shift the level
is edited in the text (program) editor. Type Back if you want to cancel
modifications, or OK if you confirm the modifications. If you confirm
the modifications, the commandlines below the current level will
automatically be reevaled. This way, if you modify for example
a level like A:=1
, all levels below that depend on the value
of A
will be up to date. If you want to do that several times,
it is best to introduce a parameter with the Toolbox Parameter wizzard. Then
pressing + or  on the assume(...)
or parameter
level
will modify the value of the parameter (press * or / for faster move).
8.2 Variables
Press vars
to see which variables are assigned to a value.
Select a variable
name, press EXE to copy it to the commandline, Del will input the command
that erases the variable (confirm with EXE). restart
will
purge all variables at once (press shift EXE 0
to clear the history
and start a fresh new session). assume
is a command to
make assumptions on a variable, like assume(x>5)
.
8.3 Archiving and exchanging with Xcas
On the calculator, go back to the history (type Back if you are in the
programming editor or the 2d expression editor).
From the shiftEXE menu, you can save/restore sessions in the
calculator scriptstore. If you save a session that is not too long,
a QR code is displayed that can be used to clone the session
inside Xcas for Firefox.
Session filenames have the _xw.py
suffix, they
are not real Python scripts, that’s just a trick to be recognized
if you want to publish them on Numworks servers. They
can be copied to your computer
using the connectivity kit
from this link,
They may be opened with Xcas or Xcas for Firefox.
From Xcas, choose the File menu then Numworks
From
Xcas for Firefox, press the Load button.
Conversely you can save a session from Xcas (choose File, Export to Khicas) or from Xcas for Firefox (choose Export at the right of the session name).
Python scripts may be saved to the Numworks RAM scriptstore, using the shiftEXE menu. They are shared with the builtin Python application of the Numworks. In addition, you can archive them to the user flash on the Numworks, using shiftEXE 1 0. Scripts stored in the user flash can be accessed readonly from KhiCAS even if they are not copied to the RAM scriptstore.
9 Keyboard shortcuts.
These shortcuts are valid inside the shell and text programming editor. With default configuration:
 HOME: back to main Numworks menu
 Back: cancel (if there is something to cancel) or switch from shell to editor
 Toolbox: commands menu
 shiftEXE: $\chi$CAS menu
shift *
: table of ASCII characters vars: variables list
 shift1shift6: see legend at screen bottom,
 shift7: matrix fast menu
 shift8: complex fast menu
 shift9: arithmetic fast menu
 shift(: list fast menu
 shift): function fast menu
 shift) 8: switch from Xcas interpreter to MicroPython interpreter
 shift0: misc fast menu (probabilities and periodic table)
 shift.: real fast menu
 shift$10^x$: polynomial fast menu and Galois Field command
 shift Ans (or shiftEXE 1): $\chi$CAS applications (Geometry, Spreadsheet, ...)
shift /
:%
inside shell,
You can modify fast menus shortcuts by editing the file
FMENU.py
. Delete the file
to reset to default configuration.
In programming editor
 shift then cursor key: move to begin/end of line or file
 shift and cursor key simultaneously: select. Move the cursor to the selection end, type Back to remove the selection (it will be copied to clipboard) or again shiftcopy to copy selection to clipboard without removal. Type Back to cancel selection.
 OK: if a search/replace is currently active (Toolbox 6) find next word occurence. Otherwise parse/execute.
 EXE: add a newline.
 Del: remove selection or previous character if no selection active
10 Remarks
If KhiCAS is inside a long computation, you should be able to interrupt it by pressing Back. If it does not interrupt, try the HOME key. If that does not work, you may have to press the reset button, but beware that this will disable $\chi$CAS on locked Numworks calculators, which means you will have to connect to a computer and reinstall the small launcher application/
The memory available for computations is about 128K with an empty session, it is displayed in the statusline. You can defragment memory (keeping variables and history) by pressing HOME then restarting $\chi$CAS. For a fresh restart, press vars, select restart then EXE, then shiftEXE Clear history, then HOME.
11 $\chi$CAS applications
11.1 MicroPython
You can select the shell interpreter by shiftEXE ln or switch interpreter with shift) 8. The menu background color of the shell reflects the active interpreter (yellow=MicroPython, magenta or cyan for Xcas native or Xcas Python compatible).
This MicroPython implementation has the following modules: turtle, graphic (both with filled objects), matplotl, arit (integer arithmetic), linalg/numpy (linear algebra, matrices), ulab (scipy compatibility), cas (CAS from Python).
11.2 3d and 4d graphs
$\chi$CAS can plot
2 variables function or parametric plots, cones, solids, planes, ...
For example type Toolbox * 5 shift2 EXE
to draw a cube or shift 1
to select the plot command,
and enter x^2y^2
.
For fonctions plots from $\mathbb{C}$ to
$\mathbb{C}$, run the plot
command with argument
a complex valued expression of 2 variables (real and imaginary parts)
like for example plot((x+i*y)^29)
. For
expression depending directly on the complex variable
(without requiring real/imaginary part), run the
plot3d
command, for example
plot3d(x^29)
(the plot(x^29)
command would not
work, because it is already used for a graph from $\mathbb{R}$ to
$\mathbb{R}$). The modulus is represented along the $Oz$ axis and
the argument using raimbow colors: from $\pi$
in blue magenta to 0 in green (through yellow orange) and from
0 to $\pi$ via cyan.
If you need precise options, run the plotfunc
command, for example
plotfunc((x+i*y)^31,[x=2..2,y=2..2],nstep=500)
will plot $z \rightarrow z^31$ from a square in the complex plane
centered at origin, size 4 with a 500 small reectangles discretization.
Beware, 3d plots require much memory, you should avoid simultaneous plots (polyhedrons, lines, planes or spheres do not require much memory, only plots and objects handled by a plot like cones). You can modify the rendering precision with shift2 (faster, less precise) or shift3 (slower, more precise).
If you just want one time a higher
precision rendering, type ^
and be patient. If you want to
interrupt this rendering, press Back. Use the cursor keys to change the
viewpoint, 5 to reset to default viewpoint, and 
or +
to zoom in/out.
While a cursor key is
kept pressed, the precision is lower, when the key is released the
last position is redrawn with the default precision.
11.3 Interactive geometry application
The geometry application lets you construct figures in the 2d plane or in 3d space. It is possible to move one point of the figure and observe how the construction evolves, illustrating some properties (dynamic geometry). Pure geometric constructions may be mixed with function graphs and other analytic constructions. This application has two view: the graphic view where the figure is rendered and the symbolic view where you see the Xcas instructions to construct the figure. The philosophy is similar to Geogebra, but with Xcas commands instead.
You will find here a short description of this application, cf. here for a more complete documentation of the geometry application, with a few screenshots.
11.3.1 Modes, graphical and symbolic view
Type shiftAns or Toolbox to display the list
of additional applications, then EXE then select an existing figure
or create a new 2d or 3d figure. You may also open the
geometry application from an existing graph displayed from the shell
(for example after running plot(sin(x))
)
by typing shiftEXE then Save figure.
At startup, you are in graphical view in frame mode. The cursor key will modify the viewpoint (move the frame in 2d, rotate viewpoint in 3d). Press Toolbox to change mode. Type OK to switch to symbolic view or back. For example, type Toolbox 3 to enter point mode, move the pointer and press EXE where you want to create a point. Or type Toolbox 5 to enter triangle mode move the pointer to each vertex and press EXE on each vertex. You can move the pointer with the keypad (use shift cursor key for a fast move), or if there is an existing point, type the name (e.g. type ALPHA A to move the pointer to the point A if it has already been defined).
In a 3d figure, objects will be created in the yellow plane. Press 4 or 6 to move this plane. It is recommended to keep a viewpoint with $Oz$ vertical (therefore change viewpoint only with the right and left cursor keys that make a rotation of axis $Oz$).
Dynamic geometry howto: switch to pointer mode (Toolbox 2), move near an exising point and select it with EXE, then move the point with the cursor keys, you will see how the whole figure depends on that point, this helps conjectures or illustration of some geometric properties, like the fact that 3 lines of a triangle have a common intersection.
If you type Back in the graphical view, it will reset mode to frame mode
if you were not in frame mode, or it will switch to symbolic view if
you were in frame mode. In the symbolic view, you can modifiy existing
commands or create new geometric objects with new commandlines (one line
per object). You can save the construction in text format
from shiftEXE menu, note
that the file generated will have a .py
extension
despite the fact that
it is not a Python script.
Type Back again to leave the geometry application.
When leaving the geometry application, the figure is saved in an Xcas variable that has the same identifier than the filename displayed in the symbolic view. You can erase this Xcas variable if you want to clear the figure.
Example : circumcircle.
From KhiCAS shell, type shiftEXE 1 then select new figure 2d EXE.
Type Toolbox 5 Triangle, EXE to create the first vertex, move the pointer
with cursor keys and type EXE for the second vertex, move the pointer
again and type EXE to create the 3rd vertex and the triangle.
Long version, construction of the center:
Type Toolbox 7, select 8 Perpen bisector, move the pointer so that
only one edge of the triangle is selected (this is displayed
at the bottom right, something like perpen_bisector D5,D
,
type EXE will create the perpendicular bisector. Move the pointer
to another edge of the triangle, type EXE to create the 2nd bisector.
You may optionnaly create the 3rd bisector.
Then type Toolbox 6, select 4 Single intersection. Move the pointer
to a perpen bisector, type EXE, move the pointer to another perpen
bisector and type EXE. This will create the circumcircle center.
Type Toolbox 4, move the pointer to the center (with the cursor keys
or by typing ALPHA H or the center name if it is not H), then EXE,
move to one of the triangle vertex and press EXE.
Short version with the circumcircle
command:
Type Toolbox 9, select circumcircle, select each vertex with
pointer move + EXE (ALPHA A EXE ALPHA B EXE ALPHA C EXE, replace
A, B, C with the vertices names).
Symbolic view version:
If you are in the graphical view, type Back to move to the symbolic view.
Move to the script end and add a newline if required (shift EXE).
Enter
c:=circonscrit(A,B,C)
EXE
3d Example
Type shiftEXE 1 from the shell, then select new 3d figure.
Then Back or OK to switch to the symbolic view. Then alpha c shift =
Toolbox uparrow twice, select 3D, EXE 5 for cube, Toolbox for help on the cube
command, press shift2 to copy+paste the first example in the symbolic
view. You should see
c=cube([0,0,0],[1,0,0],[0,1,0])
Type OK, this display a small cube, type + a few times to zoom in. Then
OK to switch back to symbolic view.
Type EXE to begin a new commandline.
Now we define the vertices of the cube with
A,B,C,D,E,F,G,H:=
(type alpha shift A , alpha shift B etc.).
Then type Toolbox and uparrow 3 times
to select Geometry then uparrow 4 times to select
sommets
EXE, put c as argument to get sommets(c)
.
Type OK to display the cube and the vertices with their names.
Type OK again to go back to symbolic view. Then EXE to
enter a new commandline, that will define the plane ABC.
Type ALPHA P = then shift2 to open the fast menu lines and 8, this will
copy plane(
.
This command takes 3 points as argument (or a cartesian equation), here
A, B, G, P=plan(A,B,G,
. We now add a color to the plane
with the shift3 disp fast menu
display=filled+green
. Check by OK OK.
Go to the next line (EXE) and create segment DE
ALPHA S = shift2 select segment command with EXE, type D, E,
and give a color
S=segment(D,E,color=cyan)
The whole construction should be
c=cube([0,0,0],[1,0,0],[0,1,0]) A,B,C,D,E,F,G,H=sommets(c) P=plan(A,B,G,display=filled+green) S=segment(D,E,display=cyan)
Type OK to display it and use the keypad to change the viewpoint.
Type OK or Back to go back to symbolic view and Back to leave the
geometry application. Type shift1 to save the figure if you did not
save it from the shiftEXE menu.
You can access analytic geometry information from KhiCAS shell, for
example equation(P)
(Toolbox select Geometry submenu) will
return the cartesian equation of the plane $P$, or
is_orthogonal(P,S)
(Toolbox Geometry)
will confirm that the plane $P$
is orthogonal to the segment $S$ (this should be apparent from
3d rendering).
11.3.2 Cursors
Cursors are parametric values that live in a given inteval and may be
moved by 1% steps from the graphical view. They are created
with the element
command in the symbolic view or from Toolbox
menu in the graphical view.
Example : quadratic explorer
This example demonstrates how the curve of the parabola of equation
$y=ax^2+bx+c$ depends on the value of $a,b,c$.
Create 3 cursors from Toolbox menu while you are inside the graphical view
(for each cursor Toolbox uparrow 4 times EXE EXE). In the symbolic view
you should have something like
a:=element(1..1) b:=element(0..1,0.5) c:=element(1..1)
then add the parabole graph, from graphical view,
type Toolbox 0 (for 10 Curves)
and select plot, or from the symbolic view
shift 6 5 select plot
fill inside the parenthesis with a*x^2+b*x+c
(beware,
do not forget the *
), then EXE.
From the graphical view, you should see 3 cursors
a
, b
and c
and the corresponding graph.
You can now modify the value of $a,b,c$ and see how it affects the shape
of the parabola. Type Toolbox 2 (pointer mode),
then a (or b or c) EXE
to select $a$ (or ($b$ or $c$).
Type EXE then the right and left arrow keys,
EXE again to stop moving the cursor.
A lot of variations may be done, some of them simpler with one or two cursors
and a curve depending on one or two parameters. For example a line equation
explorer with line(y=a*x+b)
or a trigonometic explorer with
plot(sin(a*x+b))
.
11.3.3 Measures and legends
From the graphical view, type Toolbox and select 13 Measure. You can compute and display a measure at some point of the figure. For example after creating a triangle, one can display the perimeter of the triangle or its area. Type Toolbox then uparrow twice EXE. Move the pointer near the triangle, type EXE, move the pointer where you want to display the measure and type EXE.
From the symbolic view, you can display a legend with the
legend()
command.
The first argument of legend may be a point of the figure, or
a vector of 2 integers giving the absolute position in pixels
(measured from the top left corner). The second argument
is the legend, it may be a string or any expression.
If the legend is a numeric value, it can be used as a numeric parameter
for commands that require such an argument, like transformations
(angle of rotation, homothety ratio...)
r:=legend([20,40],"2")
homothety(A,extract_measure(r),B)
11.3.4 Traces
The trace()
command lets you keep track of all the positions of
a geometric object when the figure is recomputed while moving a point
Example Enveloppe of the normals to a parametric curve (here an ellipse)
E:=plotparam([cos(t),2*sin(t)],t=pi..pi) a:=element(pi..pi) M:=element(E,a) T:=tangent(M) N:=perpendiculaire(M,T) trace(N)
If you change the value of $a$ (Toolbox 2 for pointer mode, a),
you will see a curve that separates the area of normals to the curve
and a free area, this is the enveloppe of normals, it is also
the evolute of the ellipse
evolute(E,color=red)
You can remove the traces in the graphical view from the shiftEXE menu
(last item).
11.4 CAS spreadsheet
The spreadsheet is launched from the application menu (shiftEXE EXE or shiftAns shortcut).
Unlike pure numeric spreadsheet, the CAS spreadsheet can handle exact or
symbolic values. You can compute cells whose values are
fractions, square roots or expressions containing variables like
$x,y...$.
A cell can contain any valid Xcas value, numbers, strings, etc.
If you enter a list of values, or an Xcas command returning a list
of values, the list will fill consecutives cells (downwards or to the
right, according to the setup). For example type shift1 range(
10 EXE, this will fill 10 cells with numbers from 0 to 9.
Defining a cell content with reference to other cells
is similar to other spreadsheet, begin with
=
, and enter an expression that may contain cell references
(characters :
and $
are available from shift3 menu,
:
is also accessible with shift $\rightarrow$). While editing
the cell content, you can select another cell by pressing the up or
down cursor key followed by any other cursor key. To select a range,
move to the begin of selection cell,
press shiftarrow key then move to the end of selection and type EXE.
While defining a cell, any Xcas commands may be used, you can get them from Toolbox menu, or fast menus (shift1 etc.). Programming Xcas structures may also be used as well as Xcas functions that you have defined. Beware that MicroPython functions are not supported.
A cell can be defined with a command returning a graphic result. Type shift6 to display the graphic corresponding to the graphical output of the whole spreadsheet.
12 Copyright and Thanks to.
 Giac and $\chi$CAS, computing kernel (c) B. Parisse and R. De Graeve, 2024.
 $\chi$CAS interface adapted by B. Parisse from Eigenmath source code by Gabrial Maia and from Xcas source code.
 Initial port
OS Epsilon 15.5
de la Numworks, (c) 2021 Numworks, license
Creative Commons AttributionNonCommercial
ShareAlike 4.0 International Public License
Modifications by Damien Nicolet and Bernard Parisse, (c) 2019, 2021 (Delta and Khi projects), same license. Modifications by Omega and Upsilon (c) 2024 same license  $\chi$CAS license GPL2. See details in
the
LICENSE.GPL2
file, inside khicasio.zip or GPL2 on the Free Software Foundation website. The source code of $\chi$CAS is available at Numworks section of my webpage (see section 13).  Thanks to Damien Nicolet who first ported giac to a Numworks N0100 with hardware modifications, and later built the Epsilon External app for unlocked Numworks N0110.
 The periodic table is (c) Maxime Friess and redistributed under GPL2 with his authorization.
 Thanks to the mysterious ScarlettSpell who created the (discontinued) Nwagyu website with the first KhiCAS external app for locked Numworks. It was unfortunately not stable and installation was more tricky than the current install method, that was the main reason for me to make this port.
 Thanks to the active members of tiplanet and Planete Casio for answering questions and testing during the time I developed $\chi$CAS. Special thanks to LePhenixNoir (Prizm/35+eii help), Nemhardy (Prizm), and to critor for articles, tests and advertising.
 Thanks to Yann Couturier for insightfull discussions about Epsilon 16 and above (locked Numworks).
13 Developer infos.
The simulator installation for the impatient is described in 1.2. The detailled installation procedure follows :

Windows users :
First method : install WSL or a Linux distribution inside a virtualization software like VirtualBox, and follow Linux instructions.
Second method : First install Msys2/mingw64 then open from Msys2 menu a mingw64 terminal. In the Options menu of the windows, click keys, check Ctrlshiftletter shortcut, this way you can paste in the terminal with CtrlshiftV. Run :pacman S git wget mingww64x86_64gcc mingww64x86_64freetype mingww64x86_64pkgconfig mingww64x86_64libusb make mingww64x86_64python3 mingww64x86_64libjpegturbo mingww64x86_64libpng mingww64x86_64imagemagick mingww64x86_64librsvg mingww64x86_64inkscape mingww64x86_64python3pip mingww64x86_64pythonlz4 mingww64x86_64libpng gmp mpfr echo "export PATH=/mingw64/bin:$PATH" >> .bashrc pip3 install pypng stringcase
Check that you can compile Epsilon without KhiCASgit clone https://github.com/parisseb/epsilon cd epsilon make PLATFORM=simulator
If everything is ok, runwget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/ext.tar.bz2 tar xfj ext.tar.bz2 wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/nwsimu.tgz tar xfz nwsimu.tgz
Now
either download
MPFI
unarchive it
tar xfj /chemin/vers/mpfi1.5.4.tar.bz2
configure with./configure prefix=/usr
runmake
andmake install
,  or remove
lmpfi
in themkwin
script
./mkwin
(instead ofmk
).If everything went well, type
./epsilon.exe
fromepsilon
directory. The simulator should display. 
either download
MPFI
unarchive it
 Native MacOS compilation is more complicated
because we will build a universal binary for 2 architectures
arm64 and x86. The first step is to install homebrew and
dependencies for both, on a recent Mac (arm64), open
a Terminal (type Terminal in launchpad) and copypaste
(with commandC commandV)
/bin/bash c "$(curl fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)" brew install numworks/tap/epsilonsdk brew install libpng gmp mpfr mpfi arch x86_64 /bin/bash c "$(curl fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)" arch x86_64 /usr/local/bin/brew install libpng gmp mpfr mpfi
Thengit clone https://github.com/parisseb/epsilon cd epsilon wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/ext.tar.bz2 tar xfj ext.tar.bz2 wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/nwsimu.tgz tar xfz nwsimu.tgz ./mkmac ln sf output/release/simulator/macos/epsilon.app epsilon.app/Contents/MacOS/Epsilon
Note that Mac OS Intel users can also install UTM then install a Debian distribution, but Epsilon 22 does not compile on an ARM Mac with UTM.  Now assuming we are on a Debian based Linux,
install Epsilon dependencies
from a Terminal or Konsole, copypaste (select commands, press CtrlC,
then in the Terminal press shiftCtrlV simultaneously) the following commands:
sudo aptget install wget buildessential git imagemagick libx11dev libxextdev libfreetype6dev libpngdev libjpegdev pkgconfig python3 python3pip sudo aptget install gcc g++ libgmpdev libmpfrdev libmpfidev libparidev libgsl0dev libxextdev libpngdev libjpegdev libreadlinedev libncurses5dev mesacommondev libx11dev libxtdev libxftdev libntldev libgl1mesadev libgldev libaodev hevea debhelper libecm1dev libnauty2dev libcliquerdev libresample1dev libxineramadev libsamplerate0dev libfltk1.3dev pip3 install lz4 pypng stringcase
then copypaste from a Terminal (or Konsole)git clone https://github.com/parisseb/epsilon cd epsilon wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/ext.tar.bz2 tar xfj ext.tar.bz2 wget https://wwwfourier.univgrenoblealpes.fr/~parisse/numworks/nwsimu.tgz tar xfz nwsimu.tgz ./mk ln sf output/release/simulator/linux/epsilon.bin simu
Note that compilation with mk is done in two steps: first a normal compilation of Epsilon that will error (because it does not link to Xcas libraries) then a link step with Xcas libraries, this final step should not error.If everything went well, type
./simu
fromepsilon
directory. The simulator should display.
Once the simulator is compiled, you can modify Xcas source code in
the src
directory, and you can debug the simulator with
gdb
.
We describe here the external app build process for Epsilon 22/23. $\chi$CAS is a large application (size 4M or 5M), it can not be handled like a “normal” external app as supported by Numworks (upper limit 2.6M because they must be in one of the 2 “slots” of 4M of the Numworks). Moreover, the current protection mechanism of the Numworks erase all external apps at each reset or crash and we do not want to reflash a large app each time this happens. Therefore, $\chi$CAS is divided in 2 files (short version) or 3 files (large version), with a launcher Numworks external app (of size a few K) that will start $\chi$CAS code in the second slot of the Numworks, overwriting one of the two copies of Epsilon firmware. The long version is compiled with data located at the end of slot A, the short version has data located in slot B together with the code.
Source code for the hardware calc is available in the two archives launcher and KhiCAS.
The launcher should not need recompilation.
If you really want to modify it, install Numworks EADK then
compile by make
, this will generates a standard
Numworks external app in output/khicas.nwa
, this app
will install from
Numworks external app site.
It is linked to Numworks EADK with a few additions for missing functions
in order to match the same API as the old External unlocked N0110 API
extern "C" void (* const apiPointers[])(void) = { (void (*)(void)) extapp_millis, (void (*)(void)) extapp_msleep, (void (*)(void)) extapp_scanKeyboard, (void (*)(void)) extapp_pushRect, (void (*)(void)) extapp_pushRectUniform, // 4 (void (*)(void)) extapp_pullRect, (void (*)(void)) extapp_drawTextLarge, (void (*)(void)) extapp_drawTextSmall, (void (*)(void)) extapp_waitForVBlank, // 8 (void (*)(void)) extapp_clipboardStore, (void (*)(void)) extapp_clipboardText, (void (*)(void)) extapp_fileListWithExtension, (void (*)(void)) extapp_fileExists, // 12 (void (*)(void)) extapp_fileErase, (void (*)(void)) extapp_fileRead, (void (*)(void)) extapp_fileWrite, (void (*)(void)) extapp_lockAlpha, // 16 (void (*)(void)) extapp_resetKeyboard, (void (*)(void)) extapp_getKey, (void (*)(void)) extapp_restorebackup, (void (*)(void)) extapp_erasesector, // 20 (void (*)(void)) extapp_writememory, (void (*)(void)) extapp_inexammode, (void (*)(void)) extapp_isalphaactive, (void (*)(void)) extapp_kbdstatus, // 24 (void (*)(void)) nullptr, };
This array address is passed as a parameter to extapp_start
in khib/startup.c
uint32_t _extapp_start(const uint32_t api_version, const void * api_base, void * heap, const uint32_t heap_size);
this function is responsible for copying these parameters, including
the apiPointers array, used by KhiCAS CSDK in khib/api.c
,
initialize static RAM, and call extapp_main
in khib/main.c
, this function calls
ext_main
that calls caseval("*")
which is a convention in Giac/Xcas library to start the interactive shell.
KhiCAS can be compiled in 2 versions : the short version without
full online help will fit in Numworks 2nd slot
starting at 0x90400000, and the long version
that generates two binary files, the first one starting at 0x90260000
ending at 0x903f0000 (readonly data),
and the second one starting at 0x90400000 (code).
Binaries are stored in a tar archive file, where script files
can be added, that will be accessible readonly on the calculator.
Run ./mkb
or ./mkab
.
An additionnal tarfile can be sent to the calc at 0x90200000
with data/scripts that can be read or modified from the calculator.
There are 4 ld scriptfiles (2 versions and 2 calculator models, where
N0110 and N0115 are identical)
n01?0.ld, n01?0ab.ld
.
Compilation is done by pair, with target khi110b.tar khi120b.tar
or
khi110ab.tar khi120ab.tar
with compile commandline g++ define
DNUMWORKS_SLOTB
or
DNUMWORKS_SLOTAB
.
Static RAM is located 16K before the end of RAM for external apps
(13K are used now), and the launcher allocates 128K for KhiCAS malloc heap.
Memory modem

RAM heap starts at
0x2?012A28
with Epsilon 22.2.1 (replace ? by 0 or 4 depending on mdel)  static RAM:
0x2?033000
(16K reserved, 13K used)  flash tar file R/W:
0x90200000
(6*64K available)  flash
.rodata 0x902600000x903f0000
:khia
file, read only data for long version  flash
.text 0x904000000x907f0000
(about 0.5M free for RO data tarfile in long version), filekhi1?0ab.tar
(long), or filekhi1?0b.tar
(short)
Local dfu command to flash without Internet access
dfuutil i 0 a 0 s 0x90400000 D khi120b.tar (short) or (long) dfuutil i 0 a 0 s 0x90400000 D khi120ab.tar dfuutil i 0 a 0 s 0x90260000 D khia script exemples: dfuutil i 0 a 0 s 0x90200000 D khi92
In order to reflash the launcher app locally, get it once, when KhiCAS is visible in the Numorks home menu, on a N0120:
#! /bin/bash dfuutil i 0 a 0 s 0x90190000:0x10000:force U sector19
on a N0110/N0115:
#! /bin/bash dfuutil i 0 a 0 s 0x90180000:0x10000:force U sector18
then reflash a N0120 with:
#! /bin/bash dfuutil i 0 a 0 s 0x90190000 D sector19
and a N0110/N0115
#! /bin/bash dfuutil i 0 a 0 s 0x90180000 D sector18
Remarks :

KhiCAS can be compiled in a short version in French by
running
./mkfr
, this version is 4M90K. It could be further shortened by removing MicroPython support (removeDMICROPY_LIB
in Makefile).  The launcher compulation could probably be faster and could
work without Internet access by bypassing the Numworks
linker, with a ld file using a fixed sector in flash
(
0x90190000
for N0120 Epsilon 22) and the lowest address of the stack for static RAM (0x2?380000
) since the stack has room available. EADK calls should be replaced by SVC calls, and some header code should be added to be recognized as a Numworks external appion/src/device/userland/drivers/external_apps.cpp ion/include/ion/external_apps.h /* The ExternalApp start with its info layout as: *  4 bytes: a magic code 0xBABECODE *  4 bytes: the API level of the AppInfo layout *  4 bytes: the address of the app name *  4 bytes: the size of the compressed icon *  4 bytes: the address of the compressed icon data *  4 bytes: the address of the entry point *  4 bytes: the size of the external app including the AppInfo header *  4 bytes: the same magic code 0xBABECODE */ apps/home/controller.cpp: affichage et lancement par switchToExternalApp apps/apps_container.cpp:void AppsContainer::switchToExternalApp(Ion::ExternalApps::App app)