Giac is a C++ library that has types for symbolic algebraic manipulations. Xcas is a GUI linked with Giac that provides the functionnalities of a general purpose computer algebra system. Giac's name derive from http://www.ginac.de, another C++ library for symbolic algebraic computations.

If you want to use `xcas/giac`

like another CAS and your OS is
Intel x86 GNU/Linux or Intel StrongARM GNU/Linux or Windows 9x or Mac OS
X.4(+), then
you don't need to worry about compilation. Instead you can install
precompiled binaries:

- x86 GNU/Linux as a normal user:
ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/xcas_user.tgz
Unpack the archive with

`tar xvfz xcas_user.tgz`then

`cd xcas`and

`./xcas` - x86 GNU/Linux if you have root access:
ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/xcas_root.tgz
Unpack the archive from the
`/`

directory - ARM GNU/Linux: ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/xcas_ipaq.tgz
- Windows 9x:
ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/xcasinst.exe.
Run
`xcas`

from the Start menu. - Mac OS X:
ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/xcas_osx4.dmg.gz.
Run
`xcas`

from the Applications.

Get Giac source at ftp://ftp-fourier.univ-grenoble-alpes.fr/xcas/giac_stable.tgz
or http://perso.wanadoo.fr/bernard.parisse/.
Check that your C++ compiler understand the C++ ANSI 3 norm. For
example `gcc`

version 2.95 or later will work. If the GMP GNU Math
Precision Library is not installed on your system, install it:
http://www.gnu.org/directory/gnump.html. If you are using GNU/Linux,
the GMP library is most probably installed but the headers files
might not, check for a package named something like `gmp-devel`

.

- If you want numerical functions you should install the Gnu Scientific Library available at http://sources.redhat.com/gsl
- If you want to use NTL for some polynomial operations (currently
factorization), get version >= 5.2 at http://www.shoup.net. Then
check that you configured with namespace enabled (this is not the
default) and with GMP enabled (not the default, but this is not mandatory)
If you are not sure of your install go in the NTL directory and type
make clean ./configure NTL_GMP_LIP=on NTL_STD_CXX=on make make install

- If you want advanced arithmetic functions, get PARI at
http://www.parigp-home.de.
If you plan to use an old version of PARI WITHOUT NTL then you MUST MAKE THE
FOLLOWING PATCHES in the PARI source directory:
- File
`src/basemath/polarit2.c`

: remove the word`static`

from the declaration:static GEN combine_factors(...)

- File
`src/headers/paridecl.h`

: Add the line`GEN combine_factors(GEN a, GEN famod, GEN p, long klim, long hint);`

in the

`* polarit2.c`

section. - Recompile (
`make all`) and reinstall PARI (`make install`

) and check that`libpari.a`

has been updated or copy it explicitely from the`O<your_os>`

directory. - Replace in
`/usr/local/include/pari/pariinl.h`

`labs`

by`std::abs`

otherwise you might get compiler errors.

`long pari_mem_size=10000000;`

- File
- If you want GUI support, check that you have FLTK 1.1 installed (available at http://www.fltk.org).
- TeXmacs provides an interface for giac. You can get it at http://www.texmacs.org. After installing giac, run texmacs and use Insert->Session->giac.

The `./configure `

shell-script recognizes the following options:

- –enable-debug Allow vecteurs printing and add some debugging code
- –enable-fltk GUI support
- –enable-gsl Use the Gnu Scientific Library for floating point (e.g. special functions..)
- –enable-sscl Allow inclusion of code for semi-classical algorithms (Moyal product, ...) Not available yet
- –enable-ntl Allow inclusion of NTL code
- –enable-pari Allow inclusion of PARI code

These options can be turned off using `--disable-option-name`

instead of
`--enable-option-name`

. By default `configure`

will use these
options if the libraries are available on your system.

For full speed binaries, before calling `configure`

do (with bash
as shell)

`$ export CXXFLAGS="-O3 -fexpensive-optimizations -malign-loops=2 -malign-jumps=2 -malign-functions=2"`

or (with tcsh as shell)

`$ setenv CXXFLAGS "-O3 -fexpensive-optimizations -malign-loops=2 -malign-jumps=2 -malign-functions=2"`

Like with any autoconfiguring GNU software, you can type :

` ./configure `

[add options as needed: try `./configure -help` for option info]

` make `

` make check `

[become root if necessary]

` make install `

Tips:

- If you don't want optimizations, set the environment variable
`CXXFLAGS`to`-g`

before calling configure, with tcsh`setenv CXXFLAGS -g`, with bash`export CXXFLAGS=-g`. - If you want the commandline icas only run
`./configure --disable-gui``make` - If you want to build xcas for the ARM processor with the Linux familiar
distribution (e.g. for an iPaq http://www.handhelds.org)
assuming you have the skiff toolchain installed and FLTK installed.
Check that
`config.h`

defines HAVE_LIBFLTK and does not define HAVE_LIBGSL and HAVE_LIBGSLCBLAS unless you have these libraries too, then`make -f Makefile.ipaq`Note that I never succeded to build with optimization for the iPaq.

- Windows
You can compile the library version of giac like under Unix. Or assuming you have the cygwin tools, gmp and FLTK installed (see http://sources.redhat.com/cygwin for cygwin, run cygwin, go in the

`src`

directory and run`make -f Makefile.win`After that, you may run

`xcas.exe`

standalone, provided`/usr/bin/cygwin1.dll`

has been copied in the path (e.g. in the same directory as`xcas.exe`

)

- If you test giac after compilation with
`make check`

, please note that the answer assume PARI and NTL are enabled. Otherwise you will get some errors because factoring will not return the factors in the same order. - Optimization requires much memory for compilation. If you are low
in memory edit
`src/Makefile`

and if necessary replace the line :`CXXFLAGS = -g -O2`

by :`CXXFLAGS = -g`

- If you get an error like
`autoheader: Symbol 'CONSTANT_DEBUG_SUPPORT' is not covered by ...`run

`autoheader --localdir=.` - If you get error when compiling
`modpoly.cc`

, it's most certainly because you compiled NTL without namespaces. Recompile it (see section) - If you get a linker error about combine_factors not found in
`modfactor.o`

it's because you did not modify PARI correctly or forgot to re-install the PARI libraries (see section) - Cygwin compilation of Giac with PARI 2.1.1 requires you to make
some hand work. I could not get the dynamic version of PARI library compiling.
Therefore I had to do the install by hand
cp libpari.a /usr/local/lib mkdir /usr/local/include/pari cp src/headers/*.h /usr/local/include/pari cp Ocygwin/*.h /usr/local/include/pari

Then I got an error compiling

`pari.cc`

that dispeared by commenting the offending line in the header`/usr/local/include/pari/paricom.h`

After that all went OK.

`xcas`

is an user-interface to giac that is similar to a calculator.
A readline interface named `cas`

is also available.

You can use but you don't need to have a keyboard to use xcas, it is designed to be used on a PDA as well. Use the green shift button to get the button-keyboard.

The window is composed from left and up to right and down of:

- The main menu-bar: at the left: session management, configuration and help, at the right the commands by theme
- The session menu: file and edit operations. In the Edit menu, the Add item lets you add levels of different kinds: commandlines, comments, 2-d and 3-d geometry and graphs, spreadsheet, program editor
- The session, with a blank commandline at startup
- The buttons: help (?), switch for scientific keyboard (kbd), status button (in red, click here to change the CAS configuration)

The on-line help gives a short description of all the CAS commands with examples that can be pasted to the commandline. A more complete description is available by clicking on Details. Command completion is enabled in commandlines with the Tab key.

Printing may be done natively to Postscript or with a working
`LaTeX`

installation (with `pstricks`

for 2-d graphs).

A list of commands of the CAS system.

The `gcd`

and `lcm`

commands apply to both argument types : they
return the greatest common divisor or the least common multiplicator.
Other arithmetic commands must begin with an `i`

if you want
to use them with integers, otherwise the arguments will be considered
as constant polynomials.

Given two integers `a`

and `b`

, the euclidean integer division
is defined by the equality :

a=b*q+r

where usually `r`

is taken between 0 and `b-1`

, or
in the symmetric representation, between `-b/2`

and `b/2`

.
The functions `iquo(a,b)`

and `irem(a,b)`

return respectively
`q`

and `r`

, or `iquorem(a,b)`

return both in a vector.
The `smod(a,b)`

function will return `r`

using the symmetric
remainder convention.

The `gcd(a,b)`

function returns the greatest common divisor
`d`

of two integers `a`

and `b`

. If you need two integers
`u`

and `v`

such that:

a*u+b*v=d

you should call `egcd(a,b)`

instead, it will return `[u,v,d]`

.

The `ichinrem([a,n],[b,m])`

call where `n`

and `m`

are prime together will return a vector `[c,n*m]`

such that
`c=a (mod n)`

and `c=b (mod m)`

.

The `is_prime(a)`

function will return 0 if `a`

is not prime.
It will return 2 if `a`

is known to be prime, and 1 if `a`

is a (strong) pseudo-prime. If you have compiled `xcas`

with PARI
support, you will get a prime certificate instead (see PARI documentation for
more information).

The `nextprime(a)`

and `prevprime(a)`

will return the next
or previous (pseudo-)prime, given an integer `a`

.

The `ifactor(a)`

function returns a factorization of `a`

.
It is a good idea to compile with PARI support if you plan to factor
relatively large integers (with prime factors having more than 20 digits).

Additional integer functions provided by `xcas`

are

`jacobi(a,b)`

and`legendre(a,b)`

, see the GMP documentation for more details.`pa2b2(p)`

return`[a,b]`

so that`p=a*a+b*b`

if`p=1 (mod 4)`

is prime.

Polynomials have two representations: symbolic representation or
by a vector of coefficients. In the symbolic representation you might
add the variable name as an additionnal parameter to the functions
you call, otherwise the default variable is used. For the vector
representation, it is recommended to use the right delimiter `poly1[`

instead of `[`

so that usual operations (addition, ...) behave
correctly (i.e. not like vectors or matrices).

`quo(a,b)`

`rem(a,b)`

and`quorem(a,b)`

return respectively`q`

,`r`

and`[q,r]`

polynomials so that`a=b*q+r`

and`degree(r)<degree(b)`

`gcd(a,b)`

return the greatest common divisor of two polynomials`egcd(a,b)`

is the extended euclidean GCD algorithm, like for integers it returns a list of 3 polynomials`u,v,d`

such that`au+bv=d`

.`chinrem`

return the chinese remainder for polynomials written as lists. The 2 arguments are two lists made of a polynomial modulo another polynomial (where the modulo polynomials must be prime together). The answer is the polynomial modulo the product of the modulo polynomials that reduce to the original polynomials modulo the original modulo polynomials`cyclotomic`

takes an integer n as argument and returns the n-th cyclotomic polynomial.

The `normal`

command rewrites a rational fraction as a ratio of two
coprime polynomials. If an expression is not rational, it is first
rationalized by substitution of transcendental expressions (e.g.
`sin(x)`

by a temporary identifier. Algebraic expressions
(e.g. `sqrt(x)`

) are normalized too.

The `factor`

command factorize polynomials. Like above a non
polynomial expression is first rationalized. You can choose the main
variable with respect to which the polynomial will be factorized by
adding it as second argument of `factor`

.

The `texpand`

function is called to expand transcendental
expressions like `exp(x+y)=exp(x)*exp(y)`

or similar rules
for trigonometric functions. The `tlin`

function does
the reverse operation for trigonometric functions, as the `lin`

function does it for exponentials.

The `halftan`

function rewrites trigonometric expressions
in terms of the tangent of the half angle. The `hyp2exp`

function rewrites hyperbolic functions in terms of exponentials.

The differentiation instruction is `diff(expression,variable)`

.
The undefined antiderivative is obtained using
`integrate(expression,variable)`

. If you need defined integration
between bounds `a`

and `b`

, choose
`integrate(expression,variable,a,b)`

for exact integration
or `romberg(expression,variable,a,b)`

for numeric integration.

Example of defined integration are Fourier coefficients of periodic
functions. They are provided using `fourier_an`

and `fourier_bn`

for trigonometric coefficients or using `fourier_cn`

for
complex exponentials coefficients.

Some discrete antiderivatives may be obtained using the
`sum(variable,expression)`

call.

For a limit the syntax is
`limit(expression,variable,limitpoint[,direction])`

.
For a series expansion
`series(expression,variable,limitpoint,order[,direction])`

.
`giac`

implementation of `limit`

and `series`

is based
on the mrv algorithm.

The `solve(expression,variable)`

call is used to find exact
solutions of (polynomial-)like equations. Use `newton`

instead
for numeric solutions (of a wider range of equations).

Arithmetic operations on matrices and vectors are done using the usual
operators. The scalar product of two vectors is obtained using the `*`

operator.

Gaussian elimination (Gauss-Bareiss) over a matrix is performed
using `rref(m)`

. The kernel of a linear application with matrix
m is obtained with `ker(m)`

. A system of linear equations (written
symbolically in a vector) can be solved via
`linsolve([equations],[variables])`

.

The determinant of a matrix may be obtained using two algorithms,
either Gauss-Bareiss invoking `det(m)`

, or by computing minors
`det_minor(m)`

. Actually, a last method is provided using the
computation of the constant coefficient of the characteristic polynomial
using Fadeev-Leverrier algorithm.

The characteristic polynomial of a matrix may be computed by Fadeev-Leverrier
algorithm calling `pcar(m)`

. For matrices withe coefficients in
a finite field, `pcar_hessenberg(m)`

is a better choice (`O(n^3)`

complexity where `n`

is the size of the matrix).

Eigenvalues and eigenvectors are computed using respectively `egvl(m)`

and `egv(m)`

. The Jordan normal form is obtained invoking
`jordan(m)`

.

Quadratic forms (written symbolically) can be reduced to sum and differences
of squares using `gauss(expression,[variables])`

.

There is some support for isometries: `mkisom`

may be used to
make an isometry from its proper elements as `isom(m)`

return the
proper elements of an isometry.

Add a figure (Edit menu of the session, Add item, then select geometry and graph 2-d or 3-d). As other objects, you can create geometrical objects anatically using the commandlines at the left. You may also create points, segments, etc. with the mouse (or the stylus) or move a geometrical object depending on the mouse mode (Pointer, point, segment, circle, etc.)

To configure or print a graph, use the menu at the right of the graph.

Add a spreadsheet (Edit menu of the session, Add item, spreadsheet). Cells may have a formal value, or eval to a geometric 2-d object that will be displayed in a dynamically linked 2-d graph.

The xcas and icas program provide an interpreted language that is similar to
popular other CAS programming language. This scripting language is
available in 4 flavours: C-like syntax (default) or compatibility
mode for simple Maple, Mupad or TI programs. We describe only the C-like
syntax. Instructions must end with a semi-column `;`

. Groups of
instructions may be combined like in C with brackets.

You can define a program in a commandline, but it is recommended to use a Program Editor (Edit->Add->Program menuitem of the session menubar) if it is larger than a few lines.

Click on the status button and select the programming style.
Alternatively, the command `maple_mode(0)`

or `maple_mode(1)`

or
`maple_mode(2)`

may be used to switch the language flavour
respectively from C-like to Maple-like or Mupad-like mode. Note that this
command takes effect only when the current parser session is finished
which means when the next command is processed in interative mode or at
the end of the current file in batch mode, hence you should not begin a script
file with this command. In batch mode you can achieve the mode switch by
setting the environment variable `GIAC_MAPLE_MODE`

, for example with
tcsh: `setenv GIAC_MAPLE_MODE 1`
or with bash `export GIAC_MAPLE_MODE=1`
will switch to the Maple-like language. Additionnally you can enter
the `maple_mode(1)`

command in the `.xcasrc`

of your home directory
to change the default behavior. Or inside `xcas`

you can run
the `Import`

command of the `File`

menu and select the flavour.
The `Export`

command can be used to translate the current level
of the history inside `xcas`

to a file, or the `View as`

command
of the `Edit`

menu to translate to the Help output window.

The language accept local and global variables, variables are not typed.
Global variables do not need to be declared, local variables must be declared
at the beginning of a function by the keyword `local`

followed by
the names of the local variables separated by commas `,`

with a final
semi-columns `;`

The affectation sign is `:=`

like popular CAS and unlike C.
For large vectors, lists and matrices, you may also use `=<`

to make
in-place modifications (in other words by reference), but be aware
that all references of the object will be modified.
Other operations (e.g. {+ - * /}) and function calls are done like in C
or like in an interactive session.
As in C, the equality test is `==`

. The single equal sign `=`

is used to return an equation (note that
an equation will be transformed in a test
in some situations where an equation could not be expected).
The other tests are `!=`

for non equal, `< <= > >=`

for
real value comparisons. You can combine tests with `&&`

or `and`

,
and `||`

or `or`

. The boolean negation is `!`

or `not`

.

The loop keywoard is like in C

`for (initialization;while_condition;increment){ loop_block }`

You can break a loop inside the loop block with `break;`

.
You can skip immediately to the next iteration with `continue;`

.

The conditionnal keywoard is like in C

`if (condition) { bloc_if_true } [ else { bloc_if_false } ]`

Additionnaly, multiple-cases is translated like in C

`swith (variable){ case (value_1): ... break; default: ... ; } `

Functions are declared and implemeted together like this

`function_name(parameters):={ definition }`

Parameters are like local variables with an additional initialization from the values of the parameters inside the calling instruction.

`return return_value;`

should be used to return the value
of the function.

It is not possible to pass arguments by reference, only by value.

If one of these variables `GIAC_MAPLE`

, `GIAC_MUPAD`

,
`GIAC_C`

or `GIAC_TI`

is defined, the corresponding
syntax mode will be in effect. If `XCAS_RPN`

is defined,
then xcas will start in RPN mode.

The variable `XCAS_ROOT`

may be used for a custom xcas installation,
it should point to the directory where xcas is installed. `XCAS_LOCALE`

should point to the directory where the locales are. `XCAS_TMP`

may be defined for temporary exchange files between xcas processes,
if not defined it will use the home directory.

The variable `PARI_SIZE`

may be used to define the memory
available for pari.

The variable `BROWSER`

may be used for the HTML documentation browser.

The variable `LANG`

may be used for internationalization.

The variable `GIAC_TIME`

and `GIAC_TEX`

may be used
in giac readline interface to ask for timing and tex output.
`GIAC_DEBUG`

will give some info on the internals used.

In this chapter we will first describe the generic data type of giac,
the `gen`

class. Then we describe the most important data
types than `gen`

dispatches to (polynomials, vectors, symbolic
objects and gen unary functions). At this point, the reader should be
able to code using `giac`

, hence we describe how to integrate
code to `giac`

by inclusion in the library or as a separate
runtime loadable library (called module). The last item describes
how you can add new mathematical objects, e.g. quaternions,
inside the `gen`

type.

Giac uses the C++ language because it is easier to write algebraic
operations using usual operators, for example `a+b*x`

is easier
to understand and modify than `add(a,mul(b,x))`

, but it does not
require that you learn object oriented programming. In fact it is more
a C library using C++ features that makes programming easier (like the
I/O streams and the Standard Template Library). However you will need
a recent C++ compiler, e.g. `gcc`

version 2.95 or later.

`gen`

is the class used to represent mathematical objects
(`#include <giac/gen.h>`

). It's a C union, made either of “direct”
objects like `int`

or `double`

or of pointers to heap allocated objects that are reference counted.
Memory allocation is handled by the class itself (except for
user-defined object types). You can check
the actual type of a variable of type `gen`

, e.g. `gen e;`

,
using it's `type`

field (e.g. `if (e.type==...)`

). This
`type`

field of a `gen`

is an `int`

.

The `gen`

might be~:

- an immediate int (
`e.type==_INT_`

) - a double (
`e.type==_DOUBLE_`

) - an arbitrary precision integer (
`e.type==_ZINT`

) - a complex number (
`e.type==_CPLX`

), a pointer to two objects of type`gen`

the real and imaginary parts - a global name (
`e.type==_IDNT`

), with a pointer to an`identificateur`

type - a symbolic object (
`e.type==_SYMB`

), with a pointer to a`symbolic`

type - a vector object (in fact it is a list) (
`e.type==_VECT`

), with a pointer to a`vecteur`

type - a function object (
`e.type==_FUNC`

), with a pointer to a`unary_function_ptr`

type

Some other types are available (e.g. a pointer to `gen_user`

an object you can derive to make your own class, or arbitrary precision
floating point numbers `_REAL`

), for a complete
description look at `giac/gen.h`

(if you have installed `giac`

the path to the include files is `/usr/local/include/giac`

unless you
override the default, if you did not install it, the path is the path
to the `src`

directory of the source code distribution).

If you want to access the underlying type, after checking that the type is correct, you can do the following:

- for immediate int:
`int i=e.val;`

- for double:
`double d=e._DOUBLE_val;`

- for arbitray precision integers:
`mpz_t * m=e._ZINTptr;`

- for complex numbers:
`gen realpart=*e._CPLXptr,impart=*(e._CPLXptr+1);`

- for identificateur:
`identificateur i=*e._IDNTptr;`

- for symbolics:
`symbolic s=*e._SYMBptr;`

- for composites:
`vecteur v=*e._VECTptr;`

- for function objects:
`unary_function_ptr u=*e._FUNCptr`

In addition to the main `type`

, each `gen`

has a `subtype`

.
This subtype is used sometimes to select different behaviour, e.g.
adding a constant to a vector might add the constant to all terms for
some geometric objects represented using vectors, only to the term of
the diagonal of a square matrix, or to the last term for dense polynomials.
See `giac/dispatch.h`

for the description of the subtypes.

Polynomials are available as:

- sparse multivariate polynomials
`polynome`

, header files are`gausspol.h`

,`poly.h`

,`monomial.h`

- dense univariate polynomials:
`poly1`

or alias`modpoly`

used for modular univariate polynomials. The type used is the same as for vectors and matrices. Header files are`giac/modfactor.h`

and`giac/modpoly.h`

.

A `gen`

can be a polynomials if it's `type`

field is
respectively `_POLY`

(sparse) or `_VECT`

(dense).
Conversion functions to and from the symbolic representation with
respect to global names are declared in `giac/sym2poly.cc/h`

.

The type used for vectors and matrices is the same, it's a
`std::vector<gen>`

(unless you have configured with
`--enable-debug`

). The header file is `giac/vecteur.h`

.
A `gen`

can be a vector if it's `type`

field is
`_VECT`

.

Symbolic objects are trees. The `sommet`

is a `unary_function_ptr`

(a class pointing to the function). The `feuille`

is either
an atomic `gen`

(for a function with one argument) or a composite
(`feuille.type==_VECT`

) for a function with more than one argument
(these functions appears therefore as a function with one argument which
is the list of all it's arguments).

In the giac library, every function is viewed as a function taking one
argument and returning one argument. Almost every Xcas functions have
a C++ equivalent with the same name preceded by a _.
If a Xcas function has more than one argument, these arguments
are packed in a vector which is the first argument of the C++ function.
Most C++ functions require a second argument, which is
a context pointer. This context pointer
encapsulate all the context (e.g. complex vs real mode, or all the
variables that are assigned or assumed). You can use
`giac::context0`

as global context pointer or define a context
`giac::context ct;`

and use `&ct`

as last argument to the function.

The files `usual.cc/.h`

give examples of declaration e.g. for
exponential and trigonometric functions. Unary functions have the
following members~:

- a fonction taking a
`gen`

and a`context *`

and returning an`gen`

which does the job - partial derivatives of this function if they exist
- a special Taylor expansion if it's needed (see e.g.
`taylor_asin`

). This is always the case if your function is defined at infinity. Note that this function is called at initialization so that you can include code in it for example to add your function to the symbolic preprocessing step of the`limit/series`

algorithm. - a string identifier for printing. If you want the parser to
recognize your function you must add a line in
`input_lexer.ll`

(see for example`"sin"`

) or you must register it (see below). - two special printing function if normal printing (normal printing means printing the function name followed by the argument(s) in parentheses) is not the right way to print. A null pointer means using normal printing.

`unary_function_eval`

is defined, you must construct
a `unary_function_ptr`

to be able to use it inside symbolics.
When declaring the `unary_function_ptr`

,
you may give an optional argument to specify a behavior for the evaluation
of arguments (quoting or special parser rules).
In this case, you may give a second optionnal argument
to register your function dynamically in the list of function names
recognized by the lexer. Be sure to link the object file so that
initialization occurs after the initialization of `input_lexer.ll`

,
it means you must put your object file before `input_lexer.o`

when linking (see for example the position of `moyal.o`

in
the `Makefile.am`

file, `moyal`

is one example where dynamic registering is done).
You have of course the option to declare the function name
statically in the file `input_lexer.ll`

but this is not recommended.

Here is one example of a dynamically linkable function named
`example`

which takes 2 arguments and returns the sum divided
by the product if the argument are integers and return itself otherwise.
The C++ header `example.h`

code looks like

#ifndef __EXAMPLE_H #define __EXAMPLE_H #include <giac/config.h> #include <giac/gen.h> #include <giac/unary.h> #ifndef NO_NAMESPACE_GIAC namespace giac { #endif // ndef NO_NAMESPACE_GIAC gen example(const gen & a,const gen & b,GIAC_CONTEXT); gen _example(const gen & args,GIAC_CONTEXT); extern const unary_function_ptr * const at_example ; #ifndef NO_NAMESPACE_GIAC } // namespace giac #endif // ndef NO_NAMESPACE_GIAC #endif // __EXAMPLE_H

The C++ source code looks like:

using namespace std; #include "example.h" #include <giac/giac.h> #ifndef NO_NAMESPACE_GIAC namespace giac { #endif // ndef NO_NAMESPACE_GIAC gen example(const gen & a,const gen & b,GIAC_CONTEXT){ if (is_integer(a) && is_integer(b)) return (a+b)/(a*b); return symbolic(at_example,makesequence(a,b)); } gen _example(const gen & args,GIAC_CONTEXT){ if ( (args.type!=_VECT) || (args._VECTptr->size()!=2) ) return gensizeerr(contextptr); // type checking : args must be a vector of size 2 vecteur & v=*args._VECTptr; return example(v[0],v[1],contextptr); } const string _example_s("example"); static define_unary_function_eval (__example,&_example,_example_s); define_unary_function_ptr5( at_example ,alias_at_example,&__example,0,true); #ifndef NO_NAMESPACE_GIAC } #endif // ndef NO_NAMESPACE_GIAC

Compile it with

c++ -g -c example.cc

To test your code, you should write the following `test.cc`

program

#include "example.h" using namespace std; using namespace giac; int main(){ gen args; context ct; cout << "Enter arguments of example function, for example 2,3 "; cin >> args; cout << "Result: " << _example(args,&ct) << endl; }

Compile it with the command

c++ -g example.o test.cc -lgiac -lgmp

You might need to link to other libraries e.g.
`-lreadline -lhistory -lcurses`

depedning on your installation.
Then run `a.out`

. Here you would test e.g. with `[1,2]`

.

You can debug your program as usual, e.g. with
`gdb a.out`

, it is recommended to create a `.gdbinit`

file
in the current directory so that you can use the `v`

command
to print giac data, the `.gdbinit`

file should contain :

echo Defining v as print command for giac types\n define v print ($arg0).dbgprint() end

When your function is tested, you can add it to the library. Edit
the file `Makefile.am`

of the `src`

subdirectory
of `giac`

: just add `example.cc`

before `input_lexer.cc`

in the `libgiac_la_SOURCES`

line and add `example.h`

in the
`giacinclude_HEADERS`

line.

To rebuild the library go in the `giac`

directory and type
`automake; make`

If you want to share your function(s) with other people, you must
license it under the GPL (because it will be linked to GPL-ed code).
Add the GPL header to the files, and send them to the `giac`

contribution e-mail, currently `mailto:parisse@fourier.univ-grenoble-alpes.fr`

/* * Copyright (C) 2007 Your name * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */

Another way to share your code could be to build a dynamic library
that can be loaded at runtime using facilities of `<dlfcns.h>`

.
Warning: modules do not work with static binaries. Be sure
to have dynamic binaries (this is the default when you compile giac,
but the packaged `xcas`

distributed as a binary is build static to
avoid incompatible libraries).

Let us define a function named `mydll`

in the file `mydll.cc`

like
this :

#include <giac/config.h> #include <giac/giac.h> #ifndef NO_NAMESPACE_GIAC namespace giac { #endif // ndef NO_NAMESPACE_GIAC const string _mydll_s("mydll"); gen _mydll(const gen & args,GIAC_CONTEXT){ return sin(ln(args,contextptr),contextptr); } unary_function_eval __mydll(0,&giac::_mydll,_mydll_s); unary_function_ptr at_mydll (&__mydll,0,true); // auto-register #ifndef NO_NAMESPACE_GIAC } // namespace giac #endif // ndef NO_NAMESPACE_GIAC

Compile it like this

c++ -fPIC -DPIC -g -c mydll.cc -o mydll.lo cc -shared mydll.lo -lc -Wl,-soname -Wl,libgiac_mydll.so.0 -o libgiac_mydll.so.0.0.0 rm -f libgiac_mydll.so.0 && ln -s libgiac_mydll.so.0.0.0 libgiac_mydll.so.0 rm -f libgiac_mydll.so && ln -s libgiac_mydll.so.0.0.0 libgiac_mydll.so

The library is loadable at runtime in a session using the command
`insmod("mydll")`

assuming it is stored in a directory available
from `LD_LIBRARY_PATH`

or in `/etc/ld.so.conf`

otherwise
you must put a path to the library file (beginning with `./`

if
it is in the current directory), something like
`insmod("/path_to/libgiac_mydll.so")`

A nice way to test your code is to add the following line in your
`~/.xcasrc`

file :

insmod("path_to_libmydll/libmydll.so");

where you replace `path_to_libmydll.so`

with the actual path to
`libmydll.so`

for example `/home/joe`

if your login name is
`joe`

and `mydll`

is in your home directory.
Then if you are using `emacs`

as editor, put as first line of
the file `mydll.cc`

// -*- mode:C++ ; compile-command: "g++ -I.. -fPIC -DPIC -g -c mydll.cc -o mydll.lo && ln -sf mydll.lo mydll.o && gcc -shared mydll.lo -lc -Wl,-soname -Wl,libmydll.so.0 -o libmydll.so.0.0.0 && ln -sf libmydll.so.0.0.0 libmydll.so.0 && ln -sf libmydll.so.0.0.0 libmydll.so" -*-

Now you can compile it with `Compile`

of the menu `Tools`

and the resulting code is automatically loaded when you launch a new
session with `xcas`

or `cas`

which makes testing a breath.

The class `gen_user`

can be derived so that you can include
your own data inside `gen`

. Look at the declaration of `gen_user`

in the file `gen.h`

and at the example of the quaternions
in the files `quater.h`

and `quater.cc`

.

Type the following text with your favorite editor

#include <giac/config.h> #include <giac/giac.h> using namespace std; using namespace giac; int main(){ context ct; gen e("x^2-1",&ct); e=eval(e,1,&ct); cout << _factor(e,&ct) << endl; }

save it e.g. as `tryit.cc`

and compile it with

`c++ -g tryit.cc -lgiac -lgmp`

If you get unresolved symbol, then `readline`

is probably enabled
and you should compile like that

`c++ -g tryit.cc -lgiac -lgmp -lreadline -lcurses`

You can now run `a.out`

which will print the factorisation of
`x^2-1`

.

You can also run the program step by step using gdb. We
recommended that you copy the file `.gdbinit`

from the `src`

directory of the giac distribution, because it enables using
`v varname`

to print the variable `varname`

of type `gen`

.

Some explanations of the code:

- the
`#include <giac/giac.h>`

directive includes all the headers of giac (which includes some STL headers like`string`

or`vector`

). - The
`using namespace`

directive are not mandatory, if you don't use them, you need to modify some of the code, e.g. use`std::string`

instead of`string`

or`giac::gen`

instead of`gen`

. - Variables of type
`gen`

can be constructed from strings (using the parser), from some C types (like`int`

or`double`

), from the STL type`std::complex<double>`

or from streams (using the parser). - Operations like
`+, -, *`

are defined on the`gen`

type but the division is not redefined to avoid confusion between integers (use`iquo`

) and double C division (use`rdiv`

). For powers, use`pow`

as usual.

- gen: Gen
- Matrices: Vectors and matrices
- Polynomials: Polynomials
- Symbolics: Symbolics
- Unary functions: Unary functions
- User defined data: User defined data
- Vectors: Vectors and matrices

- 1 Installing Giac/Xcas
- 2 Using xcas, an user-interface to giac
- 2.1 The interface
- 2.2 Computer algebra system commands
- 2.3 Geometry
- 2.4 Spreadsheet
- 2.5 The xcas scripting language
- 2.6 Selecting the language mode
- 2.7 Data
- 2.8 Environment variables

- 3 The gen class
- 4 Some examples of C++ program using giac
- 5 A first simple example
- Concept Index