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Making a C++ program with the Giac library

The easiest way if you have a Debian-based distribution (debian, ubuntu, ...) is probably to install the giac debian package and add the required libraries headers, something like
apt-get install libgmp3-dev xlibmesa3-dev libpng12-dev
You will also need the NTL headers which are not available as debian packages, therefore you should install NTL as explained below.
On other distributions, you will have to compile giac from source.
The source code of giac has an examples/demo folder, where you will find a test program named pgcd.cc that you should be able to compile (g++ pgcd.cc -lgiac -lgmp) once all headers are correctly installed.
Now look at the info documentation of Giac for data structures (like the gen type), etc.

Compiling Giac from source