2.1 How to use it from within C++

The GiNaC open framework for symbolic computation within the C++ programming language does not try to define a language of its own as conventional CAS do. Instead, it extends the capabilities of C++ by symbolic manipulations. Here is how to generate and print a simple (and rather pointless) bivariate polynomial with some large coefficients:

#include <iostream>
#include <ginac/ginac.h>
using namespace std;
using namespace GiNaC;

int main()
{
    symbol x("x"), y("y");
    ex poly;

    for (int i=0; i<3; ++i)
        poly += factorial(i+16)*pow(x,i)*pow(y,2-i);

    cout << poly << endl;
    return 0;
}

Assuming the file is called ‘hello.cc’, on our system we can compile and run it like this:

$ c++ hello.cc -o hello -lcln -lginac
$ ./hello
355687428096000*x*y+20922789888000*y^2+6402373705728000*x^2

(See section Package tools, for tools that help you when creating a software package that uses GiNaC.)

Next, there is a more meaningful C++ program that calls a function which generates Hermite polynomials in a specified free variable.

#include <iostream>
#include <ginac/ginac.h>
using namespace std;
using namespace GiNaC;

ex HermitePoly(const symbol & x, int n)
{
    ex HKer=exp(-pow(x, 2));
    // uses the identity H_n(x) == (-1)^n exp(x^2) (d/dx)^n exp(-x^2)
    return normal(pow(-1, n) * diff(HKer, x, n) / HKer);
}

int main()
{
    symbol z("z");

    for (int i=0; i<6; ++i)
        cout << "H_" << i << "(z) == " << HermitePoly(z,i) << endl;

    return 0;
}

When run, this will type out

H_0(z) == 1
H_1(z) == 2*z
H_2(z) == 4*z^2-2
H_3(z) == -12*z+8*z^3
H_4(z) == -48*z^2+16*z^4+12
H_5(z) == 120*z-160*z^3+32*z^5

This method of generating the coefficients is of course far from optimal for production purposes.

In order to show some more examples of what GiNaC can do we will now use the ginsh, a simple GiNaC interactive shell that provides a convenient window into GiNaC's capabilities.