PyGiNaC

PyGiNaC is a Python module that acts as an interface to the C++ library GiNaC. This open-source framework enables symbolic computation within C++. PyGiNaC is built by leveraging the Boost.Python library, and currently, the package is considered to be in an "alpha" state. It means that the GiNaC classes are only partially exposed, many parts of the regression test suite are unconverted, and no documentation exists as of yet. However, these drawbacks are expected to change shortly.

To the best of our knowledge, PyGiNaC has two predecessors - one written by Pearu Peterson a few years back and another by Ondrej Certik. Despite not being complete, PyGiNaC can perform some impressive computations. For instance, solving a linear system of equations using the Python interpreter is straightforward, as seen in this example -

>>> x = symbol('x')
>>> y = symbol('y')
>>> lsolve([3*x + 5*y == 2, 5*x+y == -3], [x,y])
[, ]
>>> [str(x) for x in lsolve([3*x + 5*y == 2, 5*x+y == -3], [x,y])]
['x==-17/22', 'y==19/22']
>>>

PyGiNaC also handles power series of functions, as demonstrated below -

>>> x = symbol('x')
>>> print sin(x).series(x==0, 8)
1*x+(-1/6)*x**3+1/120*x**5+(-1/5040)*x**7+Order(x**8)
>>>

Moreover, PyGiNaC lets you try out a modified version of one of Ramanujan's identities. As shown below, the example has been ripped off from the GiNaC's regression test suite -

>>> e1 = pow(1 + pow(3,numeric(1,5)) - pow(3,numeric(2,5)),3)
>>> e2 = expand(e1 - 10 + 5*pow(3,numeric(3,5)))
>>> print e2.expand()
0
>>>

Here, the numeric(3,5) refers to a fraction 3/5.