PARI/GP is a widely used computer algebra system designed for fast
computations in number theory (factorizations, algebraic number theory,
elliptic curves, modular forms, L functions...), but also contains a
large number of other useful functions to compute with mathematical
entities such as matrices, polynomials, power series, algebraic numbers
etc., and a lot of transcendental functions. PARI is also available as
a C library to allow for faster computations.