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.