PARI is a widely used computer algebra system designed for fasti computations in number theory (factorizations, algebraic number theory, elliptic curves...), 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/GP is an advanced programmable calculator, which computes symbolically as long as possible, numerically where needed, and contains a wealth of number-theoretic functions.