Computer algebra system for high-performance number theory computations

<rendered-html><p>PARI/GP is a widely used computer algebra system designed for fast 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 is also available as a C library to allow for faster computations.</p> <p>Originally developed by Henri Cohen and his co-workers (Université Bordeaux I, France), PARI is now under the GPL and maintained by Karim Belabas with the help of many volunteer contributors.</p> <ul> <li>PARI is a C library, allowing fast computations.</li> <li>gp is an easy-to-use interactive shell giving access to the PARI functions.</li> <li>GP is the name of gp’s scripting language.</li> <li>gp2c, the GP-to-C compiler, combines the best of both worlds by compiling GP scripts to the C language and transparently loading the resulting functions into gp. (gp2c-compiled scripts will typically run 3 or 4 times faster.) gp2c currently only understands a subset of the GP language.</li> </ul> </rendered-html>