PARI/GP

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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.

Originally (1985-1996) developed at Université Bordeaux I by a team led by Henri Cohen, PARI-GP is maintained since 1995 by Karim Belabas (Université Bordeaux 1) with the help of many volunteer contributors.

PARI/GP is free software, distributed under the GPL license.

PARI is a C library, allowing fast computations.
gp is an interactive shell giving access to PARI functions, much easier to use.
GP is the name of gp' s scripting language
gp2c the GP-to-C compiler makes the best of both worlds, compiling GP scripts to the C language, and loading the resulting functions in gp (gp2c-compiled scripts will typically run 3 or 4 times faster). The compiler currently only understands a subset of the GP language.

These pages contain, or link to, a number of resources for PARI/GP, which I found could be useful. You might also be interested in the main PARI site

Resources for PARI/GP:

A few screenshots of gp, running in an X terminal: [1], [2], (to be continued).

Front ends / interfaces

SAGE (GPL) is an impressive Python framework acting as a front-end for many mathematical software. Developped by William Stein and many others.
GNU TeXmacs (GPL) is a powerful Wysiwyg editor, which can be used as a graphical frontend for computer algebra systems, in particular gp (screenshot). Developped by Joris van der Hoeven and many others.
Math::Pari is a Perl interface for PARI. See here for most recent versions.
CLISP (an ANSI Common Lisp) offers an interface to PARI.
How to get PARI/GP running on an iPad.
Pari-TTY is a Windows-specific GUI for PARI, written by Gottfried Helms.
PariGUIde (GPL) is a nice looking Graphical User Interface for gp, based on the Qt library. Available for Windows and Linux. Written by Hartmut Ring. (No longer maintained.)
A successor MathGUIde is now based on Python, with a PARI plugin.

Related stuff

GMP (C, LGPL), CLN (C++, GPL) [multiprecision], NTL (C++, GPL) [polynomial arithmetic, lattice reduction], LiDiA (C++, freely available, not free) [number theory], GiNaC (C++, GPL) [computer algebra] are other good libraries to write number theoretic programs.
Magma and KANT/KASH are other useful packages to do algebraic number theory (and much more in the case of Magma, which contains KANT). KANT is freely available (not free), Magma is a proprietary commercial system (non-profit, cost recovery).
GAP (GPL) is a nice system in discrete algebra and computational group theory.

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Karim Belabas
Sat Sep 18 17:46:11 MEST 2004