PARI/GP – computer algebra system for number theory

PARI/GP is a computer algebra system specialising in number theory. It provides efficient algorithms for integer factorisation, algebraic number theory, elliptic curves, modular forms and related branches of mathematics. The system also handles matrices, polynomials, power series, algebraic numbers and high-precision numerical calculations.

The software comprises several complementary components. PARI is a library of mathematical functions that can be called directly from other programs. gp is an interactive command-line environment for using those functions, while GP is its associated scripting language. The gp2c compiler translates supported GP code into C, allowing computationally demanding procedures to execute more efficiently.

PARI/GP is particularly valuable to researchers working with exact arithmetic and specialised number-theoretic algorithms. Its interactive environment can be used for exploratory calculations, while scripts and library interfaces support longer computations and integration into other mathematical software.

This is free and open source software.

Key Features

• Fast integer arithmetic, factorisation and primality testing.
• Algorithms for algebraic number fields, ideals and class groups.
• Arithmetic and analysis of elliptic curves.
• Computation with modular forms, modular symbols and L-functions.
• Calculations involving p-adic numbers and local fields.
• Polynomial arithmetic, factorisation and root finding.
• Power series and formal series computations.
• Matrix operations and linear algebra over different coefficient domains.
• High-precision real and complex arithmetic.
• Transcendental functions, numerical integration and summation.
• Interactive calculations through the gp command-line interpreter.
• GP scripting for functions, loops and repeatable computations.
• gp2c compiler for translating supported GP programs into C.
• PARI library for calling mathematical routines from external programs.
• Parallel computation facilities for suitable mathematical algorithms.
• Cross-platform support – runs on Linux, macOS, and Windows.

Website: pari.math.u-bordeaux.fr
Support:
Developer: PARI development team at the University of Bordeaux
License: GNU General Public License v2.0

PARI/GP is written in C. Learn C with our recommended free books and free tutorials.

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