Open science prize for PARI/GP open source mathematics software

The founding team

Initially developed by Henri Cohen and his team at theUniversity of Bordeaux I, PARI/GP is currently licensed under the GNU General Public License (GNU GPL), and has been maintained by Karim Belabas since 1994, with the help of numerous volunteer contributors. Bill Allombert joined the project around 1998. Today, Aurel Page is the software's scientific director.

Introduction to the software

PARI/GP is a formal calculation system widely used by the international number theorist community. Designed for fast arithmetic calculations (factorizations, algebraic number theory, elliptic curves, modular forms, L-functions), it also contains a large number of functions for matrix and polynomial calculations, integration or numerical summation, as well as numerous transcendental functions. To optimize its computational performance, PARI is also available as a library in the C programming language.

• PARI is a C library, enabling fast calculations.
• gp is an interpreter, giving access to PARI routines, but much simpler and more intuitive to use.
• GP is the name of the language understood by gp.
• gp2c is a compiler that translates the GP language into the C language. This combines the advantages of gp and PARI, by compiling GP scripts in C, then loading the corresponding functions into gp transparently (a script compiled by gp2c will typically be four times faster). At present, gp2c can only handle part of the GP language.

According to Bill Allombert, “the name of the software comes from historical reasons. “Pari“ refers to both ‘arithmetic program‘  and ‘Pascal's wager’, since the software was originally written in the Pascal programming language. As for “gp”, “great programmable”, Bill Allombert explains, “we're referring to the calculator”. The software was originally called ‘gc ‘ for ‘great calculator ‘, in reference to the UNIX commands  ‘bc ‘ for ’basic calculator ” and “ dc ” for “desk calculator ”. “As a joke, we determined the suffix "gpc" to refer to ’"great programmable calculator” and then shortened it to “ gp”. It's stuck ever since!

Technical specifics

“ The scientific perimeter is pyramidal,” explains Bill Allombert. “The lower layers are accessible to mathematicians without having to do very high maths. This is the case, for example, with multi-precision calculation, which is fairly basic but useful for many scientists. One of the advantages of PARI/GP software is that it's very compact, yet does a lot of things: it can be integrated into other programs without compromising the latter ”.

Winner in the “ community ”category

Awarded the open science prize for free research software in the “community” category, PARI/GP software stands out for its solidarity and knowledge-sharing actions aimed at fellow scientists. Every year, and since 2012, the team plans a highlight during a week in January. Bill Allombert describes the program: “ In the morning, we organize tutorials and presentations on new software features. There are also presentations on possible optimizations by various speakers. In the afternoons, the groups are divided into different rooms and work out their individual PARI/GP problems. We give each other advice on how to move forward, and help each other out .

In addition to this annual highlight, more occasional workshops for students are organized in various countries (France, India, Italy, Morocco, Turkey, etc.).

Managing contributions

“We don't have a defined protocol for contributions,” says Aurel Page, ”everything goes through us, and we discuss it . The reason for this is that most contributions are written in GP, requiring conversion to C since PARI is written in this language. The software counts nearly 60 contributors from many countries: Germany, the United States of America, France, Japan, the Netherlands, the Philippines... A diversity that is a sign of the software's richness.

Since 2018, PARI/GP has been increasingly cited in research articles, in line with evolving bibliographic standards.

Discover the list of contributions