Category:PARI/GP: Difference between revisions

PARI/GP
This programming language may be used to instruct a computer to perform a task.

Official website

Execution method:	Interpreted or compiled
Garbage collected:	Yes
Parameter passing methods:	By reference, By value
Type strength:	Weak
Type checking:	Dynamic
Lang tag(s):	parigp, c
See Also:	PARI/GP compared to other languages

Listed below are all of the tasks on Rosetta Code which have been solved using PARI/GP.

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/GP is composed of two parts: a C library called PARI and an interface, gp, to this library. GP scripts are concise, easy to write, and resemble mathematical language. (Terminology: the scripting language of gp is called GP.)

PARI was written by Henri Cohen and others at Université de Bordeaux and is now maintained by Karim Belabas. gp was originally written by Dominique Bernardi, then maintained and enhanced by Karim Belabas and Ilya Zakharevich, and finally rewritten by Bill Allombert.

Getting PARI/GP

PARI/GP can be used in many different operating systems. This is a reasonably comprehensive list of currently-supported systems; for other systems, please use the mailing lists.

Coding with PARI

The most common way to use PARI is through the gp calculator, using its own scripting language, GP. But there are other interfaces to PARI beside gp:

• PariGP on EmacsWiki, PariEmacs
• Pari-tty
• pariGUIde
• vim-notebook (see also the author's video on using gp from vim)
• Jupyter kernel

If you want to program with PARI, many languages are supported:

• C: PARI is written in C, so it's very easy to either write your own programs or extend gp using C.
  • The gp2c utility converts GP scripts into executable C code.
  • For use with the Gnu Mpc library, there is also Pari-Gnump.
  • PariTwine is a glue library for various math libraries including GMP, GNU MPFR, GNU MPC, FLINT, ARB and CMH.
• C++: PARI can be used directly in C++. The code is intentionally written in a C++-compatible style. -fpermissive may be useful when compiling with g++.
• Python:
  • SageMath (or SAGE) is a Python-based system that includes GP among others
  • pari-python
  • cypari/cypari2 is a fork of the GP component of SageMath (see also the voluminous CyPari2 Documentation)
• Perl:
  • Math::Pari
  • GPP
• Common Lisp: Use Pari (CLISP).
• Mathematica: A quick tutorial using MathLink is available.

See also

• Wikipedia:PARI/GP

Resources

General

• Official FAQ
• PARI/GP FAQ
• Ateliers PARI/GP: Conference slides and other resources
• Comparison with Magma, GAP, and Singular

Tutorials

• Official tutorial by The PARI Group (58 pp., 2018)
• Tutorial on Elliptic Curves by Bill Allombert and Karim Belabas (5 pp., 2016)
• Beginning PARI Programming for CSE/MATH 467 by W. Dale Brownawell (7 pp., 2014)
• Class notes including PARI/GP tutorial and sample code by Masha Vlasenko (2013)
• Tutorial by Siman Wong (6 pp., 2009)
• Exploring binary numbers with PARI/GP calculator by Rick Regan (appx. 4 pp., 2009)
• Class notes, parts 12345sieve by Benjamin L. Levitt (41 pp., 2009; now offline?)
• Introduction by Keith Conrad (7 pp., 2008)
• PARI/GP programming for basic cryptography by Minh Van Nguyen (appx. 3 pp., 2008); also appears in an extended version (9 pp., 2008)
• Tutorial by Robert B. Ash (20 pp., 2007)
• The Pari Package On Linux, by Klaus-Peter Nischke (3 pp., 1995)
• Pari/GP Tutorial by Akinola Richard Olatokunbo (now offline; archived version)
• Parallel Computation by Bill Allombert

Non-English language

• French tutorials (slides) by Bill Allombert (2017):
  • Introduction à PARI/GP (13 pp.)
  • Programmation GP (11 pp.)
  • Théorie algébrique des nombres (31 pp.)
  • Théorie algébrique des nombres avancée (22 pp.)
  • Courbes elliptiques sur les corps finis (4 pp.)
• Erste Schritte mit PARI/GP by Lars Fischer (13 pp., 2007; German)
• Pari Gp مع NotPad++ by NoorDeen Rahmani (2020; 2:46; Arabic) -- setting up Notepad++ for syntax highlighting for PARI/GP.

Video tutorials

• Pari/GP Tutorial: Basics by Leandro Junes (2020, 19:04)
• Video demo of RSA in PARI/GP by Maren1955 (2014, 17:39)
• Video tutorials, parts 1 2 3 4 (2011, appx. 20 minutes)

Papers on PARI/GP

• Karim Belabas and Henri Cohen, Modular Forms in Pari/GP, Research in the Mathematical Sciences 5:37 (2018)
• Henri Cohen, Expansions at Cusps and Petersson Products in Pari/GP, Elliptic Integrals, Functions, and Modular Forms in Quantum Field Theory, Nov 2017, Zeuthen, Germany. Springer Wien, Elliptic Integrals, Functions, and Modular Forms in Quantum Field Theory. (2018)
• Karim Belabas and Jean-François Jaulent, The logarithmic class group package in PARI/GP, Mathematical Publications of Besançon, Algebra and Number Theory (2016), pp. 5–18.
• Bill Alombert, A new interpretor for PARI/GP, Journal de Théorie des Nombres de Bordeaux 20:3 (2008), pp. 531–541. (English)
• Paul Zimmermann, The Ups and Downs of PARI/GP in the last 20 years, Explicit Methods in Number Theory, October 15th-19th 2007
• Robert H. Lewis and Michael Wester, Comparison of polynomial-oriented computer algebra systems, ACM SIGSAM Bulletin 33:4 (1999), pp. 5-13.
• Henri Cohen, Computing in algebraic number fields. In P. L. Butzer (ed.) et al., Karl der Grosse und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Band 2: Mathematisches Wissen. Turnhout: Brepols. 505-520 (1998)