RosettaCodeData/Lang/PARI-GP/00-LANG.txt

{{language|PARI/GP
|exec=both<!-- interpreted with gp or compiled via gp2c -->
|site=http://pari.math.u-bordeaux.fr/
|gc=yes<!-- GP is garbage-collected; PARI does this manually using an internal heap -->
|parampass=both<!-- by reference is limited in GP but the limits do not apply in PARI -->
|strength=weak
|checking=dynamic
|hopl=no
|LCT=yes
|tags=parigp, c
}}
{{language programming paradigm|Dynamic}}
{{language programming paradigm|Functional}}
{{language programming paradigm|Procedural}}

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; Aurel Page is the current project leader.  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 [https://pari.math.u-bordeaux.fr/lists-index.html mailing lists].

{| class="wikitable"
|-
! Operating system
! Kind
! Type of install
! Link
! How to install
|-
| rowspan="3" | Windows
| various
| installer (stable or development)
| [http://pari.math.u-bordeaux.fr/download.html#windows official site]
| run installer
|-
| XP, Vista, 7, 8, 10
| standalone binaries (stable or development)
| [http://pari.math.u-bordeaux.fr/download.html#windows official site]
| run
|-
| various
| standalone binaries (daily)
| [http://pari.math.u-bordeaux.fr/pub/pari/windows/snapshots/ official site]
| run
|-
| rowspan="7" | Linux
| Ubuntu/Debian
| package manager
| [https://packages.debian.org/stretch/pari-gp Debian packages]
| <code>sudo apt-get install pari-gp</code>
|-
| Fedora
| package manager
| [https://apps.fedoraproject.org/packages/pari-gp Fedora packages]
| <code>sudo dnf install pari-gp</code>
|-
| Arch
| package manager
| [https://www.archlinux.org/packages/community/x86_64/pari/ Arch packages]
| <code>sudo pacman -S pari</code>
|-
| RHEL/CentOS
| package manager
|
| <code>sudo yum install pari-gp</code>
|-
| FreeBSD
| package manager
| [https://svnweb.freebsd.org/ports/head/math/pari/?view=log FreeBSD Ports Search]
| <code>sudo pkg install pari-2.11.3,2</code>
|-
| various
| package manager
| [https://formulae.brew.sh/formula-linux/pari Homebrew formula]
| <code>brew install pari</code>
|-
| various
| build from source
| [http://pari.math.u-bordeaux.fr/download.html official site]
| [http://math.crg4.com/software.html#pari Building PARI/GP in Linux]
|-
| rowspan="4" | macOS
| at least El Capitan (10.11)
| DMG installer (stable or development)
| [http://pari.math.u-bordeaux.fr/download.html#macos official site]
| Open dmg, drag to Applications (note: window may start minimized)
|-
| at least El Capitan (10.11)
| standalone binary (stable or development)
| [http://pari.math.u-bordeaux.fr/download.html#macos official site]
| run
|-
| unknown, at least OS X (10.?)
| package manager
| [https://ports.macports.org/port/pari/ MacPorts] (and [https://github.com/macports/macports-ports/blob/master/math/pari/Portfile portfile])
| <code>sudo port install pari</code>
|-
| unknown
| package manager
| [https://formulae.brew.sh/formula/pari Homebrew formula]
| <code>brew install pari</code>
|-
| rowspan="5" | Android
| various
| package manager
| [https://f-droid.org/packages/fr.ubordeaux.math.paridroid/ f-droid]
| Install via F-Droid client or install APK directly
|-
| various
| package manager
| [https://play.google.com/store/apps/details?id=fr.ubordeaux.math.paridroid&hl=en Google Play]
|
|-
| various
| precompiled binary
| [http://pari.math.u-bordeaux.fr/download.html#paridroid official site]
|
|-
| various
| build from source
| [https://github.com/FreeMonad/paridroid github]
| [https://github.com/FreeMonad/paridroid/wiki/Build-Environment Building] and [https://github.com/FreeMonad/paridroid/wiki/Installation Installing] (note: requires Android SDK Tools and Android NDK)
|-
| various
| build from source
| [http://pari.math.u-bordeaux.fr/cgi-bin/gitweb.cgi?p=paridroid.git;a=summary official site]
| [https://pari.math.u-bordeaux.fr/paridroid/index.html Installing PariDroid]
|-
| rowspan="2" | iOS
| ?
| Build from source on [https://ish.app/ iSH]
| [https://pari.math.u-bordeaux.fr/archives/pari-users-2111/msg00021.html Mailing list post]
| Turn on iSh Disable Screen Dimming Setting, then <code>apt get git gcc && git clone https://pari.math.u-bordeaux.fr/git/pari.git && cd pari && ./Configure && make install</code>
|-
| iOS 8+
| app
| [https://itunes.apple.com/us/app/sage-math/id496492945?mt=8 sage-math]
| Click the "+" in the top-right to start a new program, then click and hold on "Sage" at the top until the "Select Language" dropdown appears, then choose GP. (You can also use the wrapper function <code class="language-sage">pari</code> in a Sage snippet.)
|-
| rowspan="4" | online
| Chrome, Firefox, Internet Explorer
| local Javascript
| [http://pari.math.u-bordeaux.fr/gp.html Emscripten]
|
|-
| Chrome, Firefox
| local Javascript
| [http://pari.math.u-bordeaux.fr/gpexpwasm.html WebAssembly]
|
|-
| Chrome, Firefox, Internet Explorer
| client/server
| [https://www.tutorialspoint.com/execute_pari_online.php coding ground]
|
|-
| various
| client/server
| [https://cocalc.com/ CoCalc]
| [http://youtu.be/CzB6T7Nvc-s How to use PARI/GP in the SageMathCloud] (SageMathCloud is now CoCalc)
|}

== 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:
* [http://www.emacswiki.org/emacs/PariGP PariGP on EmacsWiki], [http://math.univ-lille1.fr/~ramare/ServeurPerso/GP-PARI/ PariEmacs]
* [http://go.helms-net.de/sw/paritty/pari_tty_einf_en.html Pari-tty]
* [http://www.skalatan.de/pariguide/ pariGUIde]
* [https://github.com/baruchel/vim-notebook vim-notebook] (see also [https://www.youtube.com/watch?v=vHiCpRQiJuU the author's video on using gp from vim])
* [https://github.com/jdemeyer/pari_jupyter 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 [http://pari.math.u-bordeaux.fr/pub/pari/manuals/gp2c/gp2c.html gp2c] utility converts GP scripts into executable C code.
** For use with the Gnu Mpc library, there is also [http://www.multiprecision.org/?prog=pari-gnump Pari-Gnump].
** [https://www.multiprecision.org/paritwine/ 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. <code>-fpermissive</code> may be useful when compiling with g++.
* [[Python]]:
** [http://www.sagemath.org/ SageMath] (or SAGE) is a Python-based system that includes GP among others
** [http://code.google.com/p/pari-python/ pari-python]
** [https://pypi.python.org/pypi/cypari/ cypari]/[https://github.com/sagemath/cypari2 cypari2] is a fork of the GP component of SageMath (see also the voluminous [https://buildmedia.readthedocs.org/media/pdf/cypari2/latest/cypari2.pdf CyPari2 Documentation])
* [[Perl]]:
** [http://search.cpan.org/dist/Math-Pari/ Math::Pari]
** [https://github.com/FreeMonad/GPP GPP]
* [[Common Lisp]]: Use [http://clisp.sourceforge.net/impnotes/pari.html Pari] ([[CLISP]]).
* [[Mathematica]]: A [http://pari.math.u-bordeaux.fr/dochtml/mathlink.html quick tutorial using MathLink] is available.

== See also ==
*[[wp:PARI/GP|Wikipedia:PARI/GP]]

== Resources ==
=== General ===
*[http://pari.math.u-bordeaux.fr/faq.html Official FAQ]
*[http://www.math.utah.edu/faq/pari/pari.html PARI/GP FAQ]
*[http://pari.math.u-bordeaux.fr/ateliers.html Ateliers PARI/GP]: Conference slides and other resources
*[http://hyperpolyglot.org/more-computer-algebra Comparison with Magma, GAP, and Singular]

=== Tutorials ===
*[http://pari.math.u-bordeaux.fr/pub/pari/manuals/2.11.1/tutorial.pdf Official tutorial] by The PARI Group (58 pp., 2018)
*[http://www.math.u-bordeaux.fr/~ballombe/talks/bordeaux-20150924.pdf Tutorial on Elliptic Curves] by Bill Allombert and Karim Belabas (5 pp., 2016)
*[http://www.personal.psu.edu/bug/467/pariinfo.pdf Beginning PARI Programming for CSE/MATH 467] by W. Dale Brownawell (7 pp., 2014)
*[http://www.maths.tcd.ie/~vlasenko/MA2316/ Class notes] including PARI/GP tutorial and sample code by Masha Vlasenko (2013)
*[http://people.math.umass.edu/~siman/09.791N/tutorial.pdf Tutorial] by Siman Wong (6 pp., 2009)
*[http://www.exploringbinary.com/exploring-binary-numbers-with-parigp-calculator/ Exploring binary numbers with PARI/GP calculator] by Rick Regan (appx. 4 pp., 2009)
* Class notes, parts [http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_01.pdf 1][http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_02.pdf 2][http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_03.pdf 3][http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_04.pdf 4][http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_05.pdf 5][http://myweb.csuchico.edu/~blevitt/math230/230coursedocs/230notes/230notes_sieve.pdf sieve] by Benjamin L. Levitt (41 pp., 2009; now offline?)
*[http://www.math.uconn.edu/~kconrad/math5230f08/parihandout.pdf Introduction] by Keith Conrad (7 pp., 2008)
*[http://mvngu.wordpress.com/2008/08/01/parigp-programming-for-basic-cryptography/ PARI/GP programming for basic cryptography] by Minh Van Nguyen (appx. 3 pp., 2008); also appears in an [https://bitbucket.org/mvngu/www/downloads/2008-11-25_numtheory-crypto-gp.pdf extended version] (9 pp., 2008)
*[http://www.math.uiuc.edu/~r-ash/GPTutorial.pdf Tutorial] by Robert B. Ash (20 pp., 2007)
*[http://www.linuxjournal.com/article/1068 The Pari Package On Linux], by Klaus-Peter Nischke (3 pp., 1995)
*[http://users.aims.ac.za/~richard/faq/index.php Pari/GP Tutorial] by Akinola Richard Olatokunbo (now offline; [https://web.archive.org/web/20170324230906/http://users.aims.ac.za/~richard/faq/index.php archived version])
*[https://pari.math.u-bordeaux.fr/Events/PARI2019/talks/parallel.pdf Parallel Computation] by Bill Allombert

==== Non-English language ====
*French tutorials (slides) by Bill Allombert (2017):
** [https://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/init.pdf Introduction à PARI/GP] (13 pp.)
** [https://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/prog.pdf Programmation GP] (11 pp.)
** [https://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/TAN.pdf Théorie algébrique des nombres] (31 pp.)
** [https://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/TAN2.pdf Théorie algébrique des nombres avancée] (22 pp.)
** [https://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/ecc.pdf Courbes elliptiques sur les corps finis] (4 pp.)
*[http://w3.countnumber.de/fischer/res-ZT2007/PariByExample.pdf Erste Schritte mit PARI/GP] by Lars Fischer (13 pp., 2007; German)
* [https://www.youtube.com/watch?v=I_GfMUGAlns Pari Gp مع NotPad++] by NoorDeen Rahmani (2020; 2:46; Arabic) -- setting up Notepad++ for syntax highlighting for PARI/GP.

==== Video tutorials ====
* [https://www.youtube.com/watch?v=RQLqQHu7i0Y Pari/GP Tutorial: Basics] by Leandro Junes (2020, 19:04)
* [https://www.youtube.com/watch?v=FeG0BYRrDOE&t=12m Video demo of RSA in PARI/GP] by Maren1955 (2014, 17:39)
* Video tutorials, parts [http://www.youtube.com/watch?v=0G-9JzlrzBM 1] [http://www.youtube.com/watch?v=d7i0rv59hns 2] [http://www.youtube.com/watch?v=wCyU2n-G-pk 3] [http://www.youtube.com/watch?v=WOCuBvK8O6Q 4] (2011, appx. 20 minutes)

== Syntax highlighting ==
* [https://github.com/notepad-plus-plus/userDefinedLanguages/blob/master/UDLs/PARI-GP_by-third_maths.xml Notepad++]
* [https://www.youtube.com/watch?v=I_GfMUGAlns Pari Gp مع NotPad++] (Arabic tutorial)

=== Papers on PARI/GP ===
* Karim Belabas and Henri Cohen, [https://arxiv.org/abs/1810.00547 Modular Forms in Pari/GP], ''Research in the Mathematical Sciences'' '''5''':37 (2018)
* Henri Cohen, [https://arxiv.org/abs/1809.10908 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, [https://www.math.u-bordeaux.fr/~jjaulent/Articles/bnflog.ps The logarithmic class group package in PARI/GP], ''Mathematical Publications of Besançon, Algebra and Number Theory'' (2016), pp. 5&ndash;18.
* Bill Alombert, [http://www.math.u-bordeaux.fr/~allomber/darkpaper.pdf A new interpretor for PARI/GP], ''Journal de Théorie des Nombres de Bordeaux'' '''20''':3 (2008), pp. 531&ndash;541. (English)
* Paul Zimmermann, [http://www.loria.fr/~zimmerma/talks/henri.pdf 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, [https://home.bway.net/lewis/cacomp.ps 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)

[[Category:Mathematical programming languages]]