Category:PARI/GP
![Language](http://static.miraheze.org/rosettacodewiki/thumb/2/27/Rcode-button-language-crushed.png/64px-Rcode-button-language-crushed.png)
This programming language may be used to instruct a computer to perform a task.
Official website |
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Execution method: | Interpreted or compiled |
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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 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.
Operating system | Kind | Type of install | Link | How to install |
---|---|---|---|---|
Windows | various | installer (stable or development) | official site | run installer |
XP, Vista, 7, 8, 10 | standalone binaries (stable or development) | official site | run | |
various | standalone binaries (daily) | official site | run | |
Linux | Ubuntu/Debian | package manager | Debian packages | sudo apt-get install pari-gp
|
Fedora | package manager | Fedora packages | sudo dnf install pari-gp
| |
Arch | package manager | Arch packages | sudo pacman -S pari
| |
RHEL/CentOS | package manager | sudo yum install pari-gp
| ||
FreeBSD | package manager | FreeBSD Ports Search | sudo pkg install pari-2.11.3,2
| |
various | package manager | Homebrew formula | brew install pari
| |
various | build from source | official site | Building PARI/GP in Linux | |
macOS | at least El Capitan (10.11) | DMG installer (stable or development) | official site | Open dmg, drag to Applications (note: window may start minimized) |
at least El Capitan (10.11) | standalone binary (stable or development) | official site | run | |
unknown, at least OS X (10.?) | package manager | MacPorts (and portfile) | sudo port install pari
| |
unknown | package manager | Homebrew formula | brew install pari
| |
Android | various | package manager | f-droid | Install via F-Droid client or install APK directly |
various | package manager | Google Play | ||
various | precompiled binary | official site | ||
various | build from source | github | Building and Installing (note: requires Android SDK Tools and Android NDK) | |
various | build from source | official site | (need build/install instructions) | |
iOS | iOS 8+ | app | 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 pari in a Sage snippet.)
|
online | Chrome, Firefox, Internet Explorer | local Javascript | Emscripten | |
Chrome, Firefox | local Javascript | WebAssembly | ||
Chrome, Firefox, Internet Explorer | client/server | compile online | ||
various | client/server | CoCalc | 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:
- 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.
- C++: PARI can be used directly in C++. The code is intentionally written in a C++-compatible style.
-fpermissive
is sometimes 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:
- Common Lisp: Use Pari (CLISP).
- Mathematica: A quick tutorial using MathLink is available.
See also
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)
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)
Subcategories
This category has the following 3 subcategories, out of 3 total.
@
- PARI/GP Implementations (empty)
- PARI/GP User (12 P)
Pages in category "PARI/GP"
The following 200 pages are in this category, out of 607 total.
(previous page) (next page)F
G
- Gamma function
- Gaussian elimination
- General FizzBuzz
- Generate Chess960 starting position
- Generate lower case ASCII alphabet
- Generator/Exponential
- Generic swap
- Get system command output
- Giuga numbers
- Gray code
- Greatest common divisor
- Greatest element of a list
- Greatest subsequential sum
- Greedy algorithm for Egyptian fractions
- Guess the number
- Guess the number/With feedback
- Guess the number/With feedback (player)
- GUI/Maximum window dimensions
H
- Hailstone sequence
- Hamming numbers
- Happy numbers
- Harmonic series
- Harshad or Niven series
- Hash from two arrays
- Haversine formula
- Hello world/Graphical
- Hello world/Newbie
- Hello world/Newline omission
- Hello world/Standard error
- Hello world/Text
- Heronian triangles
- Hickerson series of almost integers
- Higher-order functions
- History variables
- Hofstadter Q sequence
- Hofstadter-Conway $10,000 sequence
- Holidays related to Easter
- Home primes
- Horner's rule for polynomial evaluation
- Hostname
I
- Identity matrix
- Idiomatically determine all the characters that can be used for symbols
- Idiomatically determine all the lowercase and uppercase letters
- Idoneal numbers
- Implicit type conversion
- Include a file
- Increment a numerical string
- Infinity
- Input/Output for lines of text
- Input/Output for pairs of numbers
- Integer comparison
- Integer overflow
- Integer roots
- Integer sequence
- Interactive programming (repl)
- Introspection
- Inverted syntax
- Iterated digits squaring
K
L
- Langton's ant
- Largest int from concatenated ints
- Largest prime factor
- Last Friday of each month
- Leap year
- Least common multiple
- Left factorials
- Letter frequency
- Levenshtein distance
- Linear congruential generator
- List comprehensions
- Literals/Floating point
- Literals/Integer
- Literals/String
- Logical operations
- Long multiplication
- Look-and-say sequence
- Loop over multiple arrays simultaneously
- Loops/Break
- Loops/Continue
- Loops/Do-while
- Loops/Downward for
- Loops/For
- Loops/For with a specified step
- Loops/Foreach
- Loops/Infinite
- Loops/N plus one half
- Loops/Nested
- Loops/While
- LU decomposition
- Lucas-Carmichael numbers
- Lucas-Lehmer test
- Ludic numbers
M
- Machine code
- Magic squares of doubly even order
- Magic squares of odd order
- Mandelbrot set
- Map range
- Matrix multiplication
- Matrix transposition
- Matrix-exponentiation operator
- Maximum triangle path sum
- MD4
- MD5
- Meissel–Mertens constant
- Memory allocation
- Menu
- Mersenne primes
- Metaprogramming
- Middle three digits
- Miller–Rabin primality test
- Minimum number of cells after, before, above and below NxN squares
- Modular arithmetic
- Modular exponentiation
- Modular inverse
- Monte Carlo methods
- Monty Hall problem
- Morse code
- Motzkin numbers
- Multifactorial
- Multiline shebang
- Multiple regression
- Multiplication tables
- Multiplicative order
- Mutual recursion
- Möbius function
N
- N'th
- N-smooth numbers
- Narcissist
- Narcissistic decimal number
- Neighbour primes
- Nice primes
- Non-continuous subsequences
- Non-decimal radices/Convert
- Non-decimal radices/Input
- Non-decimal radices/Output
- Nth root
- Null object
- Number names
- Number reversal game
- Numbers whose count of divisors is prime
- Numeric error propagation
- Numerical integration
- Numerical integration/Gauss-Legendre Quadrature
O
P
- Palindrome detection
- Palindromic primes
- Pan base non-primes
- Pangram checker
- Paraffins
- Parallel calculations
- Parse command-line arguments
- Parsing/RPN calculator algorithm
- Partial function application
- Partition an integer x into n primes
- Pascal matrix generation
- Pascal's triangle
- Pascal's triangle/Puzzle
- Password generator
- Pathological floating point problems
- Perfect numbers
- Perfect shuffle
- Permutations
- Permutations/Derangements
- Permutations/Rank of a permutation
- Execution method/Interpreted
- Execution method/Compiled
- Garbage collection/Yes
- Parameter passing/By reference
- Parameter passing/By value
- Typing/Weak
- Typing/Checking/Dynamic
- Programming Languages
- Programming paradigm/Dynamic
- Programming paradigm/Functional
- Programming paradigm/Procedural
- Mathematical programming languages