# Category:PARI/GP

**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 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 Bordeaux I 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 Alombert.

## Using PARI/GP

PARI/GP can be downloaded at its official website's download page.

Windows precompiled binaries are available: an installer, stand-alone stable and development versions, plus a nightly build with the very latest changes.

Mac users may find it convenient to download the version from Fink.

Linux users can install PARI/GP with their favorite package manager (RPM, dpkg, apt, etc.) or build it from source. Instructions are available for compiling.

Android phones and tablets can use paridroid (also on github).

While an iPhone/iPad version has not been developed, sage-math includes PARI and GP commands can be invoked with the wrapper function `pari`

.

Finally, gp can be used online through compile online or the SageMath cloud (see How to use PARI/GP in the SageMathCloud).

## 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:

If you want to write a program rather than script a calculator, 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.
- 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: SAGE is a Python-based system that includes PARI among others; there is a pari-python library as well.
- Perl: Use Math::Pari or GPP.
- Common Lisp: Use Pari (CLISP).

## See also

## Resources

### General

- PARI/GP FAQ
- Resources for PARI/GP
- Atelier PARI/GP 2012: Conference slides

### Tutorials

- Official tutorial by C. Batut, K. Belabas, D. Bernardi, H. Cohen, M. Olivier (52 pp., 2011)
- Class notes, parts 12345sieve by Benjamin L. Levitt (41 pp., 2009)
- Tutorial by Robert B. Ash (20 pp., 2007)
- Tutorial by Siman Wong (6 pp., 2009)
- Introduction by Keith Conrad (7 pp., 2008)
- The Pari Package On Linux, by Klaus-Peter Nischke (3 pp., 1995)
- PARI/GP programming for basic cryptography by Minh Van Nguyen (appx. 3 pp., 2008)
- Exploring binary numbers with PARI/GP calculator by Rick Regan (appx. 4 pp., 2009)
- Video tutorials, parts 1 2 3 4 (appx. 20 minutes, 2011)

### Papers on PARI/GP

- 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

## 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)### 2

### A

- A+B
- ABC problem
- Abstract type
- Abundant, deficient and perfect number classifications
- Accumulator factory
- Ackermann function
- Address of a variable
- AKS test for primes
- Aliquot sequence classifications
- Almost prime
- Amb
- Amicable pairs
- Anagrams/Deranged anagrams
- Angle difference between two bearings
- Anonymous recursion
- Anti-primes
- Apply a callback to an array
- Apéry's constant
- Arbitrary-precision integers (included)
- Archimedean spiral
- Arena storage pool
- Arithmetic-geometric mean
- Arithmetic-geometric mean/Calculate Pi
- Arithmetic/Complex
- Arithmetic/Integer
- Arithmetic/Rational
- Array concatenation
- Array length
- Arrays
- Assertions
- Associative array/Creation
- Associative array/Iteration
- Atomic updates
- Average loop length
- Averages/Arithmetic mean
- Averages/Mean angle
- Averages/Mean time of day
- Averages/Median
- Averages/Mode
- Averages/Pythagorean means
- Averages/Root mean square
- Averages/Simple moving average

### B

### C

- Caesar cipher
- Calkin-Wilf sequence
- Call a foreign-language function
- Call a function
- Call a function in a shared library
- Calmo numbers
- Card shuffles
- Carmichael 3 strong pseudoprimes
- Case-sensitivity of identifiers
- Casting out nines
- Catalan numbers
- Catalan numbers/Pascal's triangle
- Catamorphism
- Chaos game
- Character codes
- Check Machin-like formulas
- Check that file exists
- Chernick's Carmichael numbers
- Chinese remainder theorem
- Cholesky decomposition
- Chowla numbers
- Circles of given radius through two points
- Closest-pair problem
- Closures/Value capture
- Code segment unload
- Collections
- Combinations
- Combinations and permutations
- Combinations with repetitions
- Comma quibbling
- Comments
- Compare a list of strings
- Composite numbers k with no single digit factors whose factors are all substrings of k
- Compound data type
- Concurrent computing
- Conditional structures
- Conjugate transpose
- Constrained random points on a circle
- Continued fraction
- Continued fraction/Arithmetic/Construct from rational number
- Convert decimal number to rational
- Convert seconds to compound duration
- Conway's Game of Life
- Copy a string
- Count in factors
- Count in octal
- Count occurrences of a substring
- Count the coins
- Cramer's rule
- CRC-32
- Create a file
- Create a two-dimensional array at runtime
- Create an HTML table
- CSV data manipulation
- Cuban primes
- Cullen and Woodall numbers
- Cumulative standard deviation
- Currying
- Curzon numbers
- Cyclotomic polynomial

### D

- Day of the week
- Deal cards for FreeCell
- Deceptive numbers
- Deepcopy
- Delete a file
- Deming's funnel
- Department numbers
- Detect division by zero
- Determinant and permanent
- Determine if a string is numeric
- Digit fifth powers
- Digital root
- Digital root/Multiplicative digital root
- Dijkstra's algorithm
- Distance and Bearing
- Documentation
- Dot product
- Dragon curve
- Draw a cuboid
- Duffinian numbers
- Dutch national flag problem
- Dynamic variable names

### E

- Egyptian division
- Element-wise operations
- Elliptic curve arithmetic
- Emirp primes
- Empty directory
- Empty program
- Empty string
- Enforced immutability
- Entropy
- Entropy/Narcissist
- Environment variables
- Equilibrium index
- Ethiopian multiplication
- Euclid-Mullin sequence
- Euler's constant 0.5772...
- Euler's sum of powers conjecture
- Evaluate binomial coefficients
- Even or odd
- Evolutionary algorithm
- Exceptions
- Exceptions/Catch an exception thrown in a nested call
- Executable library
- Execute a system command
- Execute Brain****
- Execute HQ9+
- Exponentiation operator
- Exponentiation order
- Extend your language
- Extensible prime generator
- Extreme floating point values

### F

- Factorial
- Factors of a Mersenne number
- Factors of an integer
- Farey sequence
- Fast Fourier transform
- Faulhaber's formula
- Fermat numbers
- Fibonacci n-step number sequences
- Fibonacci sequence
- Fibonacci word
- Fibonacci word/fractal
- File extension is in extensions list
- File input/output
- Filter
- Find adjacent primes which differ by a square integer
- Find common directory path
- Find first and last set bit of a long integer
- Find largest left truncatable prime in a given base
- Find limit of recursion
- Find palindromic numbers in both binary and ternary bases
- Find prime numbers of the form n*n*n+2
- Find squares n where n+1 is prime
- Find the last Sunday of each month
- Find the missing permutation
- First-class functions
- First-class functions/Use numbers analogously
- Five weekends

- 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