The Fast Library for Number Theory (FLINT) is a C

library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (soft copies) materials, and may be a physical location or a vir ...

for

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

applications. The two major areas of functionality currently implemented in FLINT are

polynomial arithmetic In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An ex ...

over the

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language o ...

and a

quadratic sieve The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerab ...

. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is released under the

GNU General Public License The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the Four Freedoms (Free software), four freedoms to run, study, share, and modify the software. The license was th ...

. It is developed by William Hart of the

University of Kaiserslautern Technical University of Kaiserslautern (German: ''Technische Universität Kaiserslautern'', also known as TU Kaiserslautern or TUK) is a public university, public research university in Kaiserslautern, Germany. There are numerous institutes arou ...

(formerly

University of Warwick The University of Warwick ( ; abbreviated as ''Warw.'' in post-nominal letters) is a public research university on the outskirts of Coventry between the West Midlands (county), West Midlands and Warwickshire, England. The university was founded i ...

) and

David Harvey David W. Harvey (born 31 October 1935) is a British-born Marxist economic geographer, podcaster and Distinguished Professor of anthropology and geography at the Graduate Center of the City University of New York (CUNY). He received his P ...

University of New South Wales The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensive ...

(formerly

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

) to address the speed limitations of the PARI and

NTL NTL may refer to: Companies * NTL Incorporated and NTL Internet, later Virgin Media, communications media company ** NTL Ireland, later Virgin Media Ireland * Arqiva, UK company formerly ''NTL Broadcast'' and ''National Transcommunications L ...

libraries.Page 10 of th
Project Description
fo
UW 2006 COMPMATH Proposal
by William Stein

Design Philosophy

* Asymptotically Fast Algorithms * Implementations Fast as or Faster than Alternatives * Written in Pure C * Reliance on GMP * Extensively Tested * Extensively Profiled * Support for Parallel Computation

Functionality

* Polynomial Arithmetic over the Integers * Quadratic Sieve

References

;Notes
FLINT 1.0.9: Fast Library for Number Theory
by William Hart and David Harvey
Video
of the talk Parallel Computation in Number Theory (30 January 2007) by William Hart
Video
of the tal
FLINT and Fast Polynomial Arithmetic
(13 June 2007) By David Harvey
Video
of the talk A short talk on short division (1 October 2007) by William Hart
Video
of the talk Algebraic Number Theory with FLINT (11 November 2007) by William Hart {{refend Computational number theory Free software programmed in C Integer factorization algorithms Numerical software