precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists with coefficients...
8 KB (1,036 words) - 18:54, 7 June 2024
the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the...
123 KB (15,119 words) - 08:05, 21 August 2024
general algorithm for integer factorization, any integer can be factored into its constituent prime factors by repeated application of this algorithm. The...
25 KB (2,981 words) - 18:28, 21 June 2024
Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also...
28 KB (4,452 words) - 21:55, 14 August 2024
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...
41 KB (5,886 words) - 09:59, 12 August 2024
The algorithm can be used to find integer solutions to many problems. In particular, the LLL algorithm forms a core of one of the integer relation algorithms...
15 KB (2,128 words) - 15:42, 2 April 2024
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and...
13 KB (1,723 words) - 03:26, 18 June 2024
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a divide-and-conquer...
13 KB (2,044 words) - 21:24, 21 July 2024
Linear programming (redirect from 0-1 integer programming)
(reciprocal) licenses: MINTO (Mixed Integer Optimizer, an integer programming solver which uses branch and bound algorithm) has publicly available source code...
61 KB (6,667 words) - 07:20, 23 August 2024
Let y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt...
16 KB (2,410 words) - 03:37, 13 December 2023
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or...
38 KB (5,354 words) - 15:36, 29 June 2024
optimal bound, although this remains a conjecture today. Integer multiplication algorithms can also be used to multiply polynomials by means of the method...
47 KB (6,801 words) - 03:33, 25 July 2024
(GCD) of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with...
17 KB (1,993 words) - 02:27, 26 July 2024
AKS primality test (redirect from AKS algorithm)
with the AKS algorithm. The AKS primality test is based upon the following theorem: Given an integer n ≥ 2 {\displaystyle n\geq 2} and integer a {\displaystyle...
20 KB (2,448 words) - 20:19, 19 March 2024
Gaussian integers share many properties with integers: they form a Euclidean domain, and have thus a Euclidean division and a Euclidean algorithm; this implies...
35 KB (4,795 words) - 03:23, 20 December 2023
Greatest common divisor (section Euclid's algorithm)
of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest...
35 KB (4,710 words) - 01:08, 5 August 2024
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen...
26 KB (4,601 words) - 22:35, 6 August 2024
Modular arithmetic (redirect from Integers mod n)
if there is an integer k such that a − b = k m. Congruence modulo m is a congruence relation, meaning that it is an equivalence relation that is compatible...
29 KB (3,602 words) - 18:28, 25 August 2024
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning...
9 KB (1,250 words) - 01:11, 18 April 2024
discrete logarithms in a finite abelian group whose order is a smooth integer. The algorithm was introduced by Roland Silver, but first published by Stephen...
7 KB (1,035 words) - 06:27, 5 June 2024
exponential-time algorithm, practical only for small groups G. More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization...
17 KB (2,043 words) - 22:45, 29 July 2024
more of the unknowns must be an integer then it is classified in integer programming. A linear programming algorithm can solve such a problem if it can...
62 KB (7,323 words) - 20:13, 26 August 2024
Pi (section Computer era and iterative algorithms)
Ramanujan–Sato series. In 2006, mathematician Simon Plouffe used the PSLQ integer relation algorithm to generate several new formulae for π, conforming to the following...
146 KB (17,419 words) - 20:13, 25 August 2024
kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced...
9 KB (1,287 words) - 11:50, 3 September 2023
Fisher–Yates shuffle (redirect from Algorithm P)
following algorithm (for a zero-based array). -- To shuffle an array a of n elements (indices 0..n-1): for i from n−1 down to 1 do j ← random integer such...
36 KB (4,398 words) - 16:06, 26 August 2024
"ABC ABCDAB ABCDABCDABDE". At any given time, the algorithm is in a state determined by two integers: m, denoting the position within S where the prospective...
33 KB (4,068 words) - 01:45, 15 July 2024
Quadratic sieve (category Integer factorization algorithms)
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field...
27 KB (4,487 words) - 16:24, 29 June 2024
RSA (cryptosystem) (redirect from RSA algorithm)
calculated through the Euclidean algorithm, since lcm(a, b) = |ab|/gcd(a, b). λ(n) is kept secret. Choose an integer e such that 1 < e < λ(n) and gcd(e...
61 KB (7,877 words) - 15:19, 2 August 2024
theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by...
5 KB (831 words) - 21:06, 30 September 2022
Fürer's algorithm: an integer multiplication algorithm for very large numbers possessing a very low asymptotic complexity Karatsuba algorithm: an efficient...
71 KB (7,827 words) - 18:40, 18 August 2024