division algorithm
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8 matching pages
1: 1.11 Zeros of Polynomials
§1.11(i) Division Algorithm
…2: 27.19 Methods of Computation: Factorization
3: 27.18 Methods of Computation: Primes
4: 3.10 Continued Fractions
Quotient-Difference Algorithm
… ► … ►To compute the of (3.10.2) we perform the iterated divisions … ►Steed’s Algorithm
… ►Alternatives to Steed’s algorithm are the Lentz algorithm Lentz (1976) and the modified Lentz algorithm Thompson and Barnett (1986). …5: 27.22 Software
Mathematica. PrimeQ combines strong pseudoprime tests for the bases 2 and 3 and a Lucas pseudoprime test. No known composite numbers pass these three tests, and Bleichenbacher (1996) has shown that this combination of tests proves primality for integers below . Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard , and then cfrac after trial division. See §27.19. ecm is available also, and the Multiple Polynomial Quadratic sieve is expected in a future release.
For additional Mathematica routines for factorization and primality testing, including several different pseudoprime tests, see Bressoud and Wagon (2000).
Wolfram’s Mathworld. Descriptions, references, and Mathematica algorithms for factorization and primality testing.