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1: 16 Generalized Hypergeometric Functions & Meijer G-Function
Chapter 16 Generalized Hypergeometric Functions and Meijer -Function
…2: 27.15 Chinese Remainder Theorem
3: 20 Theta Functions
4: Adri B. Olde Daalhuis
5: 32.12 Asymptotic Approximations for Complex Variables
6: 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).
7: Staff
Richard A. Askey, University of Wisconsin, Chaps. 1, 5, 16
Adri B. Olde Daalhuis, University of Edinburgh, Chaps. 13, 15, 16
Adri B. Olde Daalhuis, The University of Edinburgh, for Chaps. 13, 15, 16