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Wilf?Zeilberger algorithm

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1: 27.19 Methods of Computation: Factorization
Deterministic algorithms are slow but are guaranteed to find the factorization within a known period of time. …Fermat’s algorithm is another; see Bressoud (1989, §5.1). Type I probabilistic algorithms include the Brent–Pollard rho algorithm (also called Monte Carlo method), the Pollard p 1 algorithm, and the Elliptic Curve Method (ecm). Descriptions of these algorithms are given in Crandall and Pomerance (2005, §§5.2, 5.4, and 7.4). … These algorithms include the Continued Fraction Algorithm (cfrac), the Multiple Polynomial Quadratic Sieve (mpqs), the General Number Field Sieve (gnfs), and the Special Number Field Sieve (snfs). …
2: 35.12 Software
In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. … For an algorithm to evaluate zonal polynomials, and an implementation of the algorithm in Maple by Zeilberger, see Lapointe and Vinet (1996).
3: 17.19 Software
In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …
4: 26.22 Software
In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …
  • Stony Brook Algorithm Repository (website).

  • For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).
    5: 27.18 Methods of Computation: Primes
    Two simple algorithms for proving primality require a knowledge of all or part of the factorization of n 1 , n + 1 , or both; see Crandall and Pomerance (2005, §§4.1–4.2). These algorithms are used for testing primality of Mersenne numbers, 2 n 1 , and Fermat numbers, 2 2 n + 1 . … The APR (Adleman–Pomerance–Rumely) algorithm for primality testing is based on Jacobi sums. … The AKS (Agrawal–Kayal–Saxena) algorithm is the first deterministic, polynomial-time, primality test. … The ECPP (Elliptic Curve Primality Proving) algorithm handles primes with over 20,000 digits. …
    6: 21.11 Software
    In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …
    7: 3.10 Continued Fractions
    Quotient-Difference Algorithm
    In general this algorithm is more stable than the forward algorithm; see Jones and Thron (1974). …
    Steed’s Algorithm
    Alternatives to Steed’s algorithm are the Lentz algorithm Lentz (1976) and the modified Lentz algorithm Thompson and Barnett (1986). …
    8: 35.10 Methods of Computation
    Koev and Edelman (2006) utilizes combinatorial identities for the zonal polynomials to develop computational algorithms for approximating the series expansion (35.8.1). These algorithms are extremely efficient, converge rapidly even for large values of m , and have complexity linear in m .
    9: 18.42 Software
    In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …
    10: 20.16 Software
    In this section we provide links to the research literature describing the implementation of algorithms in software for the evaluation of functions described in this chapter. …