# Wilf?Zeilberger algorithm

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## 1—10 of 89 matching pages

##### 1: 27.19 Methods of Computation: Factorization

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►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

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►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.
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►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

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►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.
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##### 4: 26.22 Software

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►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.
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►For algorithms for counting and analyzing combinatorial structures see Knuth (1993), Nijenhuis and Wilf (1975), and Stanton and White (1986).

Stony Brook Algorithm Repository (website).

##### 5: 27.18 Methods of Computation: Primes

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►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

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►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.
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##### 7: 3.10 Continued Fractions

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###### 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

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►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

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►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.
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