cfrac证书在银行有用吗?〖办证V信ATV1819〗follow

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1: 27.19 Methods of Computation: Factorization

… ►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). A description of cfrac is given in Bressoud and Wagon (2000). …The largest composite numbers that have been factored by other Type II probabilistic algorithms are a 63-digit integer by cfrac, a 135-digit integer by mpqs, and a 182-digit integer by gnfs. …

2: 27.22 Software

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Maple. isprime combines a strong pseudoprime test and a Lucas pseudoprime test. ifactor uses cfrac (§27.19) after exhausting trial division. Brent–Pollard rho, Square Forms Factorization, and ecm are available also; see §27.19.

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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 ${10}^{16}$. Provable PrimeQ uses the Atkin–Goldwasser–Kilian–Morain Elliptic Curve Method to prove primality. FactorInteger tries Brent–Pollard rho, Pollard $p-1$, 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).

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3: Ira Gessel

… ►In November 2015, Gessel was named Associate Editor of the following DLMF Chapter …

4: Sidebar 7.SB1: Diffraction from a Straightedge

… ►The intensity distribution follows ${|ℱ\left(x\right)|}^2$, where $ℱ$ is the Fresnel integral (See 7.3.4). …

5: Simon Ruijsenaars

… ►In November 2015, Ruijsenaars was named Senior Associate Editor of the DLMF and Associate Editor of the following DLMF Chapters …

6: 12.20 Approximations

… ►As special cases of these results a Chebyshev-series expansion for $U(a,x)$ valid when follows from (12.7.14), and Chebyshev-series expansions for $U(a,x)$ and $V(a,x)$ valid when $0\le x\le \lambda$ follow from (12.4.1), (12.4.2), (12.7.12), and (12.7.13). …

7: 29.22 Software

… ►The following Maple programs were provided by the author. … ►The following Maple programs were provided by the author. …

8: Adri B. Olde Daalhuis

… ►Olde Daalhuis has published numerous papers in asymptotics and special functions and in addition to his responsibilities as Mathematics Editor of the DLMF, he is the author or coauthor of the following DLMF Chapters …

9: Karl Dilcher

… ►Dilcher is author of the following DLMF Chapter …

10: T. Mark Dunster

… ►Dunster is author of the following DLMF Chapter …