Singular Manual: atkins_lib

> | ### D.12.2 atkins_lib Library: atkins.lib Purpose: Procedures for teaching cryptography Author: Stefan Steidel, steidel@mathematik.uni-kl.de Note: The library contains auxiliary procedures to compute the elliptic curve primality test of Atkin and the Atkin's Test itself. The library is intended to be used for teaching purposes but not for serious computations. Sufficiently high printlevel allows to control each step, thus illustrating the algorithms at work. Procedures:
> D.12.2.1 newTest |  | checks if number D already exists in list L
> D.12.2.2 bubblesort |  | sorts elements of the list L
> D.12.2.3 disc |  | generates a list of negative discriminants
> D.12.2.4 Cornacchia |  | computes solution (x,y) for x^2+d*y^2=p
> D.12.2.5 CornacchiaModified |  | computes solution (x,y) for x^2+|D|*y^2=4p
> D.12.2.6 maximum |  | computes the maximal number contained in L
> D.12.2.7 sqr |  | computes the square root of w w.r.t. accuracy k
> D.12.2.8 expo |  | computes exp(z)
> D.12.2.9 jOft |  | computes the j-invariant of t
> D.12.2.10 round |  | rounds r to the nearest number out of Z
> D.12.2.11 HilbertClassPoly |  | computes the Hilbert Class Polynomial
> D.12.2.12 rootsModp |  | computes roots of the polynomial P modulo p
> D.12.2.13 wUnit |  | computes the number of units in Q(sqr(D))
> D.12.2.14 Atkin |  | tries to prove that N is prime

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