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D.12.2.14 Atkin
Procedure from library atkins.lib (see atkins_lib).
- Return:
- 1, if N is prime,
-1, if N is not prime,
0, if the algorithm is not applicable, since there are too few discriminants
- Assume:
- N is coprime to 6 and different from 1
- Note:
- K/2 is input for the procedure "disc",
K is input for the procedure "HilbertClassPoly",
B describes the number of recursions being calculated.
The basis of the algorithm is the following theorem:
Let N be an integer coprime to 6 and different from 1 and E be an
ellipic curve modulo N. Assume that we know an integer m and a
point P of E(Z/NZ) satisfying the following conditions.
(1) There exists a prime divisor q of m such that q > (4-th root(N)+1)^2.
(2) m*P = O(E) = (0:1:0).
(3) (m/q)*P = (x:y:t) with t element of (Z/NZ)*.
Then N is prime.
Example:
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