Inhaltsverzeichnis

Development of
Algorithmic Constructions

15:25:11
Deutsch
28.Mar 2024

29 31 33
√10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29

Number p= Adjoined square root=

Calculation

A=√20
(a+bAI)² = a²-b²A² + 2abAI mod p
|(a+bAI)| = (a+bAI)(a-bAI) = a²+b²A² mod p

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29


Calculation of the metric is the distance from the point x+yAI to the point (p-1)/2+[(p-1)/2]AI
center:=(p-1)/2
if x>center then x:=p - x
if y>center then y:=p - y
diff_x:=center-x
diff_y:=center-y
metric:=diff_x^2+diff_y^2*A^2 mod p

Number = 31, Adjoined = √20, Exponent = 1, Jacobi (20, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√20
Number of elements = 1

Number = 31, Adjoined = √20, Exponent = 1, Jacobi (20, 31) = 131 = 3 mod 4, 31 = 7 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

(a+bAI)^19=21+28A

|20+26AI|
=1
metric = 30

sum of all metrics = 30