Inhaltsverzeichnis

Development of
Algorithmic Constructions

18:27:39
Deutsch
19.May 2019

29 31 33
√2 √3 √5 √6 √7 √8

Number p= Adjoined square root=

Calculation

A=√3
(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 = √3, Exponent = 1, Jacobi (3, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√3
Number of elements = 30

Number = 31, Adjoined = √3, Exponent = 1, Jacobi (3, 31) = -1, 31 = 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

|30+0AI|
=1
|28+7AI|
=1
metric = 5
|28+24AI|
=1
metric = 5
|25+3AI|
=1
metric = 2
|25+28AI|
=1
metric = 2
|23+14AI|
=1
metric = 10
|23+17AI|
=1
metric = 10
|22+5AI|
=1
metric = 5
|22+26AI|
=1
metric = 5
|19+2AI|
=1
metric = 10
|19+29AI|
=1
metric = 10
|17+11AI|
=1
metric = 6
|17+20AI|
=1
metric = 6
|16+15AI|
=1
metric = 1
|16+16AI|
=1
metric = 1
|15+15AI|
=1
metric = 1
|15+16AI|
=1
metric = 1
|14+11AI|
=1
metric = 6
|14+20AI|
=1
metric = 6
|12+2AI|
=1
metric = 10
|12+29AI|
=1
metric = 10
|9+5AI|
=1
metric = 5
|9+26AI|
=1
metric = 5
|8+14AI|
=1
metric = 10
|8+17AI|
=1
metric = 10
|6+3AI|
=1
metric = 2
|6+28AI|
=1
metric = 2
|3+7AI|
=1
metric = 5
|3+24AI|
=1
metric = 5
|1+0AI|
=1

sum of all metrics = 156