Inhaltsverzeichnis

Development of
Algorithmic Constructions

14:03:23
Deutsch
3.Dec 2022

33 35 37
√2 √3 √5 √6 √7 √8 √10 √11

Number p= Adjoined square root=

Calculation

A=√2
(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
Square 3

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 = 35, Adjoined = √2, Exponent = 3, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

34
034√2
Number of elements = 16
Number of red elements = 12
Number of elements / Number of red elements = 1.3333333333333

Number = 35, Adjoined = √2, Exponent = 3, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

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

href=3. root

|34+0AI|
=1
|29+0AI|
=1
|26+10AI|
=1
metric = 2
|26+25AI|
=1
metric = 2
|21+5AI|
=1
metric = 18
|21+30AI|
=1
metric = 18
|19+10AI|
=1
metric = 6
|19+25AI|
=1
metric = 6
|16+10AI|
=1
metric = 6
|16+25AI|
=1
metric = 6
|14+5AI|
=1
metric = 18
|14+30AI|
=1
metric = 18
|9+10AI|
=1
metric = 2
|9+25AI|
=1
metric = 2
|6+0AI|
=1
|1+0AI|
=1

sum of all metrics = 104