Inhaltsverzeichnis

Development of
Algorithmic Constructions
22:20:54
Deutsch
19.Apr 2024
27 29 31
√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 = 29, Adjoined = √2, Exponent = 3, Jacobi (2, 29) = -1, 29 = 1 mod 4, 29 = 5 mod 8

28
028√2
Number of elements = 10

Number = 29, Adjoined = √2, Exponent = 3, Jacobi (2, 29) = -1, 29 = 1 mod 4, 29 = 5 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

|28+0AI|
=1
|26+5AI|
=1
metric = 2		|26+24AI|
=1
metric = 2
|17+1AI|
=1
metric = 6		|17+28AI|
=1
metric = 6
|12+1AI|
=1
metric = 6		|12+28AI|
=1
metric = 6
|3+5AI|
=1
metric = 2		|3+24AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 32