Inhaltsverzeichnis

Development of
Algorithmic Constructions

11:49:27
Deutsch
29.Mar 2024

27 29 31
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15

Number p= Adjoined square root=

Calculation

A=√6
(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 = 29, Adjoined = √6, Exponent = 1, Jacobi (6, 29) = 129 = 1 mod 4, 29 = 5 mod 8

28
028√6
Number of elements = 28

Number = 29, Adjoined = √6, Exponent = 1, Jacobi (6, 29) = 129 = 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

|28+0AI|
=1
|24+5AI|
=1
metric = 2
|24+24AI|
=1
metric = 2
|23+12AI|
=1
metric = 2
|23+17AI|
=1
metric = 2
|21+2AI|
=1
metric = 2
|21+27AI|
=1
metric = 2
|20+8AI|
=1
metric = 10
|20+21AI|
=1
metric = 10
|18+3AI|
=1
metric = 10
|18+26AI|
=1
metric = 10
|16+1AI|
=1
metric = 1
|16+28AI|
=1
metric = 1
|13+1AI|
=1
metric = 1
|13+28AI|
=1
metric = 1
|11+3AI|
=1
metric = 10
|11+26AI|
=1
metric = 10
|9+8AI|
=1
metric = 10
|9+21AI|
=1
metric = 10
|8+2AI|
=1
metric = 2
|8+27AI|
=1
metric = 2
|6+12AI|
=1
metric = 2
|6+17AI|
=1
metric = 2
|5+5AI|
=1
metric = 2
|5+24AI|
=1
metric = 2
|1+0AI|
=1
|0+11AI|
=1
|0+18AI|
=1

sum of all metrics = 108