Inhaltsverzeichnis

Development of
Algorithmic Constructions

08:07:28
Deutsch
30.Nov 2021

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21

Number p= Adjoined square root=

Calculation

A=√12
(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 = √12, Exponent = 1, Jacobi (12, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√12
Number of elements = 30

Number = 31, Adjoined = √12, Exponent = 1, Jacobi (12, 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+12AI|
=1
metric = 3
|28+19AI|
=1
metric = 3
|25+14AI|
=1
metric = 1
|25+17AI|
=1
metric = 1
|23+7AI|
=1
metric = 10
|23+24AI|
=1
metric = 10
|22+13AI|
=1
metric = 3
|22+18AI|
=1
metric = 3
|19+1AI|
=1
metric = 5
|19+30AI|
=1
metric = 5
|17+10AI|
=1
metric = 3
|17+21AI|
=1
metric = 3
|16+8AI|
=1
metric = 30
|16+23AI|
=1
metric = 30
|15+8AI|
=1
metric = 30
|15+23AI|
=1
metric = 30
|14+10AI|
=1
metric = 3
|14+21AI|
=1
metric = 3
|12+1AI|
=1
metric = 5
|12+30AI|
=1
metric = 5
|9+13AI|
=1
metric = 3
|9+18AI|
=1
metric = 3
|8+7AI|
=1
metric = 10
|8+24AI|
=1
metric = 10
|6+14AI|
=1
metric = 1
|6+17AI|
=1
metric = 1
|3+12AI|
=1
metric = 3
|3+19AI|
=1
metric = 3
|1+0AI|
=1

sum of all metrics = 220