Inhaltsverzeichnis

Development of
Algorithmic Constructions

07:35:54
Deutsch
30.Nov 2021

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

Number p= Adjoined square root=

Calculation

A=√11
(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 = √11, Exponent = 1, Jacobi (11, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√11
Number of elements = 30

Number = 31, Adjoined = √11, Exponent = 1, Jacobi (11, 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+9AI|
=1
metric = 6
|28+22AI|
=1
metric = 6
|25+5AI|
=1
metric = 3
|25+26AI|
=1
metric = 3
|23+13AI|
=1
metric = 1
|23+18AI|
=1
metric = 1
|22+2AI|
=1
metric = 3
|22+29AI|
=1
metric = 3
|19+7AI|
=1
metric = 1
|19+24AI|
=1
metric = 1
|17+8AI|
=1
metric = 6
|17+23AI|
=1
metric = 6
|16+6AI|
=1
metric = 2
|16+25AI|
=1
metric = 2
|15+6AI|
=1
metric = 2
|15+25AI|
=1
metric = 2
|14+8AI|
=1
metric = 6
|14+23AI|
=1
metric = 6
|12+7AI|
=1
metric = 1
|12+24AI|
=1
metric = 1
|9+2AI|
=1
metric = 3
|9+29AI|
=1
metric = 3
|8+13AI|
=1
metric = 1
|8+18AI|
=1
metric = 1
|6+5AI|
=1
metric = 3
|6+26AI|
=1
metric = 3
|3+9AI|
=1
metric = 6
|3+22AI|
=1
metric = 6
|1+0AI|
=1

sum of all metrics = 88