Inhaltsverzeichnis

Development of
Algorithmic Constructions

09:47:35
Deutsch
4.Oct 2022

29 31 33
√8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27

Number p= Adjoined square root=

Calculation

A=√18
(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 2

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 = √18, Exponent = 2, Jacobi (18, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√18
Number of elements = 16

Number = 31, Adjoined = √18, Exponent = 2, Jacobi (18, 31) = 131 = 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
Square 2

href=2. root

|30+0AI|
=1
|27+5AI|
=1
metric = 30
|27+26AI|
=1
metric = 30
|24+7AI|
=1
metric = 6
|24+24AI|
=1
metric = 6
|18+1AI|
=1
metric = 2
|18+30AI|
=1
metric = 2
|13+1AI|
=1
metric = 2
|13+30AI|
=1
metric = 2
|7+7AI|
=1
metric = 6
|7+24AI|
=1
metric = 6
|4+5AI|
=1
metric = 30
|4+26AI|
=1
metric = 30
|1+0AI|
=1
|0+9AI|
=1
|0+22AI|
=1

sum of all metrics = 152