Inhaltsverzeichnis

Development of
Algorithmic Constructions

13:51:56
Deutsch
3.Dec 2022

31 33 35
√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 = 33, Adjoined = √11, Exponent = 1, Jacobi (11, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√11
Number of elements = 44
Number of red elements = 40
Number of elements / Number of red elements = 1.1

Number = 33, Adjoined = √11, Exponent = 1, Jacobi (11, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

|32+0AI|
=1
|32+3AI|
=1
metric = 2
|32+6AI|
=1
metric = 2
|32+9AI|
=1
metric = 2
|32+12AI|
=1
metric = 2
|32+15AI|
=1
metric = 2
|32+18AI|
=1
metric = 2
|32+21AI|
=1
metric = 2
|32+24AI|
=1
metric = 2
|32+27AI|
=1
metric = 2
|32+30AI|
=1
metric = 2
|23+0AI|
=1
|23+3AI|
=1
metric = 2
|23+6AI|
=1
metric = 2
|23+9AI|
=1
metric = 2
|23+12AI|
=1
metric = 2
|23+15AI|
=1
metric = 2
|23+18AI|
=1
metric = 2
|23+21AI|
=1
metric = 2
|23+24AI|
=1
metric = 2
|23+27AI|
=1
metric = 2
|23+30AI|
=1
metric = 2
|10+0AI|
=1
|10+3AI|
=1
metric = 2
|10+6AI|
=1
metric = 2
|10+9AI|
=1
metric = 2
|10+12AI|
=1
metric = 2
|10+15AI|
=1
metric = 2
|10+18AI|
=1
metric = 2
|10+21AI|
=1
metric = 2
|10+24AI|
=1
metric = 2
|10+27AI|
=1
metric = 2
|10+30AI|
=1
metric = 2
|1+0AI|
=1
|1+3AI|
=1
metric = 2
|1+6AI|
=1
metric = 2
|1+9AI|
=1
metric = 2
|1+12AI|
=1
metric = 2
|1+15AI|
=1
metric = 2
|1+18AI|
=1
metric = 2
|1+21AI|
=1
metric = 2
|1+24AI|
=1
metric = 2
|1+27AI|
=1
metric = 2
|1+30AI|
=1
metric = 2

sum of all metrics = 80