Inhaltsverzeichnis

Development of
Algorithmic Constructions

14:32:22
Deutsch
3.Dec 2022

31 33 35
√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 = 33, Adjoined = √12, Exponent = 1, Jacobi (12, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√12
Number of elements = 72
Number of red elements = 36
Number of elements / Number of red elements = 2

Number = 33, Adjoined = √12, Exponent = 1, Jacobi (12, 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+11AI|
=1
metric = 2
|32+22AI|
=1
metric = 2
|28+3AI|
=1
metric = 2
|28+8AI|
=1
metric = 2
|28+14AI|
=1
metric = 2
|28+19AI|
=1
metric = 2
|28+25AI|
=1
metric = 2
|28+30AI|
=1
metric = 2
|25+5AI|
=1
metric = 2
|25+6AI|
=1
metric = 2
|25+16AI|
=1
metric = 2
|25+17AI|
=1
metric = 2
|25+27AI|
=1
metric = 2
|25+28AI|
=1
metric = 2
|23+0AI|
=1
|23+11AI|
=1
metric = 2
|23+22AI|
=1
metric = 2
|22+1AI|
=1
metric = 2
|22+10AI|
=1
metric = 2
|22+12AI|
=1
metric = 2
|22+21AI|
=1
metric = 2
|22+23AI|
=1
metric = 2
|22+32AI|
=1
metric = 2
|19+5AI|
=1
metric = 2
|19+6AI|
=1
metric = 17
|19+16AI|
=1
metric = 2
|19+17AI|
=1
metric = 2
|19+27AI|
=1
metric = 17
|19+28AI|
=1
metric = 2
|17+3AI|
=1
metric = 2
|17+8AI|
=1
metric = 2
|17+14AI|
=1
metric = 2
|17+19AI|
=1
metric = 2
|17+25AI|
=1
metric = 2
|17+30AI|
=1
metric = 2
|16+3AI|
=1
metric = 2
|16+8AI|
=1
metric = 2
|16+14AI|
=1
metric = 2
|16+19AI|
=1
metric = 2
|16+25AI|
=1
metric = 2
|16+30AI|
=1
metric = 2
|14+5AI|
=1
metric = 2
|14+6AI|
=1
metric = 17
|14+16AI|
=1
metric = 2
|14+17AI|
=1
metric = 2
|14+27AI|
=1
metric = 17
|14+28AI|
=1
metric = 2
|11+1AI|
=1
metric = 2
|11+10AI|
=1
metric = 2
|11+12AI|
=1
metric = 2
|11+21AI|
=1
metric = 2
|11+23AI|
=1
metric = 2
|11+32AI|
=1
metric = 2
|10+0AI|
=1
|10+11AI|
=1
metric = 2
|10+22AI|
=1
metric = 2
|8+5AI|
=1
metric = 2
|8+6AI|
=1
metric = 2
|8+16AI|
=1
metric = 2
|8+17AI|
=1
metric = 2
|8+27AI|
=1
metric = 2
|8+28AI|
=1
metric = 2
|5+3AI|
=1
metric = 2
|5+8AI|
=1
metric = 2
|5+14AI|
=1
metric = 2
|5+19AI|
=1
metric = 2
|5+25AI|
=1
metric = 2
|5+30AI|
=1
metric = 2
|1+0AI|
=1
|1+11AI|
=1
metric = 2
|1+22AI|
=1
metric = 2

sum of all metrics = 196