Inhaltsverzeichnis

Development of
Algorithmic Constructions

13:51:16
Deutsch
3.Dec 2022

31 33 35
√2 √3 √5 √6 √7 √8 √10 √11 √12

Number p= Adjoined square root=

Calculation

A=√3
(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 = √3, Exponent = 1, Jacobi (3, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√3
Number of elements = 72
Number of red elements = 36
Number of elements / Number of red elements = 2

Number = 33, Adjoined = √3, Exponent = 1, Jacobi (3, 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+5AI|
=1
metric = 2
|28+6AI|
=1
metric = 2
|28+16AI|
=1
metric = 2
|28+17AI|
=1
metric = 2
|28+27AI|
=1
metric = 2
|28+28AI|
=1
metric = 2
|25+1AI|
=1
metric = 2
|25+10AI|
=1
metric = 2
|25+12AI|
=1
metric = 2
|25+21AI|
=1
metric = 2
|25+23AI|
=1
metric = 2
|25+32AI|
=1
metric = 2
|23+0AI|
=1
|23+11AI|
=1
metric = 2
|23+22AI|
=1
metric = 2
|22+2AI|
=1
metric = 2
|22+9AI|
=1
metric = 2
|22+13AI|
=1
metric = 2
|22+20AI|
=1
metric = 2
|22+24AI|
=1
metric = 2
|22+31AI|
=1
metric = 2
|19+1AI|
=1
metric = 2
|19+10AI|
=1
metric = 2
|19+12AI|
=1
metric = 2
|19+21AI|
=1
metric = 2
|19+23AI|
=1
metric = 2
|19+32AI|
=1
metric = 2
|17+5AI|
=1
metric = 1
|17+6AI|
=1
metric = 2
|17+16AI|
=1
metric = 1
|17+17AI|
=1
metric = 1
|17+27AI|
=1
metric = 2
|17+28AI|
=1
metric = 1
|16+5AI|
=1
metric = 1
|16+6AI|
=1
metric = 2
|16+16AI|
=1
metric = 1
|16+17AI|
=1
metric = 1
|16+27AI|
=1
metric = 2
|16+28AI|
=1
metric = 1
|14+1AI|
=1
metric = 2
|14+10AI|
=1
metric = 2
|14+12AI|
=1
metric = 2
|14+21AI|
=1
metric = 2
|14+23AI|
=1
metric = 2
|14+32AI|
=1
metric = 2
|11+2AI|
=1
metric = 2
|11+9AI|
=1
metric = 2
|11+13AI|
=1
metric = 2
|11+20AI|
=1
metric = 2
|11+24AI|
=1
metric = 2
|11+31AI|
=1
metric = 2
|10+0AI|
=1
|10+11AI|
=1
metric = 2
|10+22AI|
=1
metric = 2
|8+1AI|
=1
metric = 2
|8+10AI|
=1
metric = 2
|8+12AI|
=1
metric = 2
|8+21AI|
=1
metric = 2
|8+23AI|
=1
metric = 2
|8+32AI|
=1
metric = 2
|5+5AI|
=1
metric = 2
|5+6AI|
=1
metric = 2
|5+16AI|
=1
metric = 2
|5+17AI|
=1
metric = 2
|5+27AI|
=1
metric = 2
|5+28AI|
=1
metric = 2
|1+0AI|
=1
|1+11AI|
=1
metric = 2
|1+22AI|
=1
metric = 2

sum of all metrics = 128