Inhaltsverzeichnis

Development of
Algorithmic Constructions

23:14:25
Deutsch
16.Oct 2021

31 33 35
√2 √3 √5 √6 √7 √8

Number p= Adjoined square root=

Calculation

A=√5
(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 = √5, Exponent = 1, Jacobi (5, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√5
Number of elements = 24
Number of red elements = 20
Number of elements / Number of red elements = 1.2

Number = 33, Adjoined = √5, Exponent = 1, Jacobi (5, 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
|28+9AI|
=1
metric = 2
|28+24AI|
=1
metric = 2
|25+15AI|
=1
metric = 2
|25+18AI|
=1
metric = 2
|23+0AI|
=1
|22+3AI|
=1
metric = 2
|22+30AI|
=1
metric = 2
|19+15AI|
=1
metric = 2
|19+18AI|
=1
metric = 2
|17+9AI|
=1
metric = 2
|17+24AI|
=1
metric = 2
|16+9AI|
=1
metric = 2
|16+24AI|
=1
metric = 2
|14+15AI|
=1
metric = 2
|14+18AI|
=1
metric = 2
|11+3AI|
=1
metric = 2
|11+30AI|
=1
metric = 2
|10+0AI|
=1
|8+15AI|
=1
metric = 2
|8+18AI|
=1
metric = 2
|5+9AI|
=1
metric = 2
|5+24AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 40