Inhaltsverzeichnis

Development of
Algorithmic Constructions
11:31:57
Deutsch
20.Apr 2024
31 33 35
√3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22

Number p= Adjoined square root=

Calculation

A=√13
(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 = 33, Adjoined = √13, Exponent = 2, Jacobi (13, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√13
Number of elements = 10
Number of red elements = 8
Number of elements / Number of red elements = 1.25

Number = 33, Adjoined = √13, Exponent = 2, Jacobi (13, 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
Square 2

href=2. root

|31+9AI|
=1
metric = 2		|31+24AI|
=1
metric = 2
|29+3AI|
=1
metric = 2		|29+30AI|
=1
metric = 2
|23+0AI|
=1
|20+9AI|
=1
metric = 2		|20+24AI|
=1
metric = 2
|7+3AI|
=1
metric = 2		|7+30AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 16