Inhaltsverzeichnis

Development of
Algorithmic Constructions

13:48:14
Deutsch
28.Mar 2024

31 33 35
√11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30

Number p= Adjoined square root=

Calculation

A=√21
(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 = √21, Exponent = 1, Jacobi (21, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√21
Number of elements = 60
Number of red elements = 24
Number of elements / Number of red elements = 2.5

Number = 33, Adjoined = √21, Exponent = 1, Jacobi (21, 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
|31+5AI|
=1
metric = 2
|31+6AI|
=1
metric = 2
|31+16AI|
=1
metric = 2
|31+17AI|
=1
metric = 2
|31+27AI|
=1
metric = 2
|31+28AI|
=1
metric = 2
|29+2AI|
=1
metric = 2
|29+9AI|
=1
metric = 2
|29+13AI|
=1
metric = 2
|29+20AI|
=1
metric = 2
|29+24AI|
=1
metric = 2
|29+31AI|
=1
metric = 2
|26+2AI|
=1
metric = 2
|26+9AI|
=1
metric = 2
|26+13AI|
=1
metric = 2
|26+20AI|
=1
metric = 2
|26+24AI|
=1
metric = 2
|26+31AI|
=1
metric = 2
|23+0AI|
=1
|23+11AI|
=1
metric = 1
|23+22AI|
=1
metric = 1
|20+5AI|
=1
metric = 2
|20+6AI|
=1
metric = 2
|20+16AI|
=1
metric = 2
|20+17AI|
=1
metric = 2
|20+27AI|
=1
metric = 2
|20+28AI|
=1
metric = 2
|13+5AI|
=1
metric = 2
|13+6AI|
=1
metric = 2
|13+16AI|
=1
metric = 2
|13+17AI|
=1
metric = 2
|13+27AI|
=1
metric = 2
|13+28AI|
=1
metric = 2
|10+0AI|
=1
|10+11AI|
=1
metric = 1
|10+22AI|
=1
metric = 1
|7+2AI|
=1
metric = 2
|7+9AI|
=1
metric = 2
|7+13AI|
=1
metric = 2
|7+20AI|
=1
metric = 2
|7+24AI|
=1
metric = 2
|7+31AI|
=1
metric = 2
|4+2AI|
=1
metric = 2
|4+9AI|
=1
metric = 2
|4+13AI|
=1
metric = 2
|4+20AI|
=1
metric = 2
|4+24AI|
=1
metric = 2
|4+31AI|
=1
metric = 2
|2+5AI|
=1
metric = 2
|2+6AI|
=1
metric = 2
|2+16AI|
=1
metric = 2
|2+17AI|
=1
metric = 2
|2+27AI|
=1
metric = 2
|2+28AI|
=1
metric = 2
|1+0AI|
=1
|1+11AI|
=1
metric = 2
|1+22AI|
=1
metric = 2

sum of all metrics = 108