Inhaltsverzeichnis

Development of
Algorithmic Constructions

12:59:37
Deutsch
3.Dec 2022

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


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 = 1, Jacobi (13, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

32
032√13
Number of elements = 40
Number of red elements = 36
Number of elements / Number of red elements = 1.1111111111111

Number = 33, Adjoined = √13, Exponent = 1, 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

|32+0AI|
=1
|31+9AI|
=1
metric = 2
|31+24AI|
=1
metric = 2
|29+3AI|
=1
metric = 2
|29+30AI|
=1
metric = 2
|26+3AI|
=1
metric = 2
|26+30AI|
=1
metric = 2
|24+2AI|
=1
metric = 2
|24+13AI|
=1
metric = 2
|24+20AI|
=1
metric = 2
|24+31AI|
=1
metric = 2
|23+0AI|
=1
|21+11AI|
=1
metric = 2
|21+22AI|
=1
metric = 2
|20+9AI|
=1
metric = 2
|20+24AI|
=1
metric = 2
|18+8AI|
=1
metric = 2
|18+14AI|
=1
metric = 2
|18+19AI|
=1
metric = 2
|18+25AI|
=1
metric = 2
|15+8AI|
=1
metric = 2
|15+14AI|
=1
metric = 2
|15+19AI|
=1
metric = 2
|15+25AI|
=1
metric = 2
|13+9AI|
=1
metric = 2
|13+24AI|
=1
metric = 2
|12+11AI|
=1
metric = 2
|12+22AI|
=1
metric = 2
|10+0AI|
=1
|9+2AI|
=1
metric = 2
|9+13AI|
=1
metric = 2
|9+20AI|
=1
metric = 2
|9+31AI|
=1
metric = 2
|7+3AI|
=1
metric = 2
|7+30AI|
=1
metric = 2
|4+3AI|
=1
metric = 2
|4+30AI|
=1
metric = 2
|2+9AI|
=1
metric = 2
|2+24AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 72