Inhaltsverzeichnis

Development of
Algorithmic Constructions

12:56:06
Deutsch
3.Dec 2022

29 31 33
√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 = 31, Adjoined = √13, Exponent = 1, Jacobi (13, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√13
Number of elements = 30

Number = 31, Adjoined = √13, Exponent = 1, Jacobi (13, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

|30+0AI|
=1
|28+11AI|
=1
metric = 10
|28+20AI|
=1
metric = 10
|25+13AI|
=1
metric = 3
|25+18AI|
=1
metric = 3
|23+9AI|
=1
metric = 10
|23+22AI|
=1
metric = 10
|22+1AI|
=1
metric = 10
|22+30AI|
=1
metric = 10
|19+12AI|
=1
metric = 2
|19+19AI|
=1
metric = 2
|17+4AI|
=1
metric = 6
|17+27AI|
=1
metric = 6
|16+3AI|
=1
metric = 6
|16+28AI|
=1
metric = 6
|15+3AI|
=1
metric = 6
|15+28AI|
=1
metric = 6
|14+4AI|
=1
metric = 6
|14+27AI|
=1
metric = 6
|12+12AI|
=1
metric = 2
|12+19AI|
=1
metric = 2
|9+1AI|
=1
metric = 10
|9+30AI|
=1
metric = 10
|8+9AI|
=1
metric = 10
|8+22AI|
=1
metric = 10
|6+13AI|
=1
metric = 3
|6+18AI|
=1
metric = 3
|3+11AI|
=1
metric = 10
|3+20AI|
=1
metric = 10
|1+0AI|
=1

sum of all metrics = 188