Inhaltsverzeichnis

Development of
Algorithmic Constructions

01:41:18
Deutsch
4.Oct 2022

29 31 33
√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 = 31, Adjoined = √21, Exponent = 1, Jacobi (21, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√21
Number of elements = 30

Number = 31, Adjoined = √21, Exponent = 1, Jacobi (21, 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+10AI|
=1
metric = 6
|28+21AI|
=1
metric = 6
|25+9AI|
=1
metric = 1
|25+22AI|
=1
metric = 1
|23+11AI|
=1
metric = 6
|23+20AI|
=1
metric = 6
|22+15AI|
=1
metric = 5
|22+16AI|
=1
metric = 5
|19+6AI|
=1
metric = 5
|19+25AI|
=1
metric = 5
|17+2AI|
=1
metric = 15
|17+29AI|
=1
metric = 15
|16+14AI|
=1
metric = 10
|16+17AI|
=1
metric = 10
|15+14AI|
=1
metric = 10
|15+17AI|
=1
metric = 10
|14+2AI|
=1
metric = 15
|14+29AI|
=1
metric = 15
|12+6AI|
=1
metric = 5
|12+25AI|
=1
metric = 5
|9+15AI|
=1
metric = 5
|9+16AI|
=1
metric = 5
|8+11AI|
=1
metric = 6
|8+20AI|
=1
metric = 6
|6+9AI|
=1
metric = 1
|6+22AI|
=1
metric = 1
|3+10AI|
=1
metric = 6
|3+21AI|
=1
metric = 6
|1+0AI|
=1

sum of all metrics = 192