Inhaltsverzeichnis

Development of
Algorithmic Constructions

02:55:00
Deutsch
4.Oct 2022

29 31 33
√13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32

Number p= Adjoined square root=

Calculation

A=√23
(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 = √23, Exponent = 1, Jacobi (23, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√23
Number of elements = 30

Number = 31, Adjoined = √23, Exponent = 1, Jacobi (23, 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+1AI|
=1
metric = 2
|28+30AI|
=1
metric = 2
|25+4AI|
=1
metric = 6
|25+27AI|
=1
metric = 6
|23+2AI|
=1
metric = 30
|23+29AI|
=1
metric = 30
|22+14AI|
=1
metric = 3
|22+17AI|
=1
metric = 3
|19+13AI|
=1
metric = 2
|19+18AI|
=1
metric = 2
|17+6AI|
=1
metric = 3
|17+25AI|
=1
metric = 3
|16+11AI|
=1
metric = 3
|16+20AI|
=1
metric = 3
|15+11AI|
=1
metric = 3
|15+20AI|
=1
metric = 3
|14+6AI|
=1
metric = 3
|14+25AI|
=1
metric = 3
|12+13AI|
=1
metric = 2
|12+18AI|
=1
metric = 2
|9+14AI|
=1
metric = 3
|9+17AI|
=1
metric = 3
|8+2AI|
=1
metric = 30
|8+29AI|
=1
metric = 30
|6+4AI|
=1
metric = 6
|6+27AI|
=1
metric = 6
|3+1AI|
=1
metric = 2
|3+30AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 196