Inhaltsverzeichnis

Development of
Algorithmic Constructions

09:59:13
Deutsch
4.Oct 2022

29 31 33
√17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35

Number p= Adjoined square root=

Calculation

A=√27
(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 = √27, Exponent = 1, Jacobi (27, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√27
Number of elements = 30

Number = 31, Adjoined = √27, Exponent = 1, Jacobi (27, 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+8AI|
=1
metric = 10
|28+23AI|
=1
metric = 10
|25+1AI|
=1
metric = 10
|25+30AI|
=1
metric = 10
|23+15AI|
=1
metric = 6
|23+16AI|
=1
metric = 6
|22+12AI|
=1
metric = 1
|22+19AI|
=1
metric = 1
|19+11AI|
=1
metric = 6
|19+20AI|
=1
metric = 6
|17+14AI|
=1
metric = 3
|17+17AI|
=1
metric = 3
|16+5AI|
=1
metric = 3
|16+26AI|
=1
metric = 3
|15+5AI|
=1
metric = 3
|15+26AI|
=1
metric = 3
|14+14AI|
=1
metric = 3
|14+17AI|
=1
metric = 3
|12+11AI|
=1
metric = 6
|12+20AI|
=1
metric = 6
|9+12AI|
=1
metric = 1
|9+19AI|
=1
metric = 1
|8+15AI|
=1
metric = 6
|8+16AI|
=1
metric = 6
|6+1AI|
=1
metric = 10
|6+30AI|
=1
metric = 10
|3+8AI|
=1
metric = 10
|3+23AI|
=1
metric = 10
|1+0AI|
=1

sum of all metrics = 156