Inhaltsverzeichnis

Development of
Algorithmic Constructions
17:00:54
Deutsch
20.Apr 2024
29 31 33
√20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35 √37 √38 √39

Number p= Adjoined square root=

Calculation

A=√30
(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 = √30, Exponent = 1, Jacobi (30, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√30
Number of elements = 30

Number = 31, Adjoined = √30, Exponent = 1, Jacobi (30, 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+15AI|
=1
metric = 10		|28+16AI|
=1
metric = 10
|25+2AI|
=1
metric = 5		|25+29AI|
=1
metric = 5
|23+1AI|
=1
metric = 2		|23+30AI|
=1
metric = 2
|22+7AI|
=1
metric = 3		|22+24AI|
=1
metric = 3
|19+9AI|
=1
metric = 3		|19+22AI|
=1
metric = 3
|17+3AI|
=1
metric = 6		|17+28AI|
=1
metric = 6
|16+10AI|
=1
metric = 6		|16+21AI|
=1
metric = 6
|15+10AI|
=1
metric = 6		|15+21AI|
=1
metric = 6
|14+3AI|
=1
metric = 6		|14+28AI|
=1
metric = 6
|12+9AI|
=1
metric = 3		|12+22AI|
=1
metric = 3
|9+7AI|
=1
metric = 3		|9+24AI|
=1
metric = 3
|8+1AI|
=1
metric = 2		|8+30AI|
=1
metric = 2
|6+2AI|
=1
metric = 5		|6+29AI|
=1
metric = 5
|3+15AI|
=1
metric = 10		|3+16AI|
=1
metric = 10
|1+0AI|
=1

sum of all metrics = 140