Inhaltsverzeichnis

Development of
Algorithmic Constructions
01:30:45
Deutsch
3.Oct 2023
29 31 33
√14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33

Number p= Adjoined square root=

Calculation

A=√24
(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 = √24, Exponent = 1, Jacobi (24, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√24
Number of elements = 30

Number = 31, Adjoined = √24, Exponent = 1, Jacobi (24, 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+14AI|
=1
metric = 6		|28+17AI|
=1
metric = 6
|25+6AI|
=1
metric = 10		|25+25AI|
=1
metric = 10
|23+3AI|
=1
metric = 2		|23+28AI|
=1
metric = 2
|22+10AI|
=1
metric = 15		|22+21AI|
=1
metric = 15
|19+4AI|
=1
metric = 30		|19+27AI|
=1
metric = 30
|17+9AI|
=1
metric = 3		|17+22AI|
=1
metric = 3
|16+1AI|
=1
metric = 2		|16+30AI|
=1
metric = 2
|15+1AI|
=1
metric = 2		|15+30AI|
=1
metric = 2
|14+9AI|
=1
metric = 3		|14+22AI|
=1
metric = 3
|12+4AI|
=1
metric = 30		|12+27AI|
=1
metric = 30
|9+10AI|
=1
metric = 15		|9+21AI|
=1
metric = 15
|8+3AI|
=1
metric = 2		|8+28AI|
=1
metric = 2
|6+6AI|
=1
metric = 10		|6+25AI|
=1
metric = 10
|3+14AI|
=1
metric = 6		|3+17AI|
=1
metric = 6
|1+0AI|
=1

sum of all metrics = 272