Inhaltsverzeichnis

Development of
Algorithmic Constructions

20:53:46
Deutsch
28.Mar 2024

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17

Number p= Adjoined square root=

Calculation

A=√8
(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
Square 3

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 = √8, Exponent = 3, Jacobi (8, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√8
Number of elements = 32

Number = 31, Adjoined = √8, Exponent = 3, Jacobi (8, 31) = 131 = 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
Square 3

href=3. root

|30+0AI|
=1
|29+9AI|
=1
metric = 2
|29+22AI|
=1
metric = 2
|27+8AI|
=1
metric = 2
|27+23AI|
=1
metric = 2
|26+11AI|
=1
metric = 10
|26+20AI|
=1
metric = 10
|24+5AI|
=1
metric = 3
|24+26AI|
=1
metric = 3
|21+10AI|
=1
metric = 2
|21+21AI|
=1
metric = 2
|20+4AI|
=1
metric = 2
|20+27AI|
=1
metric = 2
|18+14AI|
=1
metric = 6
|18+17AI|
=1
metric = 6
|13+14AI|
=1
metric = 6
|13+17AI|
=1
metric = 6
|11+4AI|
=1
metric = 2
|11+27AI|
=1
metric = 2
|10+10AI|
=1
metric = 2
|10+21AI|
=1
metric = 2
|7+5AI|
=1
metric = 3
|7+26AI|
=1
metric = 3
|5+11AI|
=1
metric = 10
|5+20AI|
=1
metric = 10
|4+8AI|
=1
metric = 2
|4+23AI|
=1
metric = 2
|2+9AI|
=1
metric = 2
|2+22AI|
=1
metric = 2
|1+0AI|
=1
|0+2AI|
=1
|0+29AI|
=1

sum of all metrics = 108