Inhaltsverzeichnis

Development of
Algorithmic Constructions

23:19:21
Deutsch
16.Oct 2021

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

Number p= Adjoined square root=

Calculation

A=√7
(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 = √7, Exponent = 1, Jacobi (7, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√7
Number of elements = 32

Number = 31, Adjoined = √7, Exponent = 1, Jacobi (7, 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

|30+0AI|
=1
|29+2AI|
=1
metric = 6
|29+29AI|
=1
metric = 6
|27+12AI|
=1
metric = 2
|27+19AI|
=1
metric = 2
|26+1AI|
=1
metric = 15
|26+30AI|
=1
metric = 15
|24+8AI|
=1
metric = 3
|24+23AI|
=1
metric = 3
|21+15AI|
=1
metric = 6
|21+16AI|
=1
metric = 6
|20+6AI|
=1
metric = 6
|20+25AI|
=1
metric = 6
|18+10AI|
=1
metric = 6
|18+21AI|
=1
metric = 6
|13+10AI|
=1
metric = 6
|13+21AI|
=1
metric = 6
|11+6AI|
=1
metric = 6
|11+25AI|
=1
metric = 6
|10+15AI|
=1
metric = 6
|10+16AI|
=1
metric = 6
|7+8AI|
=1
metric = 3
|7+23AI|
=1
metric = 3
|5+1AI|
=1
metric = 15
|5+30AI|
=1
metric = 15
|4+12AI|
=1
metric = 2
|4+19AI|
=1
metric = 2
|2+2AI|
=1
metric = 6
|2+29AI|
=1
metric = 6
|1+0AI|
=1
|0+3AI|
=1
|0+28AI|
=1

sum of all metrics = 176