Inhaltsverzeichnis

Development of
Algorithmic Constructions

13:49:25
Deutsch
28.Mar 2024

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
Square 2 Square 5 Square 19

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 = 190, Jacobi (7, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√7
Number of elements = 16

Number = 31, Adjoined = √7, Exponent = 190, 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
Square 2 Square 5 Square 19

href=5. root

|30+0AI|
=1
|27+12AI|
=1
metric = 2
|27+19AI|
=1
metric = 2
|24+8AI|
=1
metric = 3
|24+23AI|
=1
metric = 3
|18+10AI|
=1
metric = 6
|18+21AI|
=1
metric = 6
|13+10AI|
=1
metric = 6
|13+21AI|
=1
metric = 6
|7+8AI|
=1
metric = 3
|7+23AI|
=1
metric = 3
|4+12AI|
=1
metric = 2
|4+19AI|
=1
metric = 2
|1+0AI|
=1
|0+3AI|
=1
|0+28AI|
=1

sum of all metrics = 44