Inhaltsverzeichnis

Development of
Algorithmic Constructions

14:52:35
Deutsch
18.Aug 2022

29 31 33
√10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28

Number p= Adjoined square root=

Calculation

A=√19
(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 = √19, Exponent = 1, Jacobi (19, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√19
Number of elements = 32

Number = 31, Adjoined = √19, Exponent = 1, Jacobi (19, 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+15AI|
=1
metric = 2
|29+16AI|
=1
metric = 2
|27+3AI|
=1
metric = 5
|27+28AI|
=1
metric = 5
|26+8AI|
=1
metric = 2
|26+23AI|
=1
metric = 2
|24+2AI|
=1
metric = 10
|24+29AI|
=1
metric = 10
|21+4AI|
=1
metric = 30
|21+27AI|
=1
metric = 30
|20+14AI|
=1
metric = 3
|20+17AI|
=1
metric = 3
|18+13AI|
=1
metric = 6
|18+18AI|
=1
metric = 6
|13+13AI|
=1
metric = 6
|13+18AI|
=1
metric = 6
|11+14AI|
=1
metric = 3
|11+17AI|
=1
metric = 3
|10+4AI|
=1
metric = 30
|10+27AI|
=1
metric = 30
|7+2AI|
=1
metric = 10
|7+29AI|
=1
metric = 10
|5+8AI|
=1
metric = 2
|5+23AI|
=1
metric = 2
|4+3AI|
=1
metric = 5
|4+28AI|
=1
metric = 5
|2+15AI|
=1
metric = 2
|2+16AI|
=1
metric = 2
|1+0AI|
=1
|0+7AI|
=1
|0+24AI|
=1

sum of all metrics = 232