Inhaltsverzeichnis

Development of
Algorithmic Constructions

09:48:12
Deutsch
4.Oct 2022

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

Number p= Adjoined square root=

Calculation

A=√20
(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 17

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 = √20, Exponent = 17, Jacobi (20, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√20
Number of elements = 32

Number = 31, Adjoined = √20, Exponent = 17, Jacobi (20, 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 17

href=17. root

|30+0AI|
=1
|29+12AI|
=1
metric = 2
|29+19AI|
=1
metric = 2
|27+10AI|
=1
metric = 30
|27+21AI|
=1
metric = 30
|26+6AI|
=1
metric = 15
|26+25AI|
=1
metric = 15
|24+14AI|
=1
metric = 3
|24+17AI|
=1
metric = 3
|21+3AI|
=1
metric = 3
|21+28AI|
=1
metric = 3
|20+5AI|
=1
metric = 30
|20+26AI|
=1
metric = 30
|18+2AI|
=1
metric = 5
|18+29AI|
=1
metric = 5
|13+2AI|
=1
metric = 5
|13+29AI|
=1
metric = 5
|11+5AI|
=1
metric = 30
|11+26AI|
=1
metric = 30
|10+3AI|
=1
metric = 3
|10+28AI|
=1
metric = 3
|7+14AI|
=1
metric = 3
|7+17AI|
=1
metric = 3
|5+6AI|
=1
metric = 15
|5+25AI|
=1
metric = 15
|4+10AI|
=1
metric = 30
|4+21AI|
=1
metric = 30
|2+12AI|
=1
metric = 2
|2+19AI|
=1
metric = 2
|1+0AI|
=1
|0+13AI|
=1
|0+18AI|
=1

sum of all metrics = 352