Inhaltsverzeichnis

Development of
Algorithmic Constructions

08:19:08
Deutsch
4.Oct 2022

29 31 33
√18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35 √37

Number p= Adjoined square root=

Calculation

A=√28
(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 = √28, Exponent = 1, Jacobi (28, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√28
Number of elements = 32

Number = 31, Adjoined = √28, Exponent = 1, Jacobi (28, 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+1AI|
=1
metric = 15
|29+30AI|
=1
metric = 15
|27+6AI|
=1
metric = 2
|27+25AI|
=1
metric = 2
|26+15AI|
=1
metric = 6
|26+16AI|
=1
metric = 6
|24+4AI|
=1
metric = 10
|24+27AI|
=1
metric = 10
|21+8AI|
=1
metric = 2
|21+23AI|
=1
metric = 2
|20+3AI|
=1
metric = 6
|20+28AI|
=1
metric = 6
|18+5AI|
=1
metric = 2
|18+26AI|
=1
metric = 2
|13+5AI|
=1
metric = 2
|13+26AI|
=1
metric = 2
|11+3AI|
=1
metric = 6
|11+28AI|
=1
metric = 6
|10+8AI|
=1
metric = 2
|10+23AI|
=1
metric = 2
|7+4AI|
=1
metric = 10
|7+27AI|
=1
metric = 10
|5+15AI|
=1
metric = 6
|5+16AI|
=1
metric = 6
|4+6AI|
=1
metric = 2
|4+25AI|
=1
metric = 2
|2+1AI|
=1
metric = 15
|2+30AI|
=1
metric = 15
|1+0AI|
=1
|0+14AI|
=1
|0+17AI|
=1

sum of all metrics = 172