Inhaltsverzeichnis

Development of
Algorithmic Constructions

08:06:55
Deutsch
4.Oct 2022

31 33 35
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17

Number p= Adjoined square root=

Calculation

A=√8
(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 = 33, Adjoined = √8, Exponent = 1, Jacobi (8, 33) = 133 = 1 mod 4, 33 = 1 mod 8

32
032√8
Number of elements = 20
Number of red elements = 16
Number of elements / Number of red elements = 1.25

Number = 33, Adjoined = √8, Exponent = 1, Jacobi (8, 33) = 133 = 1 mod 4, 33 = 1 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

|32+0AI|
=1
|31+12AI|
=1
metric = 2
|31+21AI|
=1
metric = 2
|29+15AI|
=1
metric = 2
|29+18AI|
=1
metric = 2
|26+15AI|
=1
metric = 2
|26+18AI|
=1
metric = 2
|23+0AI|
=1
|20+12AI|
=1
metric = 2
|20+21AI|
=1
metric = 2
|13+12AI|
=1
metric = 2
|13+21AI|
=1
metric = 2
|10+0AI|
=1
|7+15AI|
=1
metric = 2
|7+18AI|
=1
metric = 2
|4+15AI|
=1
metric = 2
|4+18AI|
=1
metric = 2
|2+12AI|
=1
metric = 2
|2+21AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 32