Inhaltsverzeichnis

Development of
Algorithmic Constructions

23:22:23
Deutsch
16.Oct 2021

27 29 31
√2 √3 √5 √6 √7 √8

Number p= Adjoined square root=

Calculation

A=√2
(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 = 29, Adjoined = √2, Exponent = 1, Jacobi (2, 29) = -1, 29 = 1 mod 4, 29 = 5 mod 8

28
028√2
Number of elements = 30

Number = 29, Adjoined = √2, Exponent = 1, Jacobi (2, 29) = -1, 29 = 1 mod 4, 29 = 5 mod 8

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

|28+0AI|
=1
|27+10AI|
=1
metric = 3
|27+19AI|
=1
metric = 3
|26+5AI|
=1
metric = 2
|26+24AI|
=1
metric = 2
|25+6AI|
=1
metric = 5
|25+23AI|
=1
metric = 5
|22+11AI|
=1
metric = 10
|22+18AI|
=1
metric = 10
|19+9AI|
=1
metric = 3
|19+20AI|
=1
metric = 3
|17+1AI|
=1
metric = 6
|17+28AI|
=1
metric = 6
|15+2AI|
=1
metric = 3
|15+27AI|
=1
metric = 3
|14+2AI|
=1
metric = 3
|14+27AI|
=1
metric = 3
|12+1AI|
=1
metric = 6
|12+28AI|
=1
metric = 6
|10+9AI|
=1
metric = 3
|10+20AI|
=1
metric = 3
|7+11AI|
=1
metric = 10
|7+18AI|
=1
metric = 10
|4+6AI|
=1
metric = 5
|4+23AI|
=1
metric = 5
|3+5AI|
=1
metric = 2
|3+24AI|
=1
metric = 2
|2+10AI|
=1
metric = 3
|2+19AI|
=1
metric = 3
|1+0AI|
=1

sum of all metrics = 128