Inhaltsverzeichnis

Development of
Algorithmic Constructions

22:27:58
Deutsch
16.Oct 2021

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11

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 = 31, Adjoined = √2, Exponent = 1, Jacobi (2, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√2
Number of elements = 32

Number = 31, Adjoined = √2, Exponent = 1, Jacobi (2, 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+13AI|
=1
metric = 3
|29+18AI|
=1
metric = 3
|27+15AI|
=1
metric = 3
|27+16AI|
=1
metric = 3
|26+9AI|
=1
metric = 2
|26+22AI|
=1
metric = 2
|24+10AI|
=1
metric = 10
|24+21AI|
=1
metric = 10
|21+11AI|
=1
metric = 5
|21+20AI|
=1
metric = 5
|20+8AI|
=1
metric = 10
|20+23AI|
=1
metric = 10
|18+3AI|
=1
metric = 6
|18+28AI|
=1
metric = 6
|13+3AI|
=1
metric = 6
|13+28AI|
=1
metric = 6
|11+8AI|
=1
metric = 10
|11+23AI|
=1
metric = 10
|10+11AI|
=1
metric = 5
|10+20AI|
=1
metric = 5
|7+10AI|
=1
metric = 10
|7+21AI|
=1
metric = 10
|5+9AI|
=1
metric = 2
|5+22AI|
=1
metric = 2
|4+15AI|
=1
metric = 3
|4+16AI|
=1
metric = 3
|2+13AI|
=1
metric = 3
|2+18AI|
=1
metric = 3
|1+0AI|
=1
|0+4AI|
=1
|0+27AI|
=1

sum of all metrics = 156