Inhaltsverzeichnis

Development of
Algorithmic Constructions

06:48:28
Deutsch
30.Nov 2021

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19

Number p= Adjoined square root=

Calculation

A=√10
(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 = √10, Exponent = 1, Jacobi (10, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√10
Number of elements = 32

Number = 31, Adjoined = √10, Exponent = 1, Jacobi (10, 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+3AI|
=1
metric = 3
|29+28AI|
=1
metric = 3
|27+13AI|
=1
metric = 6
|27+18AI|
=1
metric = 6
|26+14AI|
=1
metric = 2
|26+17AI|
=1
metric = 2
|24+12AI|
=1
metric = 30
|24+19AI|
=1
metric = 30
|21+7AI|
=1
metric = 2
|21+24AI|
=1
metric = 2
|20+9AI|
=1
metric = 3
|20+22AI|
=1
metric = 3
|18+15AI|
=1
metric = 3
|18+16AI|
=1
metric = 3
|13+15AI|
=1
metric = 3
|13+16AI|
=1
metric = 3
|11+9AI|
=1
metric = 3
|11+22AI|
=1
metric = 3
|10+7AI|
=1
metric = 2
|10+24AI|
=1
metric = 2
|7+12AI|
=1
metric = 30
|7+19AI|
=1
metric = 30
|5+14AI|
=1
metric = 2
|5+17AI|
=1
metric = 2
|4+13AI|
=1
metric = 6
|4+18AI|
=1
metric = 6
|2+3AI|
=1
metric = 3
|2+28AI|
=1
metric = 3
|1+0AI|
=1
|0+11AI|
=1
|0+20AI|
=1

sum of all metrics = 196