# Development ofAlgorithmic Constructions

 07:42:29 25.Sep 2023

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12

 Number p= Adjoined square root=

### Calculation

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

 30 0 30√3
Number of elements = 2

### Number = 31, Adjoined = √3, Exponent = 1, Jacobi (3, 31) = -1, 31 = 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

### (a+bAI)^2=6+28A

 |22+26AI|=1 metric = 5 |9+5AI|=1 metric = 5

sum of all metrics = 10