# Development ofAlgorithmic Constructions

 12:45:58 3.Dec 2022

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

### 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
Square 7

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

 30 0 30√3
Number of elements = 30

### Number = 31, Adjoined = √3, Exponent = 7, 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
Square 7

### href=7. root

 |30+0AI|=1 |28+7AI|=1 metric = 5 |28+24AI|=1 metric = 5 |25+3AI|=1 metric = 2 |25+28AI|=1 metric = 2 |23+14AI|=1 metric = 10 |23+17AI|=1 metric = 10 |22+5AI|=1 metric = 5 |22+26AI|=1 metric = 5 |19+2AI|=1 metric = 10 |19+29AI|=1 metric = 10 |17+11AI|=1 metric = 6 |17+20AI|=1 metric = 6 |16+15AI|=1 metric = 1 |16+16AI|=1 metric = 1 |15+15AI|=1 metric = 1 |15+16AI|=1 metric = 1 |14+11AI|=1 metric = 6 |14+20AI|=1 metric = 6 |12+2AI|=1 metric = 10 |12+29AI|=1 metric = 10 |9+5AI|=1 metric = 5 |9+26AI|=1 metric = 5 |8+14AI|=1 metric = 10 |8+17AI|=1 metric = 10 |6+3AI|=1 metric = 2 |6+28AI|=1 metric = 2 |3+7AI|=1 metric = 5 |3+24AI|=1 metric = 5 |1+0AI|=1

sum of all metrics = 156