# Development ofAlgorithmic Constructions

 13:45:22 3.Dec 2022

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20

### Calculation

A=√11
(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 = √11, Exponent = 1, Jacobi (11, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

 30 0 30√11
Number of elements = 30

### Number = 31, Adjoined = √11, Exponent = 1, Jacobi (11, 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

 |30+0AI|=1 |28+9AI|=1 metric = 6 |28+22AI|=1 metric = 6 |25+5AI|=1 metric = 3 |25+26AI|=1 metric = 3 |23+13AI|=1 metric = 1 |23+18AI|=1 metric = 1 |22+2AI|=1 metric = 3 |22+29AI|=1 metric = 3 |19+7AI|=1 metric = 1 |19+24AI|=1 metric = 1 |17+8AI|=1 metric = 6 |17+23AI|=1 metric = 6 |16+6AI|=1 metric = 2 |16+25AI|=1 metric = 2 |15+6AI|=1 metric = 2 |15+25AI|=1 metric = 2 |14+8AI|=1 metric = 6 |14+23AI|=1 metric = 6 |12+7AI|=1 metric = 1 |12+24AI|=1 metric = 1 |9+2AI|=1 metric = 3 |9+29AI|=1 metric = 3 |8+13AI|=1 metric = 1 |8+18AI|=1 metric = 1 |6+5AI|=1 metric = 3 |6+26AI|=1 metric = 3 |3+9AI|=1 metric = 6 |3+22AI|=1 metric = 6 |1+0AI|=1

sum of all metrics = 88