# Development ofAlgorithmic Constructions

 13:32:40 3.Dec 2022

29 31 33
√5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23

### Calculation

A=√14
(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 = √14, Exponent = 1, Jacobi (14, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√14
Number of elements = 32

### Number = 31, Adjoined = √14, Exponent = 1, Jacobi (14, 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+8AI|=1 metric = 6 |29+23AI|=1 metric = 6 |27+14AI|=1 metric = 10 |27+17AI|=1 metric = 10 |26+4AI|=1 metric = 3 |26+27AI|=1 metric = 3 |24+1AI|=1 metric = 6 |24+30AI|=1 metric = 6 |21+2AI|=1 metric = 3 |21+29AI|=1 metric = 3 |20+7AI|=1 metric = 6 |20+24AI|=1 metric = 6 |18+9AI|=1 metric = 6 |18+22AI|=1 metric = 6 |13+9AI|=1 metric = 6 |13+22AI|=1 metric = 6 |11+7AI|=1 metric = 6 |11+24AI|=1 metric = 6 |10+2AI|=1 metric = 3 |10+29AI|=1 metric = 3 |7+1AI|=1 metric = 6 |7+30AI|=1 metric = 6 |5+4AI|=1 metric = 3 |5+27AI|=1 metric = 3 |4+14AI|=1 metric = 10 |4+17AI|=1 metric = 10 |2+8AI|=1 metric = 6 |2+23AI|=1 metric = 6 |1+0AI|=1 |0+12AI|=1 |0+19AI|=1

sum of all metrics = 160