# Development ofAlgorithmic Constructions

 12:46:27 29.Nov 2022

29 31 33
√8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27

### Calculation

A=√18
(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 = √18, Exponent = 1, Jacobi (18, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√18
Number of elements = 32

### Number = 31, Adjoined = √18, Exponent = 1, Jacobi (18, 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+6AI|=1 metric = 15 |29+25AI|=1 metric = 15 |27+5AI|=1 metric = 30 |27+26AI|=1 metric = 30 |26+3AI|=1 metric = 5 |26+28AI|=1 metric = 5 |24+7AI|=1 metric = 6 |24+24AI|=1 metric = 6 |21+14AI|=1 metric = 6 |21+17AI|=1 metric = 6 |20+13AI|=1 metric = 5 |20+18AI|=1 metric = 5 |18+1AI|=1 metric = 2 |18+30AI|=1 metric = 2 |13+1AI|=1 metric = 2 |13+30AI|=1 metric = 2 |11+13AI|=1 metric = 5 |11+18AI|=1 metric = 5 |10+14AI|=1 metric = 6 |10+17AI|=1 metric = 6 |7+7AI|=1 metric = 6 |7+24AI|=1 metric = 6 |5+3AI|=1 metric = 5 |5+28AI|=1 metric = 5 |4+5AI|=1 metric = 30 |4+26AI|=1 metric = 30 |2+6AI|=1 metric = 15 |2+25AI|=1 metric = 15 |1+0AI|=1 |0+9AI|=1 |0+22AI|=1

sum of all metrics = 276