# Development ofAlgorithmic Constructions

 08:55:29 25.Sep 2023

29 31 33
√10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28

### Calculation

A=√19
(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 17

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 = √19, Exponent = 17, Jacobi (19, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√19
Number of elements = 32

### Number = 31, Adjoined = √19, Exponent = 17, Jacobi (19, 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
Square 17

### href=17. root

 |30+0AI|=1 |29+15AI|=1 metric = 2 |29+16AI|=1 metric = 2 |27+3AI|=1 metric = 5 |27+28AI|=1 metric = 5 |26+8AI|=1 metric = 2 |26+23AI|=1 metric = 2 |24+2AI|=1 metric = 10 |24+29AI|=1 metric = 10 |21+4AI|=1 metric = 30 |21+27AI|=1 metric = 30 |20+14AI|=1 metric = 3 |20+17AI|=1 metric = 3 |18+13AI|=1 metric = 6 |18+18AI|=1 metric = 6 |13+13AI|=1 metric = 6 |13+18AI|=1 metric = 6 |11+14AI|=1 metric = 3 |11+17AI|=1 metric = 3 |10+4AI|=1 metric = 30 |10+27AI|=1 metric = 30 |7+2AI|=1 metric = 10 |7+29AI|=1 metric = 10 |5+8AI|=1 metric = 2 |5+23AI|=1 metric = 2 |4+3AI|=1 metric = 5 |4+28AI|=1 metric = 5 |2+15AI|=1 metric = 2 |2+16AI|=1 metric = 2 |1+0AI|=1 |0+7AI|=1 |0+24AI|=1

sum of all metrics = 232