# Development ofAlgorithmic Constructions

 16:28:52 18.Aug 2022

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

 Number p= Adjoined square root=

### Calculation

A=√20
(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 = √20, Exponent = 1, Jacobi (20, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√20
Number of elements = 32

### Number = 31, Adjoined = √20, Exponent = 1, Jacobi (20, 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+12AI|=1 metric = 2 |29+19AI|=1 metric = 2 |27+10AI|=1 metric = 30 |27+21AI|=1 metric = 30 |26+6AI|=1 metric = 15 |26+25AI|=1 metric = 15 |24+14AI|=1 metric = 3 |24+17AI|=1 metric = 3 |21+3AI|=1 metric = 3 |21+28AI|=1 metric = 3 |20+5AI|=1 metric = 30 |20+26AI|=1 metric = 30 |18+2AI|=1 metric = 5 |18+29AI|=1 metric = 5 |13+2AI|=1 metric = 5 |13+29AI|=1 metric = 5 |11+5AI|=1 metric = 30 |11+26AI|=1 metric = 30 |10+3AI|=1 metric = 3 |10+28AI|=1 metric = 3 |7+14AI|=1 metric = 3 |7+17AI|=1 metric = 3 |5+6AI|=1 metric = 15 |5+25AI|=1 metric = 15 |4+10AI|=1 metric = 30 |4+21AI|=1 metric = 30 |2+12AI|=1 metric = 2 |2+19AI|=1 metric = 2 |1+0AI|=1 |0+13AI|=1 |0+18AI|=1

sum of all metrics = 352