# Development ofAlgorithmic Constructions

 13:37:38 2.Apr 2023

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

 Number p= Adjoined square root=

### Calculation

A=√7
(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 5

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 = √7, Exponent = 5, Jacobi (7, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√7
Number of elements = 32

### Number = 31, Adjoined = √7, Exponent = 5, Jacobi (7, 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 5

### href=5. root

 |30+0AI|=1 |29+2AI|=1 metric = 6 |29+29AI|=1 metric = 6 |27+12AI|=1 metric = 2 |27+19AI|=1 metric = 2 |26+1AI|=1 metric = 15 |26+30AI|=1 metric = 15 |24+8AI|=1 metric = 3 |24+23AI|=1 metric = 3 |21+15AI|=1 metric = 6 |21+16AI|=1 metric = 6 |20+6AI|=1 metric = 6 |20+25AI|=1 metric = 6 |18+10AI|=1 metric = 6 |18+21AI|=1 metric = 6 |13+10AI|=1 metric = 6 |13+21AI|=1 metric = 6 |11+6AI|=1 metric = 6 |11+25AI|=1 metric = 6 |10+15AI|=1 metric = 6 |10+16AI|=1 metric = 6 |7+8AI|=1 metric = 3 |7+23AI|=1 metric = 3 |5+1AI|=1 metric = 15 |5+30AI|=1 metric = 15 |4+12AI|=1 metric = 2 |4+19AI|=1 metric = 2 |2+2AI|=1 metric = 6 |2+29AI|=1 metric = 6 |1+0AI|=1 |0+3AI|=1 |0+28AI|=1

sum of all metrics = 176