# Development ofAlgorithmic Constructions

 12:37:24 3.Dec 2022

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

 Number p= Adjoined square root=

### Calculation

A=√6
(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 = √6, Exponent = 1, Jacobi (6, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

 30 0 30√6
Number of elements = 30

### Number = 31, Adjoined = √6, Exponent = 1, Jacobi (6, 31) = -1, 31 = 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 |28+3AI|=1 metric = 15 |28+28AI|=1 metric = 15 |25+12AI|=1 metric = 10 |25+19AI|=1 metric = 10 |23+6AI|=1 metric = 2 |23+25AI|=1 metric = 2 |22+11AI|=1 metric = 2 |22+20AI|=1 metric = 2 |19+8AI|=1 metric = 6 |19+23AI|=1 metric = 6 |17+13AI|=1 metric = 6 |17+18AI|=1 metric = 6 |16+2AI|=1 metric = 3 |16+29AI|=1 metric = 3 |15+2AI|=1 metric = 3 |15+29AI|=1 metric = 3 |14+13AI|=1 metric = 6 |14+18AI|=1 metric = 6 |12+8AI|=1 metric = 6 |12+23AI|=1 metric = 6 |9+11AI|=1 metric = 2 |9+20AI|=1 metric = 2 |8+6AI|=1 metric = 2 |8+25AI|=1 metric = 2 |6+12AI|=1 metric = 10 |6+19AI|=1 metric = 10 |3+3AI|=1 metric = 15 |3+28AI|=1 metric = 15 |1+0AI|=1

sum of all metrics = 176