# Development ofAlgorithmic Constructions

 08:55:56 25.Sep 2023

29 31 33
√17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35

### Calculation

A=√26
(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 = √26, Exponent = 1, Jacobi (26, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

 30 0 30√26
Number of elements = 30

### Number = 31, Adjoined = √26, Exponent = 1, Jacobi (26, 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+13AI|=1 metric = 1 |28+18AI|=1 metric = 1 |25+10AI|=1 metric = 6 |25+21AI|=1 metric = 6 |23+5AI|=1 metric = 2 |23+26AI|=1 metric = 2 |22+4AI|=1 metric = 10 |22+27AI|=1 metric = 10 |19+14AI|=1 metric = 3 |19+17AI|=1 metric = 3 |17+15AI|=1 metric = 30 |17+16AI|=1 metric = 30 |16+12AI|=1 metric = 2 |16+19AI|=1 metric = 2 |15+12AI|=1 metric = 2 |15+19AI|=1 metric = 2 |14+15AI|=1 metric = 30 |14+16AI|=1 metric = 30 |12+14AI|=1 metric = 3 |12+17AI|=1 metric = 3 |9+4AI|=1 metric = 10 |9+27AI|=1 metric = 10 |8+5AI|=1 metric = 2 |8+26AI|=1 metric = 2 |6+10AI|=1 metric = 6 |6+21AI|=1 metric = 6 |3+13AI|=1 metric = 1 |3+18AI|=1 metric = 1 |1+0AI|=1

sum of all metrics = 216