# Development ofAlgorithmic Constructions

 01:30:45 3.Oct 2023

29 31 33
√14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33

### Calculation

A=√24
(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 = √24, Exponent = 1, Jacobi (24, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

 30 0 30√24
Number of elements = 30

### Number = 31, Adjoined = √24, Exponent = 1, Jacobi (24, 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+14AI|=1 metric = 6 |28+17AI|=1 metric = 6 |25+6AI|=1 metric = 10 |25+25AI|=1 metric = 10 |23+3AI|=1 metric = 2 |23+28AI|=1 metric = 2 |22+10AI|=1 metric = 15 |22+21AI|=1 metric = 15 |19+4AI|=1 metric = 30 |19+27AI|=1 metric = 30 |17+9AI|=1 metric = 3 |17+22AI|=1 metric = 3 |16+1AI|=1 metric = 2 |16+30AI|=1 metric = 2 |15+1AI|=1 metric = 2 |15+30AI|=1 metric = 2 |14+9AI|=1 metric = 3 |14+22AI|=1 metric = 3 |12+4AI|=1 metric = 30 |12+27AI|=1 metric = 30 |9+10AI|=1 metric = 15 |9+21AI|=1 metric = 15 |8+3AI|=1 metric = 2 |8+28AI|=1 metric = 2 |6+6AI|=1 metric = 10 |6+25AI|=1 metric = 10 |3+14AI|=1 metric = 6 |3+17AI|=1 metric = 6 |1+0AI|=1

sum of all metrics = 272