# Development ofAlgorithmic Constructions

 13:49:28 3.Dec 2022

31 33 35
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14

### Calculation

A=√5
(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 = 33, Adjoined = √5, Exponent = 1, Jacobi (5, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

 32 0 32√5
Number of elements = 24
Number of red elements = 20
Number of elements / Number of red elements = 1.2

### Number = 33, Adjoined = √5, Exponent = 1, Jacobi (5, 33) = -1, 33 = 1 mod 4, 33 = 1 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

 |32+0AI|=1 |28+9AI|=1 metric = 2 |28+24AI|=1 metric = 2 |25+15AI|=1 metric = 2 |25+18AI|=1 metric = 2 |23+0AI|=1 |22+3AI|=1 metric = 2 |22+30AI|=1 metric = 2 |19+15AI|=1 metric = 2 |19+18AI|=1 metric = 2 |17+9AI|=1 metric = 2 |17+24AI|=1 metric = 2 |16+9AI|=1 metric = 2 |16+24AI|=1 metric = 2 |14+15AI|=1 metric = 2 |14+18AI|=1 metric = 2 |11+3AI|=1 metric = 2 |11+30AI|=1 metric = 2 |10+0AI|=1 |8+15AI|=1 metric = 2 |8+18AI|=1 metric = 2 |5+9AI|=1 metric = 2 |5+24AI|=1 metric = 2 |1+0AI|=1

sum of all metrics = 40