# Development ofAlgorithmic Constructions

 14:03:23 3.Dec 2022

33 35 37
√2 √3 √5 √6 √7 √8 √10 √11

### Calculation

A=√2
(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 3

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 = 35, Adjoined = √2, Exponent = 3, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

 34 0 34√2
Number of elements = 16
Number of red elements = 12
Number of elements / Number of red elements = 1.3333333333333

### Number = 35, Adjoined = √2, Exponent = 3, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

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

### href=3. root

 |34+0AI|=1 |29+0AI|=1 |26+10AI|=1 metric = 2 |26+25AI|=1 metric = 2 |21+5AI|=1 metric = 18 |21+30AI|=1 metric = 18 |19+10AI|=1 metric = 6 |19+25AI|=1 metric = 6 |16+10AI|=1 metric = 6 |16+25AI|=1 metric = 6 |14+5AI|=1 metric = 18 |14+30AI|=1 metric = 18 |9+10AI|=1 metric = 2 |9+25AI|=1 metric = 2 |6+0AI|=1 |1+0AI|=1

sum of all metrics = 104