# Development ofAlgorithmic Constructions

 12:02:34 29.Nov 2022

29 31 33
√7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20 √21 √22 √23 √24 √26

### Calculation

A=√17
(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 = √17, Exponent = 1, Jacobi (17, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

 30 0 30√17
Number of elements = 30

### Number = 31, Adjoined = √17, Exponent = 1, Jacobi (17, 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+6AI|=1 metric = 2 |28+25AI|=1 metric = 2 |25+7AI|=1 metric = 3 |25+24AI|=1 metric = 3 |23+12AI|=1 metric = 15 |23+19AI|=1 metric = 15 |22+9AI|=1 metric = 3 |22+22AI|=1 metric = 3 |19+15AI|=1 metric = 3 |19+16AI|=1 metric = 3 |17+5AI|=1 metric = 3 |17+26AI|=1 metric = 3 |16+4AI|=1 metric = 10 |16+27AI|=1 metric = 10 |15+4AI|=1 metric = 10 |15+27AI|=1 metric = 10 |14+5AI|=1 metric = 3 |14+26AI|=1 metric = 3 |12+15AI|=1 metric = 3 |12+16AI|=1 metric = 3 |9+9AI|=1 metric = 3 |9+22AI|=1 metric = 3 |8+12AI|=1 metric = 15 |8+19AI|=1 metric = 15 |6+7AI|=1 metric = 3 |6+24AI|=1 metric = 3 |3+6AI|=1 metric = 2 |3+25AI|=1 metric = 2 |1+0AI|=1

sum of all metrics = 156