# Development ofAlgorithmic Constructions

 03:03:44 3.Oct 2023

33 35 37
√2 √3 √5 √6 √7 √8

### 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

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

 34 0 34√2
Number of elements = 48
Number of red elements = 28
Number of elements / Number of red elements = 1.7142857142857

### Number = 35, Adjoined = √2, Exponent = 1, 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

 |34+0AI|=1 |33+4AI|=1 metric = 4 |33+11AI|=1 metric = 18 |33+24AI|=1 metric = 18 |33+31AI|=1 metric = 4 |29+0AI|=1 |28+9AI|=1 metric = 18 |28+16AI|=1 metric = 4 |28+19AI|=1 metric = 4 |28+26AI|=1 metric = 18 |27+14AI|=1 metric = 6 |27+21AI|=1 metric = 6 |26+10AI|=1 metric = 2 |26+25AI|=1 metric = 2 |23+4AI|=1 metric = 2 |23+11AI|=1 metric = 9 |23+24AI|=1 metric = 9 |23+31AI|=1 metric = 2 |22+14AI|=1 metric = 2 |22+21AI|=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 |13+14AI|=1 metric = 2 |13+21AI|=1 metric = 2 |12+4AI|=1 metric = 2 |12+11AI|=1 metric = 9 |12+24AI|=1 metric = 9 |12+31AI|=1 metric = 2 |9+10AI|=1 metric = 2 |9+25AI|=1 metric = 2 |8+14AI|=1 metric = 6 |8+21AI|=1 metric = 6 |7+9AI|=1 metric = 18 |7+16AI|=1 metric = 4 |7+19AI|=1 metric = 4 |7+26AI|=1 metric = 18 |6+0AI|=1 |2+4AI|=1 metric = 4 |2+11AI|=1 metric = 18 |2+24AI|=1 metric = 18 |2+31AI|=1 metric = 4 |1+0AI|=1

sum of all metrics = 356