Development ofAlgorithmic Constructions

 22:18:20 29.Nov 2023

31 33 35
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17

Calculation

A=√8
(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 = √8, Exponent = 1, Jacobi (8, 33) = 133 = 1 mod 4, 33 = 1 mod 8

 32 0 32√8
Number of elements = 20
Number of red elements = 16
Number of elements / Number of red elements = 1.25

Number = 33, Adjoined = √8, Exponent = 1, Jacobi (8, 33) = 133 = 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 |31+12AI|=1 metric = 2 |31+21AI|=1 metric = 2 |29+15AI|=1 metric = 2 |29+18AI|=1 metric = 2 |26+15AI|=1 metric = 2 |26+18AI|=1 metric = 2 |23+0AI|=1 |20+12AI|=1 metric = 2 |20+21AI|=1 metric = 2 |13+12AI|=1 metric = 2 |13+21AI|=1 metric = 2 |10+0AI|=1 |7+15AI|=1 metric = 2 |7+18AI|=1 metric = 2 |4+15AI|=1 metric = 2 |4+18AI|=1 metric = 2 |2+12AI|=1 metric = 2 |2+21AI|=1 metric = 2 |1+0AI|=1

sum of all metrics = 32