# Development ofAlgorithmic Constructions

 14:01:10 3.Dec 2022

29 31 33
√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 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 = √2, Exponent = 29, Jacobi (2, 31) = 131 = 3 mod 4, 31 = 7 mod 8

 30 0 30√2
Number of elements = 32

### Number = 31, Adjoined = √2, Exponent = 29, Jacobi (2, 31) = 131 = 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
Square 29

### href=29. root

 |30+0AI|=1 |29+13AI|=1 metric = 3 |29+18AI|=1 metric = 3 |27+15AI|=1 metric = 3 |27+16AI|=1 metric = 3 |26+9AI|=1 metric = 2 |26+22AI|=1 metric = 2 |24+10AI|=1 metric = 10 |24+21AI|=1 metric = 10 |21+11AI|=1 metric = 5 |21+20AI|=1 metric = 5 |20+8AI|=1 metric = 10 |20+23AI|=1 metric = 10 |18+3AI|=1 metric = 6 |18+28AI|=1 metric = 6 |13+3AI|=1 metric = 6 |13+28AI|=1 metric = 6 |11+8AI|=1 metric = 10 |11+23AI|=1 metric = 10 |10+11AI|=1 metric = 5 |10+20AI|=1 metric = 5 |7+10AI|=1 metric = 10 |7+21AI|=1 metric = 10 |5+9AI|=1 metric = 2 |5+22AI|=1 metric = 2 |4+15AI|=1 metric = 3 |4+16AI|=1 metric = 3 |2+13AI|=1 metric = 3 |2+18AI|=1 metric = 3 |1+0AI|=1 |0+4AI|=1 |0+27AI|=1

sum of all metrics = 156