Development of
Algorithmic Constructions

A=√3
(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 13

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

30
0	30√3

Number of elements = 30

|28+7AI|
=1
metric = 5

|28+24AI|
=1
metric = 5

|25+3AI|
=1
metric = 2

|25+28AI|
=1
metric = 2

|23+14AI|
=1
metric = 10

|23+17AI|
=1
metric = 10

|22+5AI|
=1
metric = 5

|22+26AI|
=1
metric = 5

|19+2AI|
=1
metric = 10

|19+29AI|
=1
metric = 10

|17+11AI|
=1
metric = 6

|17+20AI|
=1
metric = 6

|16+15AI|
=1
metric = 1

|16+16AI|
=1
metric = 1

|15+15AI|
=1
metric = 1

|15+16AI|
=1
metric = 1

|14+11AI|
=1
metric = 6

|14+20AI|
=1
metric = 6

|12+2AI|
=1
metric = 10

|12+29AI|
=1
metric = 10

|9+5AI|
=1
metric = 5

|9+26AI|
=1
metric = 5

|8+14AI|
=1
metric = 10

|8+17AI|
=1
metric = 10

|6+3AI|
=1
metric = 2

|6+28AI|
=1
metric = 2

|3+7AI|
=1
metric = 5

|3+24AI|
=1
metric = 5

sum of all metrics = 156

Development ofAlgorithmic Constructions