Inhaltsverzeichnis

Development of
Algorithmic Constructions

09:53:25
Deutsch
4.Oct 2022

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

Number p= Adjoined square root=

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
Square 17

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

30
030√17
Number of elements = 30

Number = 31, Adjoined = √17, Exponent = 17, 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
Square 17

href=17. root

|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