Inhaltsverzeichnis

Development of
Algorithmic Constructions

02:42:46
Deutsch
4.Oct 2022

29 31 33
√17 √18 √19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35

Number p= Adjoined square root=

Calculation

A=√26
(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 = 31, Adjoined = √26, Exponent = 1, Jacobi (26, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√26
Number of elements = 30

Number = 31, Adjoined = √26, Exponent = 1, Jacobi (26, 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

|30+0AI|
=1
|28+13AI|
=1
metric = 1
|28+18AI|
=1
metric = 1
|25+10AI|
=1
metric = 6
|25+21AI|
=1
metric = 6
|23+5AI|
=1
metric = 2
|23+26AI|
=1
metric = 2
|22+4AI|
=1
metric = 10
|22+27AI|
=1
metric = 10
|19+14AI|
=1
metric = 3
|19+17AI|
=1
metric = 3
|17+15AI|
=1
metric = 30
|17+16AI|
=1
metric = 30
|16+12AI|
=1
metric = 2
|16+19AI|
=1
metric = 2
|15+12AI|
=1
metric = 2
|15+19AI|
=1
metric = 2
|14+15AI|
=1
metric = 30
|14+16AI|
=1
metric = 30
|12+14AI|
=1
metric = 3
|12+17AI|
=1
metric = 3
|9+4AI|
=1
metric = 10
|9+27AI|
=1
metric = 10
|8+5AI|
=1
metric = 2
|8+26AI|
=1
metric = 2
|6+10AI|
=1
metric = 6
|6+21AI|
=1
metric = 6
|3+13AI|
=1
metric = 1
|3+18AI|
=1
metric = 1
|1+0AI|
=1

sum of all metrics = 216