Inhaltsverzeichnis

Development of
Algorithmic Constructions

13:34:51
Deutsch
3.Dec 2022

29 31 33
√19 √20 √21 √22 √23 √24 √26 √27 √28 √29 √30 √31 √32 √33 √34 √35 √37 √38

Number p= Adjoined square root=

Calculation

A=√29
(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 = √29, Exponent = 1, Jacobi (29, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√29
Number of elements = 30

Number = 31, Adjoined = √29, Exponent = 1, Jacobi (29, 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+2AI|
=1
metric = 2
|28+29AI|
=1
metric = 2
|25+8AI|
=1
metric = 2
|25+23AI|
=1
metric = 2
|23+4AI|
=1
metric = 6
|23+27AI|
=1
metric = 6
|22+3AI|
=1
metric = 3
|22+28AI|
=1
metric = 3
|19+5AI|
=1
metric = 5
|19+26AI|
=1
metric = 5
|17+12AI|
=1
metric = 2
|17+19AI|
=1
metric = 2
|16+9AI|
=1
metric = 10
|16+22AI|
=1
metric = 10
|15+9AI|
=1
metric = 10
|15+22AI|
=1
metric = 10
|14+12AI|
=1
metric = 2
|14+19AI|
=1
metric = 2
|12+5AI|
=1
metric = 5
|12+26AI|
=1
metric = 5
|9+3AI|
=1
metric = 3
|9+28AI|
=1
metric = 3
|8+4AI|
=1
metric = 6
|8+27AI|
=1
metric = 6
|6+8AI|
=1
metric = 2
|6+23AI|
=1
metric = 2
|3+2AI|
=1
metric = 2
|3+29AI|
=1
metric = 2
|1+0AI|
=1

sum of all metrics = 120