Inhaltsverzeichnis

Development of
Algorithmic Constructions

20:16:29
Deutsch
28.Mar 2024

29 31 33
√27 √28 √29 √30 √31 √32 √33 √34 √35 √37 √38 √39 √40 √41 √42 √43 √44 √45 √46

Number p= Adjoined square root=

Calculation

A=√37
(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 = √37, Exponent = 1, Jacobi (37, 31) = -1, 31 = 3 mod 4, 31 = 7 mod 8

30
030√37
Number of elements = 30

Number = 31, Adjoined = √37, Exponent = 1, Jacobi (37, 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+3AI|
=1
metric = 15
|28+28AI|
=1
metric = 15
|25+12AI|
=1
metric = 10
|25+19AI|
=1
metric = 10
|23+6AI|
=1
metric = 2
|23+25AI|
=1
metric = 2
|22+11AI|
=1
metric = 2
|22+20AI|
=1
metric = 2
|19+8AI|
=1
metric = 6
|19+23AI|
=1
metric = 6
|17+13AI|
=1
metric = 6
|17+18AI|
=1
metric = 6
|16+2AI|
=1
metric = 3
|16+29AI|
=1
metric = 3
|15+2AI|
=1
metric = 3
|15+29AI|
=1
metric = 3
|14+13AI|
=1
metric = 6
|14+18AI|
=1
metric = 6
|12+8AI|
=1
metric = 6
|12+23AI|
=1
metric = 6
|9+11AI|
=1
metric = 2
|9+20AI|
=1
metric = 2
|8+6AI|
=1
metric = 2
|8+25AI|
=1
metric = 2
|6+12AI|
=1
metric = 10
|6+19AI|
=1
metric = 10
|3+3AI|
=1
metric = 15
|3+28AI|
=1
metric = 15
|1+0AI|
=1

sum of all metrics = 176