Inhaltsverzeichnis

Development of
Algorithmic Constructions
07:13:01
Deutsch
19.Apr 2024
25 27 29
√2 √3 √5 √6 √7 √8

Number p= Adjoined square root=

Calculation

A=√2
(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 = 27, Adjoined = √2, Exponent = 1, Jacobi (2, 27) = -1, 27 = 3 mod 4, 27 = 3 mod 8

26
026√2
Number of elements = 18
Number of red elements = 16
Number of elements / Number of red elements = 1.125

Number = 27, Adjoined = √2, Exponent = 1, Jacobi (2, 27) = -1, 27 = 3 mod 4, 27 = 3 mod 8

Potence 2 Potence 3 Potence 5 Potence 7 Potence 11 Potence 13 Potence 17 Potence 19 Potence 23 Potence 29

|26+0AI|
=1
|26+9AI|
=1
metric = 14		|26+18AI|
=1
metric = 14
|19+3AI|
=1
metric = 2		|19+6AI|
=1
metric = 4		|19+12AI|
=1
metric = 1		|19+15AI|
=1
metric = 1		|19+21AI|
=1
metric = 4		|19+24AI|
=1
metric = 2
|8+3AI|
=1
metric = 2		|8+6AI|
=1
metric = 4		|8+12AI|
=1
metric = 1		|8+15AI|
=1
metric = 1		|8+21AI|
=1
metric = 4		|8+24AI|
=1
metric = 2
|1+0AI|
=1
|1+9AI|
=1
metric = 14		|1+18AI|
=1
metric = 14

sum of all metrics = 84