Inhaltsverzeichnis

Development of
Algorithmic Constructions
03:03:44
Deutsch
3.Oct 2023
33 35 37
√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 = 35, Adjoined = √2, Exponent = 1, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

34
034√2
Number of elements = 48
Number of red elements = 28
Number of elements / Number of red elements = 1.7142857142857

Number = 35, Adjoined = √2, Exponent = 1, Jacobi (2, 35) = -1, 35 = 3 mod 4, 35 = 3 mod 8

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

|34+0AI|
=1
|33+4AI|
=1
metric = 4		|33+11AI|
=1
metric = 18		|33+24AI|
=1
metric = 18		|33+31AI|
=1
metric = 4
|29+0AI|
=1
|28+9AI|
=1
metric = 18		|28+16AI|
=1
metric = 4		|28+19AI|
=1
metric = 4		|28+26AI|
=1
metric = 18
|27+14AI|
=1
metric = 6		|27+21AI|
=1
metric = 6
|26+10AI|
=1
metric = 2		|26+25AI|
=1
metric = 2
|23+4AI|
=1
metric = 2		|23+11AI|
=1
metric = 9		|23+24AI|
=1
metric = 9		|23+31AI|
=1
metric = 2
|22+14AI|
=1
metric = 2		|22+21AI|
=1
metric = 2
|21+5AI|
=1
metric = 18		|21+30AI|
=1
metric = 18
|19+10AI|
=1
metric = 6		|19+25AI|
=1
metric = 6
|16+10AI|
=1
metric = 6		|16+25AI|
=1
metric = 6
|14+5AI|
=1
metric = 18		|14+30AI|
=1
metric = 18
|13+14AI|
=1
metric = 2		|13+21AI|
=1
metric = 2
|12+4AI|
=1
metric = 2		|12+11AI|
=1
metric = 9		|12+24AI|
=1
metric = 9		|12+31AI|
=1
metric = 2
|9+10AI|
=1
metric = 2		|9+25AI|
=1
metric = 2
|8+14AI|
=1
metric = 6		|8+21AI|
=1
metric = 6
|7+9AI|
=1
metric = 18		|7+16AI|
=1
metric = 4		|7+19AI|
=1
metric = 4		|7+26AI|
=1
metric = 18
|6+0AI|
=1
|2+4AI|
=1
metric = 4		|2+11AI|
=1
metric = 18		|2+24AI|
=1
metric = 18		|2+31AI|
=1
metric = 4
|1+0AI|
=1

sum of all metrics = 356