Inhaltsverzeichnis

Development of
Algorithmic Constructions
07:11:08
Deutsch
19.Apr 2024
33 35 37
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14 √15 √17 √18 √19 √20

Number p= Adjoined square root=

Calculation

A=√11
(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 = √11, Exponent = 1, Jacobi (11, 35) = 135 = 3 mod 4, 35 = 3 mod 8

34
034√11
Number of elements = 32
Number of red elements = 24
Number of elements / Number of red elements = 1.3333333333333

Number = 35, Adjoined = √11, Exponent = 1, Jacobi (11, 35) = 135 = 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
|30+1AI|
=1
metric = 4		|30+6AI|
=1
metric = 6		|30+29AI|
=1
metric = 6		|30+34AI|
=1
metric = 4
|29+0AI|
=1
|26+15AI|
=1
metric = 4		|26+20AI|
=1
metric = 4
|21+10AI|
=1
metric = 12		|21+25AI|
=1
metric = 12
|20+14AI|
=1
metric = 3		|20+21AI|
=1
metric = 3
|19+15AI|
=1
metric = 2		|19+20AI|
=1
metric = 2
|16+15AI|
=1
metric = 2		|16+20AI|
=1
metric = 2
|15+14AI|
=1
metric = 3		|15+21AI|
=1
metric = 3
|14+10AI|
=1
metric = 12		|14+25AI|
=1
metric = 12
|9+15AI|
=1
metric = 4		|9+20AI|
=1
metric = 4
|6+0AI|
=1
|5+1AI|
=1
metric = 4		|5+6AI|
=1
metric = 6		|5+29AI|
=1
metric = 6		|5+34AI|
=1
metric = 4
|1+0AI|
=1
|0+4AI|
=1
|0+11AI|
=1
|0+24AI|
=1
|0+31AI|
=1

sum of all metrics = 124