Inhaltsverzeichnis

Development of
Algorithmic Constructions

23:20:35
Deutsch
16.Oct 2021

29 31 33
√2 √3 √5 √6 √7 √8 √10 √11 √12 √13 √14

Number p= Adjoined square root=

Calculation

A=√5
(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 = √5, Exponent = 1, Jacobi (5, 31) = 131 = 3 mod 4, 31 = 7 mod 8

30
030√5
Number of elements = 32

Number = 31, Adjoined = √5, Exponent = 1, Jacobi (5, 31) = 131 = 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
|29+7AI|
=1
metric = 6
|29+24AI|
=1
metric = 6
|27+11AI|
=1
metric = 15
|27+20AI|
=1
metric = 15
|26+12AI|
=1
metric = 10
|26+19AI|
=1
metric = 10
|24+3AI|
=1
metric = 3
|24+28AI|
=1
metric = 3
|21+6AI|
=1
metric = 3
|21+25AI|
=1
metric = 3
|20+10AI|
=1
metric = 2
|20+21AI|
=1
metric = 2
|18+4AI|
=1
metric = 10
|18+27AI|
=1
metric = 10
|13+4AI|
=1
metric = 10
|13+27AI|
=1
metric = 10
|11+10AI|
=1
metric = 2
|11+21AI|
=1
metric = 2
|10+6AI|
=1
metric = 3
|10+25AI|
=1
metric = 3
|7+3AI|
=1
metric = 3
|7+28AI|
=1
metric = 3
|5+12AI|
=1
metric = 10
|5+19AI|
=1
metric = 10
|4+11AI|
=1
metric = 15
|4+20AI|
=1
metric = 15
|2+7AI|
=1
metric = 6
|2+24AI|
=1
metric = 6
|1+0AI|
=1
|0+5AI|
=1
|0+26AI|
=1

sum of all metrics = 196