Modulo-Potenz-Polygone
Author: Prof. Dr. Dörte Haftendorn

Aufeinanderfolgende Potenzen von a werden verbunden.

Ursprüngliche Anregung 2008 von Reimund Albers, Uni Bremen.

Ha 2010

Start, k=0

11 Billiarden geht nicht mehr

O = (0, 0)
Null = (0, -1)
c = Circle(O, Null)
n = 23 (slider from 0 to 50, step 1)
pkt = Sequence((cos(((i * 2) * 3.141592653589793 / n) - 3.141592653589793 / 2), sin(((i * 2) * 3.141592653589793 / n) - 3.141592653589793 / 2)), i, 0, n)
a = 7 (slider from 0 to 50, step 1)
k = 15 (slider from 0 to 50, step 1)
LiZn = Sequence(Mod[a^(i), n], i, 0, k)
LiZ = Sequence(a^(i), i, 0, k)
Eins = Element(pkt, 2)
Text3: "Modul Z(" + n + ")"
Liste1 = Sequence(Segment[Element[pkt, Mod[a^(i), n] + 1], Element[pkt, Mod[a^(i + 1), n] + 1]], i, 0, k - 1)
Text6: "Bis zur " + k + "-ten Potenz von " + a
Text4: "Potenzen von " + a + ".
Powers of " + a + "."
Text2: "Powers of " + a + " in Z(" + n + ")= " + LiZn + ""
Text1: "Potenzen von " + a + " in Z= " + LiZ + ""
erg = Mod(a^(k), n)
Text9: "mod(a^k,n)=" + (LaTeX[erg]) + ""