Gruppen

Zyklische Gruppe

ZyklischeGruppe[n_] := 
      Table[Mod[i + j, n], {i, 0, n - 1}, {j, 0, n - 1}]

ZyklischeGruppe[10]

Multiplikationstafel[n_] := 
      Table[Mod[i*j, n], {i, n - 1}, {j, n - 1}]

Multiplikationstafel[10]

mult = Multiplikationstafel[5]

Clear[Vertauschung ]
Vertauschung[A_, j_, k_] := 
      Module[{Aj, Ak, B}, 
Aj = 
          A[[j]]; 
Ak = 
          A[[k]]; 
B = 
          ReplacePart[A, Ak, j]; 
B = 
          ReplacePart[B, Aj, k]]

Umbenennung[A_, j_, k_] := 
      Transpose[
        Vertauschung[Transpose[Vertauschung[A, j, k]], j, k]]

Umbenennung[mult, 3, 4]

Multiplikationstafel[13]

Komplexe Zahlen

p = (x +  I y) (u + I v)

ComplexExpand[p]

ComplexExpand[Re[p]]

ComplexExpand[Im[p]]

ComplexExpand[(1/(x +  I y))]

Abs[x +  I y]

ComplexExpand[%]

Table[(I^n), {n, 0, 20}]

Polynome

Polynomdivision

f = 3  (t^3) + 2  t + 1

g = (t^2) - 4  t

q = PolynomialQuotient[f, g, t]

r = PolynomialRemainder[f, g, t]

Test

(f/g) == q + (r/g)

(f/g) == q + (r/g) // Simplify

(f/g) - (q + (r/g)) // Together