Nebenrechnungen in der Vorlesung MAT3 am 23.11.2006

<<   Math/poliesModP4.m

f  =   .

f[x_]  := Mod [ x^2  + x + 1, 7]

(* 
      Suchen der Nullstellen von f *) 
Table [{x, f[x]},  {x, 0, 6}]

Table [{alpha,  
        PolynomialRemainderP [x^2  + x +  1,  x - alpha, x, 
          7]}, 
{alpha, 0, 6}]

f  =  x^3  +  x^2  -  5 x

Wir können f(5)auf zwei Arten berechnen

PolynomialRemainderP [f, x - 5,  x,  11]

f

f  /.  x  ->  5

Mod [%,  11]

f  =  x^2  +  x  +  1

f  /.  x  ->  2

PolynomialQuotientP [f,  x - 2,  x,  7]

PolynomialRemainderP [f, x - 2, x, 7]

F [x_]  :=  x^2  +  1

F [I]

I * I

PolynomialRemainderP [x^5,  x^2  +  4  x  +  3, x,  
      5]

PolynomialRemainderP[x^3, x^2 + 4  x + 3, x, 5]

PolynomialRemainderP [x^10  +  x^3,  x^2 + 4  x + 3, x, 
      5]

PolynomialRemainderP [x^24 - 1, x^2 + 4  x + 3, x, 5]

PolynomialRemainderP [x^2  +  x,  x^2 + x + 1, x, 2]

PolynomialRemainderP [x^2, x^2 + x + 1, x, 2]

f  =  x^3  + x  +  1

a   =  x^2 * (x^2  +  11 x)

PolynomialRemainderP [a,  f, x, 13]

PolynomialExtendedGCDP [x + 2,  x^2 + x + 1, x, 
      3]