Rechnungen der Vorlesung CMS vom 30.11.2006

f  =  x^2  +  4  x  +  3

<<  poliesModP4.m

PolynomialRemainderP [(x + 2) (x - 3),  
      x^2  +  4  x  + 3,  x,  7]

PolynomialExtendedGCDP [x^2 + 4  x + 3,  4  x + 2, x, 7]

r  =  4  x * (4  x  +  2)

PolynomialRemainderP [r,  f, x, 7]

Wir versuchen, ein irreduzibles Polynom vom Grad 5 ueber Z_7 zu finden.

f  =  x^5  + 4  x^3  +  4

PolynomialExtendedGCDP [f,  x^7 - x, x, 7]

PolynomialExtendedGCDP [f,  x^49 - x, x, 7]

BaseForm [123, 2]

FindIrreduciblePoly [var_,  grad_,  
        p_] := 
Module [{f,  i}, 
i  = 
          1; 
f  =  
          var^grad  +  
            RandomPoly [var,  grad - 1,  p]; 
While [
          Not [IsIrreduciblePoly [f,  var,  
              p]], 
i  =  
            i  +  1; 
f  = 
            var^grad  +  
              RandomPoly [var,  grad - 1,  p]]; 
{f, 
          i}]

FindIrreduciblePoly [x,  25,  101]

h  =  %%

h[[1]]

Timing [IsIrreduciblePoly [h[[1]],  x,  101]]

FindIrreduciblePoly [x, 3, 7]