Rechnungen zur Vorlesung am 9.11.2006

GCD [0, 0]

f  =  -8 x  +  4 x^2  +  6  x^3  -  5  x^4  + 
        x^5

g  =  4  - 4 x  -  x^2  +  x^3

f1  = PolynomialRemainder [f, g, x]

g1  =  PolynomialRemainder [g, f1, x]

f2  =  PolynomialRemainder [f1,  g1, x]

ggT  =  Simplify[25 / 16 * g1]

f  =  
      Expand [(x^2  +  x  +  8) * (x^3  + 4  x  +  
              2)]

g  =  
      Expand [(x^2  +  x  +  8) * (x^4  - x^3  + 2  x^2  +  
              7)]

f

g

g1  =  PolynomialRemainder [g, f, x]

f1  =  PolynomialRemainder [f, g1, x]

g2  =  PolynomialRemainder [g1, f1, x]

f2  =  PolynomialRemainder [f1,  g2, x]

ggT  =  Simplify [(361/2417) * g2]

f

g

PolynomialQuotient [f, g, x]

PolynomialRemainder [f, g, x]

zeile3  =  {-24 + 32  x - 10  x^2,  
        1,  -x^2  + 4  x  - 6}

zeile2  =  {g, 0, 1}

zeile4  =  
      zeile2  -  
        PolynomialQuotient [zeile2 [[1]],  zeile3 [[1]],  x] * 
          zeile3

zeile4a  =  Simplify [zeile4]

<<  poliesModP4.m

result  =  
      GCDPoliesP [1 + x^3  + x^5,  1 + x + x^3, x, 2]

matrix = result [[1]]

MatrixForm [matrix]