Re: diohantische Gleichung

["Udo und Susanne Krause" <su.krause@XXXXXXX.ch>]

Hallo zusammen

> Wie steht es mit
>
> Reduce[2 x + 3 y + 4 z + 5 w == 20 && x >= 0 && y >= 0 && z >= 0 &&w  >=  
> 0, {x, y, z, w}, Integers]

mit anderen Worten

In[6]:= FrobeniusSolve[Range[2, 5], 20]
Out[6]= {{0, 0, 0, 4}, {0, 0, 5, 0}, {0, 1, 3, 1}, {0, 2, 1, 2}, {0,
  4, 2, 0}, {0, 5, 0, 1}, {1, 0, 2, 2}, {1, 1, 0, 3}, {1, 2, 3,
  0}, {1, 3, 1, 1}, {1, 6, 0, 0}, {2, 0, 4, 0}, {2, 1, 2, 1}, {2, 2,
  0, 2}, {2, 4, 1, 0}, {3, 0, 1, 2}, {3, 2, 2, 0}, {3, 3, 0, 1}, {4,
  0, 3, 0}, {4, 1, 1, 1}, {4, 4, 0, 0}, {5, 0, 0, 2}, {5, 2, 1,
  0}, {6, 0, 2, 0}, {6, 1, 0, 1}, {7, 2, 0, 0}, {8, 0, 1, 0}, {10, 0,
  0, 0}}

In[14]:= FrobeniusSolve[Range[2, 5], 20] ==
  Reduce[2 x + 3 y + 4 z + 5 w == 20 && x >= 0 && y >= 0 && z >= 0 &&
    w >= 0, {x, y, z, w}, Integers] /. {Or -> List, And -> List,
  Equal[__, x_Integer] -> x}
Out[14]= True

Gruss
Udo.