> c[1]:=-(x[1]+x[2]+x[3]+x[4]); 
> c[2]:=x[1]*x[2]+x[1]*x[3]+x[1]*x[4]+x[2]*x[3]+x[2]*x[4]+x[3]*x[4];
> c[3]:=-(x[1]*x[2]*x[3]+x[1]*x[2]*x[4]+x[1]*x[3]*x[4]+x[2]*x[3]*x[4]); 
> c[4]:=x[1]*x[2]*x[3]*x[4];
> 

                  c[1] := -x[1] - x[2] - x[3] - x[4]


  c[2] := x[1] x[2] + x[1] x[3] + x[1] x[4] + x[2] x[3] + x[2] x[4]

         + x[3] x[4]


  c[3] := -x[1] x[2] x[3] - x[1] x[2] x[4] - x[1] x[3] x[4]

         - x[2] x[3] x[4]


                     c[4] := x[1] x[2] x[3] x[4]

> Loesung:=solve({1/5+c[2]/3+c[4]=0, c[1]/5+c[3]/3=0,
> 1/7+c[2]/5+c[4]/3=0, c[1]/7+c[3]/5=0}, {x[1],x[2],x[3],x[4]}):
> Loesung:=evalf(convert(Loesung[1],'radical'));
> 

  Loesung := {x[3] = 0.3399810437, x[1] = -0.8611363116,

        x[2] = -0.3399810437, x[4] = 0.8611363116}

# Diese Sttzstellen stimmen berein mit den Nullstellen des
# LEGENDRE-Polynoms P(4,x):
> with(orthopoly,P):
> p[4]:=P(4,x);
> 

                                       4         2
                   p[4] := 3/8 + 35/8 x  - 15/4 x

> solve(p[4]=0):
> Nullstellen:=evalf(%);
> 

  Nullstellen :=

        -0.8611363114, 0.8611363114, -0.3399810437, 0.3399810437

> plot(p[4],x=-1..1,scaling=constrained,color=black,resolution=1200);
> 

> 
