bug with factorize in alg ext of deg 6 in char 32003

[gorzel]

> ring R3s = (0,s),(x,y),dp;
> minpoly = s2-s+1;
> poly G3 = x3+y3+(-s-1)*x2+(s-2)*xy+(-s-1)*y2+(s+1)*x+(s+1)*y+(-s);
> factorize(G3);
[1]:
   _[1]=1
   _[2]=x+y+(-s)
   _[3]=x+(-s)*y+(s-1)
   _[4]=x+(s-1)*y+(-s)
[2]:
   1,1,1,1

Now consider this cubic extension of \sqrt{-3} as defined above:

>  ring R6s = (32003,s),(x,y),dp;
>  minpoly = (s6-11914s5+3952s4-5439s3-15290s2-15431s+15606);
> factorize(x2-x+1);
[1]:
   _[1]=1
   _[2]=x+(-7372s5+12678s4+6785s3+12049s2+6154s+14657)
   _[3]=x+(7372s5-12678s4-6785s3-12049s2-6154s-14658)
[2]:
   1,1,1

The same polynomial from above should again factorize, isn't it? But factorize takes very long and gives a wrong result: The s is entirely missing and not all factors are irreducible:

> poly G3 = x3+y3+(-s-1)*x2+(s-2)*xy+(-s-1)*y2+(s+1)*x+(s+1)*y+(-s);
> factorize(G3);
[1]:
   _[1]=1
   _[2]=x+y
   _[3]=x2-xy+y2
[2]:
   1,1,1
> factorize(x2-xy+y2);
[1]:
   _[1]=1
   _[2]=(-7372s5+12678s4+6785s3+12049s2+6154s+14657)*x+y
   _[3]=(7372s5-12678s4-6785s3-12049s2-6154s-14658)*x+y
[2]:
   1,1,1

[mlee]

Fixed with 15724