> Can an ideal contain fractions?
No. Fractions are not elements of the ring of polynomials (but of the field of rational functions).
>Moreover, what does singular with the following input:
The division is performed in the ring of polynomials giving zero as the second and the third generators of I.
If you want to solve the system of equations
x^2+y-w = 0,
x^2+z = 0,
x^3-y = 0,
1-y-z^2 <> 0,
x+y+z+w <> 0,
we recommend the following:
ideal I = x^2+y-w,x^2+z,x^3-y;
ideal J = 1-y-z^2, x+y+z+w;
See the description of facstd for details.