**Quote:**

> Can an ideal contain fractions?

No. Fractions are not elements of the ring of polynomials (but of the field of rational functions).

**Quote:**

>Moreover, what does singular with the following input:

>

**Code:**

ring R=0,(x,y,z,w),dp;

ideal I=x^2+y-w,(x^2+z)/(1-y-z^2),(x^3-y)/(x+y+z+w);

std(I);

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:

**Code:**

ring R=0,(x,y,z,w),dp;

ideal I = x^2+y-w,x^2+z,x^3-y;

ideal J = 1-y-z^2, x+y+z+w;

facstd(I,J);

See the description of facstd for details.

Regards,