It is possible to an ideal contain fractions?

Luis Bandeira · Thu Aug 11, 2005 5:31 pm

Can an ideal contain fractions? Moreover, what does singular with the following input:

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);

email: lmzb@uevora.pt
Posted in old Singular Forum on: 2002-12-20 18:43:57+01

Re: It is possible for an ideal to contain fractions?

levandov · Thu Aug 11, 2005 8:55 pm

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,