Singular

[quote]> Can an ideal contain fractions?[/quote]
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);[/code][/quote]

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);[/code]

See the description of facstd for details.

Regards,

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