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| It is possible to an ideal contain fractions? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1347 |
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| Author: | Luis Bandeira [ Thu Aug 11, 2005 5:31 pm ] |
| Post subject: | It is possible to an ideal contain fractions? |
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 |
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| Author: | levandov [ Thu Aug 11, 2005 8:55 pm ] |
| Post subject: | Re: It is possible for an ideal to contain fractions? |
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, |
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