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 Font size: Tiny Small Normal Large Huge Font colour [quote="Luis Bandeira"]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[/quote]
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Topic review - It is possible to an ideal contain fractions?
Author Message
 levandov
 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 equationsx^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, [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 equationsx^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,
 Posted: Thu Aug 11, 2005 8:55 pm
 Luis Bandeira
 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.ptPosted in old Singular Forum on: 2002-12-20 18:43:57+01 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.ptPosted in old Singular Forum on: 2002-12-20 18:43:57+01
 Posted: Thu Aug 11, 2005 5:31 pm

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