Hi Simon, thanks for replying, your example: y*I.0 -2*y^3*I.1 -x*I.2 is x*y^2 which lies in ideal [x*y^3, 2*x^2 + x*y, 3*x*y, 2*y^2] as y * (3*x*y) - x * (2*y^2) = x*y^2, so it has to be reduced to zero. Am I right? Please tell me which command should I use to avoid bugs. Is it the parameter (algorithm='toy:buchberger2') ? Bye,
On Fri, Jul 30, 2010 at 1:07 PM, Simon King <[email protected]> wrote: > PS: > > On 30 Jul., 12:57, Simon King <[email protected]> wrote: > > No, you are wrong. Your expected answer is definitely not correct, > > But certainly there is something wrong in Singular/libsingular (which > by default is used in Sage to compute Gröbner bases) as well: > > sage: > (I.groebner_basis(algorithm='toy:buchberger2')*R).interreduced_basis() > [2*x^2 + x*y, 3*x*y, 2*y^2] > sage: > (I.groebner_basis(algorithm='toy:buchberger')*R).interreduced_basis() > [2*x^2 + x*y, 3*x*y, 2*y^2] > sage: > (I.groebner_basis(algorithm='singular:std')*R).interreduced_basis() > [x^2*y, x*y^2, 2*x^2 + x*y, 3*x*y, 2*y^2] > sage: > (I.groebner_basis(algorithm='libsingular:std')*R).interreduced_basis() > [x^2*y, x*y^2, 2*x^2 + x*y, 3*x*y, 2*y^2] > sage: > (I.groebner_basis(algorithm='libsingular:slimgb')*R).interreduced_basis() > [2*x^2 + x*y, 3*x*y, 2*y^2] > > So, it looks like both toy:buchberger and toy:buchberger2 and slimgb > coincide - and they are in majority. But again, they are wrong: > > sage: (y*I.0 -2*y^3*I.1 -x*I. > 2).reduce(I.groebner_basis(algorithm='libsingular:slimgb')) > x*y^2 > > So, this will actually be several bug reports to Singular. > > Thank you for pointing us to this! > Simon > > -- > To post to this group, send an email to [email protected] > To unsubscribe from this group, send an email to > [email protected]<sage-devel%[email protected]> > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
