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] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
