Hi Dusan, On Jul 30, 12:58 pm, Dušan Orlović <[email protected]> wrote: > 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?
Yes. I wrote "y*I.0 -2*y^3*I.1 -x*I.2" in order to demonstrate that we really have an element of the ideal that is not reduced to zero, in order to assert that the answer you expected was not a Groebner basis in degree reverse lexicographic order (and x>y, by the way). > Please tell me which command should I use to avoid bugs. > Is it the parameter (algorithm='toy:buchberger2') ? As the name says, 'toy:...' is a toy, hardly useful for any serious computation. And, as I demonstrated in my previous post, the answer given with toy:buchberger and toy:buchberger2 and (surprisingly) libsingular:slimgb are wrong. It is hard to say how to avoid bugs. Groebner bases over the integers are relatively new in Singular (hence, also new in Sage), and therefore it does not surprise me that there are still a couple of bugs to discover. But I don't know where the bug is actually located. Theoretically, it could also be in "reduce". The best way to avoid bugs? Well, one should never blindly trust any computer algebra system. Doing a verification by hand (as you did) is certainly a good approach, as long as the examples are small enough. I just arrived in my office, I am now doing some tests, also involving other computer algebra systems. I'll report back when I opened a trac ticket for this. Cheers, 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
