On Thursday, February 16, 2017 at 5:32:42 AM UTC, Matthew Macauley wrote: > > Typing the following: > > > P.<x,y,z> = PolynomialRing(RR, 3, order='lex'); P > I = ideal(x^2+y^2+z^2-1, x^2-y+z^2, x-z); I > B = I.groebner_basis(); B > > > gives a brutal error (type it into SageMathCell and you'll see). > > > Seth Sullivant suggested that it's due to a roundoff error, because it > works with fields such as "QQ" or "GF(3)", etc. That said, I am 99% sure > that it's a relatively new error, because I have typed in those exact lines > in previous semesters (it's from a HW problem that I assigned) and I > haven't had any prior issues. >
RR is not a even a ring in a proper sense of this term (IIRC, just because of multiplication being non-associative: think what happens when rounding occurs if you do (ab)c, but not if you do a(bc)...) Certainly it's naive to expect nontrivial commutative algebra algorithms work correctly in this case. In particular, lexicographic Groebner bases are prone to coefficient growth, so for anything like toy examples you might get wrong answers. Having said this, this is a bug; and it was a bug, even more brutal (behind the curtains) one, as it was possible compute this. The backend that actually does this computation is Singular, adn it does not do floating point numbers (in this context for sure). -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
