2015-01-26 17:07 UTC+01:00, Jeroen Demeyer <jdeme...@cage.ugent.be>: > On 2015-01-26 14:22, Bruno Grenet wrote: >> In the special case of univariate polynomials over ZZ, I think there are >> two possibilities for xgcd: >> >> - either xgcd(p,q) = (g,u,v) where g = gcd(p,q) = up+vq with u,v in >> QQ[x]; >> - or xgcd(p,q) = (g×r, u, v) where g = gcd(p,q), r = res(p,q), g×r = >> up+vq with u,v in ZZ[x]. >> >> More generally, Bézout coefficients seem to be usually defined only for >> PID, and this motivates the first solution (in general, replace ZZ by a >> UFD R and QQ by its field of fractions K). The second solution has the >> advantage of staying in the same polynomial ring, and it has a clear >> definition. I would go for the second solution, with an updated >> documentation. > The second definition might be useful to have as algorithm, but I would > never call it xgcd(). Call it pseudo_xgcd() or resultant_xgcd().
I agree. But definitely distinct from the purpose of #17671. I opened #17674 for that. Vincent -- 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 sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
