On Sep 14, 3:47 pm, Sebastian Pancratz <s...@pancratz.org> wrote: > 1. > > Given rational polynomials a and b, what should gcd(a,b) return? The > problem arises since the gcd is only defined up to rational units. I > think the two sound options are either the monic normalisation, or a
I think any mathematician would first expect a monic polynomial to be returned and be quite surprised by a non-monic answer. > Personally, I would be in favour of the second choice, because in the > new implementation using FLINT, the polynomial is represented as an > integer polynomial with a positive integer denominator coprime to the > content of the numerator. If in a higher level block of code calls > are made to gcd on a frequent basis, this would be faster than if gcd > always had to return the monic version. So perhaps also offer integral_gcd and document that this is faster because it is closer to the internal representation? > - Polynomials over Z/nZ via FLINT: Not quite sure, except that gcd > (a,0) == a and gcd(0,b) == b. By the way, working in (Z/27Z)[t], gcd > (3*t+2, (3*t+2)*(t^3 + t - 1)) returns 1, which looks like a bug. In If n is not prime then $Z/nZ$ is not a PID anymore, so you can't really expect that the gcd can be represented by a single generator. The same problem arises over Z, but there people seem to be content with getting back the biggest principal ideal that extends to the correct ideal over $Q$. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
