I hope I did not offend anyone, least of all someone who had provided a patch which makes a useful efficiency improvement! But as Martin invited all sage-devel to look at that code, I did!
I'll be happy to provide a patch for the bug in is_irreducible for rational polys. (I call it a bug, though it's actually a correct implementation of a wrong definition). What Ryan suggest for is_primitive might be a good way to go; as far as I know the meaning which is relevant here, namely "irreducible and the root generates the multiplicative group of the extension" is only relevant over finite fields (and no other fields). The other meaning (coprime coefficients) is certainly not very useful over fields as it is the same as "non-zero", so we are left with the question "what, if anything, should we take is_primitive() to mean for polynomials in F[x] where F is an infinite field?" John 2009/3/18 Ryan Hinton <iob...@email.com>: > > Unfortunately, I don't know what on earth is_primitive() is doing there. > I didn't put it there. I wrote the patch to as a performance > enhancement to the _existing_ is_primitive implementation. is_primitive > was there already, so the current ticket is probably not the best place > to discuss its existence or placement. (And I didn't even touch > is_irreducible.) > > C.Witty suggested on IRC that #5535 be accepted as is, and to open > additional tickets to address John's concerns (is_primitive placement > and is_irreducible bug). He also suggested that, given the differing > meanings of "primitive polynomial" in ring theory vs. field theory, one > way to resolve the issue is to split up the polynomial classes into > "polynomials over fields" and "polynomials over rings." Then these new > base classes (and/or their derived classes) can implement is_primitive > as appropriate. > > Unfortunately, I'm not enough of a mathematician to address the problems > (I've learned most of what I know about these issues from Wikipedia over > the last few days), so I'll assign the new trac tickets to John for now. > > In the mean time, does anyone object to the patch for trac #5535 that > gives a huge speed improvement but allows a user to get garbage out if > they put garbage in? :-) > > Thanks! > > - Ryan > > John Cremona wrote: >> What on earth is that function is_primitive() doing there? If you >> asked me to define what it means for a univariate polynomial over a >> ring to be primitive then I would say that it means that the >> coefficients generate the unit ideal. >> >> The function there seems to be a different concept only relevant for >> polynomials over finite fields. So why is it in class Polynomial? >> >> It gets worse: >> >> sage: R.<x> = QQ[] >> sage: f=3*x^2-6 >> sage: f.is_irreducible() >> False >> >> This is WRONG. I thought I fixed that months ago, but here it is >> again. The implementation >> >> def is_irreducible(self): >> S = PolynomialRing(ZZ, self.variable_name()) >> return S(self.denominator()*self).is_irreducible() >> >> would fail any first year undergraduate exam I was responsible for. >> >> John >> >> 2009/3/16 Martin Albrecht <m...@informatik.uni-bremen.de>: >>> Hi there, >>> >>> http://trac.sagemath.org/sage_trac/ticket/5535 >>> >>> adds a neat way of shooting yourself in the foot in the name of performance, >>> so I wonder if anyone has any hard feelings about that? I suggested to >>> include this in Sage (Ryan had a local version for his application), so I >>> think it is worth it. >>> >>> Thoughts? >>> Martin >>> -- >>> name: Martin Albrecht >>> _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 >>> _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF >>> _www: http://www.informatik.uni-bremen.de/~malb >>> _jab: martinralbre...@jabber.ccc.de >>> >>> >> >> > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
