The is_primitive issues is now described in trac #5561. Owners are welcome!
John Cremona wrote: > 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 -~----------~----~----~----~------~----~------~--~---
