[sage-devel] Re: Number fields without generators
On Aug 20, 12:32 pm, William Stein wrote: > Number fields defined by polynomials that are not monic *and* integral > are not supported by PARI. OK, thanks for the explanation. > It would probably be a 2-3 day project for somebody to make Sage fully > support fields Hmm, I don't think I am that somebody. ;-) Thanks, William and John, for the help. I should have enough now to at least spruce up the eigen-stuff code appropriately, and insert some doctests that will fail when that somebody gets that project implemented. Rob -- 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
Re: [sage-devel] Re: Number fields without generators
Also Rob, the real name for the field is M._NumberField_relative__gens (or similar). John On Sat, Aug 20, 2011 at 8:32 PM, William Stein wrote: > On Sat, Aug 20, 2011 at 10:58 AM, Rob Beezer wrote: >> Thanks for the sleuthing and ideas, John. Yes, I should have used a >> monic polynomial in my example since the original problem I have is >> with factors of a characteristic polynomial (and get similar >> behavior). >> >> I also get >> >> sage: M._gens is None >> True >> >> The eigenspace code (and probably eigenvalues, too) assume the root >> field has just one generator, so there is more to do there perhaps. >> >> Is that indicative of anything? I'll dig deeper and see if I can get >> to the bottom of this. Maybe at Bug Days 32. ;-) > > Number fields defined by polynomials that are not monic *and* integral > are not supported by PARI. > Trying to define them in Sage right now should just give a big error > on creation, but currently doesn't. > It would probably be a 2-3 day project for somebody to make Sage fully > support fields defined by arbitrary > polynomials though, by secretely using the function > > sage.schemes.elliptic_curves.heegner.make_monic > > This project would save people from a lot of headaches, and *has* to > happen. It just a matter of time until somebody does it. > > -- William > > > >> >> Rob >> >> -- >> 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 >> > > > > -- > William Stein > Professor of Mathematics > University of Washington > http://wstein.org > > -- > 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 > -- 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
Re: [sage-devel] Re: Number fields without generators
On Sat, Aug 20, 2011 at 10:58 AM, Rob Beezer wrote: > Thanks for the sleuthing and ideas, John. Yes, I should have used a > monic polynomial in my example since the original problem I have is > with factors of a characteristic polynomial (and get similar > behavior). > > I also get > > sage: M._gens is None > True > > The eigenspace code (and probably eigenvalues, too) assume the root > field has just one generator, so there is more to do there perhaps. > > Is that indicative of anything? I'll dig deeper and see if I can get > to the bottom of this. Maybe at Bug Days 32. ;-) Number fields defined by polynomials that are not monic *and* integral are not supported by PARI. Trying to define them in Sage right now should just give a big error on creation, but currently doesn't. It would probably be a 2-3 day project for somebody to make Sage fully support fields defined by arbitrary polynomials though, by secretely using the function sage.schemes.elliptic_curves.heegner.make_monic This project would save people from a lot of headaches, and *has* to happen. It just a matter of time until somebody does it. -- William > > Rob > > -- > 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 > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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
[sage-devel] Re: Number fields without generators
Thanks for the sleuthing and ideas, John. Yes, I should have used a monic polynomial in my example since the original problem I have is with factors of a characteristic polynomial (and get similar behavior). I also get sage: M._gens is None True The eigenspace code (and probably eigenvalues, too) assume the root field has just one generator, so there is more to do there perhaps. Is that indicative of anything? I'll dig deeper and see if I can get to the bottom of this. Maybe at Bug Days 32. ;-) Rob -- 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
