Hi everyone: I'm applying for a grant from the New Zealand government to fund some Sage development in the area of computational algebraic and analytic geometry. For part of the application i need to report on the 'state of the field'. Part of my response to this will be to mention that Sage doesn't have an implementation of factorization, ideal, and variety calculations over QQbar. To double-check, is this true? Related to that, do any major computer algebra systems (Singular included) have such implementations?
Alex On Dec 5 2008, 10:55 am, "William Stein" <wst...@gmail.com> wrote: > On Thu, Dec 4, 2008 at 1:48 PM, AlexRaichev<tortoise.s...@gmail.com> wrote: > > > Thanks for your help, Carl. Where did you find the documentation for > > the command number_field_elements_from_algebraics(c)? > > I'm guessing Carl knew about that command since he implemented it. > > Typing > > sage: help(sage.rings.qqbar) > > in Sage is pretty helpful too. > > > Yes, i'd find it very useful to have ideal and variety > > computations over QQbar implemented. I don't have the know-how or the > > time at present to do this myself, but i am learning more about Sage > > every day and my next job might support this endeavor more than my > > present one. So perhaps in the future i can work on this. > > > Alex > > Awesome. I hope you get said next job! > > -- William > > > > > > > On Dec 4, 9:31 am, Carl Witty <cwi...@newtonlabs.com> wrote: > >> On Nov 30, 1:27 pm, AlexRaichev<tortoise.s...@gmail.com> wrote: > > >> > > It would be helpful if you could give a more concrete example, e.g., a > >> > > session > >> > > where you have some elements, and finally want to do something with > >> > > them. > > >> > That's good idea, William. Let me back up to and change my question > >> > to a more fundamental one. How does one compute in QQbar with Sage? > >> > For example, how about factoring a polynomial, computing a radical > >> > ideal, or computing a variety (see below)? I get the same error for > >> > all these: "no conversion of this ring to a Singular ring defined". > > >> > Alex > > >> None of these things are implemented for polynomials over QQbar; and > >> as far as I know there are no plans to implement them. > > >> Simpler variants of a couple of your problems are implemented: > > >> For univariate polynomials, you can find the roots with .roots > >> (ring=QQbar), and it's trivial to compute the factorization from > >> there. > > >> You can compute the variety (over QQbar) of a zero-dimensional ideal > >> of polynomials with rational coefficients, using .variety(ring=QQbar). > > >> It would be great to have more functionality implemented for > >> polynomials over QQbar; is that something you would be interested in > >> contributing? > > >> Carl > > -- > William Stein > Associate Professor of Mathematics > University of Washingtonhttp://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
