On Sep 17, 2007, at 9:00 PM, William Stein wrote: > This is being cc'd to sage-devel, since no reason not to. It's me > and Robert Bradshaw working on reworking the algebraic number > theory code in Sage (we've done a lot now). > > On 9/17/07, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > BTW, I've been working on quadratic number field elements... > > That's a good idea. > I have been working on grant proposals all day long. > I'm going to switch gears and work on the ANT package > soon. I'll probably work only on getting all the doctests > not in the number_field directory to pass, since much > was broken by my changes. > > I also want to make ZZ[a,b,c] > work, if a,b,c are algebraic integers. > > It would also be really neat to have a function that can > compute the minimal polynomial of a symbolic element: > sage: a = sqrt(2) > sage: a.minpoly() > x^2 - 2 > sage: a = 5^(1/3) > sage: a.minpoly() > x^3 - 5 > > One possibility would be to numerically approximate a, > use pari's algdep to get a candidate minpoly f, then > do bool(f(a) == 0). If it works, we're golden. If not, > we give up. Since bool(f(a) == 0) errors on the side of > caution, this would probably be fine.
That sounds like a really slick idea. > With that, we could do > > ZZ[sqrt(2), 5^(1/7), sqrt(7)] > > and it would work. Thoughts? I think this would make for a really natural way of constructing number fields. I am still of the mind that I would like sqrt(2).parent () to be an order in a number field (with an embedding into C choosing the positive root), assuming the coercion model was robust enough to find resonable compositums of these things. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
