On Wed, Aug 26, 2009 at 9:31 AM, William Stein<[email protected]> wrote: > On Wed, Aug 26, 2009 at 7:20 AM, john_perry_usm<[email protected]> wrote: >> >> Just yesterday I bumped up against factoring univariate polynomials in >> QQbar (*not* CC). Being able to factor in QQbar would have a broad >> impact (or maybe not, but at least on one ticket I was studying), but >> I don't know about feasibility. > > Any polynomial over QQbar is automatically a polynomial over K, for > some number fields K, since there are only finitely many > coefficiencts. So from an algorithmic point of view, this is
Wow, I just realized that I utterly completely misunderstood your (clear) post. Please disregard my comments below. > equivalent to polynomial factorization over numbers fields (though > there may be a complexity issue in transforming the problem, depending > on how your elements of QQbar are represented). This is already > implemented in Sage: > > sage: K.<a> = QQ[sqrt(2)] > sage: R.<x,y> = K[] > sage: f = (x+y)*(x^3-a*y); f > x^4 + x^3*y + (-sqrt2)*x*y + (-sqrt2)*y^2 > sage: f.factor() > (x + y) * (x^3 + (-sqrt2)*y) > > >> >> regards >> john perry >> >> On Aug 25, 1:56 pm, William Stein <[email protected]> wrote: >>> Hello, >>> >>> Grant proposal season is upon us, and things are in the works. >>> Imagine somebody said to you: >>> >>> "Please send me a list of items you would like us to fund. What I >>> need is just a sentence or two (at most a >>> paragraph) describing the work ... and a ballpark estimate of the cost." >>> >>> Feel free to post in this thread any wishlist ideas along these lines >>> that you might have. They could make there way into a proposal that >>> might get funded, and Sage development would consequently benefit >>> greatly. >>> >>> Thanks! >>> >>> William >>> >>> -- >>> William Stein >>> Associate Professor of Mathematics >>> University of Washingtonhttp://wstein.org >> >> >> > > > > -- > William Stein > Associate Professor of Mathematics > University of Washington > http://wstein.org > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
