On Oct 22, 8:06 am, William Stein <wst...@gmail.com> wrote:
> Is there a research paper explaining the finite field approach to
> QQbar?  It would be good to mention it here, since implementing
> similar functionality Sage for computing with QQbar would be a good
> project for somebody.

MR2578343 (2011d:13043)  Steel, Allan K.  Computing with algebraically
closed fields.
 J. Symbolic Comput.  45  (2010),  no. 3, 342--372.


MR2041106 (2005b:12016)  Steel, Allan . A new scheme for computing
with algebraically closed fields.
 Algorithmic number theory (Sydney, 2002),
 491--505, Lecture Notes in Comput. Sci., 2369, Springer, Berlin,
2002.


For primary decomposition:

MR2167699 (2006f:13023)  Steel, Allan . Conquering inseparability:
primary decomposition and multivariate factorization over algebraic
function fields of positive characteristic.
 J. Symbolic Comput.  40  (2005),  no. 3, 1053--1075.

although for the application under consideration here, you've probably
already lost when you run into inseparability problems.
>
> William
>
>
>
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> --
> William Stein
> Professor of Mathematics
> University of Washingtonhttp://wstein.org

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