#15600: Exact computations in QQbar spend unreasonable amounts of time in
do_polred
-------------------------------+------------------------
Reporter: mmezzarobba | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: performance | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
-------------------------------+------------------------
Comment (by mmezzarobba):
I asked Karim Belabas. Here is what I understand of his answer:
* the cost of `polredbest` for a polynomial of degree `n` with
coefficients of bit size `B` is roughly `n^5 B^2`;
* the best it can do is to reduce the cost of subsequent computations in
the extension by a factor of roughly `B^2`;
* it is essentially never worth calling it on polynomials of moderately
large degree;
* ...except before performing very expensive operations (typically
`bnfinit()`) on the extension, when there is reason to expect that it will
find a defining polynomial of very small height.
On a related note, I noticed that `QQbar` often calls `polredbest` on
polynomials of the form `p(x^k)` where `k` can be pretty large. Karim
suggested that the Pari function `rnfpolredbest` could be useful in this
case.
--
Ticket URL: <http://trac.sagemath.org/ticket/15600#comment:3>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
