Re: Strange performance of matdet

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Fri, Sep 07, 2012 at 01:56:32PM +0200, Jernej Azarija wrote:
> Hello!
> 
> This question  is motivated by the following discussion on sage
> https://groups.google.com/forum/?hl=en-GB&fromgroups=#!topic/sage-devel/uneXpZnRs-U
> in which it was noted that there exist a symmetric integer 34x34
> matrix such that it takes matdet  ~8minutes to compute the answer
> while it takes less than a second to compute the determinant using the
> classical Gaussian elimination.
> 
> The matrix in question is the following:

Well, ??matdet states that using the flag 1 is preferable for such matrices.
(but ?matdet states the opposite).

Anyway, the slowdown in Gauss-Bareiss was introduced in the commit below
which purpose was to handle better matrices over multivariate polynomials.

commit 2155b84a43a0977b19c5740cb281c2baec8ed4bc
Author: Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr>
Date:   Thu Apr 14 09:34:42 2011 +0000

    develop wrt to "sparse" row/column in det

In the 2.6 branch, we use a modular algorithm instead but only for matrices
at least 40x40.

Cheers,
Bill.