|Bill Allombert on Fri, 07 Sep 2012 14:21:52 +0200|
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|Re: Strange performance of matdet|
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.