On 10/26/12 6:25 AM, Volker Braun wrote:
The matrix is over RR (MPFR software floats). M.change_ring(RDF).det()
gives the right answer.
There is no special det() implementation for RR, we compute the
Hessenberg form and from that characteristic polynomial. Sage uses
Gaussian elimination to compute the Hessenberg form, and this is known
to be numerically unstable in unfavorable cases
(http://www.jstor.org/stable/2004967). I guess your matrix is one of
these cases; there is no overflow, its a numerical instability.
Yep. If you're doing computations with numerical matrices, you should
always use RDF or CDF matrices. In this case, RDF/CDF matrices use LU
factorization and then compute the determinant from that, using the
scipy.linalg.determinant function (which in turn uses LAPACK).
Thanks,
Jason
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