On Jul 13, 8:32 pm, William Stein <wst...@gmail.com> wrote:
> Sage is probably just using some completely generic general
> implementation of "kernel" for matrices.

Yes, that is correct.  It's a totally generic routine and it stands a
very good chance of giving an incorrect result with entries from RDF.

The LU routine for RDF/CDF matrices uses the NumPy/SciPy libraries.
At the moment, it only accepts square matrices, but with the
positively-reviewed patch at

http://trac.sagemath.org/sage_trac/ticket/10839

it will accept rectangular matrices.  For an over-sized example, I get

sage: M = matrix(RDF, 400, 400, lambda i,j: i+j)
sage: time x = M.LU()
Time: CPU 0.02 s, Wall: 0.02 s

Rob

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