On Wed, Jan 25, 2012 at 11:45 AM, javier <vengor...@gmail.com> wrote: > Hi William, > > On Jan 25, 6:30 pm, William Stein <wst...@gmail.com> wrote: >> I think is_singular should raise a ValueError if the input matrix is >> not square. > > Sure, that makes sense. My main point was arguing for the convenience > of using rank rather than determinant. > >> That is probably a good idea over ZZ or QQ and probably many other >> rings, especially since for a random matrix over ZZ or QQ, rank will >> be full and Sage will quickly figure this out by reducing modulo one >> small random prime. So, even if the coefficients of A are enormous, >> the rank approach will usually be very fast, whereas computing the >> determinant will be slowed down by the size of the entries. > > Certainly, for generic matrices in rings computing the rank should be > much faster, particularly in the full-rank case. In the very > degenerate case (over ZZ) my example shows similar (if slightly > better) performance for rank. I am not sure on the difference of > performance when working numerically, though. > > Should I open a ticket and change this, or does anybody have a strong > argument for favoring the determinant use in some cases?
I'm personally for changing to use rank. > >> There was no cached_method when I wrote most of the matrix code. >> Also, I think decorators weren't supported in Cython then (?). >> >> The matrix caching code is definitely more sophisticated than what >> cached_method does though. It has to behave differently for mutable >> and immutable matrices. > > I see, so touching this would mean opening a can of worms. Better > leave it as it is for now, then. > > Cheers > Javier > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
