On Wed, Jan 20, 2010 at 9:38 AM, John Cremona <john.crem...@gmail.com> wrote: > 2010/1/20 Nicolas M. Thiery <nicolas.thi...@u-psud.fr>: >> On Wed, Jan 20, 2010 at 03:43:00AM -0800, Jason Grout wrote: >>> >I'd rather have it called `echelon_form`, so I vote for leaving >>> >echelon_form as is. Jason's current change has the merit of pleasing >>> >everyone. If there is a strong majority for further changing >>> >`echelon_form`, then please make sure to keep it available under some >>> >alternative name. >>> >>> >>> Yes, as I understood it, the original plan was to make the current >>> echelon_form instead be called hermite_form. >> >> Which would then do standard Gauss elimination over a field. Hmm. I >> find this rather misleading, so -1. echelon_form is such a nice name >> for the generic thing. But that's just my view, and I am coming late >> in the discussion. >> > > What do you mean by the "generic thing"? I have never heard the term > "echelon form" used except over a field. Over rings there are other > forms, e.g. Smith, Hermite (depending on the ring of course).
In Magma "EchelonForm" is used over rings. In that case it is the Hermite form. >From a natural mathematical point of view this makes a huge amount of sense. However, it confuses undergraduates because matrix([[1,2],[3,4]]).echelon_form() has a surprising output compared to matrix(QQ,[[1,2],[3,4]]).echelon_form() That's the reason why we are having this discussion. I argue for keeping the current design when I'm *doing* math. I argue for changing echelon_form to return something over the fraction field when I'm teaching undergraduates. William > > I don't think *anyone* is suggesting that calling hermite_form() on an > integer matrix would return the echelon form of the corresponding > rational matrix! > > John > >> Cheers, >> Nicolas >> -- >> Nicolas M. Thiéry "Isil" <nthi...@users.sf.net> >> http://Nicolas.Thiery.name/ >> >> -- >> 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 >> >> > > -- > 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 Associate Professor of Mathematics University of Washington http://wstein.org
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