On Wed, Sep 19, 2012 at 8:31 PM, Rob Beezer <goo...@beezer.cotse.net> wrote: > On Wednesday, September 19, 2012 1:52:24 PM UTC-7, Robert Bradshaw wrote: >> >> There is the issue that norm(v) does not always (often?) live in v for >> exact v. Dropping to SR can be really slow, as can dropping to >> QQ[sqrt(norm(v))], especially if several vectors are normalized then >> used together (though I'm sure we could find/write a fairly efficient >> multi-quadratic extension implantation that could be more generally >> useful). > > > Exactly. > > I'd feel a lot better about the proposed change if there was no way to ever > end up in the symbolic ring (unless, of course, your vector began there). > > Having square roots of integers be symbolic (an inexact ring) causes no end > of trouble when trying to do things like matrix decompositions over exact > rings (such as starting over QQ). At least we have QQbar for square roots > of rationals and integers. > > >> This was pointed out to me by someone who teaches undergrads and found it >> frustrating that Sage was not doing the standard normalization. > > Making things more predictable for undergrads is always a good idea. Why > don't we go all the way? Have normalization() return a vector over RDF/CDF. > I think this is what "most people would think it should do."
Going from exact to inexact has issues as well, e.g. the introduction of rounding error and equality issues. - Robert -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
