Hey Dinakar, I wrote that part of the code and was assuming the user would be checking if a root is real or imaginary. However I'm definitely for adding this feature and having a method `is_root`. We can check if an element in the root space is a root in a finite root system by (the perhaps somewhat dumb) checking if it is in the (finite) set of all roots, which Sage can generate as you're probably aware. Also what's there for is_short/long/imaginary_root follows Prop 5.10 in Kac, so we could probably combine all 3 into a simple is_root for finite, affine, and (to be implemented #15974 <http://trac.sagemath.org/ticket/15974>) hyperbolic types. Please create a ticket on trac and cc me (tscrim) and we can fix things up.
Best, Travis On Sunday, October 12, 2014 1:49:39 PM UTC-7, vdelecroix wrote: > > Hi Dinakar, > > It makes more sense to post it on sage-devel as it concerns Sage > development and not a question you have about Sage. So I did the > forward. > > Vincent > > ---------- Forwarded message ---------- > From: Dinakar Muthiah <dmut...@gmail.com <javascript:>> > Date: Sun, 12 Oct 2014 11:51:56 -0700 (PDT) > Subject: [sage-support] A mathematical mistake in > root_lattice_realizations.py > To: sage-s...@googlegroups.com <javascript:> > > I claim there is currently a mathematical mistake in the way the > "is_real_root" method in the file root_lattice_realizations.py is > implemented. There is also a parallel mistake in "is_imaginary_root". Let > me illustrate with an example: > > sage: R = RootSystem(["A",2,1]).weight_lattice() > sage: alpha = R.simple_roots() > sage: alpha[0].is_real_root() > True > sage: b = 2*alpha[0] > sage: b.is_real_root() > True > > b.is_real_root() should return false because 2*alpha[0] is not a real > root. > In particular, 2*alpha[0] is not a root. > > Looking at the implementation of "is_real_root()", it is easy to see why > this isn't working properly. > > def is_real_root(self): > r""" > Return ``True`` if ``self`` is a real root. > > A root `\alpha` is real if it is `W` conjugate to a simple > root where `W` is the corresponding Weyl group. > > EXAMPLES:: > > sage: Q = RootSystem(['B',2,1]).root_lattice() > sage: alpha = Q.simple_roots() > sage: alpha[0].is_real_root() > True > sage: elt = alpha[0] + alpha[1] + 2*alpha[2] > sage: elt.is_real_root() > False > """ > return self.norm_squared() > 0 > > self.norm_squared() is not the way to check whether an element of the root > space or weight_space is a real root. > > The problem is that there is no check to see whether self is a root. In > affine types, the following should work: > > return (self.norm_squared() > 0) and self.is_root() > > where is_root() would be a method that checks whether self is a root. But > this isn't currently implemented, and I don't know what would be the most > intelligent way to implement this. In affine types, this is fairly > straight > forward assuming you have a test for checking whether something is a root > in the finite root system, but I don't know for general Cartan types. > > What do people think about this? I have not contributed to sage in the > past, but I am interested in implementing the fix. > > Also, is there a better place for me to post this bug. I looked > here: http://wiki.sagemath.org/support/ReportingBugs, and it suggested I > post on sage-support since I don't have experience developing sage or > using > trac. > > Best, > Dinakar > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
