Hey Dan and Nicolas, On Thursday, February 20, 2014 4:43:37 AM UTC-8, Nicolas M. Thiery wrote: > > Hi Dan! > > On Wed, Feb 19, 2014 at 03:34:53PM -0800, bump wrote: > > Is the invariant inner product implemented already in the ambient > space? > > I think what is called inner product is actually the dual pairing > > between the space and its dual. This is defined in ambient_space.py. > > The point of the inner product defined in ambient_space is that it > provides both the dual pairing, if we apply it to a pair of elements > from both sides (e.g. a coroot and a root) and the invariant inner > product if we apply it to a pair of elements of the same size (e.g. a > root with another root). > > Of course it gets a bit trickier in the affine case (for the inner > products between c, \delta, \delta^check, ...); but I believe the > current inner product is likely to be what you want. See the > documentation of AffineSpace in type_affine for details, try it, and > report! > > In http://trac.sagemath.org/ticket/15384 (which is still somewhat sketchwork code), I implemented a method symmetric_form() for the root space. This should (hopefully) work for the roots, but I am doubtful that it works for pairing the fundamental weights. I haven't really attempted to really push the code yet. Here at the end of my ramblings, I don't think anyone has implemented what you want.
Personally I don't like doing things in the ambient space. Well...it's mainly for type A, since (3,2,1) should equal (2,1,0), but these give different inner products using the usual Euclidean form. Best, Travis -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
