> Would it do to coerce the two elements to the (affine extended) > ambient space, and use the inner product there? If speed is an issue, > one could cache the result on the bases. >
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. However there is a canonical isomorphism (called nu by Kac) between the Cartan subalgebra and its dual. In principle implementing that is enough but it is easiest to describe in terms of the roots, not the fundamental weights. Dan -- 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.
