I found that the G2 fundamental weights in combinat/root_systems.py are the negatives of what they should be.
http://sagetrac.org/sage_trac/ticket/2808 I should have added some justification for this conclusion in the trac report. Instead I'm giving it here. You can look the weights up in Bourbaki, Lie Groups and Lie Algebras Ch 4-6 (Appendix) and you can also check the inner products of the weights with the simple roots (which are correct). The inner product of the i-th fundamental weight with the j-th simple root should be positive if i=j and zero otherwise. I checked that all the other root systems are right by examining the output following program on the ambient lattices. This change had no effect on the output of the Weyl dimension formula. def test_lattice(L): rank = L.ct[1] roots = L.simple_roots() weights = L.fundamental_weights() return [[i,j, roots[i].inner_product(weights[j])] for i in range(rank) for j in range(rank)] Since this is a genuine bug and trivial to fix I gave it priority major. Let me know if that was wrong. Dan --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
