I've been looking around in the documentation for root systems. It's not clear to me whether the individual roots in the system are accessible objects. For example, I can take the root system F4.
sage: rs=RootSystem("F4") sage: r1=rs.root_lattice().positive_roots() sage: r2=rs.weight_lattice().positive_roots() sage: r3=rs.ambient_space().positive_roots() sage: r1 A recursively enumerated set with a graded structure (breadth first search) sage: r2 A recursively enumerated set with a graded structure (breadth first search) sage: r3 [(1, 0, 0, 0), (0, 1, 0, 0), ... (1/2, -1/2, -1/2, -1/2)] sage: it1=r1.breadth_first_search_iterator() sage: it2=r2.breadth_first_search_iterator() sage: a1r1=next(it1) sage: a1r2=next(it2) sage: a1r3=r3[0] sage: a1r1 alpha[1] sage: a1r2 2*Lambda[1] - Lambda[2] sage: a1r3 (1, 0, 0, 0) sage: a1r1==a1r2 True sage: a1r1 is a1r2 False sage: a1r1 == a1r3 False sage: a1r2==a1r3 False If I understand what's going on, a1r1, a1r2 and a1r3 above are three distinct representations of the same mathematical object (the first simple root of F4). My question is whether there is a way to access the root directly? (Say you have some function which takes a root or pair of roots as input which you want to implement...) -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.