Hi Anne, Mark, Jesus,
I just pushed an updated version of #13724 which should fix the
issues/missing features of relabelled cartan types:
sage: ct = CartanType(["G",2]).relabel({1:2,2:1})
sage: ct.affine()
['G', 2, 1] relabelled by {0: 0, 1: 2, 2: 1}
sage: ct.symmetrizer()
Finite family {1: 3, 2: 1}
sage: ct.root_system().ambient_space()
Ambient space of the Root system of type ['G', 2] relabelled by {0: 0, 1:
2, 2: 1}
Please try out and shake it up!
One thing I haven't done yet is to handle the dual of G_2 and F4:
sage: ct = CartanType(['G',2]).dual()
sage: ct.affine()
One option would be to define the dual of G_2 as a relabelled G_2 (and
the same for F4), which would be two trivial methods to add. I am just
wondering whether there is any useful info we would loose by not
knowing that they are dual types.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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