# Revision history [back]

Depending on what you want to do, you can use the theorem which says that the Weyl group acts simply transitively on the set of choices of simple roots (or positive root systems, or Weyl chambers..) in order to translate back and forth between the choice that is attached to RootSystem( .. ) by default and any other choice:

sage: R=RootSystem(['A',Integer(2)])
sage: space=R.ambient_space()
sage: space.simple_roots()
Finite family {1: (1, -1, 0), 2: (0, 1, -1)}
sage: W = space.weyl_group()
sage: w0 = W.long_element()
sage: minus_sr = [ w0.action(s) for s in space.simple_roots() ]; minus_sr
[(0, -1, 1), (-1, 1, 0)]