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Here is a problem that I cannot seem to understand.

R=RootSystem(['A', 2])
F=R.ambient_space().fundamental_weights()
D=R.ambient_space().simple_roots()

F=Finite family {1: (1, 0, 0), 2: (1, 1, 0)}
D = Finite family {1: (1, -1, 0), 2: (0, 1, -1)}

I need to write a program I would need the weyl group action on some weights and roots at the same time. How can this be done? Thank you for your time in advance.

Here is a problem that I cannot seem to understand.

R=RootSystem(['A', 2])
F=R.ambient_space().fundamental_weights()
D=R.ambient_space().simple_roots()

F=Finite family {1: (1, 0, 0), 2: (1, 1, 0)}
D = Finite D=Finite family {1: (1, -1, 0), 2: (0, 1, -1)}

I need to write a program I would need the weyl group action on some weights and roots at the same time. How can this be done? Thank you for your time in advance.

Here is a problem that I cannot seem to understand.

R=RootSystem(['A', 2])
F=R.ambient_space().fundamental_weights()
D=R.ambient_space().simple_roots()

F=Finite family {1: (1, 0, 0), 2: (1, 1, 0)}
D=Finite family {1: (1, -1, 0), 2: (0, 1, -1)}

I need to write a program I would need the weyl group action on some weights and roots at the same time. How can this be done? Thank you for your time in advance.

W= R.ambient_space(). weyl_group()
S= W.gens()
s1, s2= S
s1.action(F[1]) 

 
ValueError                                Traceback (most recent call last)
<ipython-input-12-4b0b8fd74264> in <module>()
---- 1 s1.action(F[Integer(1)])
 
/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/combinat/root_system/weyl_group.pyc in action(self, v)
    843         """
    844         if v not in self.domain():
--> 845             raise ValueError("{} is not in the domain".format(v))
    846         return self.domain().from_vector(self.__matrixv.to_vector())
    847 
ValueError: Lambda[1] is not in the domain

L = R. weight_lattice()
F=L.fundamental_weights()
f= L.to_ambient_space-morphism()
s1.action(f(F[1]))
(1,0,0)