def fundamental_weights(self):
"""
EXAMPLES::
sage: RootSystem("A2xB2").ambient_space().fundamental_weights()
Finite family {1: (1, 0, 0, 0, 0), 2: (1, 1, 0, 0, 0), 3: (0, 0, 0, 1, 0), 4: (0, 0, 0, 1/2, 1/2)}
"""
fw = []
for i, ambient_space in enumerate(self.ambient_spaces()):
fw.extend(self.inject_weights(i, v) for v in ambient_space.fundamental_weights())
return Family(dict([i,fw[i-1]] for i in range(1,len(fw)+1)))
def fundamental_weights(self):
"""
EXAMPLES::
sage: RootSystem("A2xB2").ambient_space().fundamental_weights()
Finite family {1: (1, 0, 0, 0, 0), 2: (1, 1, 0, 0, 0), 3: (0, 0, 0, 1, 0), 4: (0, 0, 0, 1/2, 1/2)}
"""
fw = []
for i, ambient_space in enumerate(self.ambient_spaces()):
fw.extend(self.inject_weights(i, v) for v in ambient_space.fundamental_weights())
return Family(dict([i,fw[i-1]] for i in range(1,len(fw)+1)))