Even though your t
looks like it's a dictionary with integer keys and tuples of integer values, that's not what it is:
sage: t
{1: (1, 0, 0, 0, 0, 0, 0, 0, 0), 2: (1, 1, 1, 1, 1, 1, 1, 1, 0)}
sage: map(type, t)
[int, int]
sage: map(type, t.values())
[sage.combinat.root_system.ambient_space.AmbientSpace_with_category.element_class,
sage.combinat.root_system.ambient_space.AmbientSpace_with_category.element_class]
sage: parent(t[1])
Ambient space of the Root system of type ['A', 8]
If you want to get at the vector of coefficients, you can use .to_vector()
. For example, we have
sage: t[1]
(1, 0, 0, 0, 0, 0, 0, 0, 0)
sage: type(t[1])
<class 'sage.combinat.root_system.ambient_space.AmbientSpace_with_category.element_class'>
sage: list(t[1])
[(0, 1)]
but
sage: t[1].to_vector()
(1, 0, 0, 0, 0, 0, 0, 0, 0)
sage: type(t[1].to_vector())
<type 'sage.modules.vector_rational_dense.Vector_rational_dense'>
sage: list(t[1].to_vector())
[1, 0, 0, 0, 0, 0, 0, 0, 0]