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- from sympy.liealgebras.root_system import RootSystem
- from sympy.liealgebras.type_a import TypeA
- from sympy.matrices import Matrix
- def test_root_system():
- c = RootSystem("A3")
- assert c.cartan_type == TypeA(3)
- assert c.simple_roots() == {1: [1, -1, 0, 0], 2: [0, 1, -1, 0], 3: [0, 0, 1, -1]}
- assert c.root_space() == "alpha[1] + alpha[2] + alpha[3]"
- assert c.cartan_matrix() == Matrix([[ 2, -1, 0], [-1, 2, -1], [ 0, -1, 2]])
- assert c.dynkin_diagram() == "0---0---0\n1 2 3"
- assert c.add_simple_roots(1, 2) == [1, 0, -1, 0]
- assert c.all_roots() == {1: [1, -1, 0, 0], 2: [1, 0, -1, 0],
- 3: [1, 0, 0, -1], 4: [0, 1, -1, 0], 5: [0, 1, 0, -1],
- 6: [0, 0, 1, -1], 7: [-1, 1, 0, 0], 8: [-1, 0, 1, 0],
- 9: [-1, 0, 0, 1], 10: [0, -1, 1, 0],
- 11: [0, -1, 0, 1], 12: [0, 0, -1, 1]}
- assert c.add_as_roots([1, 0, -1, 0], [0, 0, 1, -1]) == [1, 0, 0, -1]
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