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