def test_type_A(): c = CartanType("A3") m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2]) assert m == c.cartan_matrix() assert c.basis() == 8 assert c.roots() == 12 assert c.dimension() == 4 assert c.simple_root(1) == [1, -1, 0, 0] assert c.highest_root() == [1, 0, 0, -1] assert c.lie_algebra() == "su(4)"
def test_type_A(): c = CartanType("A3") m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2]) assert m == c.cartan_matrix() assert c.basis() == 8 assert c.roots() == 12 assert c.dimension() == 4 assert c.simple_root(1) == [1, -1, 0, 0] assert c.highest_root() == [1, 0, 0, -1] assert c.lie_algebra() == "su(4)"
def test_type_A(): c = CartanType("A3") m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2]) assert m == c.cartan_matrix() assert c.basis() == 8 assert c.roots() == 12 assert c.dimension() == 4 assert c.simple_root(1) == [1, -1, 0, 0] assert c.highest_root() == [1, 0, 0, -1] assert c.lie_algebra() == "su(4)" diag = "0---0---0\n1 2 3" assert c.dynkin_diagram() == diag assert c.positive_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]}
def test_type_A(): c = CartanType("A3") m = Matrix(3, 3, [2, -1, 0, -1, 2, -1, 0, -1, 2]) assert m == c.cartan_matrix() assert c.basis() == 8 assert c.roots() == 12 assert c.dimension() == 4 assert c.simple_root(1) == [1, -1, 0, 0] assert c.highest_root() == [1, 0, 0, -1] assert c.lie_algebra() == "su(4)" diag = "0---0---0\n1 2 3" assert c.dynkin_diagram() == diag assert c.positive_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], }