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- from sympy.liealgebras.weyl_group import WeylGroup
- from sympy.matrices import Matrix
- def test_weyl_group():
- c = WeylGroup("A3")
- assert c.matrix_form('r1*r2') == Matrix([[0, 0, 1, 0], [1, 0, 0, 0],
- [0, 1, 0, 0], [0, 0, 0, 1]])
- assert c.generators() == ['r1', 'r2', 'r3']
- assert c.group_order() == 24.0
- assert c.group_name() == "S4: the symmetric group acting on 4 elements."
- assert c.coxeter_diagram() == "0---0---0\n1 2 3"
- assert c.element_order('r1*r2*r3') == 4
- assert c.element_order('r1*r3*r2*r3') == 3
- d = WeylGroup("B5")
- assert d.group_order() == 3840
- assert d.element_order('r1*r2*r4*r5') == 12
- assert d.matrix_form('r2*r3') == Matrix([[0, 0, 1, 0, 0], [1, 0, 0, 0, 0],
- [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]])
- assert d.element_order('r1*r2*r1*r3*r5') == 6
- e = WeylGroup("D5")
- assert e.element_order('r2*r3*r5') == 4
- assert e.matrix_form('r2*r3*r5') == Matrix([[1, 0, 0, 0, 0], [0, 0, 0, 0, -1],
- [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 0]])
- f = WeylGroup("G2")
- assert f.element_order('r1*r2*r1*r2') == 3
- assert f.element_order('r2*r1*r1*r2') == 1
- assert f.matrix_form('r1*r2*r1*r2') == Matrix([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
- g = WeylGroup("F4")
- assert g.matrix_form('r2*r3') == Matrix([[1, 0, 0, 0], [0, 1, 0, 0],
- [0, 0, 0, -1], [0, 0, 1, 0]])
- assert g.element_order('r2*r3') == 4
- h = WeylGroup("E6")
- assert h.group_order() == 51840
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