Python CartanType.lie_algebra Examples

Example #1

File: test_type_C.py Project: msgoff/sympy

def test_type_C():
    c = CartanType("C4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -2, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(4) == [0, 0, 0, 2]
    assert c.roots() == 32
    assert c.basis() == 36
    assert c.lie_algebra() == "sp(8)"
    t = CartanType(["C", 3])
    assert t.dimension() == 3
    diag = "0---0---0=<=0\n1   2   3   4"
    assert c.dynkin_diagram() == diag
    assert c.positive_roots() == {
        1: [1, -1, 0, 0],
        2: [1, 1, 0, 0],
        3: [1, 0, -1, 0],
        4: [1, 0, 1, 0],
        5: [1, 0, 0, -1],
        6: [1, 0, 0, 1],
        7: [0, 1, -1, 0],
        8: [0, 1, 1, 0],
        9: [0, 1, 0, -1],
        10: [0, 1, 0, 1],
        11: [0, 0, 1, -1],
        12: [0, 0, 1, 1],
        13: [2, 0, 0, 0],
        14: [0, 2, 0, 0],
        15: [0, 0, 2, 0],
        16: [0, 0, 0, 2],
    }

Example #2

File: test_type_D.py Project: twobitlogic/sympy

def test_type_D():
    c = CartanType("D4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, -1, 0, -1, 2, 0, 0, -1, 0 , 2])
    assert c.cartan_matrix() == m
    assert c.basis() == 6
    assert c.lie_algebra() == "so(8)"
    assert c.roots() == 24
    assert c.simple_root(3) == [0, 0, 1, -1]

Example #3

File: test_type_B.py Project: twobitlogic/sympy

def test_type_B():
    c = CartanType("B3")
    m = Matrix(3, 3, [2, -1, 0, -1, 2, -2, 0, -1, 2])
    assert m == c.cartan_matrix()
    assert c.dimension() == 3
    assert c.roots() == 18
    assert c.simple_root(3) == [0, 0, 1]
    assert c.basis() == 3
    assert c.lie_algebra() == "so(6)"

Example #4

File: test_type_B.py Project: QuaBoo/sympy

def test_type_B():
    c = CartanType("B3")
    m = Matrix(3, 3, [2, -1, 0, -1, 2, -2, 0, -1, 2])
    assert m == c.cartan_matrix()
    assert c.dimension() == 3
    assert c.roots() == 18
    assert c.simple_root(3) == [0, 0, 1]
    assert c.basis() == 3
    assert c.lie_algebra() == "so(6)"

Example #5

File: test_type_D.py Project: cdsousa/sympy

def test_type_D():
    c = CartanType("D4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, -1, 0, -1, 2, 0, 0, -1, 0 , 2])
    assert c.cartan_matrix() == m
    assert c.basis() == 6
    assert c.lie_algebra() == "so(8)"
    assert c.roots() == 24
    assert c.simple_root(3) == [0, 0, 1, -1]
    diag = "    3\n    0\n    |\n    |\n0---0---0\n1   2   4"
    assert diag == c.dynkin_diagram()

Example #6

File: test_type_A.py Project: twobitlogic/sympy

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)"

Example #7

File: test_type_A.py Project: QuaBoo/sympy

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)"

Example #8

File: test_type_C.py Project: twobitlogic/sympy

def test_type_C():
    c = CartanType("C4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -2, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(4) == [0, 0, 0, 2]
    assert c.roots() == 32
    assert c.basis() == 36
    assert c.lie_algebra() == "sp(8)"
    t = CartanType(['C', 3])
    assert t.dimension() == 3

Example #9

File: test_type_D.py Project: A-turing-machine/sympy

def test_type_D():
    c = CartanType("D4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, -1, 0, -1, 2, 0, 0, -1, 0 , 2])
    assert c.cartan_matrix() == m
    assert c.basis() == 6
    assert c.lie_algebra() == "so(8)"
    assert c.roots() == 24
    assert c.simple_root(3) == [0, 0, 1, -1]
    diag = "    3\n    0\n    |\n    |\n0---0---0\n1   2   4"
    assert diag == c.dynkin_diagram()
    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 1, 0, 0],
            3: [1, 0, -1, 0], 4: [1, 0, 1, 0], 5: [1, 0, 0, -1], 6: [1, 0, 0, 1],
            7: [0, 1, -1, 0], 8: [0, 1, 1, 0], 9: [0, 1, 0, -1], 10: [0, 1, 0, 1],
            11: [0, 0, 1, -1], 12: [0, 0, 1, 1]}

Example #10

File: test_type_A.py Project: A-turing-machine/sympy

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]}

Example #11

File: test_type_B.py Project: A-turing-machine/sympy

def test_type_B():
    c = CartanType("B3")
    m = Matrix(3, 3, [2, -1, 0, -1, 2, -2, 0, -1, 2])
    assert m == c.cartan_matrix()
    assert c.dimension() == 3
    assert c.roots() == 18
    assert c.simple_root(3) == [0, 0, 1]
    assert c.basis() == 3
    assert c.lie_algebra() == "so(6)"
    diag = "0---0=>=0\n1   2   3"
    assert c.dynkin_diagram() == diag
    assert c.positive_roots() ==  {1: [1, -1, 0], 2: [1, 1, 0], 3: [1, 0, -1],
            4: [1, 0, 1], 5: [0, 1, -1], 6: [0, 1, 1], 7: [1, 0, 0],
            8: [0, 1, 0], 9: [0, 0, 1]}

Example #12

File: test_type_C.py Project: A-turing-machine/sympy

def test_type_C():
    c = CartanType("C4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -2, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(4) == [0, 0, 0, 2]
    assert c.roots() == 32
    assert c.basis() == 36
    assert c.lie_algebra() == "sp(8)"
    t = CartanType(['C', 3])
    assert t.dimension() == 3
    diag = "0---0---0=<=0\n1   2   3   4"
    assert c.dynkin_diagram() == diag
    assert c.positive_roots() == {1: [1, -1, 0, 0], 2: [1, 1, 0, 0],
            3: [1, 0, -1, 0], 4: [1, 0, 1, 0], 5: [1, 0, 0, -1],
            6: [1, 0, 0, 1], 7: [0, 1, -1, 0], 8: [0, 1, 1, 0],
            9: [0, 1, 0, -1], 10: [0, 1, 0, 1], 11: [0, 0, 1, -1],
            12: [0, 0, 1, 1], 13: [2, 0, 0, 0], 14: [0, 2, 0, 0], 15: [0, 0, 2, 0],
            16: [0, 0, 0, 2]}

Example #13

File: test_type_A.py Project: msgoff/sympy

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],
    }

Example #14

File: test_type_B.py Project: Azatik1000/Massey-Omura-Cryptosystem

def test_type_B():
    c = CartanType("B3")
    m = Matrix(3, 3, [2, -1, 0, -1, 2, -2, 0, -1, 2])
    assert m == c.cartan_matrix()
    assert c.dimension() == 3
    assert c.roots() == 18
    assert c.simple_root(3) == [0, 0, 1]
    assert c.basis() == 3
    assert c.lie_algebra() == "so(6)"
    diag = "0---0=>=0\n1   2   3"
    assert c.dynkin_diagram() == diag
    assert c.positive_roots() == {
        1: [1, -1, 0],
        2: [1, 1, 0],
        3: [1, 0, -1],
        4: [1, 0, 1],
        5: [0, 1, -1],
        6: [0, 1, 1],
        7: [1, 0, 0],
        8: [0, 1, 0],
        9: [0, 0, 1]
    }

Example #15

File: test_type_D.py Project: Azatik1000/Massey-Omura-Cryptosystem

def test_type_D():
    c = CartanType("D4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -1, -1, 0, -1, 2, 0, 0, -1, 0, 2])
    assert c.cartan_matrix() == m
    assert c.basis() == 6
    assert c.lie_algebra() == "so(8)"
    assert c.roots() == 24
    assert c.simple_root(3) == [0, 0, 1, -1]
    diag = "    3\n    0\n    |\n    |\n0---0---0\n1   2   4"
    assert diag == c.dynkin_diagram()
    assert c.positive_roots() == {
        1: [1, -1, 0, 0],
        2: [1, 1, 0, 0],
        3: [1, 0, -1, 0],
        4: [1, 0, 1, 0],
        5: [1, 0, 0, -1],
        6: [1, 0, 0, 1],
        7: [0, 1, -1, 0],
        8: [0, 1, 1, 0],
        9: [0, 1, 0, -1],
        10: [0, 1, 0, 1],
        11: [0, 0, 1, -1],
        12: [0, 0, 1, 1]
    }