Python CartanType.dimension Beispiele

Beispiel #1

Datei: test_type_C.py Projekt: 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],
    }

Beispiel #2

Datei: test_type_C.py Projekt: 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

Beispiel #3

def test_type_G():
    c = CartanType("G2")
    m = Matrix(2, 2, [2, -1, -3, 2])
    assert c.cartan_matrix() == m
    assert c.simple_root(2) == [1, -2, 1]
    assert c.basis() == 14
    assert c.roots() == 12
    assert c.dimension() == 3

Beispiel #4

Datei: test_type_G.py Projekt: QuaBoo/sympy

def test_type_G():
    c = CartanType("G2")
    m = Matrix(2, 2, [2, -1, -3, 2])
    assert c.cartan_matrix() == m
    assert c.simple_root(2) == [1, -2, 1]
    assert c.basis() == 14
    assert c.roots() == 12
    assert c.dimension() == 3

Beispiel #5

Datei: test_type_B.py Projekt: 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)"

Beispiel #6

Datei: test_type_F.py Projekt: QuaBoo/sympy

def test_type_F():
    c = CartanType("F4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(3) == [0, 0, 0, 1]
    assert c.simple_root(4) == [-0.5, -0.5, -0.5, -0.5]
    assert c.roots() == 48
    assert c.basis() == 52

Beispiel #7

Datei: test_type_B.py Projekt: 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)"

Beispiel #8

def test_type_F():
    c = CartanType("F4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(3) == [0, 0, 0, 1]
    assert c.simple_root(4) == [-0.5, -0.5, -0.5, -0.5]
    assert c.roots() == 48
    assert c.basis() == 52

Beispiel #9

Datei: test_type_A.py Projekt: 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)"

Beispiel #10

Datei: test_type_A.py Projekt: 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)"

Beispiel #11

Datei: test_type_C.py Projekt: 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]}

Beispiel #12

Datei: test_type_E.py Projekt: QuaBoo/sympy

def test_type_E():
    c = CartanType("E6")
    m = Matrix(6, 6, [2, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0,
        -1, 0, 2, -1, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0,
        -1, 2, -1, 0, 0, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 8
    assert c.simple_root(6) == [0, 0, 0, -1, 1, 0, 0, 0]
    assert c.roots() == 72
    assert c.basis() == 78

Beispiel #13

Datei: test_type_G.py Projekt: cdsousa/sympy

def test_type_G():
    c = CartanType("G2")
    m = Matrix(2, 2, [2, -1, -3, 2])
    assert c.cartan_matrix() == m
    assert c.simple_root(2) == [1, -2, 1]
    assert c.basis() == 14
    assert c.roots() == 12
    assert c.dimension() == 3
    diag = "0≡<≡0\n1   2"
    assert diag == c.dynkin_diagram()

Beispiel #14

def test_type_E():
    c = CartanType("E6")
    m = Matrix(
        6,
        6,
        [
            2,
            0,
            -1,
            0,
            0,
            0,
            0,
            2,
            0,
            -1,
            0,
            0,
            -1,
            0,
            2,
            -1,
            0,
            0,
            0,
            -1,
            -1,
            2,
            -1,
            0,
            0,
            0,
            0,
            -1,
            2,
            -1,
            0,
            0,
            0,
            0,
            -1,
            2,
        ],
    )
    assert c.cartan_matrix() == m
    assert c.dimension() == 8
    assert c.simple_root(6) == [0, 0, 0, -1, 1, 0, 0, 0]
    assert c.roots() == 72
    assert c.basis() == 78
    diag = " " * 8 + "2\n" + " " * 8 + "0\n" + " " * 8 + "|\n" + " " * 8 + "|\n"
    diag += "---".join("0" for i in range(1, 6)) + "\n"
    diag += "1   " + "   ".join(str(i) for i in range(3, 7))
    assert c.dynkin_diagram() == diag
    posroots = c.positive_roots()
    assert posroots[8] == [1, 0, 0, 0, 1, 0, 0, 0]

Beispiel #15

Datei: test_type_E.py Projekt: twobitlogic/sympy

def test_type_E():
    c = CartanType("E6")
    m = Matrix(6, 6, [
        2, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -1, 0, 2, -1, 0, 0, 0, -1, -1, 2,
        -1, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, -1, 2
    ])
    assert c.cartan_matrix() == m
    assert c.dimension() == 8
    assert c.simple_root(6) == [0, 0, 0, -1, 1, 0, 0, 0]
    assert c.roots() == 72
    assert c.basis() == 78

Beispiel #16

def test_type_G():
    c = CartanType("G2")
    m = Matrix(2, 2, [2, -1, -3, 2])
    assert c.cartan_matrix() == m
    assert c.simple_root(2) == [1, -2, 1]
    assert c.basis() == 14
    assert c.roots() == 12
    assert c.dimension() == 3
    diag = "0≡<≡0\n1   2"
    assert diag == c.dynkin_diagram()
    assert c.positive_roots() == {1: [0, 1, -1], 2: [1, -2, 1], 3: [1, -1, 0],
            4: [1, 0, 1], 5: [1, 1, -2], 6: [2, -1, -1]}

Beispiel #17

Datei: test_type_B.py Projekt: 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]}

Beispiel #18

Datei: test_type_A.py Projekt: 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]}

Beispiel #19

Datei: test_type_E.py Projekt: cdsousa/sympy

def test_type_E():
    c = CartanType("E6")
    m = Matrix(6, 6, [2, 0, -1, 0, 0, 0, 0, 2, 0, -1, 0, 0,
        -1, 0, 2, -1, 0, 0, 0, -1, -1, 2, -1, 0, 0, 0, 0,
        -1, 2, -1, 0, 0, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 8
    assert c.simple_root(6) == [0, 0, 0, -1, 1, 0, 0, 0]
    assert c.roots() == 72
    assert c.basis() == 78
    diag = " "*8 + "2\n" + " "*8 + "0\n" + " "*8 + "|\n" + " "*8 + "|\n"
    diag += "---".join("0" for i in range(1, 6))+"\n"
    diag += "1   " + "   ".join(str(i) for i in range(3, 7))
    assert c.dynkin_diagram() == diag

Beispiel #20

def test_type_F():
    c = CartanType("F4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(1) == [1, -1, 0, 0]
    assert c.simple_root(2) == [0, 1, -1, 0]
    assert c.simple_root(3) == [0, 0, 0, 1]
    assert c.simple_root(4) == [-S(1) / 2, -S(1) / 2, -S(1) / 2, -S(1) / 2]
    assert c.roots() == 48
    assert c.basis() == 52
    diag = "0---0=>=0---0\n" + "   ".join(str(i) for i in range(1, 5))
    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: [1, 0, 0, 0],
        14: [0, 1, 0, 0],
        15: [0, 0, 1, 0],
        16: [0, 0, 0, 1],
        17: [S(1) / 2, S(1) / 2, S(1) / 2,
             S(1) / 2],
        18: [S(1) / 2, S(-1) / 2, S(1) / 2,
             S(1) / 2],
        19: [S(1) / 2, S(1) / 2, S(-1) / 2,
             S(1) / 2],
        20: [S(1) / 2, S(1) / 2, S(1) / 2,
             S(-1) / 2],
        21: [S(1) / 2, S(1) / 2, S(-1) / 2,
             S(-1) / 2],
        22: [S(1) / 2, S(-1) / 2, S(1) / 2,
             S(-1) / 2],
        23: [S(1) / 2, S(-1) / 2, S(-1) / 2,
             S(1) / 2],
        24: [S(1) / 2, S(-1) / 2, S(-1) / 2,
             S(-1) / 2]
    }

Beispiel #21

Datei: test_type_F.py Projekt: abgrilo/sympy

def test_type_F():
    c = CartanType("F4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(3) == [0, 0, 0, 1]
    assert c.simple_root(4) == [-0.5, -0.5, -0.5, -0.5]
    assert c.roots() == 48
    assert c.basis() == 52

    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: [1, 0, 0, 0], 14: [0, 1, 0, 0], 15: [0, 0, 1, 0],
            16: [0, 0, 0, 1], 17: [1/2, 1/2, 1/2, 1/2], 18: [1/2, -1/2, 1/2, 1/2],
            19: [1/2, 1/2, -1/2, 1/2], 20: [1/2, 1/2, 1/2, -1/2], 21: [1/2, 1/2, -1/2, -1/2],
            22: [1/2, -1/2, 1/2, -1/2], 23: [1/2, -1/2, -1/2, 1/2], 24: [1/2, -1/2, -1/2, -1/2]}

Beispiel #22

Datei: test_type_F.py Projekt: A-turing-machine/sympy

def test_type_F():
    c = CartanType("F4")
    m = Matrix(4, 4, [2, -1, 0, 0, -1, 2, -2, 0, 0, -1, 2, -1, 0, 0, -1, 2])
    assert c.cartan_matrix() == m
    assert c.dimension() == 4
    assert c.simple_root(3) == [0, 0, 0, 1]
    assert c.simple_root(4) == [-0.5, -0.5, -0.5, -0.5]
    assert c.roots() == 48
    assert c.basis() == 52
    diag = "0---0=>=0---0\n" + "   ".join(str(i) for i in range(1, 5))
    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: [1, 0, 0, 0], 14: [0, 1, 0, 0], 15: [0, 0, 1, 0],
            16: [0, 0, 0, 1], 17: [1/2, 1/2, 1/2, 1/2], 18: [1/2, -1/2, 1/2, 1/2],
            19: [1/2, 1/2, -1/2, 1/2], 20: [1/2, 1/2, 1/2, -1/2], 21: [1/2, 1/2, -1/2, -1/2],
            22: [1/2, -1/2, 1/2, -1/2], 23: [1/2, -1/2, -1/2, 1/2], 24: [1/2, -1/2, -1/2, -1/2]}

Beispiel #23

Datei: test_type_A.py Projekt: 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],
    }

Beispiel #24

Datei: test_type_B.py Projekt: 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]
    }