Python CartanType_standard_finite Examples

Example #1

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['E',6])
            sage: ct
            ['E', 6]
            sage: ct._repr_(compact = True)
            'E6'
            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['E', 6, 1]
            sage: ct.dual()
            ['E', 6]

        TESTS:
            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 6 and n <= 8
        CartanType_standard_finite.__init__(self, "E", n)

Example #2

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['A',4])
            sage: ct
            ['A', 4]
            sage: ct._repr_(compact = True)
            'A4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['A', 4, 1]
            sage: ct.dual()
            ['A', 4]

        TESTS::

            sage: TestSuite(ct).run()
        """
        assert n >= 0
        CartanType_standard_finite.__init__(self, "A", n)

Example #3

File: type_A.py Project: Etn40ff/sage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['A',4])
            sage: ct
            ['A', 4]
            sage: ct._repr_(compact = True)
            'A4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['A', 4, 1]
            sage: ct.dual()
            ['A', 4]

        TESTS::

            sage: TestSuite(ct).run()
        """
        assert n >= 0
        CartanType_standard_finite.__init__(self, "A", n)

Example #4

File: type_H.py Project: CETHop/sage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['H',3])
            sage: ct
            ['H', 3]
            sage: ct._repr_(compact = True)
            'H3'
            sage: ct.rank()
            3

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystallographic()
            False
            sage: ct.is_simply_laced()
            False

        TESTS::

            sage: TestSuite(ct).run()
        """
        assert n in [3, 4]
        CartanType_standard_finite.__init__(self, "H", n)

Example #5

    def __init__(self):
        """
        EXAMPLES::
        
            sage: ct = CartanType(['G',2])
            sage: ct
            ['G', 2]
            sage: ct._repr_(compact = True)
            'G2'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.dual()
            ['G', 2]^*
            sage: ct.affine()
            ['G', 2, 1]

        TESTS:
            sage: ct == loads(dumps(ct))
            True
        """
        CartanType_standard_finite.__init__(self, "G", 2)

Example #6

    def __init__(self):
        """
        EXAMPLES::

            sage: ct = CartanType(['G',2])
            sage: ct
            ['G', 2]
            sage: ct._repr_(compact = True)
            'G2'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.dual()
            ['G', 2] relabelled by {1: 2, 2: 1}
            sage: ct.affine()
            ['G', 2, 1]

        TESTS::

            sage: TestSuite(ct).run()
        """
        CartanType_standard_finite.__init__(self, "G", 2)

Example #7

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['I',5])
            sage: ct
            ['I', 5]
            sage: ct._repr_(compact = True)
            'I5'
            sage: ct.rank()
            2
            sage: ct.index_set()
            [1, 2]

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystallographic()
            False
            sage: ct.is_simply_laced()
            False

        TESTS::

            sage: TestSuite(ct).run()
        """
        assert n >= 1
        CartanType_standard_finite.__init__(self, "I", n)

Example #8

File: type_H.py Project: thalespaiva/sagelib

    def __init__(self, n):
        """
        EXAMPLES::
        
            sage: ct = CartanType(['H',3])
            sage: ct
            ['H', 3]
            sage: ct._repr_(compact = True)
            'H3'
            sage: ct.rank()
            3

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            False
            sage: ct.is_simply_laced()
            False

        TESTS:
            sage: ct == loads(dumps(ct))
            True
        """
        assert n in [3, 4]
        CartanType_standard_finite.__init__(self, "H", n)

Example #9

File: type_F.py Project: sageb0t/testsage

    def __init__(self):
        """
        EXAMPLES::

            sage: ct = CartanType(['F',4])
            sage: ct
            ['F', 4]
            sage: ct._repr_(compact = True)
            'F4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.dual()
            ['F', 4]^*
            sage: ct.affine()
            ['F', 4, 1]

        TESTS::

            sage: ct == loads(dumps(ct))
            True
        """
        CartanType_standard_finite.__init__(self, "F", 4)

Example #10

File: type_G.py Project: Babyll/sage

    def __init__(self):
        """
        EXAMPLES::

            sage: ct = CartanType(['G',2])
            sage: ct
            ['G', 2]
            sage: ct._repr_(compact = True)
            'G2'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.dual()
            ['G', 2] relabelled by {1: 2, 2: 1}
            sage: ct.affine()
            ['G', 2, 1]

        TESTS::

            sage: TestSuite(ct).run()
        """
        CartanType_standard_finite.__init__(self, "G", 2)

Example #11

File: type_I.py Project: bgxcpku/sagelib

    def __init__(self, n):
        """
        EXAMPLES::
        
            sage: ct = CartanType(['I',5])
            sage: ct
            ['I', 5]
            sage: ct._repr_(compact = True)
            'I5'
            sage: ct.rank()
            2
            sage: ct.index_set()
            [1, 2]

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            False
            sage: ct.is_simply_laced()
            False

        TESTS::

            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 1
        CartanType_standard_finite.__init__(self, "I", n)

Example #12

File: type_E.py Project: sageb0t/testsage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['E',6])
            sage: ct
            ['E', 6]
            sage: ct._repr_(compact = True)
            'E6'
            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['E', 6, 1]
            sage: ct.dual()
            ['E', 6]

        TESTS:
            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 6 and n <= 8
        CartanType_standard_finite.__init__(self, "E", n)

Example #13

File: type_E.py Project: sagemathinc/smc-sage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['E',6])
            sage: ct
            ['E', 6]
            sage: ct._repr_(compact = True)
            'E6'
            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['E', 6, 1]
            sage: ct.dual()
            ['E', 6]

        TESTS::

            sage: TestSuite(ct).run()
        """
        if n < 6 or n > 8:
            raise ValueError("Invalid Cartan Type for Type E")
        CartanType_standard_finite.__init__(self, "E", n)

Example #14

File: type_D.py Project: chiragsinghal283/sage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['D',4])
            sage: ct
            ['D', 4]
            sage: ct._repr_(compact = True)
            'D4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystallographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.dual()
            ['D', 4]
            sage: ct.affine()
            ['D', 4, 1]

            sage: ct = CartanType(['D',2])
            sage: ct.is_irreducible()
            False
            sage: ct.dual()
            ['D', 2]
            sage: ct.affine()
            Traceback (most recent call last):
            ...
            ValueError: ['D', 2, 1] is not a valid Cartan type


        TESTS::

            sage: TestSuite(ct).run()
        """
        assert n >= 2
        CartanType_standard_finite.__init__(self, "D", n)
        if n >= 3:
            self._add_abstract_superclass(CartanType_simple)

Example #15

File: type_D.py Project: chos9/sage

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['D',4])
            sage: ct
            ['D', 4]
            sage: ct._repr_(compact = True)
            'D4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            True
            sage: ct.dual()
            ['D', 4]
            sage: ct.affine()
            ['D', 4, 1]

            sage: ct = CartanType(['D',2])
            sage: ct.is_irreducible()
            False
            sage: ct.dual()
            ['D', 2]
            sage: ct.affine()
            Traceback (most recent call last):
            ...
            ValueError: ['D', 2, 1] is not a valid cartan type


        TESTS:
            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 2
        CartanType_standard_finite.__init__(self, "D", n)
        if n >= 3:
            self._add_abstract_superclass(CartanType_simple)

Example #16

File: type_B.py Project: bgxcpku/sagelib

    def __init__(self, n):
        """
        EXAMPLES::
        
            sage: ct = CartanType(['B',4])
            sage: ct
            ['B', 4]
            sage: ct._repr_(compact = True)
            'B4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.affine()
            ['B', 4, 1]
            sage: ct.dual()
            ['C', 4]

            sage: ct = CartanType(['B',1])
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['B', 1, 1]

        TESTS::

            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 1
        CartanType_standard_finite.__init__(self, "B", n)
        if n == 1:
            self._add_abstract_superclass(CartanType_simply_laced)

Example #17

    def __init__(self, n):
        """
        EXAMPLES::

            sage: ct = CartanType(['B',4])
            sage: ct
            ['B', 4]
            sage: ct._repr_(compact = True)
            'B4'

            sage: ct.is_irreducible()
            True
            sage: ct.is_finite()
            True
            sage: ct.is_affine()
            False
            sage: ct.is_crystalographic()
            True
            sage: ct.is_simply_laced()
            False
            sage: ct.affine()
            ['B', 4, 1]
            sage: ct.dual()
            ['C', 4]

            sage: ct = CartanType(['B',1])
            sage: ct.is_simply_laced()
            True
            sage: ct.affine()
            ['B', 1, 1]

        TESTS::

            sage: ct == loads(dumps(ct))
            True
        """
        assert n >= 1
        CartanType_standard_finite.__init__(self, "B", n)
        if n == 1:
            self._add_abstract_superclass(CartanType_simply_laced)