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""" Root system data for (untwisted) type B affine """ #***************************************************************************** # Copyright (C) 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>, # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #*****************************************************************************
""" EXAMPLES::
sage: ct = CartanType(['B',4,1]) sage: ct ['B', 4, 1] sage: ct._repr_(compact = True) 'B4~'
sage: ct.is_irreducible() True sage: ct.is_finite() False sage: ct.is_affine() True sage: ct.is_untwisted_affine() True sage: ct.is_crystallographic() True sage: ct.is_simply_laced() False sage: ct.classical() ['B', 4] sage: ct.dual() ['B', 4, 1]^* sage: ct.dual().is_untwisted_affine() False
TESTS::
sage: TestSuite(ct).run() """
""" Return the extended Dynkin diagram for affine type `B`.
EXAMPLES::
sage: b = CartanType(['B',3,1]).dynkin_diagram() sage: b O 0 | | O---O=>=O 1 2 3 B3~ sage: sorted(b.edges()) [(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',2,1]).dynkin_diagram(); b O=>=O=<=O 0 2 1 B2~ sage: sorted(b.edges()) [(0, 2, 2), (1, 2, 2), (2, 0, 1), (2, 1, 1)]
sage: b = CartanType(['B',1,1]).dynkin_diagram(); b O<=>O 0 1 B1~ sage: sorted(b.edges()) [(0, 1, 2), (1, 0, 2)]
"""
r""" Return a latex representation of the Dynkin diagram.
EXAMPLES::
sage: print(CartanType(['B',4,1])._latex_dynkin_diagram()) \draw (0,0.7 cm) -- (2 cm,0); \draw (0,-0.7 cm) -- (2 cm,0); \draw (2 cm,0) -- (4 cm,0); \draw (4 cm, 0.1 cm) -- +(2 cm,0); \draw (4 cm, -0.1 cm) -- +(2 cm,0); \draw[shift={(5.2, 0)}, rotate=0] (135 : 0.45cm) -- (0,0) -- (-135 : 0.45cm); \draw[fill=white] (0 cm, 0.7 cm) circle (.25cm) node[left=3pt]{$0$}; \draw[fill=white] (0 cm, -0.7 cm) circle (.25cm) node[left=3pt]{$1$}; \draw[fill=white] (2 cm, 0 cm) circle (.25cm) node[below=4pt]{$2$}; \draw[fill=white] (4 cm, 0 cm) circle (.25cm) node[below=4pt]{$3$}; \draw[fill=white] (6 cm, 0 cm) circle (.25cm) node[below=4pt]{$4$}; <BLANKLINE>
sage: print(CartanType(['B',4,1]).dual()._latex_dynkin_diagram()) \draw (0,0.7 cm) -- (2 cm,0); \draw (0,-0.7 cm) -- (2 cm,0); \draw (2 cm,0) -- (4 cm,0); \draw (4 cm, 0.1 cm) -- +(2 cm,0); \draw (4 cm, -0.1 cm) -- +(2 cm,0); \draw[shift={(4.8, 0)}, rotate=180] (135 : 0.45cm) -- (0,0) -- (-135 : 0.45cm); \draw[fill=white] (0 cm, 0.7 cm) circle (.25cm) node[left=3pt]{$0$}; \draw[fill=white] (0 cm, -0.7 cm) circle (.25cm) node[left=3pt]{$1$}; \draw[fill=white] (2 cm, 0 cm) circle (.25cm) node[below=4pt]{$2$}; \draw[fill=white] (4 cm, 0 cm) circle (.25cm) node[below=4pt]{$3$}; \draw[fill=white] (6 cm, 0 cm) circle (.25cm) node[below=4pt]{$4$}; <BLANKLINE> """ from . import cartan_type return cartan_type.CartanType(["A",1,1])._latex_dynkin_diagram(label, node, node_dist) from . import cartan_type return cartan_type.CartanType(["C",2,1])._latex_dynkin_diagram(label, node, node_dist, dual) else:
""" Return an ascii art representation of the extended Dynkin diagram.
EXAMPLES::
sage: print(CartanType(['B',3,1]).ascii_art()) O 0 | | O---O=>=O 1 2 3
sage: print(CartanType(['B',5,1]).ascii_art(label = lambda x: x+2)) O 2 | | O---O---O---O=>=O 3 4 5 6 7
sage: print(CartanType(['B',2,1]).ascii_art(label = lambda x: x+2)) O=>=O=<=O 2 4 3 sage: print(CartanType(['B',1,1]).ascii_art(label = lambda x: x+2)) O<=>O 2 3 """
""" Return the default folded Cartan type.
EXAMPLES::
sage: CartanType(['B', 4, 1])._default_folded_cartan_type() ['B', 4, 1] as a folding of ['D', 5, 1] """ return CartanTypeFolded(self, ['A', 1, 1], [[0], [1]]) [[i] for i in range(n)] + [[n, n+1]])
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