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""" Root system data for (untwisted) type C 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(['C',4,1]) sage: ct ['C', 4, 1] sage: ct._repr_(compact = True) 'C4~'
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() ['C', 4] sage: ct.dual() ['C', 4, 1]^* sage: ct.dual().is_untwisted_affine() False
TESTS::
sage: TestSuite(ct).run() """
""" Returns the extended Dynkin diagram for affine type C.
EXAMPLES::
sage: c = CartanType(['C',3,1]).dynkin_diagram() sage: c O=>=O---O=<=O 0 1 2 3 C3~ sage: sorted(c.edges()) [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
"""
r""" Return a latex representation of the Dynkin diagram.
EXAMPLES::
sage: print(CartanType(['C',4,1])._latex_dynkin_diagram()) \draw (0, 0.1 cm) -- +(2 cm,0); \draw (0, -0.1 cm) -- +(2 cm,0); \draw[shift={(1.2, 0)}, rotate=0] (135 : 0.45cm) -- (0,0) -- (-135 : 0.45cm); { \pgftransformxshift{2 cm} \draw (0 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 cm) circle (.25cm) node[below=4pt]{$1$}; \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]{$4$}; } \draw[fill=white] (0 cm, 0 cm) circle (.25cm) node[below=4pt]{$0$};
sage: print(CartanType(['C',4,1]).dual()._latex_dynkin_diagram()) \draw (0, 0.1 cm) -- +(2 cm,0); \draw (0, -0.1 cm) -- +(2 cm,0); \draw[shift={(0.8, 0)}, rotate=180] (135 : 0.45cm) -- (0,0) -- (-135 : 0.45cm); { \pgftransformxshift{2 cm} \draw (0 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 cm) circle (.25cm) node[below=4pt]{$1$}; \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]{$4$}; } \draw[fill=white] (0 cm, 0 cm) circle (.25cm) node[below=4pt]{$0$}; <BLANKLINE> """ from . import cartan_type return cartan_type.CartanType(["A",1,1])._latex_dynkin_diagram(label, node, node_dist)
else:
""" Return a ascii art representation of the extended Dynkin diagram.
EXAMPLES::
sage: print(CartanType(['C',5,1]).ascii_art(label = lambda x: x+2)) O=>=O---O---O---O=<=O 2 3 4 5 6 7
sage: print(CartanType(['C',3,1]).ascii_art()) O=>=O---O=<=O 0 1 2 3
sage: print(CartanType(['C',2,1]).ascii_art()) O=>=O=<=O 0 1 2
sage: print(CartanType(['C',1,1]).ascii_art()) O<=>O 0 1 """
""" Return the default folded Cartan type.
EXAMPLES::
sage: CartanType(['C', 3, 1])._default_folded_cartan_type() ['C', 3, 1] as a folding of ['A', 5, 1] """ return CartanTypeFolded(self, ['A', 1, 1], [[0], [1]]) [[0]] + [[i, 2*n-i] for i in range(1, n)] + [[n]])
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