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""" Root system data for (untwisted) type F affine """ #***************************************************************************** # Copyright (C) 2008-2009 Daniel Bump # Copyright (C) 2008-2009 Justin Walker # 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(['F',4,1]) sage: ct ['F', 4, 1] sage: ct._repr_(compact = True) 'F4~'
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() ['F', 4] sage: ct.dual() ['F', 4, 1]^* sage: ct.dual().is_untwisted_affine() False
TESTS::
sage: TestSuite(ct).run() """
""" Returns the extended Dynkin diagram for affine type F.
EXAMPLES::
sage: f = CartanType(['F', 4, 1]).dynkin_diagram() sage: f O---O---O=>=O---O 0 1 2 3 4 F4~ sage: sorted(f.edges()) [(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]
"""
r""" Return a latex representation of the Dynkin diagram.
EXAMPLES::
sage: print(CartanType(['F',4,1])._latex_dynkin_diagram()) \draw (0 cm,0) -- (2 cm,0); { \pgftransformxshift{2 cm} \draw (0 cm,0) -- (2 cm,0); \draw (2 cm, 0.1 cm) -- +(2 cm,0); \draw (2 cm, -0.1 cm) -- +(2 cm,0); \draw (4.0 cm,0) -- +(2 cm,0); \draw[shift={(3.2, 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> """
""" Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES::
sage: print(CartanType(['F',4,1]).ascii_art(label = lambda x: x+2)) O---O---O=>=O---O 2 3 4 5 6 """ node(label(2)), node(label(3)), node(label(4)))
""" Return the default folded Cartan type.
EXAMPLES::
sage: CartanType(['F', 4, 1])._default_folded_cartan_type() ['F', 4, 1] as a folding of ['E', 6, 1] """
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