Coverage for local/lib/python2.7/site-packages/sage/combinat/root_system/type_G_affine.py : 100%

""" 

Root system data for (untwisted) type G 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/ 

#***************************************************************************** 

from __future__ import print_function 

from __future__ import absolute_import 

from .cartan_type import CartanType_standard_untwisted_affine 

class CartanType(CartanType_standard_untwisted_affine): 

def __init__(self): 

""" 

EXAMPLES:: 

sage: ct = CartanType(['G',2,1]) 

sage: ct 

['G', 2, 1] 

sage: ct._repr_(compact = True) 

'G2~' 

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() 

['G', 2] 

sage: ct.dual() 

['G', 2, 1]^* 

sage: ct.dual().is_untwisted_affine() 

False 

TESTS:: 

sage: TestSuite(ct).run() 

""" 

CartanType_standard_untwisted_affine.__init__(self, "G",2) 

def dynkin_diagram(self): 

""" 

Returns the extended Dynkin diagram for type G. 

EXAMPLES:: 

sage: g = CartanType(['G',2,1]).dynkin_diagram() 

sage: g 

3 

O=<=O---O 

1 2 0 

G2~ 

sage: sorted(g.edges()) 

[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 3)] 

""" 

from .dynkin_diagram import DynkinDiagram_class 

g = DynkinDiagram_class(self) 

g.add_edge(1, 2) 

g.set_edge_label(2,1,3) 

g.add_edge(0, 2) 

return g 

def _latex_dynkin_diagram(self, label=lambda x: x, node=None, node_dist=2, dual=False): 

r""" 

Return a latex representation of the Dynkin diagram. 

EXAMPLES:: 

sage: print(CartanType(['G',2,1])._latex_dynkin_diagram()) 

\draw (2 cm,0) -- (4.0 cm,0); 

\draw (0, 0.15 cm) -- +(2 cm,0); 

\draw (0, -0.15 cm) -- +(2 cm,0); 

\draw (0,0) -- (2 cm,0); 

\draw (0, 0.15 cm) -- +(2 cm,0); 

\draw (0, -0.15 cm) -- +(2 cm,0); 

\draw[shift={(0.8, 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]{$0$}; 

<BLANKLINE> 

""" 

if node is None: 

node = self._latex_draw_node 

ret = "\\draw (%s cm,0) -- (%s cm,0);\n"%(node_dist, node_dist*2.0) 

ret += "\\draw (0, 0.15 cm) -- +(%s cm,0);\n"%node_dist 

ret += "\\draw (0, -0.15 cm) -- +(%s cm,0);\n"%node_dist 

ret += self.classical()._latex_dynkin_diagram(label, node, node_dist, dual) 

ret += node(2*node_dist, 0, label(0)) 

return ret 

def ascii_art(self, label=lambda i: i, node=None): 

""" 

Returns an ascii art representation of the Dynkin diagram 

EXAMPLES:: 

sage: print(CartanType(['G',2,1]).ascii_art(label = lambda x: x+2)) 

3 

O=<=O---O 

3 4 2 

""" 

if node is None: 

node = self._ascii_art_node 

ret = " 3\n{}=<={}---{}".format(node(label(1)), node(label(2)), node(label(0))) 

return ret + "\n{!s:4}{!s:4}{!s:4}".format(label(1), label(2), label(0)) 

def _default_folded_cartan_type(self): 

""" 

Return the default folded Cartan type. 

EXAMPLES:: 

sage: CartanType(['G', 2, 1])._default_folded_cartan_type() 

['G', 2, 1] as a folding of ['D', 4, 1] 

""" 

from sage.combinat.root_system.type_folded import CartanTypeFolded 

return CartanTypeFolded(self, ['D', 4, 1], [[0], [1, 3, 4], [2]])