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

""" 

Root system data for type H 

""" 

from __future__ import absolute_import 

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

# 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 .cartan_type import CartanType_standard_finite, CartanType_simple 

class CartanType(CartanType_standard_finite, CartanType_simple): 

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) 

def _latex_(self): 

r""" 

Return a latex representation of ``self``. 

EXAMPLES:: 

sage: latex(CartanType(['H',3])) 

H_3 

""" 

return "H_{}".format(self.n) 

def coxeter_diagram(self): 

""" 

Returns a Coxeter diagram for type H. 

EXAMPLES:: 

sage: ct = CartanType(['H',3]) 

sage: ct.coxeter_diagram() 

Graph on 3 vertices 

sage: sorted(ct.coxeter_diagram().edges()) 

[(1, 2, 3), (2, 3, 5)] 

sage: ct.coxeter_matrix() 

[1 3 2] 

[3 1 5] 

[2 5 1] 

sage: ct = CartanType(['H',4]) 

sage: ct.coxeter_diagram() 

Graph on 4 vertices 

sage: sorted(ct.coxeter_diagram().edges()) 

[(1, 2, 3), (2, 3, 3), (3, 4, 5)] 

sage: ct.coxeter_matrix() 

[1 3 2 2] 

[3 1 3 2] 

[2 3 1 5] 

[2 2 5 1] 

""" 

from sage.graphs.graph import Graph 

n = self.n 

g = Graph(multiedges=False) 

for i in range(1, n): 

g.add_edge(i, i+1, 3) 

g.set_edge_label(n-1, n, 5) 

return g 

def coxeter_number(self): 

""" 

Return the Coxeter number associated with ``self``. 

EXAMPLES:: 

sage: CartanType(['H',3]).coxeter_number() 

10 

sage: CartanType(['H',4]).coxeter_number() 

30 

""" 

if self.n == 3: 

return 10 

return 30