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

""" 

Root system data for type I 

""" 

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(['I',5]) 

sage: ct 

['I', 5] 

sage: ct._repr_(compact = True) 

'I5' 

sage: ct.rank() 

2 

sage: ct.index_set() 

(1, 2) 

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 >= 1 

CartanType_standard_finite.__init__(self, "I", n) 

def _latex_(self): 

r""" 

Return a latex representation of ``self``. 

EXAMPLES:: 

sage: latex(CartanType(['I',5])) 

I_2(5) 

""" 

return "I_2({})".format(self.n) 

def rank(self): 

""" 

Type `I_2(p)` is of rank 2. 

EXAMPLES:: 

sage: CartanType(['I', 5]).rank() 

2 

""" 

return 2 

def index_set(self): 

r""" 

Type `I_2(p)` is indexed by `\{1,2\}`. 

EXAMPLES:: 

sage: CartanType(['I', 5]).index_set() 

(1, 2) 

""" 

return (1, 2) 

def coxeter_diagram(self): 

""" 

Returns the Coxeter matrix for this type. 

EXAMPLES:: 

sage: ct = CartanType(['I', 4]) 

sage: ct.coxeter_diagram() 

Graph on 2 vertices 

sage: ct.coxeter_diagram().edges() 

[(1, 2, 4)] 

sage: ct.coxeter_matrix() 

[1 4] 

[4 1] 

""" 

from sage.graphs.graph import Graph 

return Graph([[1,2,self.n]], multiedges=False) 

def coxeter_number(self): 

""" 

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

EXAMPLES:: 

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

3 

sage: CartanType(['I',12]).coxeter_number() 

12 

""" 

return self.n