Coverage for local/lib/python2.7/site-packages/sage/modular/modsym/ghlist.py : 51%

r""" 

List of coset representatives for `\Gamma_H(N)` in `{\rm SL}_2(\ZZ)` 

""" 

########################################################################### 

# Sage: System for Algebra and Geometry Experimentation 

# 

# Copyright (C) 2005 William Stein <wstein@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# This code is distributed in the hope that it will be useful, 

# but WITHOUT ANY WARRANTY; without even the implied warranty of 

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 

# General Public License for more details. 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

########################################################################### 

from __future__ import absolute_import 

from sage.structure.richcmp import richcmp_method, richcmp 

from sage.structure.sage_object import SageObject 

from sage.structure.sage_object import register_unpickle_override 

from . import p1list 

@richcmp_method 

class GHlist(SageObject): 

r""" 

A class representing a list of coset representatives for `\Gamma_H(N)` in 

`{\rm SL}_2(\ZZ)`. 

TESTS:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(18,[13])) 

sage: loads(dumps(L)) == L 

True 

""" 

def __init__(self, group): 

""" 

EXAMPLES:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(8,[7])); L # indirect doctest 

List of coset representatives for Congruence Subgroup Gamma_H(8) with H generated by [7] 

""" 

self.__group = group 

N = group.level() 

v = group._coset_reduction_data()[0] 

N = group.level() 

coset_reps = set([a for a, b, _ in v if b == 1]) 

w = [group._reduce_coset(x*u, x*v) for x in coset_reps for u,v in p1list.P1List(N).list()] 

w = sorted(set(w)) 

self.__list = w 

def __getitem__(self, i): 

""" 

EXAMPLES:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(8, [5])); L[5] # indirect doctest 

(1, 3) 

""" 

return self.__list[i] 

def __richcmp__(self, other, op): 

r""" 

Compare ``self`` to ``other``. 

EXAMPLES:: 

sage: L1 = sage.modular.modsym.ghlist.GHlist(GammaH(18, [11])) 

sage: L2 = sage.modular.modsym.ghlist.GHlist(GammaH(18, [13])) 

sage: L1 > L2 

True 

sage: L1 == QQ 

False 

""" 

if not isinstance(other, GHlist): 

return NotImplemented 

else: 

return richcmp(self.__group, other.__group, op) 

def __len__(self): 

""" 

Return the length of the underlying list (the index of the group). 

EXAMPLES:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(24, [5])); len(L) # indirect doctest 

192 

""" 

return len(self.__list) 

def __repr__(self): 

""" 

String representation of self. 

EXAMPLES:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(11, [3])) 

sage: L.__repr__() 

'List of coset representatives for Congruence Subgroup Gamma_H(11) with H generated by [3]' 

""" 

return "List of coset representatives for %s" % self.__group 

def list(self): 

r""" 

Return a list of vectors representing the cosets. Do not change the 

returned list! 

EXAMPLES:: 

sage: L = sage.modular.modsym.ghlist.GHlist(GammaH(4,[])); L.list() 

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

""" 

return self.__list 

def normalize(self, u, v): 

r""" 

Given a pair `(u,v)` of integers, return the unique pair `(u', v')` 

such that the pair `(u', v')` appears in ``self.list()`` and `(u, v)` 

is equivalent to `(u', v')`. 

This will only make sense if `{\rm gcd}(u, v, N) = 1`; otherwise the 

output will not be an element of self. 

EXAMPLES:: 

sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [17, 19])).normalize(17, 6) 

(1, 6) 

sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [7, 13])).normalize(17, 6) 

(5, 6) 

sage: sage.modular.modsym.ghlist.GHlist(GammaH(24, [5, 23])).normalize(17, 6) 

(7, 18) 

""" 

return self.__group._reduce_coset(u,v) 

class _GHlist_old_pickle(GHlist): 

""" 

This class exists only for dealing with old pickles. 

This needs to handle both old-style class pickles, where there is 

no input to the class on the initial ``__init__`` call, and the 

new class pickles, we need to have ``__setstate__`` handle it. 

""" 

def __init__(self): 

""" 

For unpickling old pickles. 

TESTS:: 

sage: from sage.modular.modsym.ghlist import _GHlist_old_pickle 

sage: L = _GHlist_old_pickle() 

sage: type(L) == GHlist 

True 

""" 

self.__class__ = GHlist 

def __setstate__(self, state): 

""" 

For unpickling new pickles. 

TESTS:: 

sage: from sage.modular.modsym.ghlist import GHlist 

sage: L = GHlist(GammaH(4,[])) 

sage: Lp = loads(dumps(L)) 

sage: L == Lp 

True 

sage: type(Lp) == GHlist 

True 

""" 

# We don't really want this class, but we want to handle new 

# pickles without creating a new class 

self.__class__ = GHlist 

self.__dict__ = state # Default pickling is ``state = self.__dict__`` 

register_unpickle_override('sage.modular.modsym.ghlist', 'GHlist', 

_GHlist_old_pickle)