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r""" 

Modular abelian varieties 

""" 

from __future__ import absolute_import 

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

# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> 

# William Stein <wstein@math.ucsd.edu> 

# 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 .category_types import Category_over_base 

from .category_with_axiom import CategoryWithAxiom 

from .homsets import HomsetsCategory 

from .rings import Rings 

from .sets_cat import Sets 

 

class ModularAbelianVarieties(Category_over_base): 

""" 

The category of modular abelian varieties over a given field. 

 

EXAMPLES:: 

 

sage: ModularAbelianVarieties(QQ) 

Category of modular abelian varieties over Rational Field 

""" 

def __init__(self, Y): 

""" 

TESTS:: 

 

sage: C = ModularAbelianVarieties(QQ) 

sage: C 

Category of modular abelian varieties over Rational Field 

sage: TestSuite(C).run() 

 

sage: ModularAbelianVarieties(ZZ) 

Traceback (most recent call last): 

... 

assert Y.is_field() 

AssertionError 

""" 

assert Y.is_field() 

Category_over_base.__init__(self, Y) 

 

def base_field(self): 

""" 

EXAMPLES:: 

 

sage: ModularAbelianVarieties(QQ).base_field() 

Rational Field 

""" 

return self.base() 

 

def super_categories(self): 

""" 

EXAMPLES:: 

 

sage: ModularAbelianVarieties(QQ).super_categories() 

[Category of sets] 

""" 

return [Sets()] # FIXME 

 

class Homsets(HomsetsCategory): 

 

class Endset(CategoryWithAxiom): 

def extra_super_categories(self): 

""" 

Implement the fact that an endset of modular abelian variety is a ring. 

 

EXAMPLES:: 

 

sage: ModularAbelianVarieties(QQ).Endsets().extra_super_categories() 

[Category of rings] 

""" 

return [Rings()]