Coverage for local/lib/python2.7/site-packages/sage/categories/finite_fields.py : 29%

r""" 

Finite Fields 

""" 

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

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

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

# 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> 

# 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 sage.categories.category_with_axiom import CategoryWithAxiom 

from sage.categories.enumerated_sets import EnumeratedSets 

class FiniteFields(CategoryWithAxiom): 

""" 

The category of finite fields. 

EXAMPLES:: 

sage: K = FiniteFields(); K 

Category of finite enumerated fields 

A finite field is a finite monoid with the structure of a field; 

it is currently assumed to be enumerated:: 

sage: K.super_categories() 

[Category of fields, 

Category of finite commutative rings, 

Category of finite enumerated sets] 

Some examples of membership testing and coercion:: 

sage: FiniteField(17) in K 

True 

sage: RationalField() in K 

False 

sage: K(RationalField()) 

Traceback (most recent call last): 

... 

TypeError: unable to canonically associate a finite field to Rational Field 

TESTS:: 

sage: K is Fields().Finite() 

True 

sage: TestSuite(K).run() 

""" 

def extra_super_categories(self): 

r""" 

Any finite field is assumed to be endowed with an enumeration. 

TESTS:: 

sage: Fields().Finite().extra_super_categories() 

[Category of finite enumerated sets] 

sage: FiniteFields().is_subcategory(FiniteEnumeratedSets()) 

True 

""" 

return [EnumeratedSets().Finite()] 

def __contains__(self, x): 

""" 

EXAMPLES:: 

sage: GF(4, "a") in FiniteFields() 

True 

sage: QQ in FiniteFields() 

False 

sage: IntegerModRing(4) in FiniteFields() 

False 

""" 

from sage.categories.fields import Fields 

return x in Fields() and x.is_finite() 

# As is, this does no more than the usual __call__ of Category, but for the error message 

def _call_(self, x): 

""" 

EXAMPLES:: 

sage: FiniteFields()(GF(4, "a")) 

Finite Field in a of size 2^2 

sage: FiniteFields()(RationalField()) # indirect doctest 

Traceback (most recent call last): 

... 

TypeError: unable to canonically associate a finite field to Rational Field 

""" 

raise TypeError("unable to canonically associate a finite field to %s"%x) 

# TODO: local dvr ring? 

class ParentMethods: 

pass 

class ElementMethods: 

pass