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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/categories/finite_fields.py
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r"""

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Finite Fields

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"""

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

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#  Copyright (C) 2005      David Kohel <[email protected]>

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#                          William Stein <[email protected]>

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#                2008      Teresa Gomez-Diaz (CNRS) <[email protected]>

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#                2008-2009 Nicolas M. Thiery <nthiery at users.sf.net>

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#

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

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#                  http://www.gnu.org/licenses/

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

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from sage.misc.cachefunc import cached_method

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from sage.categories.category import Category

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from sage.rings.field import is_Field

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class FiniteFields(Category):

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    """

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    The category of finite fields

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    EXAMPLES::

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        sage: K = FiniteFields()

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        sage: K

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        Category of finite fields

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        sage: FiniteField(17) in K

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        True

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        sage: RationalField() in K

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        False

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        sage: K(RationalField())

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        Traceback (most recent call last):

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        ...

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

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    TESTS::

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        sage: TestSuite(FiniteFields()).run()

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    """

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    @cached_method

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    def super_categories(self):

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        """

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        EXAMPLES::

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            sage: FiniteFields().super_categories()

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            [Category of fields, Category of finite enumerated sets]

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        """

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        from sage.categories.all import Fields, FiniteEnumeratedSets

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        return [Fields(), FiniteEnumeratedSets()]

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    def __contains__(self, x):

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        """

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        EXAMPLES::

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            sage: GF(4, "a") in FiniteFields()

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            True

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            sage: QQ in FiniteFields()

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            False

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            sage: IntegerModRing(4) in FiniteFields()

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            False

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        """

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        return is_Field(x) and x.is_finite()

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

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    def _call_(self, x):

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        """

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        EXAMPLES::

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            sage: FiniteFields()(GF(4, "a"))

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            Finite Field in a of size 2^2

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

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            Traceback (most recent call last):

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            ...

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

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        """

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

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        # TODO: local dvr ring?

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    #@lazy_attribute

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    #def element_class(self):

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    #    """

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    #    A common super class for all elements of finite fields

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    #

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    #    EXAMPLES::

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    #

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    #        sage: C = FiniteFields().element_class; C

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    #        <type 'sage.rings.finite_rings.element_base.FiniteFieldElement'>

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    #        sage: type(C)

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    #        <type 'type'>

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    #    """

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    #    from sage.rings.finite_rings.element_base import FiniteFieldElement

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    #    return FiniteFieldElement

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    class ParentMethods:

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        pass

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    class ElementMethods:

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        pass

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