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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/rings/ideal_monoid.py
4079 views
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"""

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Monoid of ideals in a commutative ring

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"""

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from commutative_ring import is_CommutativeRing

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#from sage.structure.parent_base import ParentWithBase

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from sage.structure.parent import Parent

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import sage.rings.integer_ring

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import ideal

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from sage.categories.monoids import Monoids

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def IdealMonoid(R):

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    r"""

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    Return the monoid of ideals in the ring R.

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    EXAMPLE::

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        sage: R = QQ['x']

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        sage: sage.rings.ideal_monoid.IdealMonoid(R)

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        Monoid of ideals of Univariate Polynomial Ring in x over Rational Field

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    """

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    return IdealMonoid_c(R)

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class IdealMonoid_c(Parent):

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    r"""

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    The monoid of ideals in a commutative ring.

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    TESTS::

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        sage: R = QQ['x']

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        sage: M = sage.rings.ideal_monoid.IdealMonoid(R)

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        sage: TestSuite(M).run()

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          Failure in _test_category: 

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        ...

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        The following tests failed: _test_elements

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    (The "_test_category" test fails but I haven't the foggiest idea why.)

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    """

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    Element = ideal.Ideal_generic # this doesn't seem to do anything

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    def __init__(self, R):

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        r"""

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        TESTS::

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            sage: R = QuadraticField(-23, 'a')

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            sage: M = sage.rings.ideal_monoid.IdealMonoid(R); M # indirect doctest

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            Monoid of ideals of Number Field in a with defining polynomial x^2 + 23

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        """

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        self.__R = R

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        Parent.__init__(self, base = sage.rings.integer_ring.ZZ, category = Monoids())

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        self._populate_coercion_lists_()

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    def _repr_(self):

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        r"""

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        TESTS::

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            sage: R = QuadraticField(-23, 'a')

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            sage: M = sage.rings.ideal_monoid.IdealMonoid(R); M._repr_()

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            'Monoid of ideals of Number Field in a with defining polynomial x^2 + 23'

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        """

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        return "Monoid of ideals of %s"%self.__R

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    def ring(self):

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        r"""

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        Return the ring of which this is the ideal monoid.

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        EXAMPLE::

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            sage: R = QuadraticField(-23, 'a')

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            sage: M = sage.rings.ideal_monoid.IdealMonoid(R); M.ring() is R

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            True

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        """

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        return self.__R

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    def _element_constructor_(self, x):

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        r"""

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        Create an ideal in this monoid from ``x``.

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        EXAMPLES::

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            sage: R.<a> = QuadraticField(-23)

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            sage: M = sage.rings.ideal_monoid.IdealMonoid(R)

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            sage: M(a)   # indirect doctest

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            Fractional ideal (a)

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            sage: M([a-4, 13])

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            Fractional ideal (13, 1/2*a + 9/2)

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        """

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        try:

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            side = x.side()

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        except (AttributeError,TypeError):

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            side = None

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        try:

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            x = x.gens()

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        except AttributeError:

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            pass

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        if side is None:

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            y = self.__R.ideal(x)

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        else:

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            y = self.__R.ideal(x,side=side)

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        y._set_parent(self)

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        return y

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    def _coerce_map_from_(self, x):

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        r"""

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        Used by coercion framework.

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        EXAMPLE::

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            sage: R = QuadraticField(-23, 'a')

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            sage: M = R.ideal_monoid()

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            sage: M.has_coerce_map_from(R)

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            True

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            sage: M.has_coerce_map_from(QQ.ideal_monoid())

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            True

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            sage: M.has_coerce_map_from(Zmod(6))

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            False

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            sage: M.has_coerce_map_from(loads(dumps(M)))

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            True

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        """

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        if isinstance(x, IdealMonoid_c):

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            return self.ring().has_coerce_map_from(x.ring())

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        else:

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            return self.ring().has_coerce_map_from(x)

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    def __cmp__(self, other):

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        r"""

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        Comparison function.

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        EXAMPLE::

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            sage: R = QuadraticField(-23, 'a')

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            sage: M = R.ideal_monoid()

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            sage: M == QQ

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            False

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            sage: M == 17

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            False

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            sage: M == R.ideal_monoid()

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            True

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        """

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        if not isinstance(other, IdealMonoid_c):

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            return cmp(type(self), type(other))

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        else:

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            return cmp(self.ring(), other.ring())

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