Coverage for local/lib/python2.7/site-packages/sage/rings/ideal_monoid.py : 61%

""" 

Monoid of ideals in a commutative ring 

""" 

from __future__ import absolute_import 

from sage.structure.parent import Parent 

import sage.rings.integer_ring 

from . import ideal 

from sage.categories.monoids import Monoids 

def IdealMonoid(R): 

r""" 

Return the monoid of ideals in the ring ``R``. 

EXAMPLES:: 

sage: R = QQ['x'] 

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

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

""" 

return IdealMonoid_c(R) 

class IdealMonoid_c(Parent): 

r""" 

The monoid of ideals in a commutative ring. 

TESTS:: 

sage: R = QQ['x'] 

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

sage: TestSuite(M).run() 

Failure in _test_category: 

... 

The following tests failed: _test_elements 

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

""" 

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

def __init__(self, R): 

r""" 

Initialize ``self``. 

TESTS:: 

sage: R = QuadraticField(-23, 'a') 

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

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

""" 

self.__R = R 

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

category=Monoids()) 

self._populate_coercion_lists_() 

def _repr_(self): 

r""" 

Return a string representation of ``self``. 

TESTS:: 

sage: R = QuadraticField(-23, 'a') 

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

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

""" 

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

def ring(self): 

r""" 

Return the ring of which this is the ideal monoid. 

EXAMPLES:: 

sage: R = QuadraticField(-23, 'a') 

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

True 

""" 

return self.__R 

def _element_constructor_(self, x): 

r""" 

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

EXAMPLES:: 

sage: R.<a> = QuadraticField(-23) 

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

sage: M(a) # indirect doctest 

Fractional ideal (a) 

sage: M([a-4, 13]) 

Fractional ideal (13, 1/2*a + 9/2) 

""" 

try: 

side = x.side() 

except (AttributeError, TypeError): 

side = None 

try: 

x = x.gens() 

except AttributeError: 

pass 

if side is None: 

y = self.__R.ideal(x) 

else: 

y = self.__R.ideal(x, side=side) 

y._set_parent(self) 

return y 

def _coerce_map_from_(self, x): 

r""" 

Used by coercion framework. 

EXAMPLES:: 

sage: R = QuadraticField(-23, 'a') 

sage: M = R.ideal_monoid() 

sage: M.has_coerce_map_from(R) # indirect doctest 

True 

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

True 

sage: M.has_coerce_map_from(Zmod(6)) 

False 

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

True 

""" 

if isinstance(x, IdealMonoid_c): 

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

else: 

return self.ring().has_coerce_map_from(x) 

def __eq__(self, other): 

r""" 

Check whether ``self`` is not equal to ``other``. 

EXAMPLES:: 

sage: R = QuadraticField(-23, 'a') 

sage: M = R.ideal_monoid() 

sage: M == QQ 

False 

sage: M == 17 

False 

sage: M == R.ideal_monoid() 

True 

""" 

if not isinstance(other, IdealMonoid_c): 

return False 

else: 

return self.ring() == other.ring() 

def __ne__(self, other): 

r""" 

Check whether ``self`` is not equal to ``other``. 

EXAMPLES:: 

sage: R = QuadraticField(-23, 'a') 

sage: M = R.ideal_monoid() 

sage: M != QQ 

True 

sage: M != 17 

True 

sage: M != R.ideal_monoid() 

False 

""" 

return not (self == other)