def __init__(self, parent, ideal, element=None):
"""
Returns the ideal class of this fractional ideal.
EXAMPLE::
sage: K.<a> = NumberField(x^2 + 23,'a'); G = K.class_group()
sage: G(K.ideal(13, a + 4))
Fractional ideal class (13, 1/2*a + 17/2)
"""
self.__ideal = ideal
if element is None:
element = map(int, ideal.ideal_class_log(proof=parent._proof_flag))
AbelianGroupElement.__init__(self, parent, element)
def __init__(self, parent, ideal, element=None):
"""
Returns the ideal class of this fractional ideal.
EXAMPLE::
sage: K.<a> = NumberField(x^2 + 23,'a'); G = K.class_group()
sage: G(K.ideal(13, a + 4))
Fractional ideal class (13, 1/2*a + 17/2)
"""
self.__ideal = ideal
if element is None:
element = map(int, ideal.ideal_class_log(proof=parent._proof_flag))
AbelianGroupElement.__init__(self, parent, element)
def __init__(self, parent, exponents, value=None):
"""
Create an element
EXAMPLES::
sage: F = AbelianGroupWithValues([1,-1], [2,4])
sage: a,b = F.gens()
sage: a*b^-1 in F
True
sage: (a*b^-1).value()
-1
"""
self._value = value
AbelianGroupElement.__init__(self, parent, exponents)
def __init__(self, exponents, parent, value=None):
"""
Create an element
EXAMPLES::
sage: F = AbelianGroupWithValues([1,-1], [2,4])
sage: a,b = F.gens()
sage: a*b^-1 in F
True
sage: (a*b^-1).value()
-1
"""
self._value = value
AbelianGroupElement.__init__(self, exponents, parent)
def __init__(self, parent, ideal, element=None):
r"""
Returns the S-ideal class of this fractional ideal.
EXAMPLES::
sage: K.<a> = QuadraticField(-14)
sage: I = K.ideal(2,a)
sage: S = (I,)
sage: CS = K.S_class_group(S)
sage: J = K.ideal(7,a)
sage: G = K.ideal(3,a+1)
sage: CS(I)
Trivial S-ideal class
sage: CS(J)
Trivial S-ideal class
sage: CS(G)
Fractional S-ideal class (3, a + 1)
"""
self.__ideal = ideal
if element is None:
element = ideal.S_ideal_class_log(parent.S())
AbelianGroupElement.__init__(self, parent, element)
def __init__(self, parent, ideal, element=None):
r"""
Returns the S-ideal class of this fractional ideal.
EXAMPLES::
sage: K.<a> = QuadraticField(-14)
sage: I = K.ideal(2,a)
sage: S = (I,)
sage: CS = K.S_class_group(S)
sage: J = K.ideal(7,a)
sage: G = K.ideal(3,a+1)
sage: CS(I)
Trivial S-ideal class
sage: CS(J)
Trivial S-ideal class
sage: CS(G)
Fractional S-ideal class (3, a + 1)
"""
self.__ideal = ideal
if element is None:
element = ideal.S_ideal_class_log(parent.S())
AbelianGroupElement.__init__(self, parent, element)
