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)