def inverse(self): r""" Return the multiplicative inverse of this ideal class. EXAMPLE:: sage: K.<a> = NumberField(x^3 - 3*x + 8); G = K.class_group() sage: G(2, a).inverse() Fractional ideal class (2, a^2 + 2*a - 1) """ m = AbelianGroupElement.inverse(self) return FractionalIdealClass(self.parent(), (~self.__ideal).reduce_equiv(), m.list())
def inverse(self): r""" Return the multiplicative inverse of this ideal class. EXAMPLE:: sage: K.<a> = NumberField(x^3 - 3*x + 8); G = K.class_group() sage: G(2, a).inverse() Fractional ideal class (2, a^2 + 2*a - 1) """ m = AbelianGroupElement.inverse(self) return FractionalIdealClass(self.parent(), (~self.__ideal).reduce_equiv(), m.list())
def inverse(self): r""" Return the multiplicative inverse of this ideal class. EXAMPLES:: sage: K.<a> = NumberField(x^3 - 3*x + 8); G = K.class_group() sage: G(2, a).inverse() Fractional ideal class (2, a^2 + 2*a - 1) sage: ~G(2, a) Fractional ideal class (2, a^2 + 2*a - 1) """ m = AbelianGroupElement.inverse(self) m._value = (~self.ideal()).reduce_equiv() return m
def inverse(self): r""" Return the multiplicative inverse of this ideal class. EXAMPLE:: sage: K.<a> = NumberField(x^3 - 3*x + 8); G = K.class_group() sage: G(2, a).inverse() Fractional ideal class (2, a^2 + 2*a - 1) sage: ~G(2, a) Fractional ideal class (2, a^2 + 2*a - 1) """ m = AbelianGroupElement.inverse(self) m._value = (~self.ideal()).reduce_equiv() return m
def inverse(self): r""" Finds the inverse of the given S-ideal class. EXAMPLES:: sage: K.<a> = QuadraticField(-14) sage: I = K.ideal(2,a) sage: S = (I,) sage: CS = K.S_class_group(S) sage: G = K.ideal(3,a+1) sage: CS(G).inverse() Fractional S-ideal class (3, a + 2) """ m = AbelianGroupElement.inverse(self) inv_ideal = self.parent().number_field().class_group()(self.ideal()).inverse().ideal() return SFractionalIdealClass(self.parent(), inv_ideal , m.list())
def inverse(self): r""" Finds the inverse of the given S-ideal class. EXAMPLES:: sage: K.<a> = QuadraticField(-14) sage: I = K.ideal(2,a) sage: S = (I,) sage: CS = K.S_class_group(S) sage: G = K.ideal(3,a+1) sage: CS(G).inverse() Fractional S-ideal class (3, a + 2) """ m = AbelianGroupElement.inverse(self) inv_ideal = self.parent().number_field().class_group()( self.ideal()).inverse().ideal() return SFractionalIdealClass(self.parent(), inv_ideal, m.list())
def inverse(self): """ Return the inverse element. EXAMPLE:: sage: G.<a,b> = AbelianGroupWithValues([2,-1], [0,4]) sage: a.inverse() a^-1 sage: a.inverse().value() 1/2 sage: a.__invert__().value() 1/2 sage: (~a).value() 1/2 sage: (a*b).value() -2 sage: (a*b).inverse().value() -1/2 """ m = AbelianGroupElement.inverse(self) m._value = ~self.value() return m
def inverse(self): """ Return the inverse element. EXAMPLE:: sage: G.<a,b> = AbelianGroupWithValues([2,-1], [0,4]) sage: a.inverse() a^-1 sage: a.inverse().value() 1/2 sage: a.__invert__().value() 1/2 sage: (~a).value() 1/2 sage: (a*b).value() -2 sage: (a*b).inverse().value() -1/2 """ m = AbelianGroupElement.inverse(self) m._value = ~self.value() return m