def _div_(left, right):
"""
Divide ``left`` by ``right``
TESTS::
sage: G.<a,b> = AbelianGroupWithValues([5,2], 2)
sage: a._div_(b)
a*b^-1
sage: a/b
a*b^-1
sage: (a/b).value()
5/2
"""
m = AbelianGroupElement._div_(left, right)
m._value = left.value() / right.value()
return m
def _div_(left, right):
"""
Divide ``left`` by ``right``
TESTS::
sage: G.<a,b> = AbelianGroupWithValues([5,2], 2)
sage: a._div_(b)
a*b^-1
sage: a/b
a*b^-1
sage: (a/b).value()
5/2
"""
m = AbelianGroupElement._div_(left, right)
m._value = left.value() / right.value()
return m
def _div_(self, other):
r"""
Division of two ideal classes.
EXAMPLES::
sage: G = NumberField(x^2 + 23,'a').class_group(); G
Class group of order 3 with structure C3 of Number Field in a with defining polynomial x^2 + 23
sage: I = G.0; I
Fractional ideal class (2, 1/2*a - 1/2)
sage: I*I # indirect doctest
Fractional ideal class (2, 1/2*a + 1/2)
sage: I*I*I # indirect doctest
Trivial principal fractional ideal class
"""
m = AbelianGroupElement._div_(self, other)
m._value = (self.ideal() / other.ideal()).reduce_equiv()
return m
def _div_(self, other):
r"""
Division of two ideal classes.
EXAMPLE::
sage: G = NumberField(x^2 + 23,'a').class_group(); G
Class group of order 3 with structure C3 of Number Field in a with defining polynomial x^2 + 23
sage: I = G.0; I
Fractional ideal class (2, 1/2*a - 1/2)
sage: I*I # indirect doctest
Fractional ideal class (2, 1/2*a + 1/2)
sage: I*I*I # indirect doctest
Trivial principal fractional ideal class
"""
m = AbelianGroupElement._div_(self, other)
m._value = (self.ideal() / other.ideal()).reduce_equiv()
return m