def __pow__(self, n):
r"""
Raise this element to the power n.
EXAMPLES::
sage: K.<a> = NumberField(x^3 - 3*x + 8)
sage: C=K.class_group()
sage: c = C(2, a)
sage: c^2
Fractional ideal class (4, a)
sage: c^3
Trivial principal fractional ideal class
sage: c^1000
Fractional ideal class (2, a)
sage: (c^2)^2
Fractional ideal class (2, a)
"""
# We use MonoidElement's __pow__ routine, since that does
# repeated squaring, and hence the ideal gets reduced as
# we go along; actually computing self._value ** n would
# be disastrous.
n = n % self.order()
return MonoidElement.__pow__(self, n)
def __pow__(self, n):
r"""
Raise this element to the power n.
EXAMPLE::
sage: K.<a> = NumberField(x^3 - 3*x + 8)
sage: C=K.class_group()
sage: c = C(2, a)
sage: c^2
Fractional ideal class (2, a^2 + 2*a - 1)
sage: c^3
Trivial principal fractional ideal class
sage: c^1000
Fractional ideal class (2, a)
sage: (c^2)^2
Fractional ideal class (2, a)
"""
# We use MonoidElement's __pow__ routine, since that does
# repeated squaring, and hence the ideal gets reduced as
# we go along; actually computing self._value ** n would
# be disastrous.
n = n % self.order()
return MonoidElement.__pow__(self, n)
