def __rpow__(self, other):
if other == 1 or other == 0:
return other
elif isinstance(other, int) and other < 0:
raise ValueError("Cannot raise negative integer to Ordinal power")
else:
ordinals = []
for term in self.terms:
if len(term) > 1:
a = Ordinal([term])
b = self._raise_lower_index_to_single_term_power()
else:
a = term[0]
b = other ** a
ordinals.append(b)
return product(ordinals)
def __pow__(self, other):
if isinstance(other, int):
if other > 0:
return self._raise_to_integer_power(other)
elif other == 0:
return 1
else:
raise ValueError("Cannot raise Ordinal to negative integer power")
else:
ordinals = []
for term in other.terms:
if len(term) > 1:
a = Ordinal([term])
b = self._raise_ordinal_to_single_term_power(a)
else:
a = term[0]
b = self._raise_to_integer_power(a)
ordinals.append(b)
return product(ordinals)
def _raise_to_integer_power(self, n):
# naive approach: repeated multiplication (this
# does not scale well).
# TODO: find a formula for finite powers of ordinals.
return product(self for _ in range(n))
