def __mul__(self, other):
if isinstance(other, int):
if other < 0:
raise ValueError("can only multiply ordinals and positive integers")
elif other == 0:
return 0
else:
terms = self._multiply_by_integer(other)
return Ordinal(terms.terms)
else:
s_lead_term = self.terms[0]
terms = []
indexes = [getattr(x, "index", -1) for x in s_lead_term]
for o_term in other.terms:
try:
n = hi_lo_bisect_right(indexes, o_term[0].index)
if indexes[n - 1] == o_term[0].index:
new_stack = OrdinalStack.add_stack_powers(s_lead_term[n - 1], o_term[0])
term = s_lead_term[: n - 1] + [new_stack] + o_term[1:]
else:
term = s_lead_term[:n] + o_term
terms.append(term)
except AttributeError:
# no .index attribute so we have an integer
term = self._multiply_by_integer(o_term[0])
terms.extend(term.terms)
return Ordinal(terms)
def __add__(self, other):
if type(other) is int:
if other < 0:
raise ValueError("can only add positive integers to ordinal")
terms = self.terms[:]
if self.is_successor:
terms[-1][0] += other
else:
terms.append([other])
return Ordinal(terms)
else:
s_terms_no_mult = [term[:-1] for term in self.terms]
o_lead_term_no_mult = other.terms[0][:-1]
o_lead_term_mult = other.terms[0][-1]
n = hi_lo_bisect_right(s_terms_no_mult, o_lead_term_no_mult)
if s_terms_no_mult[n - 1] == o_lead_term_no_mult:
s_last_term_mult = self.terms[n - 1][-1]
if type(s_last_term_mult) is int and type(o_lead_term_mult) is int:
s_terms = copy.deepcopy(self.terms[:n])
s_terms[n - 1][-1] += o_lead_term_mult
terms = s_terms + other.terms[1:]
elif a < o_lead_term_mult:
s_terms = copy.deepcopy(self.terms[: n - 1])
terms = s_terms + other.terms
elif a > o_lead_term_mult:
s_terms = copy.deepcopy(self.terms[:n])
terms = s_terms + other.terms[1:]
else:
s_terms = self.terms[:n]
o_terms = other.terms
terms = s_terms + o_terms
return Ordinal(terms)