def quasisymmetrize(cls, word, zeta):
if len(word) == 0:
return Vector({(): 1})
ans = defaultdict(int)
for i in range(1, len(word) + 1):
pre = word[:i]
sub = word[i:]
z = zeta(pre)
if z != 0:
for k, v in cls.quasisymmetrize(sub, zeta).items():
ans[(i,) + k] += z * v
ans = Vector({k: v for k, v in ans.items() if v != 0})
return ans
