Private attribute but a pydantic field

Question

I want to make a attribute private but with a pydantic field:

from pydantic import BaseModel, Field, PrivateAttr, validator

class A(BaseModel):
  _a: str = "" # I want a pydantic field for this private value.

  _computed_from_a: str = PrivateAttr(default="")

  @property
  def a(self):
     return self._a

  @a.setter
  def a(self,v):
    self._a = v
    self._computed_from_a = "b" + self._a

# This returns a type Field<...> which crashes...
assert isinstance(A().a, str)

I think I cannot name a field _ with underscore because pydantic does black magic underneath. How can I achieve a private field _a which has defined setters and getters, where the getter computes some other value _computed_from_a.