Different UNIQUE constraint when a column is null

So "null" in sqlite is not a fixed value. If there's a constraint that involves a column that is null, it will always be considered unique.

Is it possible to take null into account too? My table looks like this:

CREATE TABLE test(
  parent INTEGER
  name TEXT
  UNIQUE(name, parent)
....

and I want

  UNIQUE(name, parent)
  UNIQUE(name)  if parent is null