def _split(rel: Relation, fd: FD) -> tuple:
"""
Splits a relation on a FD according to BCNF.
"""
r1 = rel.closure(fd.determinants)
r2 = rel.relation - (r1 - fd.determinants)
new_r1 = Relation()
new_r1.relation = r1
new_r1.fds = rel.get_fds_copy()
new_r2 = Relation()
new_r2.relation = r2
new_r2.fds = rel.get_fds_copy()
return new_r1, new_r2
def project_dependencies(rel: Relation) -> None:
"""
Update the fds in the relation by projecting them.
"""
new_fds = []
supers = []
for single in rel.relation:
closure = rel.closure({single})
fd = FD(f'{single}->{"".join(closure)}')
if closure == rel.relation:
supers.append(fd)
if not closure.issubset({single}):
new_fds.append(fd)
for s in powerset(rel.relation):
redundant = False
subset = set(s)
for fd in supers:
if subset.issuperset(fd.determinants):
redundant = True
break
if redundant or subset == rel.relation or not subset:
continue
closure = rel.closure(subset)
fd = FD(f'{"".join(subset)}->{"".join(closure)}')
if closure == rel.relation:
supers.append(fd)
if not closure.issubset(subset) and fd not in new_fds:
new_fds.append(fd)
rel.fds = new_fds
