def req_lists_to_insert(self, tiling: Tiling) -> Iterator[ListRequirement]:
active = tiling.active_cells
bdict = tiling.cell_basis()
for cell, length in product(active, range(1, self.maxreqlen + 1)):
basis = bdict[cell][0] + self.extra_basis
yield from ((GriddedPerm.single_cell(patt, cell), )
for patt in Av(basis).of_length(length)
if not any(patt in perm for perm in bdict[cell][1]))
def req_lists_to_insert(self, tiling: Tiling) -> Iterator[ListRequirement]:
bdict = tiling.cell_basis()
cell_with_req = ((cell, obs, reqlist[0])
for cell, (obs, reqlist) in bdict.items()
if len(reqlist) == 1)
for cell, obs, curr_req in cell_with_req:
for length in range(len(curr_req) + 1, self.maxreqlen + 1):
for patt in Av(obs + self.extra_basis).of_length(length):
if curr_req in patt:
yield (GriddedPerm.single_cell(patt, cell), )
def decomposition_function(
self, comb_class: Tiling) -> Optional[Tuple[Tiling, ...]]:
"""
The rule as the root as children if one of the cell of the tiling is the root.
"""
if self.verified(comb_class):
if not self.basis:
return ()
for obs, _ in comb_class.cell_basis().values():
if frozenset(obs) in self.symmetries:
return (Tiling.from_perms(self.basis), )
return ()
return None
def pack(comb_class: Tiling) -> StrategyPack:
if any(isinstance(ass, ComponentAssumption) for ass in comb_class.assumptions):
raise InvalidOperationError(
"Can't find generating function with component assumption."
)
# pylint: disable=import-outside-toplevel
from tilings.tilescope import TileScopePack
assert comb_class.dimensions == (1, 1)
basis, _ = comb_class.cell_basis()[(0, 0)]
if any(
any(p.contains(patt) for patt in basis)
for p in [
Perm((0, 2, 1)),
Perm((1, 2, 0)),
Perm((1, 0, 2)),
Perm((2, 0, 1)),
]
):
# subclass of Av(231) or a symmetry, use point placements!
return TileScopePack.point_and_row_and_col_placements().add_verification(
BasicVerificationStrategy(), replace=True
)
if is_insertion_encodable_maximum(basis):
return TileScopePack.regular_insertion_encoding(3)
if is_insertion_encodable_rightmost(basis):
return TileScopePack.regular_insertion_encoding(2)
# if it is the class or positive class
if not comb_class.requirements or (
len(comb_class.requirements) == 1
and len(comb_class.requirements[0]) == 1
and len(comb_class.requirements[0][0]) <= 2
):
if basis in ([Perm((0, 1, 2))], [Perm((2, 1, 0))]):
# Av(123) or Av(321) - use fusion!
return (
TileScopePack.row_and_col_placements(row_only=True)
.make_fusion(tracked=True)
.add_basis(basis)
)
if (Perm((0, 1, 2)) in basis or Perm((2, 1, 0)) in basis) and all(
len(p) <= 4 for p in basis
):
# is a subclass of Av(123) avoiding patterns of length <= 4
# experimentally showed that such clsses always terminates
return TileScopePack.row_and_col_placements().add_basis(basis)
raise InvalidOperationError(
"Cannot get a specification for one by one verification for "
f"subclass Av({basis})"
)
def req_lists_to_insert(self, tiling: Tiling) -> Iterator[ListRequirement]:
if self.one_cell_only:
assert self.maxreqlen == 1 and self.ignore_parent
cells = sorted(
frozenset(tiling.active_cells) - frozenset(tiling.positive_cells)
)
if cells:
yield (GriddedPerm.single_cell((0,), cells[0]),)
return
active = tiling.active_cells
bdict = tiling.cell_basis()
for cell, length in product(active, range(1, self.maxreqlen + 1)):
basis = bdict[cell][0] + self.extra_basis
patterns = Av(basis).of_length(length) if basis else Perm.of_length(length)
yield from (
(GriddedPerm.single_cell(patt, cell),)
for patt in patterns
if not any(patt in perm for perm in bdict[cell][1])
)
def has_topmost_insertion_encoding(tiling: Tiling) -> bool:
return tiling.dimensions[1] == 1 and all(
is_insertion_encodable_maximum(basis)
for basis, _ in tiling.cell_basis().values()
)
def has_rightmost_insertion_encoding(tiling: Tiling) -> bool:
return tiling.dimensions[0] == 1 and all(
is_insertion_encodable_rightmost(basis)
for basis, _ in tiling.cell_basis().values()
)
def verified(self, comb_class: Tiling) -> bool:
cell_bases = (frozenset(obs) for obs, _ in comb_class.cell_basis().values())
return not bool(self.symmetries.intersection(cell_bases))
