def __call__(self, comb_class: Tiling) -> Iterator[Rule]:
if comb_class.dimensions[0] > 1 and comb_class.dimensions[1] == 1:
sliding = Sliding(comb_class)
for pair in sliding.slidable_pairs():
child = (sliding.slide_column(*pair), )
yield SlidingStrategy(*pair, _NO_SYMMETRY)(comb_class, child)
if self.use_symmetries:
yield from SlidingFactory._symmetries(comb_class)
def forward_map(
self,
comb_class: Tiling,
obj: GriddedPerm,
children: Optional[Tuple[Tiling, ...]] = None,
) -> Tuple[GriddedPerm]:
maps = _AdditionalMaps.enum_to_map(self.symmetry_type,
max(comb_class.dimensions))
if self.av_123 < self.av_12:
return (maps.g_inv(
Sliding.slide_gp(maps.g_map(obj), self.av_123, self.av_12)), )
return (maps.g_inv(
Sliding.slide_gp_inverse(maps.g_map(obj), self.av_12,
self.av_123)), )
def backward_map(
self,
comb_class: Tiling,
objs: Tuple[Optional[GriddedPerm], ...],
children: Optional[Tuple[Tiling, ...]] = None,
) -> Iterator[GriddedPerm]:
maps = _AdditionalMaps.enum_to_map(self.symmetry_type,
max(comb_class.dimensions))
if self.av_12 < self.av_123:
yield from (maps.g_inv(
Sliding.slide_gp(maps.g_map(gp), self.av_12, self.av_123))
for gp in objs if gp is not None)
else:
yield from (maps.g_inv(
Sliding.slide_gp_inverse(maps.g_map(gp), self.av_123,
self.av_12)) for gp in objs
if gp is not None)
def extra_parameters(
self,
comb_class: Tiling,
children: Optional[Tuple[Tiling, ...]] = None
) -> Tuple[Dict[str, str], ...]:
if not comb_class.extra_parameters:
return super().extra_parameters(comb_class, children)
if children is None:
children = self.decomposition_function(comb_class)
child = children[0]
maps = _AdditionalMaps.enum_to_map(self.symmetry_type,
max(comb_class.dimensions))
return ({
comb_class.get_assumption_parameter(ass):
child.get_assumption_parameter(
Sliding.slide_assumption(ass, self.av_12, self.av_123,
maps.g_map, maps.g_inv))
for ass in comb_class.assumptions
}, )
def _symmetries(comb_class: Tiling) -> Iterator[Rule]:
c, r = comb_class.dimensions
if r == 1 and c > 1:
tiling = comb_class.reverse()
sliding = Sliding(tiling)
for pair in sliding.slidable_pairs():
maps = _AdditionalMaps.enum_to_map(_REVERSE, c)
child = (maps.t_inv(sliding.slide_column(*pair)), )
yield SlidingStrategy(*pair, _REVERSE)(comb_class, child)
elif r > 1 and c == 1:
tiling = comb_class.rotate90()
sliding = Sliding(tiling)
for pair in sliding.slidable_pairs():
maps = _AdditionalMaps.enum_to_map(_ROTATE, r)
child = (maps.t_inv(sliding.slide_column(*pair)), )
yield SlidingStrategy(*pair, _ROTATE)(comb_class, child)
tiling = tiling.reverse()
sliding = Sliding(tiling)
for pair in sliding.slidable_pairs():
maps = _AdditionalMaps.enum_to_map(_ROTATE_AND_REVERSE, r)
child = (maps.t_inv(sliding.slide_column(*pair)), )
yield SlidingStrategy(*pair, _ROTATE_AND_REVERSE)(comb_class,
child)
def decomposition_function(self, comb_class: Tiling) -> Tuple[Tiling]:
"""Return the slidded tiling if it slides, otherwise None."""
maps = _AdditionalMaps.enum_to_map(self.symmetry_type,
max(comb_class.dimensions))
sliding = Sliding(maps.t_map(comb_class))
return (maps.t_inv(sliding.slide_column(self.av_12, self.av_123)), )
def generate_all_slided_tilings(tiling):
sliding = Sliding(tiling)
for av_12, av_123 in sliding.slidable_pairs():
yield sliding.slide_column(av_12, av_123)
def test_slide():
tcases = [
(
Tiling(
obstructions=(
GriddedPerm((0, 1), ((2, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (0, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (1, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (1, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((1, 0), (1, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((1, 0), (1, 0), (2, 0))),
),
requirements=(),
assumptions=(),
),
Tiling(
obstructions=(
GriddedPerm((0, 1), ((1, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (0, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (1, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (2, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((1, 0), (2, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((2, 0), (2, 0), (2, 0))),
),
requirements=(),
assumptions=(),
),
(1, 2),
7,
),
(
Tiling(
obstructions=(
GriddedPerm((0, 1, 2, 3, 4), ((1, 0),) * 5),
GriddedPerm((0, 1), ((3, 0), (3, 0))),
GriddedPerm((0, 1, 2, 3, 4), ((1, 0),) * 4 + ((3, 0),)),
GriddedPerm((4, 3, 2, 1), ((0, 0),) * 4),
GriddedPerm((2, 3, 1, 0), ((2, 0),) * 4),
GriddedPerm((0, 2, 1), ((4, 0),) * 3),
GriddedPerm((1, 2, 0), ((1, 0), (2, 0), (4, 0))),
GriddedPerm((2, 1, 0), ((2, 0), (3, 0), (4, 0))),
GriddedPerm(
(4, 1, 2, 3, 0), ((0, 0), (0, 0), (1, 0), (1, 0), (4, 0))
),
GriddedPerm(
(4, 1, 2, 3, 0), ((0, 0), (0, 0), (1, 0), (3, 0), (4, 0))
),
)
),
Tiling(
obstructions=(
GriddedPerm((0, 1, 2, 3, 4), ((3, 0),) * 5),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
GriddedPerm((0, 1, 2, 3, 4), ((1, 0),) + ((3, 0),) * 4),
GriddedPerm((4, 3, 2, 1), ((0, 0),) * 4),
GriddedPerm((2, 3, 1, 0), ((2, 0),) * 4),
GriddedPerm((0, 2, 1), ((4, 0),) * 3),
GriddedPerm((1, 2, 0), ((1, 0), (2, 0), (4, 0))),
GriddedPerm((2, 1, 0), ((2, 0), (3, 0), (4, 0))),
GriddedPerm(
(4, 1, 2, 3, 0), ((0, 0), (0, 0), (3, 0), (3, 0), (4, 0))
),
GriddedPerm(
(4, 1, 2, 3, 0), ((0, 0), (0, 0), (1, 0), (3, 0), (4, 0))
),
)
),
(1, 3),
6,
),
(
Tiling(
obstructions=(
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (0, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (0, 0), (1, 0))),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
GriddedPerm((1, 2, 3, 0), ((0, 0), (0, 0), (2, 0), (2, 0))),
GriddedPerm((1, 2, 3, 0), ((0, 0), (1, 0), (2, 0), (2, 0))),
),
requirements=(((GriddedPerm((0, 2, 1), ((2, 0), (2, 0), (2, 0))),),)),
),
Tiling(
obstructions=(
GriddedPerm((0, 1, 2), ((1, 0), (1, 0), (1, 0))),
GriddedPerm((0, 1, 2), ((0, 0), (1, 0), (1, 0))),
GriddedPerm((0, 1), ((0, 0), (0, 0))),
GriddedPerm((1, 2, 3, 0), ((1, 0), (1, 0), (2, 0), (2, 0))),
GriddedPerm((1, 2, 3, 0), ((0, 0), (1, 0), (2, 0), (2, 0))),
),
requirements=(((GriddedPerm((0, 2, 1), ((2, 0), (2, 0), (2, 0))),),)),
),
(), # default
7,
),
]
for t1, t2, cols, up_to in tcases:
visited = set()
expected = set(t2.gridded_perms(up_to))
for gp in t1.gridded_perms(up_to):
sl = Sliding.slide_gp(gp, *cols)
assert sl not in visited
visited.add(sl)
assert sl in expected
expected.remove(sl)
assert len(expected) == 0
visited = set()
expected = set(t1.gridded_perms(up_to))
for gp in t2.gridded_perms(up_to):
sl = Sliding.slide_gp_inverse(gp, *cols)
assert sl not in visited
visited.add(sl)
assert sl in expected
expected.remove(sl)
assert len(expected) == 0