def get_permclass(self):
if self.is_empty():
return Av(Perm((0, )))
elif self.is_point():
return PermSet(1)
elif self.is_anything():
return PermSet()
elif self.is_avoiding() and not self.is_containing():
return Av(self.obstructions)
else:
return MockAvCoPatts(self.obstructions, self.requirements)
def verified(self, comb_class: Tiling) -> bool:
if not comb_class.dimensions == (1, 1):
return False
if not self.basis:
return True
tiling_class = Av([ob.patt for ob in comb_class.obstructions])
sym_classes = (Av(sym) for sym in self.symmetries)
is_strict_subclass = any(
tiling_class.is_subclass(cls) and cls != tiling_class for cls in sym_classes
)
return is_strict_subclass or any(
isinstance(ass, ComponentAssumption) for ass in comb_class.assumptions
)
def __str__(self) -> str:
if self.maxreqlen == 1:
return "point insertion"
if self.extra_basis:
perm_class = Av(self.extra_basis)
return f"cell insertion from {perm_class} up to length {self.maxreqlen}"
return f"cell insertion up to length {self.maxreqlen}"
def test_123_positive_fusions():
pack = TileScopePack.insertion_row_and_col_placements(
row_only=True).make_fusion(tracked=True, apply_first=True)
css = TileScope("123", pack)
spec = css.auto_search(status_update=30)
spec = spec.expand_verified()
print(spec)
assert isinstance(spec, CombinatorialSpecification)
assert [spec.count_objects_of_size(i) for i in range(20)] == [
1,
1,
2,
5,
14,
42,
132,
429,
1430,
4862,
16796,
58786,
208012,
742900,
2674440,
9694845,
35357670,
129644790,
477638700,
1767263190,
]
av = Av([Perm((0, 1, 2))])
for i in range(10):
assert set(av.of_length(i)) == set(
gp.patt for gp in spec.generate_objects_of_size(i))
assert spec.random_sample_object_of_size(i).patt in av
def __str__(self) -> str:
if self.extra_basis:
perm_class = Av(self.extra_basis)
return "requirement extension from {} up to " "length {}".format(
perm_class, self.maxreqlen)
return "requirement extension insertion up to " "length {}".format(
self.maxreqlen)
def test_132_genf():
searcher = TileScope([Perm((0, 2, 1))], point_placements)
spec = searcher.auto_search(smallest=True)
spec = spec.expand_verified()
av = Av([Perm((0, 2, 1))])
for i in range(10):
assert set(av.of_length(i)) == set(
gp.patt for gp in spec.generate_objects_of_size(i))
assert spec.random_sample_object_of_size(i).patt in av
gf = spec.get_genf()
gf = sympy.series(spec.get_genf(), n=15)
x = sympy.Symbol("x")
assert [gf.coeff(x, n) for n in range(13)] == [
1,
1,
2,
5,
14,
42,
132,
429,
1430,
4862,
16796,
58786,
208012,
]
def test_1234_fusion():
__location__ = os.path.realpath(
os.path.join(os.getcwd(), os.path.dirname(__file__)))
with open(os.path.join(__location__, "spec-1234.json")) as f:
d = json.loads(f.read())
spec = CombinatorialSpecification.from_dict(d)
assert isinstance(spec, CombinatorialSpecification)
assert not any("NOTIMPLEMENTED" in str(eq.rhs)
for eq in spec.get_equations())
assert [spec.count_objects_of_size(i) for i in range(15)] == [
1,
1,
2,
6,
23,
103,
513,
2761,
15767,
94359,
586590,
3763290,
24792705,
167078577,
1148208090,
]
av = Av([Perm((0, 1, 2, 3))])
for i in range(10):
assert set(av.of_length(i)) == set(
gp.patt for gp in spec.generate_objects_of_size(i))
assert spec.random_sample_object_of_size(i).patt in av
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 __str__(self) -> str:
if self.maxreqlen == 1:
return "point insertion"
if self.extra_basis:
perm_class = Av(self.extra_basis)
return "cell insertion from {} up to " "length {}".format(
perm_class, self.maxreqlen)
return "cell insertion up to length {}".format(self.maxreqlen)
def __str__(self) -> str:
if not self.extra_basis:
s = f"root insertion up to length {self.maxreqlen}"
else:
perm_class = Av(self.extra_basis)
s = f"root insertion from {perm_class} up to length {self.maxreqlen}"
if self.max_num_req is not None:
s += f" (up to {self.max_num_req} requirements)"
return s
def __str__(self) -> str:
if not self.extra_basis:
s = "root insertion up to length {}".format(self.maxreqlen)
else:
perm_class = Av(self.extra_basis)
s = "root insertion from {} up to length {}".format(
perm_class, self.maxreqlen)
if self.max_num_req is not None:
s += " (up to {} requirements)".format(self.max_num_req)
return s
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 test_get_elmnts_of_size_Av21_cell(self):
mt = MeshTiling({
(0, 0): Cell(frozenset({Perm((1, 0))}), frozenset()),
(1, 1): MeshTiling.point_cell
})
for size in range(1, 5):
expected_perms = set(Av([Perm((1, 0))]).of_length(size))
mt_perms = mt.get_elmnts(of_size=size)
assert (len(set(mt_perms)) == len(list(mt_perms)))
assert (set(mt_perms) == expected_perms)
def __init__(self, av_patts, co_patts):
self.base_perm_set = Av(av_patts)
if isinstance(co_patts, (Perm, MeshPatt)):
self.filter = lambda perm: perm.contains(co_patts)
elif all(isinstance(patt, (Perm, MeshPatt)) for patt in co_patts):
self.filter = lambda perm: any(
perm.contains(patt) for patt in co_patts)
else:
raise ValueError("Variable 'co_patts' not as expected: "
"'{}'".format(co_patts))
def test_reverse_equiv():
"""A specification that should use reverse equivalence."""
pack = TileScopePack(
initial_strats=[
strat.FactorFactory(),
strat.RequirementCorroborationFactory(),
strat.RequirementPlacementFactory(partial=False),
],
inferral_strats=[strat.RowColumnSeparationStrategy()],
expansion_strats=[[strat.CellInsertionFactory()]],
ver_strats=[strat.BasicVerificationStrategy()],
iterative=False,
name="test pack",
)
basis = (Perm((0, 1, 3, 2)), Perm((0, 2, 3, 1)), Perm((1, 0, 3, 2)))
# From https://oeis.org/A033321
expected_enum = [
1, 1, 2, 6, 21, 79, 311, 1265, 5275, 22431, 96900, 424068, 1876143
]
x, f = sympy.symbols("x f")
expected_min_poly = sympy.sympify("-4*f^2*x^2 + 8*f^2*x - 4*f*x - 4*f + 4")
searcher = TileScope(basis, pack)
spec = searcher.auto_search(smallest=True)
assert [spec.count_objects_of_size(i) for i in range(13)] == expected_enum
genf = spec.get_genf()
assert sympy.simplify(expected_min_poly.subs(f, genf)) == 0
assert taylor_expand(genf, 12) == expected_enum
# In order to avoid ReccursionError we go incrementally
for i in range(0, 100):
spec.count_objects_of_size(i)
assert spec.count_objects_of_size(50) == 86055297645519796258217673160170
assert (
spec.count_objects_of_size(100) ==
2733073112795720153237297124938915907723365837935699807314396095313)
len4_perms = tuple(spec.generate_objects_of_size(4))
assert len(len4_perms) == 21
assert all(p not in len4_perms for p in basis)
len8_perms = tuple(spec.generate_objects_of_size(8))
assert len(len8_perms) == 5275
assert len(set(len8_perms)) == 5275
for _ in range(10):
gp = spec.random_sample_object_of_size(10)
print(gp)
assert gp.patt.avoids(*basis)
av = Av(basis)
for i in range(10):
assert set(av.of_length(i)) == set(
gp.patt for gp in spec.generate_objects_of_size(i))
assert spec.random_sample_object_of_size(i).patt in av
def all_cell_insertions(tiling, **kwargs):
"""
The cell insertion strategy.
The cell insertion strategy is a batch strategy that considers each active
cells, excluding positive cells. For each of these cells, the strategy
considers all patterns (up to some maximum length given by maxreqlen, and
some maximum number given by maxreqnum) and returns two tilings; one which
requires the pattern in the cell and one where the pattern is obstructed.
TODO:
- Have a flag to insert into positive cells that contain the maximal
intersections
"""
maxreqlen = kwargs.get('maxreqlen')
if not maxreqlen:
maxreqlen = 1
ignore_parent = kwargs.get('ignore_parent', False)
extra_basis = kwargs.get('extra_basis')
if extra_basis is None:
extra_basis = []
if (not isinstance(extra_basis, list)
or not all(isinstance(p, Perm) for p in extra_basis)):
raise TypeError("'extra_basis' flag should be a list of Perm to avoid")
maxreqnum = kwargs.get('maxreqnum')
if not maxreqnum:
maxreqnum = 1
active = tiling.active_cells
bdict = tiling.cell_basis()
for cell in active:
if len(bdict[cell][1]) >= maxreqnum:
continue
for length in range(1, maxreqlen + 1):
for patt in Av(bdict[cell][0] + extra_basis).of_length(length):
if not any(patt in perm for perm in bdict[cell][1]):
if (tiling.dimensions != (1, 1)
or all(patt > perm for perm in bdict[cell][1])):
yield Rule(
formal_step=("Insert {} into cell {}.|{}|{}|{}|"
"".format(
patt, cell, cell[0], cell[1],
"".join(str(i) for i in patt))),
comb_classes=cell_insertion(tiling, patt, cell),
ignore_parent=ignore_parent,
inferable=[True for _ in range(2)],
possibly_empty=[True for _ in range(2)],
workable=[True for _ in range(2)],
constructor='disjoint')
def simples_avoiding(basis):
"""
Yield all simple permutations that avoid basis.
You may wish to use the 'Av' class from permuta for iterating over
permutations that avoid a given basis.
A naive approach to know when to terminate is to use the fact that every
length n simple contains a simple of length n - 1 or length n - 2.
"""
av = Av(basis)
longest = 4
length = 4
while True:
if length - 2 > longest:
break
for perm in av.of_length(length):
if perm.is_simple():
yield perm
longest = length
length += 1
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 all_requirement_extensions(tiling, **kwargs):
"""Insert longer requirements in to cells which contain a requirement"""
maxreqlen = kwargs.get('maxreqlen')
if not maxreqlen:
maxreqlen = 2
extra_basis = kwargs.get('extra_basis')
if extra_basis is None:
extra_basis = []
if (not isinstance(extra_basis, list)
or not all(isinstance(p, Perm) for p in extra_basis)):
raise TypeError("'extra_basis' flag should be a list of Perm to avoid")
active = tiling.active_cells
bdict = tiling.cell_basis()
for cell in active:
basis = bdict[cell][0]
reqs = bdict[cell][1]
if len(reqs) != 1:
continue
curr_req = reqs[0]
for length in range(len(curr_req) + 1, maxreqlen + 1):
for patt in Av(bdict[cell][0] + extra_basis).of_length(length):
if curr_req in patt:
yield Rule(
formal_step=("Insert {} into cell {}."
"".format(patt, cell)),
comb_classes=[
tiling.add_single_cell_obstruction(patt, cell),
tiling.add_single_cell_requirement(patt, cell)
],
ignore_parent=False,
possibly_empty=[
any(len(r) > 1 for r in tiling.requirements), True
],
inferable=[True for _ in range(2)],
workable=[True for _ in range(2)],
constructor='disjoint')
def subclass_verified(tiling, basis, **kwargs):
"""The subclass verified strategy.
A tiling is subclass verified if it only generates permutations in a
proper subclass of Av(basis).
"""
if tiling.dimensions == (1, 1):
return None
else:
maxlen = kwargs.get('maxpattlen', 4)
patterns = set(perm for perm in chain(
*[Av(basis).of_length(i) for i in range(maxlen + 1)]))
maxlen += tiling.maximum_length_of_minimum_gridded_perm()
for i in range(maxlen + 1):
for g in tiling.objects_of_length(i):
perm = g.patt
patterns = set(pattern for pattern in patterns
if perm.avoids(pattern))
if not patterns:
return None
return VerificationRule(formal_step=("The tiling belongs to the "
"subclass obtained by adding"
" the patterns {}."
"".format(Basis(patterns))))
def test_321_1324():
searcher = TileScope("321_1324", reginsenc)
spec = searcher.auto_search()
assert isinstance(spec, CombinatorialSpecification)
for i in range(20):
gp = spec.random_sample_object_of_size(i)
assert all(cell == (0, 0) for cell in gp.pos)
assert gp.patt.avoids(Perm((2, 1, 0)), Perm((0, 2, 1, 3)))
av = Av([Perm((2, 1, 0)), Perm((0, 2, 1, 3))])
for i in range(10):
assert set(av.of_length(i)) == set(
gp.patt for gp in spec.generate_objects_of_size(i))
assert [spec.count_objects_of_size(i) for i in range(50)] == [
1,
1,
2,
5,
13,
32,
72,
148,
281,
499,
838,
1343,
2069,
3082,
4460,
6294,
8689,
11765,
15658,
20521,
26525,
33860,
42736,
53384,
66057,
81031,
98606,
119107,
142885,
170318,
201812,
237802,
278753,
325161,
377554,
436493,
502573,
576424,
658712,
750140,
851449,
963419,
1086870,
1222663,
1371701,
1534930,
1713340,
1907966,
2119889,
2350237,
]
def formal_step(self) -> str:
cls = Av(min(self.symmetries))
if len(self.symmetries) == 1:
return f"No cell is {cls}"
return f"No cell is a symmetry of {cls}"