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_guided_searcher():
tilescope = TileScope(
"123",
TileScopePack.point_placements().make_fusion(tracked=False))
spec = tilescope.auto_search()
searcher = GuidedSearcher.from_spec(
spec,
TileScopePack.point_placements().make_fusion(tracked=True))
tracked_spec = searcher.auto_search()
tracked_spec = tracked_spec.expand_verified()
assert [tracked_spec.count_objects_of_size(i) for i in range(13)] == [
1,
1,
2,
5,
14,
42,
132,
429,
1430,
4862,
16796,
58786,
208012,
]
def test_domino():
domino = Tiling(obstructions=[
GriddedPerm((0, 2, 1), [(0, 0), (0, 0), (0, 0)]),
GriddedPerm((1, 0, 2), [(0, 1), (0, 1), (0, 1)]),
GriddedPerm((0, 2, 1, 3), [(0, 0), (0, 1), (0, 0), (0, 1)]),
])
tilescope = TileScope(
domino,
TileScopePack.row_and_col_placements().make_fusion(tracked=True,
component=True),
)
spec = tilescope.auto_search()
assert isinstance(spec, CombinatorialSpecification)
assert [spec.count_objects_of_size(i) for i in range(15)] == [
1,
2,
6,
22,
91,
408,
1938,
9614,
49335,
260130,
1402440,
7702632,
42975796,
243035536,
1390594458,
]
def forest_expansion():
"""
A forest spec that at some point became not productive once expanded.
"""
basis = "0213_1032_1302"
pack = TileScopePack.point_placements()
css = TileScope(basis, pack, ruledb=RuleDBForest())
spec = css.auto_search(status_update=30)
for rule in spec.rules_dict.values():
rule.label = spec.get_label(rule.comb_class)
spec.expand_verified()
assert [spec.count_objects_of_size(i) for i in range(13)] == [
1,
1,
2,
6,
21,
77,
287,
1079,
4082,
15522,
59280,
227240,
873886,
]
def test_expansion():
"""
This cannot be expanded automatically since it requires the positive
root that is not in the specification.
"""
pack = TileScopePack.only_root_placements(3, 1)
css = TileScope("132", pack)
spec = css.auto_search(smallest=True)
spec = spec.expand_verified()
assert sum(1 for rule in spec if isinstance(rule, ReverseRule)) == 1
assert [spec.count_objects_of_size(i) for i in range(13)] == [
1,
1,
2,
5,
14,
42,
132,
429,
1430,
4862,
16796,
58786,
208012,
]
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)))
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 test_123_interleaving():
pack = TileScopePack.point_placements().make_interleaving()
css = TileScope("123", pack)
spec = css.auto_search(status_update=30)
spec = spec.expand_verified()
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,
]
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 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)
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,
]
def test_132_elementary():
searcher = TileScope(Tiling.from_string("132"),
point_placements.make_elementary())
spec = searcher.auto_search()
assert spec.number_of_rules() == 4
spec = spec.expand_verified()
assert spec.number_of_rules() == 5
assert isinstance(spec, CombinatorialSpecification)
def search_spec(args):
"""
Search for a specification.
"""
pack = build_pack(args)
start_class = Tiling.from_string(args.basis)
css = TileScope(start_class, pack)
spec = css.auto_search(status_update=30)
logger.info("The generating function is %s", spec.get_genf())
return 0
def test_from_tiling():
t = Tiling(obstructions=[
GriddedPerm(Perm((0, 1)), ((0, 0), (0, 0))),
GriddedPerm(Perm((0, 1)), ((0, 0), (1, 1))),
GriddedPerm(Perm((0, 1)), ((1, 1), (1, 1))),
])
searcher = TileScope(t, TileScopePack.point_placements())
spec = searcher.auto_search()
print(spec)
assert sympy.simplify(spec.get_genf() - sympy.sympify("(1+x)/(1-x)")) == 0
def test_single_fusion_db():
ruledb = LimitedStrategyRuleDB(
strategies_to_limit=set([FusionStrategy]),
limit=1,
mark_verified=False,
)
searcher = TileScope("0123_0132", row_placements_fusion, ruledb=ruledb)
spec = searcher.auto_search()
assert isinstance(spec, CombinatorialSpecification)
expected_enum = [1, 1, 2, 6, 22, 90, 394, 1806, 8558, 41586, 206098]
assert [spec.count_objects_of_size(n) for n in range(11)] == expected_enum
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 test_1324():
searcher = TileScope("1324",
row_and_col_placements_component_fusion_fusion)
spec = searcher.auto_search(smallest=True)
assert spec.number_of_rules() == 9
num_fusion = 0
num_comp_fusion = 0
for rule in spec.rules_dict.values():
if isinstance(rule.strategy, FusionStrategy) and not isinstance(
rule.strategy, ComponentFusionStrategy):
num_fusion += 1
if isinstance(rule.strategy, ComponentFusionStrategy):
num_comp_fusion += 1
assert num_fusion == 1
assert num_comp_fusion == 1
assert isinstance(spec, CombinatorialSpecification)
def test_expansion():
"""
For this pack only some basic verification are needed.
"""
pack = TileScopePack.only_root_placements(3, 1)
css = TileScope("132", pack)
spec = css.auto_search(smallest=True)
for comb_class, rule in spec.rules_dict.items():
if isinstance(rule, VerificationRule):
assert isinstance(
rule.strategy,
(
strat.OneByOneVerificationStrategy,
strat.MonotoneTreeVerificationStrategy,
strat.BasicVerificationStrategy,
EmptyStrategy,
),
)
def test_132_genf():
searcher = TileScope([Perm((0, 2, 1))], point_placements)
spec = searcher.auto_search(smallest=True)
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_132_321_genf():
searcher = TileScope("132_321", point_placements)
spec = searcher.auto_search(smallest=True)
assert isinstance(spec, CombinatorialSpecification)
gf = spec.get_genf()
assert taylor_expand(gf, 15) == [
1,
1,
2,
4,
7,
11,
16,
22,
29,
37,
46,
56,
67,
79,
92,
106,
]
def test_132():
searcher = TileScope("132", point_placements)
spec = searcher.auto_search(smallest=True)
assert isinstance(spec, CombinatorialSpecification)
def test_1342_1423():
searcher = TileScope("1342_1423", point_placements_component_fusion)
spec = searcher.auto_search(smallest=True)
assert spec.number_of_rules() == 9
assert isinstance(spec, CombinatorialSpecification)
def test_123():
searcher = TileScope((Perm((0, 1, 2)), ), point_placements_fusion)
spec = searcher.auto_search(smallest=True)
assert isinstance(spec, CombinatorialSpecification)
def test_123_with_db():
searcher = TileScope("123", all_the_strategies_verify_database)
spec = searcher.auto_search(smallest=True)
assert isinstance(spec, CombinatorialSpecification)