def enum_verified(self):
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((0, 1), ((0, 1), ) * 2),
GriddedPerm((0, 1), ((0, 2), ) * 2),
GriddedPerm((0, 1), ((2, 0), ) * 2),
GriddedPerm((0, 1, 2), ((1, 1), ) * 3),
])
return MonotoneTreeEnumeration(t)
def test_get_genf_simple(self):
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((1, 0), ((1, 0), ) * 2),
])
enum = MonotoneTreeEnumeration(t)
print(t)
assert enum.verified()
assert sympy.simplify(enum.get_genf() -
sympy.sympify("1/(1-2*x)")) == 0
def test_with_finite_monotone_cell(self):
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((1, 0), ((0, 0), ) * 2),
GriddedPerm((0, 1), ((1, 0), ) * 2),
GriddedPerm((1, 0), ((1, 0), ) * 2),
])
enum = MonotoneTreeEnumeration(t)
print(t)
assert enum.verified()
assert enum.get_genf().expand() == sympy.sympify("1+2*x+2*x**2")
def test_with_finite_monotone_cell2(self):
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((1, 0), ((0, 1), ) * 2),
GriddedPerm((0, 1), ((0, 1), ) * 2),
GriddedPerm((1, 0), ((1, 1), ) * 2),
])
enum = MonotoneTreeEnumeration(t)
print(t)
assert enum.verified()
assert (sympy.sympify("x/(1-x)**4 + 1/(1-x)**2") -
enum.get_genf()).simplify() == 0
def enum_with_list_req(self):
t = Tiling(
obstructions=[
GriddedPerm((0, 1), ((0, 0), (0, 0))),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
],
requirements=[[
GriddedPerm((0, ), ((0, 0), )),
GriddedPerm((0, ), ((1, 0), )),
]],
)
return MonotoneTreeEnumeration(t)
def test_get_genf(self, enum_verified):
x = sympy.Symbol("x")
expected_gf = -(sympy.sqrt(-(4 * x**3 - 14 * x**2 + 8 * x - 1) /
(2 * x**2 - 4 * x + 1)) - 1) / (
2 * x * (x**2 - 3 * x + 1))
assert sympy.simplify(enum_verified.get_genf() - expected_gf) == 0
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((0, 1), ((1, 0), ) * 2),
])
enum_no_start = MonotoneTreeEnumeration(t)
expected_gf = -1 / ((x - 1) * (x / (x - 1) + 1))
assert sympy.simplify(enum_no_start.get_genf() - expected_gf) == 0
def test_corner(self):
t = Tiling(
obstructions=(
GriddedPerm((0, ), ((1, 1), )),
GriddedPerm((0, 1), ((0, 0), (0, 0))),
GriddedPerm((0, 1), ((0, 1), (0, 1))),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
),
requirements=((GriddedPerm((0, ), ((0, 0), )), ), ),
)
enum = MonotoneTreeEnumeration(t)
expected_enum = [0, 1, 5, 17, 50, 138, 370, 979, 2575, 6755, 17700]
assert enum.verified()
assert taylor_expand(enum.get_genf()) == expected_enum
def test_genf_with_big_finite_cell(self):
t = Tiling(obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((0, 1), ((1, 0), ) * 2),
GriddedPerm((3, 2, 1, 0), ((0, 0), ) * 4),
GriddedPerm((3, 2, 1, 0), ((1, 0), ) * 4),
])
enum = MonotoneTreeEnumeration(t)
print(t)
assert enum.verified()
genf = enum.get_genf().expand()
x = sympy.var("x")
assert (genf == 1 + 2 * x + 4 * x**2 + 8 * x**3 + 14 * x**4 +
20 * x**5 + 20 * x**6)
def test_genf_with_req(self):
t = Tiling(
obstructions=[
GriddedPerm((0, 1), ((0, 0), ) * 2),
GriddedPerm((0, 1), ((1, 0), ) * 2),
],
requirements=[
[GriddedPerm((1, 0), ((0, 0), ) * 2)],
[GriddedPerm((0, ), ((1, 0), ))],
],
)
enum = MonotoneTreeEnumeration(t)
print(t)
assert enum.verified()
genf = enum.get_genf().expand()
terms = [0, 0, 0, 3, 10, 25, 56, 119, 246, 501, 1012]
assert taylor_expand(genf) == terms
def test_not_verified(self, enum_with_list_req, onebyone_enum,
enum_with_crossing):
assert not enum_with_crossing.verified()
assert not enum_with_list_req.verified()
assert not onebyone_enum.verified()
forest_tiling = Tiling(
obstructions=[
GriddedPerm((0, ), ((0, 0), )),
GriddedPerm((0, ), ((1, 1), )),
GriddedPerm((0, ), ((2, 1), )),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
GriddedPerm((0, 1), ((2, 0), (2, 0))),
GriddedPerm((0, 1, 2), ((0, 1), (0, 1), (0, 1))),
],
requirements=[[GriddedPerm((0, ), ((0, 1), ))]],
)
assert not MonotoneTreeEnumeration(forest_tiling).verified()
def test_with_two_reqs(self):
t = Tiling(
obstructions=(
GriddedPerm((0, ), ((1, 1), )),
GriddedPerm((0, 1), ((0, 0), (0, 0))),
GriddedPerm((0, 1), ((0, 1), (0, 1))),
GriddedPerm((0, 1), ((1, 0), (1, 0))),
GriddedPerm((1, 0), ((0, 1), (0, 1))),
),
requirements=(
(GriddedPerm((0, ), ((0, 0), )), ),
(GriddedPerm((0, ), ((0, 1), )), ),
),
)
enum = MonotoneTreeEnumeration(t)
expected_enum = [0, 0, 2, 7, 19, 47, 111, 255, 575, 1279, 2815]
assert enum.verified()
assert taylor_expand(enum.get_genf()) == expected_enum
def onebyone_enum(self):
return MonotoneTreeEnumeration(Tiling.from_string("123"))