def test_H2_cylinder_diagram_contributions():
A = AbelianStratum(2).unique_component()
c1 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(1)).integral_sum_as_mzv()
c2 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(2)).integral_sum_as_mzv()
assert c1 == M(4) / 3
assert c2 == (2 * M(1, 3) + M(2, 2)) / 3
vol = c1 + c2
assert vol == masur_veech_volume(A, rational=True) * M(
2 * A.stratum().genus())
def test_H211_cylinder_diagram_contributions():
A = AbelianStratum(2, 1, 1).unique_component()
c1 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(1)).integral_sum_as_mzv()
c2 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(2)).integral_sum_as_mzv()
c3 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(3)).integral_sum_as_mzv()
assert c1 == 7 * M(8) / 180
assert c2 == (1620 * M(1, 7) + 850 * M(2, 6) + 436 * M(3, 5) +
231 * M(4, 4) + 130 * M(5, 3) + 65 * M(6, 2) + 35 * M(7) -
35 * M(8)) / 1260
def test_H31_cylinder_diagram_contributions():
# values from Table 3 of A. Zorich "Square tiled surfaces
# and Teichmueller volumes of the moduli spaces of Abelian
# differentials" (2002)
A = AbelianStratum(3, 1).unique_component()
c1 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(1)).integral_sum_as_mzv()
c2 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(2)).integral_sum_as_mzv()
c3 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(3)).integral_sum_as_mzv()
assert c1 == M(7) / 15
assert c2 == (55 * M(1, 6) + 29 * M(2, 5) + 15 * M(3, 4) + 8 * M(4, 3) +
4 * M(5, 2)) / 45
vol = 16 * M(6) / 45
def test_gothic_generic():
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1, 3)))
a = K.gen()
S = translation_surfaces.cathedral(a, a**2)
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 4
assert O.field_of_definition() == QQ
def test_gothic_exact_reals():
pytest.importorskip('pyexactreal')
from pyexactreal import ExactReals
x = polygen(QQ)
K = NumberField(x**3 - 2, 'a', embedding=AA(2)**QQ((1, 3)))
R = ExactReals(K)
S = translation_surfaces.cathedral(K.gen(), R.random_element([0.1, 0.2]))
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 4
def test_H4odd_cylinder_diagram_contributions():
A = AbelianStratum(4).odd_component()
c1 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(1)).integral_sum_as_mzv()
c2 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(2)).integral_sum_as_mzv()
c3 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(3)).integral_sum_as_mzv()
vol = c1 + c2 + c3
assert vol == A.masur_veech_volume(rational=True) * M(
2 * A.stratum().genus())
def test_minimal_stratum_components():
for g in range(2, 6):
A = AbelianStratum(2 * g - 2)
assert sum(
C.masur_veech_volume(rational=True)
for C in A.components()) == A.masur_veech_volume(rational=True)
assert sum(
C.masur_veech_volume(rational=False)
for C in A.components()) == A.masur_veech_volume(rational=False)
def test_gothic_veech():
x = polygen(QQ)
K = NumberField(x**2 - 2, 'sqrt2', embedding=AA(2)**QQ((1, 2)))
sqrt2 = K.gen()
x = QQ((1, 2))
y = 1
a = x + y * sqrt2
b = -3 * x - QQ((3, 2)) + 3 * y * sqrt2
S = translation_surfaces.cathedral(a, b)
O = GL2ROrbitClosure(S)
assert O.ambient_stratum() == AbelianStratum(2, 2, 2)
for d in O.decompositions(4, 50):
assert d.parabolic()
O.update_tangent_space_from_flow_decomposition(d)
assert O.dimension() == O.absolute_dimension() == 2
assert O.field_of_definition() == O.V2._isomorphic_vector_space.base_ring()
def stratum(self):
r"""
Return the stratum this surface belongs to.
This uses the package ``surface_dynamics``
(see http://www.labri.fr/perso/vdelecro/flatsurf_sage.html)
EXAMPLES::
sage: import flatsurf.geometry.similarity_surface_generators as sfg
sage: sfg.translation_surfaces.octagon_and_squares().stratum()
H_3(4)
"""
from surface_dynamics import AbelianStratum
from sage.rings.integer_ring import ZZ
return AbelianStratum([ZZ(a - 1) for a in self.angles()])
def test_H11_cylinder_diagram_contributions():
A = AbelianStratum(1, 1).hyperelliptic_component()
c1 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(1)).integral_sum_as_mzv()
c2 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(2)).integral_sum_as_mzv()
c3 = sum(c.volume_contribution()
for c in A.cylinder_diagrams(3)).integral_sum_as_mzv()
assert c1 == M(5) / 6
assert c2 == M(2) * M(3) / 3 - M(5) / 6
assert c3 == (2 * M(4) - M(2) * M(3)) / 3
vol = c1 + c2 + c3
assert vol == A.masur_veech_volume(rational=True) * M(
2 * A.stratum().genus())
def ambient_stratum(self):
r"""
Return the stratum of Abelian differentials this surface belongs to.
EXAMPLES::
sage: from flatsurf import EquiangularPolygons, similarity_surfaces
sage: from flatsurf import GL2ROrbitClosure # optional: pyflatsurf
sage: E = EquiangularPolygons(1, 3, 5)
sage: T = E(1)
sage: S = similarity_surfaces.billiard(T)
sage: S = S.minimal_cover(cover_type="translation")
sage: O = GL2ROrbitClosure(S) # optional: pyflatsurf
sage: O.ambient_stratum() # optional: pyflatsurf
H_3(4, 0^4)
"""
from surface_dynamics import AbelianStratum
surface = self._surface
angles = [surface.angle(v) for v in surface.vertices()]
return AbelianStratum([a-1 for a in angles])
def test_H_3_3():
H = AbelianStratum(3, 3)
check_abelian_component(H.hyperelliptic_component(), 100)
check_abelian_component(H.non_hyperelliptic_component(), 100)
def test_H_6():
H = AbelianStratum(6)
check_abelian_component(H.hyperelliptic_component(), 100)
check_abelian_component(H.even_component(), 100)
check_abelian_component(H.odd_component(), 100)
def test_H31():
A = AbelianStratum(3,1)
cylinder_diagrams_testing(A)
origami_check(A.unique_component(), 10, 10)
def test_H22():
A = AbelianStratum(2,2)
cylinder_diagrams_testing(A)
origami_check(A.hyperelliptic_component(), 10, 10)
origami_check(A.odd_component(), 10, 10)
def click(stratum, component, nb_squares_limit, multiplicities_limit,
literature):
from surface_dynamics import AbelianStratum
if not stratum.startswith("H(") or not stratum.endswith(")"):
raise click.UsageError("invalid stratum argument")
try:
H = AbelianStratum(
*[int(x.strip()) for x in stratum[2:-1].split(",")])
except ValueError:
raise click.UsageError("invalid stratum argument")
if component == "hyp" or component == "hyperelliptic":
H = H.hyperelliptic_component()
elif component == "nonhyp" or component == "non-hyperelliptic":
H = H.nonhyperelliptic_component()
elif component == "even":
H = H.even_component()
elif component == "odd":
H = H.odd_component()
elif component is not None:
raise click.UsageError("invalid component argument")
seen = set()
for c in H.cylinder_diagrams():
for n in range(c.smallest_integer_lengths()[0], nb_squares_limit):
for lh in c.widths_and_heights_iterator(n, height_one=True):
for o0 in c.cylcoord_to_origami_iterator(*lh):
o1 = o0.mirror()
o2 = o0.vertical_symmetry()
o3 = o0.horizontal_symmetry()
for o in [o0, o1, o2, o3]:
o.relabel(inplace=True)
if o0 > o1 or o0 > o2 and o0 > o3:
continue
# TODO: in case of equality above, we will generate the same
# origami twice.
cd1 = o1.cylinder_decomposition()
if any(h != 1 for _, _, _, h, _, _ in cd1):
continue
for mh in IntegerVectors(multiplicities_limit,
c.ncyls(),
min_part=1):
for mv in IntegerVectors(multiplicities_limit,
len(cd1),
min_part=1):
tv = ThurstonVeech(o.r_tuple(), o.u_tuple(),
mh, mv)
if tv in seen:
print("Skipping duplicate")
continue
if literature == "include":
pass
elif literature == "exclude":
if tv.reference():
continue
elif literature == "only":
reference = tv.reference()
if (reference is None
or "Translation covering"
in reference):
continue
else:
raise NotImplementedError(
"Unsupported literature value")
seen.add(tv)
yield tv
