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 == A.masur_veech_volume(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_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_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 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 as_pure_zeta(vol):
support = set(sum(u) for u in vol.support())
support = [
d for d in support if not vol.homogeneous_component(d).is_zero()
]
if len(support) != 1:
raise ValueError("not homogeneous")
d = support.pop()
vol = vol.homogeneous_component(d)
u = vol.phi_as_vector()
zeta = M(d)
v = zeta.phi_as_vector()
for i in range(len(u)):
if u[i]:
break
result = u[i] / v[i] * zeta
if result != vol:
raise ValueError("not pure zeta phi(vol)={} vs phi(Z({})) = {}".format(
u, d, v))
return result