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_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_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_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())