def generate_neighbour_isoSigs(self, ceiling, floor):
# tri, angle = self.getTriang()
tri, angle, branch = self.tri, self.angle, self.branch
num_tetrahedra = tri.countTetrahedra()
assert num_tetrahedra <= ceiling
assert num_tetrahedra >= floor
if num_tetrahedra < ceiling:
for face_index in range(tri.countTriangles()):
# print('face_index', face_index)
tri_copy = regina.Triangulation3(tri)
angle_copy = angle[:]
output_taut = taut_pachner.twoThreeMove(
tri_copy, angle_copy, face_index)
# print('output_taut', output_taut)
tri_copy2 = regina.Triangulation3(tri)
branch_copy = branch[:]
output_branch = branched_pachner.twoThreeMove(
tri_copy2, branch_copy, face_index)
# print('output_branch', output_branch)
if output_taut != False and output_branch != False:
tri_new, angle_new = output_taut
_, branch_new_list = output_branch
for branch_new in branch_new_list:
new_isosig = isosig_from_tri_angle_branch(
tri_new, angle_new, branch_new)
# print('new_isosig', new_isosig)
self.neighbour_moves_up_faces[new_isosig] = 'f' + str(
face_index)
self.neighbour_moves_up_tri_angle_branches[
new_isosig] = (tri_new, angle_new, branch_new)
if num_tetrahedra > floor:
# print('now do threeTwoMove')
for edge_index in range(tri.countEdges()):
# print('edge_index', edge_index)
tri_copy = regina.Triangulation3(tri)
angle_copy = angle[:]
output_taut = taut_pachner.threeTwoMove(
tri_copy, angle_copy, edge_index)
# print('output_taut', output_taut)
tri_copy2 = regina.Triangulation3(tri)
branch_copy = branch[:]
output_branch = branched_pachner.threeTwoMove(
tri_copy2, branch_copy, edge_index)
# print('output_branch', output_branch)
if output_taut != False and output_branch != False:
tri_new, angle_new = output_taut
_, branch_new = output_branch
new_isosig = isosig_from_tri_angle_branch(
tri_new, angle_new, branch_new)
# print('new_isosig', new_isosig)
self.neighbour_moves_down_edges[new_isosig] = 'e' + str(
edge_index)
self.neighbour_moves_down_tri_angle_branches[
new_isosig] = (tri_new, angle_new, branch_new)
self.neighbour_moves_tri_angle_branches = {
**self.neighbour_moves_up_tri_angle_branches,
**self.neighbour_moves_down_tri_angle_branches
} ## union of the dictionaries
def find_veering_after_drilling(tri,
angle,
tri_loop,
extra_ceiling=4,
depth=100):
branch = upper_branched_surface(tri, angle)
if tri_loop_is_boundary_parallel(
tri_loop,
tri): # if a loop is boundary parallel then we don't drill
print('loop is boundary parallel')
else:
drilled_cusp_index = drill(tri, tri_loop, angle=angle, branch=branch)
if has_essential_torus(tri):
print('sig', tri.isoSig(), 'has_essential_torus')
else:
ceiling = tri.countTetrahedra() + extra_ceiling
print('ceiling', ceiling)
start_isoSig = isosig_from_tri_angle_branch(tri, angle, branch)
print(start_isoSig, 'angle', angle, 'branch', branch,
'drilled_cusp_index', drilled_cusp_index)
graph = search_Pachner_graph_for_shortest_path(
start_isoSig,
tri,
angle,
branch,
name=None,
search_depth=depth,
ceiling=ceiling,
drilled_cusp_index=drilled_cusp_index,
check_property=False,
property=None,
save_dir=None)
def test():
# sig = 'cPcbbbiht_12'
# sig = 'dLQacccjsnk_200'
# sig = 'dLQbccchhsj_122'
# sig = 'eLAkaccddjsnak_2001'
# sig = 'eLAkbccddhhsqs_1220'
# sig = 'eLMkbcddddedde_2100'
# sig = 'eLMkbcdddhhhdu_1221'
# sig = 'eLMkbcdddhhhml_1221'
# sig = 'eLMkbcdddhhqqa_1220'
# eLMkbcdddhhqxh_1220
# eLMkbcdddhxqdu_1200
# eLMkbcdddhxqlm_1200
# eLPkaccddjnkaj_2002
# eLPkbcdddhrrcv_1200
# sig = 'gLLAQbecdfffhhnkqnc_120012'
sigs = parse_data_file('Data/veering_census.txt')
for j, sig in enumerate(sigs[:5]):
if j%100 == 0:
print(j)
tri, angle = isosig_to_tri_angle(sig)
# tri.save(sig + '.rga')
branch = upper_branched_surface(tri, angle) ### also checks for veering and transverse taut
found_loops = find_flow_cycles(tri, branch)
# print(len(found_loops))
# for loop in found_loops:
# print(loop)
# print('found_loops', found_loops)
# print(sig)
for loop in found_loops:
tri, angle = isosig_to_tri_angle(sig)
branch = upper_branched_surface(tri, angle)
tri_loop = flow_cycle_to_triangle_loop(tri, branch, loop)
if tri_loop != False:
if not tri_loop_is_boundary_parallel(tri_loop, tri):
print('sig', isosig_from_tri_angle_branch(tri, angle, branch), 'loop', loop, 'tri_loop', tri_loop)
drill(tri, tri_loop, angle = angle, branch = branch, sig = sig)
print('new angle, branch', angle, branch)
print(isosig_from_tri_angle_branch(tri, angle, branch))
def main():
depth = 100
ceiling = 8
print('depth', depth)
print('ceiling', ceiling)
target_isoSig = 'gLLPQceeffefiiaellu_012110' ### drilled
start_isoSig = 'gLLPQccdfeffhggaagb_201022' ### veering
tri, angle = isosig_to_tri_angle(start_isoSig)
branch = upper_branched_surface(tri, angle)
start_isoSig = isosig_from_tri_angle_branch(tri, angle, branch)
graph = search_Pachner_graph_for_shortest_path(start_isoSig,
tri,
angle,
branch,
target_isoSig,
name=None,
search_depth=depth,
ceiling=ceiling,
check_property=False,
property=None,
save_dir=None)
def run_tests(num_to_check=10, smaller_num_to_check = 10):
import taut
veering_isosigs = parse_data_file("Data/veering_census.txt")
print("testing is_taut")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert taut.is_taut(tri, angle), sig
print("testing isosig round trip")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
recovered_sig = taut.isosig_from_tri_angle(tri, angle)
assert sig == recovered_sig, sig
# we only test this round trip - the other round trip does not
# make sense because tri->isosig is many to one.
import transverse_taut
print("testing is_transverse_taut")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert transverse_taut.is_transverse_taut(tri, angle), sig
non_transverse_taut_isosigs = parse_data_file("Data/veering_non_transverse_taut_examples.txt")
print("testing not is_transverse_taut")
for sig in non_transverse_taut_isosigs:
tri, angle = taut.isosig_to_tri_angle(sig)
assert not transverse_taut.is_transverse_taut(tri, angle), sig
import veering
print("testing is_veering")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
assert veering.is_veering(tri, angle), sig
# tri, angle = taut.isosig_to_tri_angle("cPcbbbdxm_10")
# explore_mobius_surgery_graph(tri, angle, max_tetrahedra = 12)
# # tests to see that it makes only veering triangulations as it goes
import veering_dehn_surgery
print("testing veering_dehn_surgery")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
for face_num in veering_dehn_surgery.get_mobius_strip_indices(tri):
(tri_s, angle_s, face_num_s) = veering_dehn_surgery.veering_mobius_dehn_surgery(tri, angle, face_num)
assert veering.is_veering(tri_s, angle_s), sig
import veering_fan_excision
print("testing veering_fan_excision")
m003, _ = taut.isosig_to_tri_angle('cPcbbbdxm_10')
m004, _ = taut.isosig_to_tri_angle('cPcbbbiht_12')
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
tet_types = veering.is_veering(tri, angle, return_type = "tet_types")
if tet_types.count("toggle") == 2:
excised_tri, _ = veering_fan_excision.excise_fans(tri, angle)
assert ( excised_tri.isIsomorphicTo(m003) != None or
excised_tri.isIsomorphicTo(m004) != None ), sig
import pachner
print("testing pachner with taut structure")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
face_num = random.randrange(tri.countTriangles())
result = pachner.twoThreeMove(tri, face_num, angle = angle, return_edge = True)
if result != False:
tri2, angle2, edge_num = result
tri3, angle3 = pachner.threeTwoMove(tri2, edge_num, angle = angle2)
assert taut.isosig_from_tri_angle(tri, angle) == taut.isosig_from_tri_angle(tri3, angle3), sig
import branched_surface
import regina
print("testing branched_surface and pachner with branched surface")
for sig in random.sample(veering_isosigs, num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
tri_original = regina.Triangulation3(tri) #copy
branch = branched_surface.upper_branched_surface(tri, angle, return_lower = random.choice([True, False]))
### test branch isosig round trip
sig_with_branch = branched_surface.isosig_from_tri_angle_branch(tri, angle, branch)
tri2, angle2, branch2 = branched_surface.isosig_to_tri_angle_branch(sig_with_branch)
assert (branch == branch2) and (angle == angle2), sig
branch_original = branch[:] #copy
face_num = random.randrange(tri.countTriangles())
out = pachner.twoThreeMove(tri, face_num, branch = branch, return_edge = True)
if out != False:
tri, possible_branches, edge_num = out
tri, branch = pachner.threeTwoMove(tri, edge_num, branch = possible_branches[0])
all_isoms = tri.findAllIsomorphisms(tri_original)
all_branches = [branched_surface.apply_isom_to_branched_surface(branch, isom) for isom in all_isoms]
assert branch_original in all_branches, sig
import flow_cycles
import drill
print("testing taut and branched drill + semiflows on drillings")
for sig in random.sample(veering_isosigs, smaller_num_to_check):
tri, angle = taut.isosig_to_tri_angle(sig)
branch = branched_surface.upper_branched_surface(tri, angle) ### also checks for veering and transverse taut
found_loops = flow_cycles.find_flow_cycles(tri, branch)
for loop in random.sample(found_loops, min(len(found_loops), 5)): ## drill along at most 5 loops
tri, angle = taut.isosig_to_tri_angle(sig)
branch = branched_surface.upper_branched_surface(tri, angle)
tri_loop = flow_cycles.flow_cycle_to_triangle_loop(tri, branch, loop)
if tri_loop != False:
if not flow_cycles.tri_loop_is_boundary_parallel(tri_loop, tri):
drill.drill(tri, tri_loop, angle = angle, branch = branch, sig = sig)
assert branched_surface.has_non_sing_semiflow(tri, branch), sig
print("all basic tests passed")
try:
import snappy
import snappy_util
snappy_working = True
except:
print("failed to import from snappy?")
snappy_working = False
if snappy_working:
print("testing algebraic intersection")
census = snappy.OrientableCuspedCensus() # not a set or list, so can't use random.sample
for i in range(10):
M = random.choice(census)
n = M.num_cusps()
peripheral_curves = M.gluing_equations()[-2*n:]
for i in range(2*n):
for j in range(i, 2*n):
alg_int = snappy_util.algebraic_intersection(peripheral_curves[i], peripheral_curves[j])
if i % 2 == 0 and j == i + 1:
assert alg_int == 1, M.name()
else:
assert alg_int == 0, M.name()
if snappy_working:
import veering_drill_midsurface_bdy
print("testing veering drilling and filling")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
T, per = veering_drill_midsurface_bdy.drill_midsurface_bdy(sig)
M = snappy.Manifold(T.snapPea())
M.set_peripheral_curves("shortest")
L = snappy_util.get_slopes_from_peripherals(M, per)
M.dehn_fill(L)
N = snappy.Manifold(sig.split("_")[0])
assert M.is_isometric_to(N), sig
if snappy_working:
print("all tests depending on snappy passed")
# try:
# from hashlib import md5
# from os import remove
# import pyx
# from boundary_triangulation import draw_triangulation_boundary_from_veering_isosig
# pyx_working = True
# except:
# print("failed to import from pyx?")
# pyx_working = False
# ladders_style_sigs = {
# "cPcbbbiht_12": "f34c1fdf65db9d02994752814803ae01",
# "gLLAQbecdfffhhnkqnc_120012": "091c85b4f4877276bfd8a955b769b496",
# "kLALPPzkcbbegfhgijjhhrwaaxnxxn_1221100101": "a0f15a8454f715f492c74ce1073a13a4",
# }
# geometric_style_sigs = {
# "cPcbbbiht_12": "1e74d0b68160c4922e85a5adb20a0f1d",
# "gLLAQbecdfffhhnkqnc_120012": "856a1fce74eb64f519bcda083303bd8f",
# "kLALPPzkcbbegfhgijjhhrwaaxnxxn_1221100101": "33bd23b34c5d977a103fa50ffe63120a",
# }
# args = {
# "draw_boundary_triangulation":True,
# "draw_triangles_near_poles": False,
# "ct_depth":-1,
# "ct_epsilon":0.03,
# "global_drawing_scale": 4,
# "delta": 0.2,
# "ladder_width": 10.0,
# "ladder_height": 20.0,
# "draw_labels": True,
# }
# shapes_data = read_from_pickle("Data/veering_shapes_up_to_ten_tetrahedra.pkl")
# if pyx_working:
# for sig in ladders_style_sigs:
# print("testing boundary triangulation pictures, ladder style", sig)
# args["tet_shapes"] = shapes_data[sig]
# args["style"] = "ladders"
# file_name = draw_triangulation_boundary_from_veering_isosig(sig, args = args)
# f = open(file_name, "rb")
# file_hash = md5(f.read())
# assert file_hash.hexdigest() == ladders_style_sigs[sig]
# f.close()
# remove(file_name)
# if pyx_working:
# for sig in geometric_style_sigs:
# print("testing boundary triangulation pictures, ladder style", sig)
# args["tet_shapes"] = shapes_data[sig]
# args["style"] = "geometric"
# file_name = draw_triangulation_boundary_from_veering_isosig(sig, args = args)
# f = open(file_name, "rb")
# file_hash = md5(f.read())
# assert file_hash.hexdigest() == geometric_style_sigs[sig]
# f.close()
# remove(file_name)
# if pyx_working:
# print("all tests depending on pyx passed")
veering_polys = {
"cPcbbbiht_12": [-4, -1, 1, 4],
"eLMkbcddddedde_2100": [-2, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 2, 2],
"gLLAQbecdfffhhnkqnc_120012": [-1, -1, -1, -1, 1, 1, 1, 1],
"gLLPQcdfefefuoaaauo_022110": [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1],
}
# veering_polys = { ### old
# "cPcbbbiht_12": "a^3 - 4*a^2 + 4*a - 1",
# "eLMkbcddddedde_2100": "a^6*b - a^6 - 2*a^5*b - a^4*b^2 + a^5 + 2*a^4*b + a^3*b^2 - 2*a^3*b + a^3 + 2*a^2*b + a*b^2 - a^2 - 2*a*b - b^2 + b",
# "gLLAQbecdfffhhnkqnc_120012": "a^7 + a^6 + a^5 + a^4 - a^3 - a^2 - a - 1",
# "gLLPQcdfefefuoaaauo_022110": "a^12*b^3 - a^11*b^2 - a^10*b^3 - a^10*b^2 - a^7*b^3 - a^7*b^2 - a^6*b^3 + a^7*b + a^5*b^2 - a^6 - a^5*b - a^5 - a^2*b - a^2 - a*b + 1",
# }
taut_polys = {
"cPcbbbiht_12": [-3, 1, 1],
"eLMkbcddddedde_2100": [-1, -1, -1, 1, 1],
"iLLAwQcccedfghhhlnhcqeesr_12001122": [],
}
# taut_polys = { ### old
# "cPcbbbiht_12": "a^2 - 3*a + 1",
# "eLMkbcddddedde_2100": "a^2*b - a^2 - a*b - b^2 + b",
# "iLLAwQcccedfghhhlnhcqeesr_12001122": "0",
# }
torus_bundles = [
"cPcbbbiht_12",
"eLMkbcdddhhqqa_1220",
"gLMzQbcdefffhhqqqdl_122002",
]
measured = [
"gLLAQbecdfffhhnkqnc_120012",
"iLLALQcccedhgghhlnxkxrkaa_12001112",
"iLLAwQcccedfghhhlnhcqeesr_12001122",
]
empties = [
"fLAMcaccdeejsnaxk_20010",
"gLALQbcbeeffhhwsras_211220",
"hLALAkbcbeefgghhwsraqj_2112202",
]
try:
from sage.rings.integer_ring import ZZ
sage_working = True
except:
print("failed to import from sage?")
sage_working = False
if sage_working:
import taut_polytope
print("testing is_layered")
for sig in veering_isosigs[:17]:
assert taut_polytope.is_layered(sig), sig
for sig in veering_isosigs[17:21]:
assert not taut_polytope.is_layered(sig), sig
if sage_working:
import fibered
print("testing is_fibered")
mflds = parse_data_file("Data/mflds_which_fiber.txt")
mflds = [line.split("\t")[0:2] for line in mflds]
for (name, kind) in random.sample(mflds, num_to_check):
assert fibered.is_fibered(name) == (kind == "fibered"), name
if sage_working:
import veering_polynomial
import taut_polynomial
print("testing veering poly")
for sig in veering_polys:
p = veering_polynomial.veering_polynomial(sig)
assert check_polynomial_coefficients(p, veering_polys[sig]), sig
### Nov 2021: sage 9.4 changed how smith normal form works, which changed our polynomials
### to equivalent but not equal polynomials. To avoid this kind of change breaking things
### in the future, we changed to comparing the list of coefficients.
# assert p.__repr__() == veering_polys[sig]
print("testing taut poly")
for sig in taut_polys:
p = taut_polynomial.taut_polynomial_via_tree(sig)
assert check_polynomial_coefficients(p, taut_polys[sig]), sig
# assert p.__repr__() == taut_polys[sig]
print("testing divide")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
p = veering_polynomial.veering_polynomial(sig)
q = taut_polynomial.taut_polynomial_via_tree(sig)
if q == 0:
assert p == 0, sig
else:
assert q.divides(p), sig
if sage_working:
print("testing alex")
for sig in random.sample(veering_isosigs[:3000], num_to_check):
snap_sig = sig.split("_")[0]
M = snappy.Manifold(snap_sig)
if M.homology().betti_number() == 1:
assert taut_polynomial.taut_polynomial_via_tree(sig, mode = "alexander") == M.alexander_polynomial(), sig
if sage_working:
# would be nice to automate this - need to fetch the angle
# structure say via z_charge.py...
print("testing is_torus_bundle")
for sig in torus_bundles:
assert taut_polytope.is_torus_bundle(sig), sig
if sage_working:
# ditto
print("testing is_layered")
for sig in torus_bundles:
assert taut_polytope.is_layered(sig), sig
print("testing measured")
for sig in measured:
assert taut_polytope.LMN_tri_angle(sig) == "M", sig
print("testing empty")
for sig in empties:
assert taut_polytope.LMN_tri_angle(sig) == "N", sig
if sage_working: # warning - this takes random amounts of time!
print("testing hom dim")
for sig in random.sample(veering_isosigs[:3000], 3): # magic number
# dimension = zero if and only if nothing is carried.
assert (taut_polytope.taut_cone_homological_dim(sig) == 0) == (taut_polytope.LMN_tri_angle(sig) == "N"), sig
if sage_working:
boundary_cycles = {
("eLMkbcddddedde_2100",(2,5,5,1,3,4,7,1)): "((-7, -7, 0, 0, 4, -3, 7, 0), (7, 7, 0, 0, -4, 3, -7, 0))",
("iLLLQPcbeegefhhhhhhahahha_01110221",(0,1,0,0,0,1,0,0,0,0,0,0,1,0,1,0)): "((0, 0, -1, 1, 1, 0, 1, 1, -1, 0, 0, 0, 0, 1, 0, 1), (0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1))",
("ivvPQQcfhghgfghfaaaaaaaaa_01122000",(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)): "((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0), (-2, 0, -3, 1, 2, -1, 0, 2, -1, 0, 3, 1, -2, 1, 0, -1), (0, -2, 1, -3, 0, -1, 2, 0, -1, 2, -1, 1, 0, 1, -2, 3))",
}
taut_polys_with_cycles = {
("eLMkbcddddedde_2100", ((7, 7, 0, 0, -4, 3, -7, 0),)): [-1, -1, -1, 1, 1],
("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): [1, 1, 2],
("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): [-4, -1, -1, 1, 1],
}
# taut_polys_with_cycles = {
# ("eLMkbcddddedde_2100", ((7, 7, 0, 0, -4, 3, -7, 0),)): "a^14 - a^8 - a^7 - a^6 + 1",
# ("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): "a^2 + 2*a + 1",
# ("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): "a*b^2 - a^2 - 4*a*b - b^2 + a",
# }
taut_polys_image = {
('eLMkbcddddedde_2100', ((7, 8, -1, 0, -4, 4, -8, 0),)):[-1, -1, -1, 1, 1],
('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2),)):[-2, -2, -1, -1, 1, 1],
('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))):[-4, -1, -1, 1, 1]
}
# taut_polys_image = {
# ('eLMkbcddddedde_2100', ((7, 8, -1, 0, -4, 4, -8, 0),)):"a^16 - a^9 - a^8 - a^7 + 1",
# ('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2),)):"a*b^2*c - 2*a*b*c - b^2*c - a^2 - 2*a*b + a",
# ('ivvPQQcfhghgfghfaaaaaaaaa_01122000', ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))):"a*b^2 - a^2 - 4*a*b - b^2 + a"
# }
alex_polys_with_cycles = {
("eLMkbcddddedde_2100",((7, 7, 0, 0, -4, 3, -7, 0),)): [-2, -1, -1, -1, 1, 1, 1, 2],
("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): [-3, -1, 1, 3],
("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): [-1, -1, 1, 1],
}
# alex_polys_with_cycles = {
# ("eLMkbcddddedde_2100",((7, 7, 0, 0, -4, 3, -7, 0),)): "a^15 - a^14 + a^9 - 2*a^8 + 2*a^7 - a^6 + a - 1",
# ("iLLLQPcbeegefhhhhhhahahha_01110221", ((0, 0, 1, -1, -1, 0, -1, -1, 1, 0, 0, 0, 0, -1, 0, -1),)): "3*a^3 - a^2 + a - 3",
# ("ivvPQQcfhghgfghfaaaaaaaaa_01122000", ((1, 1, 2, 0, -1, 2, 1, -3, 0, -1, 0, -2, -1, 0, 3, -2), (1, 1, 0, 2, -1, 0, -3, 1, 2, -1, -2, 0, 3, -2, -1, 0))): "a*b^2 - a^2 - b^2 + a",
# }
if sage_working:
import taut_carried
print("testing boundary cycles")
for sig, surface in boundary_cycles:
surface_list = list(surface)
cycles = taut_carried.boundary_cycles_from_surface(sig, surface_list)
cycles = tuple(tuple(cycle) for cycle in cycles)
assert cycles.__repr__() == boundary_cycles[(sig, surface)], sig
if sage_working:
print("testing taut with cycles")
for sig, cycles in taut_polys_with_cycles:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_via_tree(sig, cycles_in)
assert check_polynomial_coefficients(p, taut_polys_with_cycles[(sig, cycles)]), sig
# assert p.__repr__() == taut_polys_with_cycles[(sig, cycles)]
if sage_working:
print("testing taut with images")
for sig, cycles in taut_polys_image:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_image(sig, cycles_in)
assert check_polynomial_coefficients(p, taut_polys_image[(sig, cycles)]), sig
# assert p.__repr__() == taut_polys_image[(sig, cycles)]
if sage_working:
print("testing alex with cycles")
for sig, cycles in alex_polys_with_cycles:
cycles_in = [list(cycle) for cycle in cycles]
p = taut_polynomial.taut_polynomial_via_tree(sig, cycles_in, mode = "alexander")
assert check_polynomial_coefficients(p, alex_polys_with_cycles[(sig, cycles)]), sig
# assert p.__repr__() == alex_polys_with_cycles[(sig, cycles)]
if sage_working:
import edge_orientability
import taut_euler_class
print("testing euler and edge orientability")
for sig in random.sample(veering_isosigs[:3000], 3):
# Theorem: If (tri, angle) is edge orientable then e = 0.
assert not ( edge_orientability.is_edge_orientable(sig) and
(taut_euler_class.order_of_euler_class_wrapper(sig) == 2) ), sig
if sage_working:
# Theorem: If (tri, angle) is edge orientable then taut poly = alex poly.
# taut_polynomial.taut_polynomial_via_tree(sig, mode = "alexander") ==
# taut_polynomial.taut_polynomial_via_tree(sig, mode = "taut")
pass
if sage_working:
print("testing exotics")
for sig in random.sample(veering_isosigs[:3000], 3):
tri, angle = taut.isosig_to_tri_angle(sig)
T = veering.veering_triangulation(tri, angle)
is_eo = T.is_edge_orientable()
for angle in T.exotic_angles():
assert taut_polytope.taut_cone_homological_dim(tri, angle) == 0, sig
assert is_eo == transverse_taut.is_transverse_taut(tri, angle), sig
### test for drill_midsurface_bdy: drill then fill, check you get the same manifold
if sage_working:
from sage.combinat.words.word_generators import words
from sage.modules.free_module_integer import IntegerLattice
from sage.modules.free_module import VectorSpace
from sage.matrix.constructor import Matrix
import z_charge
import z2_taut
import regina
ZZ2 = ZZ.quotient(ZZ(2))
sig_starts = ["b+-LR", "b++LR"]
print("testing lattice for punc torus bundle")
for i in range(3):
for sig_start in sig_starts:
sig = sig_start + str(words.RandomWord(8, 2, "LR")) # 8 is a magic number
M = snappy.Manifold(sig)
tri = regina.Triangulation3(M)
t, A = z_charge.sol_and_kernel(M)
B = z_charge.leading_trailing_deformations(M)
C = z2_taut.cohomology_loops(tri)
AA = IntegerLattice(A)
BB = IntegerLattice(B)
assert AA == BB.saturation(), sig
dim = 3*M.num_tetrahedra()
V = VectorSpace(ZZ2, dim)
AA = V.subspace(A)
BB = V.subspace(B)
CM = Matrix(ZZ2, C)
CC = CM.right_kernel()
assert AA.intersection(CC) == BB , sig
## so l-t defms are the part of the kernel that doesn't flip over
if sage_working:
print("testing charges for punc torus bundle")
for i in range(3):
for sig_start in sig_starts:
sig = sig_start + str(words.RandomWord(8, 2, "LR")) # 8 is a magic number
M = snappy.Manifold(sig)
assert z_charge.can_deal_with_reduced_angles(M), sig
if sage_working:
import carried_surface
import mutation
print("testing building carried surfaces and mutations")
sigs_weights = [
['iLLLPQccdgefhhghqrqqssvof_02221000', (0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0)],
['jLLAvQQcedehihiihiinasmkutn_011220000', (2, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 0, 1, 0)],
['jLLAvQQcedehihiihiinasmkutn_011220000', (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)],
['jLLLMPQcdgfhfhiiihshassspiq_122201101', (0, 0, 4, 0, 4, 1, 0, 2, 2, 0, 1, 0, 0, 4, 0, 4, 0, 0)]
]
strata = [
((1, 2), [2, 2]),
((2, 4), [5, 5, 1, 1]),
((0, 3), [2, 0, 0]),
((6, 1), [22])
]
orders_of_veering_symmetry_groups = [4, 2, 2, 2]
for i in range(len(sigs_weights)):
tri, angle = taut.isosig_to_tri_angle(sigs_weights[i][0])
weights = sigs_weights[i][1]
surface, edge_colours = carried_surface.build_surface(tri, angle, weights, return_edge_colours = True)
assert strata[i] == carried_surface.stratum_from_weights_surface(weights, surface)
veering_isoms = carried_surface.veering_symmetry_group(surface, edge_colours)
assert len(veering_isoms) == orders_of_veering_symmetry_groups[i]
isom = veering_isoms[1]
mutation.mutate(tri, angle, weights, isom, quiet = True)
if i == 0:
assert tri.isoSig() == 'ivLLQQccfhfeghghwadiwadrv'
#print('svof to wadrv passed')
elif i == 1:
assert tri.isoSig() == 'jvLLAQQdfghhfgiiijttmtltrcr'
#print('smkutn to tltrcr passed')
elif i == 2:
assert tri.isoSig() == 'jLLMvQQcedehhiiihiikiwnmtxk'
#print('smkutn to mtxk passed')
elif i == 3:
assert tri.isoSig() == 'jLLALMQcecdhggiiihqrwqwrafo'
#print('spiq to rafo passed')
if sage_working:
print("all tests depending on sage passed")
def generate_neighbour_isoSigs(self, ceiling, floor):
# tri, angle = self.getTriang()
tri, angle, branch = self.tri, self.angle, self.branch
num_tetrahedra = tri.countTetrahedra()
assert num_tetrahedra <= ceiling
assert num_tetrahedra >= floor
if num_tetrahedra < ceiling:
for face_index in range(tri.countTriangles()):
### only go this way if it expands the drilled cusp
face = tri.triangles()[face_index]
embed0 = face.embedding(0)
tet0 = embed0.simplex()
tet_0_face_num = embed0.face()
embed1 = face.embedding(1)
tet1 = embed1.simplex()
tet_1_face_num = embed1.face()
if (tet0.vertex(tet_0_face_num).index()
== self.drilled_cusp_index) or (
tet1.vertex(tet_1_face_num).index()
== self.drilled_cusp_index):
tri_copy = regina.Triangulation3(tri)
angle_copy = angle[:]
branch_copy = branch[:]
output = twoThreeMove(tri_copy,
face_index,
angle=angle_copy,
branch=branch_copy,
return_vertex_perm=True)
# print('2-3', face_index, output)
if output != False:
tri_new, angle_new, branches_new, vertex_perm = output
drilled_cusp_index_new = vertex_perm[
self.drilled_cusp_index]
for branch_new in branches_new:
sig_new = isosig_from_tri_angle_branch(
tri_new, angle_new, branch_new)
self.neighbour_moves_up_faces[sig_new] = 'f' + str(
face_index)
self.neighbour_moves_up_tri_angle_branch[
sig_new] = (tri_new, angle_new, branch_new,
drilled_cusp_index_new)
if num_tetrahedra > floor:
for edge_index in range(tri.countEdges()):
### only go this way if it expands the drilled cusp
edge = tri.edges()[edge_index]
if (edge.vertex(0).index() != self.drilled_cusp_index) and (
edge.vertex(1).index() != self.drilled_cusp_index):
tri_copy = regina.Triangulation3(tri)
angle_copy = angle[:]
branch_copy = branch[:]
output = threeTwoMove(tri_copy,
edge_index,
angle=angle_copy,
branch=branch_copy,
return_vertex_perm=True)
if output != False:
tri_new, angle_new, branch_new, vertex_perm = output
drilled_cusp_index_new = vertex_perm[
self.drilled_cusp_index]
sig_new = isosig_from_tri_angle_branch(
tri_new, angle_new, branch_new)
self.neighbour_moves_down_edges[sig_new] = 'e' + str(
edge_index)
self.neighbour_moves_down_tri_angle_branch[sig_new] = (
tri_new, angle_new, branch_new,
drilled_cusp_index_new)
self.neighbour_moves_tri_angle_branch = {
**self.neighbour_moves_up_tri_angle_branch,
**self.neighbour_moves_down_tri_angle_branch
} ## union of the dictionaries
def main():
depth = 100
# ceiling = 10
extra_ceiling = 5 ### above how many tetrahedra we start with
# print('depth', depth)
# print('ceiling', ceiling)
# # sig = 'cPcbbbdxm_10'
# # sig = 'dLQacccjsnk_200'
# # sig = 'dLQbccchhfo_122'
# sig = 'eLAkbccddhhsqs_1220'
# tri, angle = isosig_to_tri_angle(sig)
# branch = upper_branched_surface(tri, angle)
# # tl = flow_cycle_to_triangle_loop(tri, branch, [(0, 2)])
# # drilled_cusp_index = drill(tri, tl, angle = angle, branch = branch)
# # print('angle', angle, 'branch', branch, 'drilled_cusp_index', drilled_cusp_index)
# # # assert has_non_sing_semiflow(tri, branch)
# # # start veering: cPcbbbdxm_10_dl loop [(0, 2)] tri_loop [(2, 102)]
# # # drill: eLMkbbddddhapu_2100_fjek
# # start_isoSig = isosig_from_tri_angle_branch(tri, angle, branch)
# # assert start_isoSig == 'eLMkbbddddhapu_2100_fjek'
# # tri, angle, branch = isosig_to_tri_angle_branch(start_isoSig) ### fails??
# # graph = search_Pachner_graph_for_shortest_path(start_isoSig, tri, angle, branch, name=None, search_depth = depth, ceiling = ceiling, drilled_cusp_index = drilled_cusp_index, check_property = False, property = None, save_dir = None)
# loops = find_flow_cycles(tri, branch)
# tri_loops = [flow_cycle_to_triangle_loop(tri, branch, loop) for loop in loops]
# for i, tri_loop in enumerate(tri_loops):
# if tri_loop != False: # False means that tri_loop goes more than once along the same triangle - not currently implemented
# tri, angle = isosig_to_tri_angle(sig)
# if tri_loop_is_boundary_parallel(tri_loop, tri) == False: # if a loop is boundary parallel then we don't drill
# branch = upper_branched_surface(tri, angle)
# drilled_cusp_index = drill(tri, tri_loop, angle = angle, branch = branch)
# print('loop', loops[i], 'tri_loop', tri_loop, 'has_essential_torus', has_essential_torus(tri))
# # start_isoSig = isosig_from_tri_angle_branch(tri, angle, branch)
# # print(start_isoSig, 'angle', angle, 'branch', branch, 'drilled_cusp_index', drilled_cusp_index)
# # graph = search_Pachner_graph_for_shortest_path(start_isoSig, tri, angle, branch, name=None, search_depth = depth, ceiling = ceiling, drilled_cusp_index = drilled_cusp_index, check_property = False, property = None, save_dir = None)
sigs = parse_data_file('Data/veering_census.txt')
for j, sig in enumerate(sigs[:5]):
if j % 100 == 0:
print(j)
tri, angle = isosig_to_tri_angle(sig)
branch = upper_branched_surface(tri, angle)
loops = find_flow_cycles(tri, branch)
tri_loops = [
flow_cycle_to_triangle_loop(tri, branch, loop) for loop in loops
]
for i, tri_loop in enumerate(tri_loops):
if tri_loop != False: # False means that tri_loop goes more than once along the same triangle - not currently implemented
tri, angle = isosig_to_tri_angle(sig)
if tri_loop_is_boundary_parallel(
tri_loop, tri
) == False: # if a loop is boundary parallel then we don't drill
branch = upper_branched_surface(tri, angle)
drilled_cusp_index = drill(tri,
tri_loop,
angle=angle,
branch=branch)
if has_essential_torus(tri):
print('sig', sig, 'has_essential_torus',
has_essential_torus(tri), 'loop', loops[i],
'tri_loop', tri_loop)
else:
print('sig', sig, 'has_essential_torus',
has_essential_torus(tri), 'loop', loops[i],
'tri_loop', tri_loop)
ceiling = tri.countTetrahedra() + extra_ceiling
print('ceiling', ceiling)
start_isoSig = isosig_from_tri_angle_branch(
tri, angle, branch)
print(start_isoSig, 'angle', angle, 'branch', branch,
'drilled_cusp_index', drilled_cusp_index)
graph = search_Pachner_graph_for_shortest_path(
start_isoSig,
tri,
angle,
branch,
name=None,
search_depth=depth,
ceiling=ceiling,
drilled_cusp_index=drilled_cusp_index,
check_property=False,
property=None,
save_dir=None)
def search_Pachner_graph_for_shortest_path(start_isoSig,
tri,
angle,
branch,
name=None,
search_depth=3,
ceiling=5,
drilled_cusp_index=None,
check_property=False,
property=None,
save_dir=None):
start_node = pachner_node(start_isoSig,
tri,
angle,
branch,
drilled_cusp_index=drilled_cusp_index,
ceiling=ceiling)
start_node.came_from = None
big_dict_of_nodes = {start_isoSig: start_node}
frontier_isoSigs = set([start_isoSig])
# print(len(big_dict_of_nodes), len(frontier_isoSigs))
for counter in range(search_depth):
if len(frontier_isoSigs) == 0: #we are done...
# print('done')
break
new_frontier_isoSigs = set([])
# for each element in the frontier check to see if it appears on the big_list_of_sigs if not we add it to the big list
for cur_isoSig in frontier_isoSigs:
current_node = big_dict_of_nodes[cur_isoSig]
neighbour_isoSigs = current_node.all_neighbour_isoSigs()
for nb_isoSig in neighbour_isoSigs:
if not nb_isoSig in big_dict_of_nodes:
nb_tri, nb_angle, nb_branch, nb_drilled_cusp_index = current_node.neighbour_moves_tri_angle_branch[
nb_isoSig]
#print('nb drilled cusp', nb_drilled_cusp_index)
new_node = pachner_node(
nb_isoSig,
nb_tri,
nb_angle,
nb_branch,
drilled_cusp_index=nb_drilled_cusp_index,
ceiling=ceiling)
new_node.came_from = cur_isoSig
if counter == search_depth - 1: #last layer
new_node.is_frontier = True
new_frontier_isoSigs.add(nb_isoSig)
big_dict_of_nodes[nb_isoSig] = new_node
if is_veering(nb_tri, nb_angle):
print(
'veering!',
isosig_from_tri_angle_branch(
nb_tri, nb_angle, nb_branch))
upper_branch = upper_branched_surface(
nb_tri, nb_angle, return_lower=False)
lower_branch = upper_branched_surface(
nb_tri, nb_angle, return_lower=True)
print(
'upper:',
isosig_from_tri_angle_branch(
nb_tri, nb_angle, upper_branch))
print(
'lower:',
isosig_from_tri_angle_branch(
nb_tri, nb_angle, lower_branch))
print_path(nb_isoSig, big_dict_of_nodes)
## break
return None
frontier_isoSigs = new_frontier_isoSigs
# print(len(big_dict_of_nodes), len(frontier_isoSigs))
print('did not find veering')
return None