def __init__(self,
surface_name,
generators,
automorph,
MCG_must_contain,
word_filter=basic_filter,
manifold_filter=basic_filter,
options=None):
self.surface_name = surface_name
self.generators = generators
self.automorph = automorph
self.MCG_must_contain = MCG_must_contain
self.word_filter = word_filter
self.manifold_filter = manifold_filter
self.options = options if options is not None else Options()
self.surfaces = SimpleNamespace(
twister=snappy.twister.Surface(self.surface_name),
flipper=flipper.load(self.surface_name),
curver=curver.load(self.surface_name),
)
self.word_generator = WordGenerator(self.generators, self.automorph,
self.MCG_must_contain,
self.word_filter, self.surfaces,
self.options)
for path in [
self.options.word_parts, self.options.properties_parts,
self.options.word, self.options.properties, self.options.census
]:
os.makedirs(os.path.dirname(path), exist_ok=True)
def test_isometries(self):
tests = [('S_0_4', 2), ('S_1_1', 6), ('S_1_2', 4), ('S_2_1', 2),
('S_3_1', 2), ('E_12', 12), ('E_24', 24), ('E_36', 36)]
for surface, num_isoms in tests:
self.assertEqual(
len(flipper.load(surface).triangulation.self_isometries()),
num_isoms)
def test_sig(self):
for surface in [
'S_0_4', 'S_1_1', 'S_1_2', 'S_2_1', 'S_3_1', 'E_12', 'E_24',
'E_36'
]:
T = flipper.load(surface).triangulation
T2 = flipper.triangulation_from_iso_sig(T.iso_sig())
self.assertTrue(T.is_isometric_to(T2))
self.assertEqual(T.iso_sig(), T2.iso_sig())
def test_invariant_lamination(self):
# Add more tests here.
tests = [
('S_1_1', 'a'),
('S_1_2', 'a'),
('S_1_2', 'b'),
('S_1_2', 'c'),
('S_1_2', 'aB'),
('S_1_2', 'bbaCBAaBabcABB'),
('S_1_2', 'aCBACBacbaccbAaAAaBBcCcBBcCaBaaaABBabBcaBbCBCbaaa'),
('S_2_1', 'aaabcd'),
# ('E_12', 'aaaaBBc'), # Really slow.
# ('E_12', 'aaBaaBBc)' # Really slow.
# ('E_12', 'aaaaBBaBaBc') # Really slow useful for profiling. Current best time 102s.
]
try:
for surface, word in tests:
S = flipper.load(surface)
mapping_class = S.mapping_class(word)
mapping_class.invariant_lamination()
except flipper.AssumptionError:
pass # mapping_class is not pseudo-Anosov.
def test_random_word(self):
S = flipper.load('S_1_2')
all_words = set(S.all_words(5, equivalence='none'))
for _ in range(10):
word = S.random_word(5)
self.assertIn(word, all_words)
def test_composition(self):
S = flipper.load('S_1_2')
self.assertEqual(S.mapping_class('abababababab'),
S.mapping_class('xx'))
from time import time
import snappy
import flipper
for _, row in flipper.census('CHW').iterrows():
start_time = time()
M = snappy.Manifold(row.manifold)
N = snappy.Manifold(
flipper.load(row.surface).mapping_class(row.monodromy).bundle())
assert M.is_isometric_to(N) # Never fails for these examples.
print('Matched %s over %s with %s in %0.3fs.' %
(row.monodromy, row.surface, row.manifold, time() - start_time))
import flipper
S = flipper.load('S_1_2')
word = 'aCBACBacbaccbAaAcAaBBcCcBBcCaBaaaABBabBcaBbCBCbaaa'
h = S.mapping_class(word)
print('Built the mapping class h := \'%s\'.' % word)
print('h has order %s (where 0 == infinite).' % h.order())
print('h is %s.' % h.nielsen_thurston_type())
try:
print('h leaves L := %s projectively invariant.' %
h.invariant_lamination().projective_string())
print('and dilates it by a factor of %s.' % h.dilatation())
except flipper.AssumptionError:
print(
'We cannot find a projectively invariant lamination for h as it is not pseudo-Anosov.'
)
import flipper
length = 10
num_samples = 100
S = flipper.load('S_2_1')
for i in range(length):
pA_samples = sum(1 if S.mapping_class(i).is_pseudo_anosov() else 0
for _ in range(num_samples))
print('Length %d: %0.1f%% pA' % (i, float(pA_samples) * 100 / num_samples))
def match(surface, monodromy):
M = snappy.twister.Surface(surface).bundle(monodromy)
N = snappy.Manifold(
flipper.load(surface).mapping_class(monodromy).bundle())
return M.is_isometric_to(N)
import snappy
import flipper
# A pseudo-Anosov mapping class.
h = flipper.load('S_1_2').mapping_class('abC')
# Build Agol's veering triangulation of the bundle.
# This will fail with an AssumptionError if h is not pseudo-Anosov.
bundle = h.bundle()
print('It has %d cusp(s) with the following properties:' %
bundle.triangulation3.num_cusps)
for index, (real, fibre, degeneracy) in enumerate(
zip(bundle.cusp_types(), bundle.fibre_slopes(),
bundle.degeneracy_slopes())):
print('\tCusp %s (%s): Fibre slope %s, degeneracy slope %s' %
(index, 'Real' if real else 'Fake', fibre, degeneracy))
# Fake cusps filled.
M = snappy.Manifold(bundle)
print(M.identify())
# Can also build a non-veering triangulation of the bundle.
# This works for all mapping classes.
M2 = snappy.Manifold(h.bundle(veering=False))
print(M2.identify())
# If we don't fill the fake cusps we may get a differnt manifold.
N = snappy.Manifold(bundle.snappy_string(filled=False))
print(N.identify())
from time import time
import flipper
length = 7
S = flipper.load('S_1_2') # Get an EquippedTriangulation.
start_time = time()
all_words = list(S.all_words(length))
print('Built %d words in %0.3fs.' % (len(all_words), time() - start_time))
# In parallel:
start_time = time()
all_words2 = list(S.all_words(length, cores=2))
print('Built %d words in %0.3fs.' % (len(all_words2), time() - start_time))
assert len(all_words) == len(
set(all_words)) and set(all_words) == set(all_words2)
## this is a python executable that will be called from GH to get curve data using Connecting_Points.py
import Connecting_Points_0409 as cp
import Reordering_points as rp
import Graph_order as go
from sys import argv
import flipper
script, init_curve, mapping_class, iterations = argv
#mapping_class = 'aBeFcdAE'
#init_curve = 'b'
#iterations = 2
triangulation = [(1, 8, 0), (7, ~3, ~8), (2, 6, ~7), (5, ~2, ~6), (3, 4, ~5),
(~0, ~1, ~4)]
edges = [1, 6, 7, 8]
S = flipper.load('S_2_1')
h = S.mapping_class(mapping_class)
curve = S.lamination(init_curve)
for i in range(int(iterations)):
curve = h(curve)
oct_out = cp.octagon_only(cp.connecting(triangulation, curve.geometric), edges)
reordered = rp.reorder_list(oct_out)
perm = []
for connection in oct_out:
i = reordered.index(connection)
perm.append(i)
D = {1: 3, -2: 7, 6: 1, -7: 5, 7: 2, -8: 6, 8: 0, -9: 4}
new_out = []
for tup in reordered:
new_tup = ((D[tup[0][0]], tup[0][1]), (D[tup[1][0]], tup[1][1]))
new_out.append(new_tup)
newer_out = []
from time import time
import flipper
times = {}
surface = 'S_3_1'
length = 20
num_samples = 100
S = flipper.load(surface)
for index in range(num_samples):
monodromy = S.random_word(length)
h = S.mapping_class(monodromy)
start_time = time()
try:
h.invariant_lamination()
times[monodromy] = time() - start_time
print('%3d/%d: %s %s, Time: %0.3f' %
(index + 1, num_samples, surface, monodromy, times[monodromy]))
except flipper.AssumptionError:
times[monodromy] = time() - start_time
print('%3d/%d: %s %s, not pA, Time: %0.3f' %
(index + 1, num_samples, surface, monodromy, times[monodromy]))
print('Average time: %0.3f' % (sum(times.values()) / num_samples))
print(
'Slowest: %s, Time: %0.3f' %
(max(times, key=lambda w: times[w]).replace('.', ''), max(times.values())))
print('Total time: %0.3f' % sum(times.values()))
