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_closed_parallel_topological_type(self):
S = curver.load(2, 1)
a = S.triangulation([0, 2, 2, 2, 2, 0, 0, 0, 0])
b = S.triangulation([0, 0, 0, 0, 0, 2, 2, 2, 2])
self.assertEqual(a.topological_type(), b.topological_type())
self.assertEqual(a.topological_type(closed=True), b.topological_type(closed=True))
self.assertEqual((a+a).topological_type(), (b+b).topological_type())
self.assertEqual((a+a).topological_type(closed=True), (b+b).topological_type(closed=True))
self.assertNotEqual((a+a).topological_type(), (a+b).topological_type())
self.assertEqual((a+a).topological_type(closed=True), (a+b).topological_type(closed=True))
def test_dihedral(self, genus):
S = curver.load(genus, 2)
g = S('a_0.b_0.' + '.'.join('c_{}.b_{}'.format(i, i+1) for i in range(genus-1)) + '.p_1').simplify()
h = S('(a_0.b_0.' + '.'.join('c_{}.b_{}'.format(i, i+1) for i in range(genus-1)) + ')^{}.S_1'.format(2*genus+1)).simplify()
K = curver.kernel.FiniteSubgroup.from_generators({'g': g, 'h': h})
self.assertEqual(len(K), 4*(genus+1))
signature = [(Fraction(-genus, 2*(genus+1)), 1, [(False, 2, ['h'], 2*(genus+1)), (False, 2*(genus+1), ['hg'], 2), (True, 2*(genus+1), ['g' * (2*genus + 1)], 2)])]
self.assertEqual(K.quotient_orbifold_signature(), signature)
def test_pair(self, g, p):
assume(2 - 2 * g - p < 0)
T = curver.load(g, p).triangulation
self.assertTrue(T.is_connected())
surface = T.surface()
self.assertEqual(len(surface), 1)
S = list(surface.values())[0]
self.assertEqual(S.g, g)
self.assertEqual(S.p, p)
def main(args):
if args.sig is not None:
T = curver.triangulation_from_sig(args.sig)
else:
T = curver.load(args.genus, max(args.punctures, 1)).triangulation
P = Polyhedron.from_triangulation(T, args.upper, zeros=args.zeros)
num_integral_points = P.integral_points_count(triangulation='cddlib')
print(P)
try:
print('Polytope dimension: {}'.format(P.as_sage().dimension()))
except AttributeError:
print('Polytope dimension: Unknown')
print('Drawing from [0, {})'.format(num_integral_points))
common = dict(T=T, P=P, closed=args.punctures == 0)
iterable = (dict(index=randrange(0, num_integral_points)) for _ in range(args.num))
process(from_index, common, iterable, cores=args.cores, path=args.output)
def index(request):
error = None
order = None
classes = defaultdict(list)
non_periodic = []
if request.method == 'POST':
form = MappingClassForm(request.POST)
if form.is_valid():
try:
g = int(form.cleaned_data['genus'])
p = int(form.cleaned_data['punctures'])
words = form.cleaned_data['words']
S = curver.load(g, p)
for word in re.split('[;,]+', words):
h = S(word)
order = h.order()
if order == 0:
non_periodic.append(word)
else:
signature = h.subgroup().quotient_orbifold_signature(
)[0]
signature = Orbifold(
order, signature.euler_characteristic,
tuple(
sorted([
cone(cp, order)
for cp in signature.cone_points
])))
classes[signature].append(word)
except Exception as e:
error = str(e)
else:
form = MappingClassForm()
return render(
request, 'quotient/index.html', {
'form': form,
'error': error,
'classes': dict(classes),
'non_periodic': non_periodic,
'version': curver.__version__
})
def main(args):
if args.genus == 0 and args.punctures == 6:
common = dict(
T=curver.load(0, 6).triangulation,
P=Polyhedron(
eqns=[],
ieqs=[
[0, 1, 0, 1, -2, 0, 0], # 1 + 3 - 4 - 4
[0, -1, 1, 0, 2, 0, 0], # -1 + 2 + 4 + 4
[0, 1, 1, 0, 0, 0, -1], # 1 + 2 - 6
[0, -1, 0, 0, 1, 0, 1], # 4 + 6 - 1
[args.upper, -4, -8, -5, -4, -5, -2],
[-args.lower, 4, 8, 5, 4, 5, 2],
] + [[-1] + [0] * i + [1] + [0] * (6 - i - 1)
for i in range(6)]),
embedding=np.array([
[1, 0, 1, -1, 0, 0],
[1, 0, 1, 0, 0, 0],
[1, 1, 0, 0, 0, 0],
[1, 1, 0, 0, 1, -1],
[1, 0, 1, -2, 0, 0],
[-1, 1, 0, 2, 0, 0],
[-1, 1, 0, 2, 1, 1],
[0, 1, 0, 1, 1, 0],
[0, 0, 0, 1, 0, 0],
[0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 1],
[-1, 0, 0, 1, 0, 1],
],
dtype=object),
closed=False,
)
elif args.genus == 2 and args.punctures == 0:
common = dict(
T=curver.load(2, 1).triangulation,
P=Polyhedron(eqns=[],
ieqs=[
[-1, 1, 1, 1, 0, 0, -1],
[-1, -1, -1, -1, 1, 1, 1],
[args.upper, -7, -8, -7, -5, -5, -6],
[-args.lower, 7, 8, 7, 5, 5, 6],
] + [[-1] + [0] * i + [1] + [0] * (6 - i - 1)
for i in range(6)]),
embedding=np.array([
[2, 2, 2, 0, 0, 0],
[0, 0, 0, 1, 1, 2],
[0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 1, 1],
[0, 0, 0, 1, 0, 1],
[1, 2, 1, 0, 0, 0],
[1, 0, 1, 0, 0, 0],
[0, 1, 1, 0, 0, 0],
[1, 1, 0, 0, 0, 0],
]),
closed=True,
)
elif args.genus == 2 and args.punctures == 1:
common = dict(
T=curver.load(2, 1).triangulation,
P=Polyhedron(
eqns=[],
ieqs=[
[0, 1, 1, 0, -1, 0, 0, 0, 0], # 1 + 2 - 4
[0, 0, -1, 1, 1, 0, 0, 0, 0], # 3 + 4 - 2
[0, 0, 0, 0, 0, 1, 1, 0, -1], # 5 + 6 - 8
[0, 0, 0, 0, 0, 0, -1, 1, 1], # 7 + 8 - 6
[0, 0, 0, -1, -1, 0, 0, 1, 1], # 7 + 8 - 3 - 4
[0, 0, 0, 1, 1, 0, -1, 0, 1], # 3 + 4 + 8 - 6
[0, 0, 0, 1, 1, 0, 1, 0, -1], # 3 + 4 + 6 - 8
[args.upper, -11, -9, -9, -2, -9, -6, -6, -2],
[-args.lower, 11, 9, 9, 2, 9, 6, 6, 2],
] + [[-1] + [0] * i + [1] + [0] * (8 - i - 1)
for i in range(8)]),
embedding=np.array(
[
[0, 0, 2, 2, 0, 0, 0, 0], # 3 + 3 + 4 + 4
[0, 1, 1, 0, 0, 0, 0, 0], # 2 + 3
[0, -1, 1, 2, 0, 0, 0, 0], # 3 + 4 + 4 - 2
[1, 0, 1, 0, 0, 0, 0, 0], # 1 + 3
[1, 1, 0, 0, 0, 0, 0, 0], # 1 + 2
[0, 0, 0, 0, 0, 1, 1, 0], # 6 + 7
[0, 0, 0, 0, 0, -1, 1, 2], # 7 + 8 + 8 - 6
[0, 0, 0, 0, 1, 0, 1, 0], # 5 + 7
[0, 0, 0, 0, 1, 1, 0, 0], # 5 + 6
],
dtype=object),
closed=False,
)
elif args.genus == 3 and args.punctures == 0:
common = dict(
T=curver.load(3, 1).triangulation,
P=Polyhedron(
eqns=[],
ieqs=[
# a1, b1, c1, a2, b2, c2, a3, b3, c3, x, y, z
[-1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, +1, +1],
[-2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, +1, +1],
[-2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, +1, +1],
[-2, +2, +2, +2, 0, 0, 0, 0, 0, 0, 0, -1, -1],
[-1, 0, 0, 0, 0, -1, -1, 0, 0, 0, +1, 0, +1],
[-2, 0, 0, 0, 0, -2, 0, 0, 0, 0, +1, 0, +1],
[-2, 0, 0, 0, 0, 0, -2, 0, 0, 0, +1, 0, +1],
[-2, 0, 0, 0, +2, +2, +2, 0, 0, 0, -1, 0, -1],
[-1, 0, 0, 0, 0, 0, 0, 0, -1, -1, +1, +1, 0],
[-2, 0, 0, 0, 0, 0, 0, 0, -2, 0, +1, +1, 0],
[-2, 0, 0, 0, 0, 0, 0, 0, 0, -2, +1, +1, 0],
[-2, 0, 0, 0, 0, 0, 0, +2, +2, +2, -1, -1, 0],
[
args.upper, -4, -2, -2, -4, -2, -2, -4, -2, -2, -6, -6,
-6
],
[
-args.lower, +4, +2, +2, +4, +2, +2, +4, +2, +2, +6,
+6, +6
],
] + [[-1] + [0] * i + [1] + [0] * (12 - i - 1)
for i in range(12)]),
embedding=np.array([
#a1, b1, c1, a2, b2, c2, a3, b3, c3, x, y, z
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, +1, +1], # 0
[0, -1, -1, 0, 0, 0, 0, 0, 0, 0, +1, +1], # 1
[0, +1, +1, 0, 0, 0, 0, 0, 0, 0, 0, 0], # 2
[+1, 0, +1, 0, 0, 0, 0, 0, 0, 0, 0, 0], # 3
[+1, +1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], # 4
[0, 0, 0, 0, 0, 0, 0, 0, 0, +1, 0, +1], # 5
[0, 0, 0, 0, -1, -1, 0, 0, 0, +1, 0, +1], # 6
[0, 0, 0, 0, +1, +1, 0, 0, 0, 0, 0, 0], # 7
[0, 0, 0, +1, 0, +1, 0, 0, 0, 0, 0, 0], # 8
[0, 0, 0, +1, +1, 0, 0, 0, 0, 0, 0, 0], # 9
[0, 0, 0, 0, 0, 0, 0, 0, 0, +1, +1, 0], # 10
[0, 0, 0, 0, 0, 0, 0, -1, -1, +1, +1, 0], # 11
[0, 0, 0, 0, 0, 0, 0, +1, +1, 0, 0, 0], # 12
[0, 0, 0, 0, 0, 0, +1, 0, +1, 0, 0, 0], # 13
[0, 0, 0, 0, 0, 0, +1, +1, 0, 0, 0, 0], # 14
]),
closed=True,
)
else:
raise ValueError(
f'Intrinsic coordinates not known for S_{args.genus},{args.punctures}'
)
iterable = (dict() for _ in count())
process(func, common, iterable, cores=args.cores, path=args.output)
def memoized_load(*args):
return curver.load(*args)
def test_correct_component_of_topological_type_marked(self):
S = curver.load(2, 8)
c = S.curves['p_1'] + S.curves['p_3'] + S.curves['p_5'] + S.curves['p_7'] + S.arcs['s_2'].boundary() + S.arcs['s_4'].boundary() + S.arcs['s_6'].boundary() + S.arcs['s_2']
d = S.curves['p_1'] + S.curves['p_3'] + S.curves['p_5'] + S.curves['p_7'] + S.arcs['s_2'].boundary() + S.arcs['s_4'].boundary() + S.arcs['s_6'].boundary() + S.arcs['s_4']
self.assertNotEqual(c.topological_type(), d.topological_type())
return curver.load(*args)
@st.composite
def mcgs(draw):
g, p = draw(st.sampled_from(MCGS))
return memoized_load(g, p)
@st.composite
def mapping_classes(draw, triangulation=None, power_range=10):
return draw(encodings(triangulation, power_range, distribution=[2, 3]))
PERIODICS = [
curver.load(0, 6)('s_0.s_1.s_2.s_3.s_4'),
curver.load(0, 6)('(s_0.s_1.s_2.s_3.s_4)^2'),
curver.load(0, 6)('(s_0.s_1.s_2.s_3.s_4)^3'),
curver.load(0, 6)('s_0.s_1.S_3.S_4'),
curver.load(1, 1)('a_0.b_0'),
curver.load(1, 1)('a_0.b_0.a_0'),
curver.load(2, 1)('a_0.b_0.c_0.b_1'),
curver.load(2, 1)('a_0.b_0.c_0.b_1.a_1'),
curver.load(2, 2)('a_0.b_0.c_0.b_1.p_1'),
]
@st.composite
def periodic_mapping_classes(draw):
return draw(st.sampled_from(PERIODICS))
import argparse
parser = argparse.ArgumentParser(description='sample curves of at most a given weight')
parser.add_argument('--num', '-n', type=int, default=1000, help='number of samples to take')
parser.add_argument('--sig', '-s', type=str, help='signature of triangulation to use')
parser.add_argument('--genus', '-g', type=int, default=2, help='genus of surface to work over')
parser.add_argument('--punctures', '-p', type=int, default=0, help='num punctures of surface to work over')
parser.add_argument('--weight', '-w', type=int, default=1000000, help='max weight of a curve')
parser.add_argument('--zeros', '-z', type=int, default=35, help='which normal arcs to set to zero')
parser.add_argument('--cores', '-c', type=int, default=1, help='number of cores to use')
parser.add_argument('path', type=str, help='path to file to process')
args = parser.parse_args()
if args.sig is not None:
T = curver.triangulation_from_sig(args.sig)
else:
T = curver.load(args.genus, max(args.punctures, 1)).triangulation
P = get_polyhedron(T, args.weight, zeros=args.zeros)
num_integral_points = P.integral_points_count(triangulation='cddlib')
print(P)
try:
print('Polytope dimension: {}'.format(P.as_sage().dimension()))
except AttributeError:
print('Polytope dimension: Unknown')
print('Drawing from [0, {})'.format(num_integral_points))
common = {'T': T, 'P': P, 'closed': args.punctures == 0, 'labels': [label for label in [i for i in range(T.zeta)] + [~i for i in range(T.zeta)][::-1]]}
with open(args.path) as F:
iterable = ({'geometric': eval(line)} for line in F)
process(from_geometric, common, iterable, cores=args.cores)
