def D33():
R2 = flatsurf.Vector['eantic::renf_elem_class']
R = eantic.renf_elem
zero = R(O, 0)
one = R(O, 1)
two = R(O, 2)
one_fourth = R(O, 1) / R(O, 4)
three_fourth = R(O, 3) / R(O, 4)
eleven_fourth = R(O, 11) / R(O, 4)
fifteen_fourth = R(O, 15) / R(O, 4)
x = O.gen()
vectors = [
R2(x + one_fourth, x),
R2(-x, zero),
R2(-one_fourth, -x),
R2(x + three_fourth, 2),
R2(-x, zero),
R2(-three_fourth, -two),
R2(one, two),
R2(-one_fourth, zero),
R2(-three_fourth, -two),
R2(one, two),
R2(x - fifteen_fourth, zero),
R2(eleven_fourth - x, -two)
]
vertices = [[1, -3, 5, -4, 9, -8, 10, -12, 11, -10, 6, -5],
[3, -2, 4, -6, 8, -7, 12, -11, 7, -9, 2, -1]]
return Surface(vertices, vectors)
def hexagon():
R2 = flatsurf.Vector['eantic::renf_elem_class']
x = K.gen()
R = eantic.renf_elem
vectors = [
R2(R(K, 2), R(K, 0)),
R2(R(K, 1), x),
R2(R(K, 3), x),
R2(R(K, 1), -x),
R2(R(K, 4), R(K, 0)),
R2(R(K, 3), x)
]
vertices = [[1, 3, -4, -5, -3, -2], [2, -1, -6, 4, 5, 6]]
return Surface(vertices, vectors)
def random_hexagon(R2):
x = K.gen()
M = NumberFieldModule(K, RealNumber.rational(1), RealNumber.random(),
RealNumber.random())
# The side lengths are going to be 2, 2·μ, 2·ν where μ,ν are the random parameters of M.
one = M.gen(0)
μ = M.gen(1)
ν = M.gen(2)
# We build our vectors from (2, 0), μ·(1, √3), ν.(-1, √3).
u = R2(2 * one, 0 * one)
v = R2(μ, x * μ)
w = R2(-ν, x * ν)
vectors = [u, v, u + v, -w, u + v - w, u + v]
vertices = [[1, 3, -4, -5, -3, -2], [2, -1, -6, 4, 5, 6]]
return Surface(vertices, vectors)
def hexagon(R2):
x = K.gen()
R = R2.Coordinate
if R2 == flatsurf.Vector[cppyy.gbl.eantic.renf_elem_class]:
R = eantic.renf_elem
vectors = [
R2(R(K, 2), R(K, 0)),
R2(R(K, 1), x),
R2(R(K, 3), x),
R2(R(K, 1), -x),
R2(R(K, 4), R(K, 0)),
R2(R(K, 3), x)
]
vertices = [[1, 3, -4, -5, -3, -2], [2, -1, -6, 4, 5, 6]]
return Surface(vertices, vectors)
def L(R2):
vectors = [
R2(1, 0),
R2(1, 1),
R2(0, 1),
R2(-1, 0),
R2(-1, -1),
R2(1, 0),
R2(1, 1),
R2(0, 1),
R2(0, -1)
]
vertices = [[
1, 2, 3, 4, 5, -3, 6, 7, 8, -6, -2, 9, -4, -5, -9, -1, -7, -8
]]
return Surface(vertices, vectors)
cycles = []
while vertices:
key = next(iter(vertices.keys()))
cycle = []
while True:
cycle.append(key)
successor = vertices[key]
del vertices[key]
key = successor
if key == cycle[0]: break
cycles.append(cycle)
vertices = cycles
surface = Surface(vertices, vectors)
print(surface)
for connection in surface.saddle_connections(flatsurf.Bound(args.bound, 0)):
print("Investigating in direction %s" % (connection.vector()))
decomposition = flatsurf.makeFlowDecomposition(surface,
connection.vector())
decomposition.decompose()
if not all([
bool(component.cylinder())
for component in decomposition.components()
]):
for component in decomposition.components():
print(component)
if any([
def square(R2):
vectors = [R2(1, 0), R2(0, 1), R2(1, 1)]
vertices = [[1, 3, 2, -1, -3, -2]]
return Surface(vertices, vectors)