def clasp():
c, d = spherogram.Crossing('c'), spherogram.Crossing('d')
c[0] = d[1]
c[1] = d[0]
d2, d3 = d.crossing_strands()[2], d.crossing_strands()[3]
c2, c3 = c.crossing_strands()[2], c.crossing_strands()[3]
return Tangle(2, [c, d], [d2, d3, c3, c2])
def link_diagram(G):
face_list = faces(G)
#print(face_list)
crossing_dict = {}
for edge in G.edges: #create one crossing per edge
l = label(edge)
crossing_dict[l] = spherogram.Crossing(l)
for face in face_list: #connect along faces
for n, direction in enumerate(face):
edge = direction[0]
next_edge = face[(n + 1) % len(face)][0]
c = crossing_dict[label(edge)]
cnext = crossing_dict[label(next_edge)]
o = open_overposition(c)
u = open_underposition(cnext)
# print('c,o: ')
# print(c,o)
# print('cnext,u: ')
# print(cnext,u)
c[o] = cnext[u]
for edge in G.edges: #switch twisted edges
c = crossing_dict[label(edge)]
if edge.twisted:
c.rotate_by_90()
return spherogram.Link(crossing_dict.values())
def petaluma_knot(height_perm):
size = len(height_perm)
crossing_dict = {}
visited_dict = {}
for i in range(size - 1):
for j in range(i + 1, size):
crossing_dict[(i, j)] = sg.Crossing('c' + str(i) + str(j))
visited_dict[(i, j)] = False
end_position = 2
if height_perm[1] < height_perm[0]:
end_position = 3
old_crossing = crossing_dict[0, 1]
visited_dict[0, 1] = True
for i in range(size):
for j in strands_to_cross(size, i):
if (i, j) == (0, 1):
continue
a, b = sorted([i, j]) #must be ordered
next_crossing = crossing_dict[a, b]
ordered_or_backward = 0
if i > j:
ordered_or_backward = 1
if height_perm[i] < height_perm[
j]: # strand i passes under strand j
if not visited_dict[a, b]: #if first time crossing has come up
next_crossing[0] = old_crossing[end_position]
end_position = 2
else: #crossing has been seen before
if (
b - a
) % 2 == 1: #strand j should cross strand i right to left
next_crossing[2] = old_crossing[end_position]
end_position = 0
else: #left to right
next_crossing[0] = old_crossing[end_position]
end_position = 2
else: #strand i passes over strand j
if not visited_dict[a, b]:
next_crossing[1] = old_crossing[end_position]
end_position = 3
else: #crossing has been seen before
if (b - a) % 2 == 1: #right to left
next_crossing[1] = old_crossing[end_position]
end_position = 3
else: #left to right
next_crossing[3] = old_crossing[end_position]
end_position = 1
visited_dict[a, b] = True
old_crossing = next_crossing
first = crossing_dict[0, 1]
last = crossing_dict[size - 2, size - 1]
first_open = first.adjacent.index(None) #last open spot
last_open = last.adjacent.index(None)
first[first_open] = last[last_open]
return sg.Link(crossing_dict.values())
def unknot_search(num_attempts, backtrack_height, num_mutations):
c = spherogram.Crossing(0)
c[0] = c[1]
c[2] = c[3]
U = spherogram.Link([c])
for i in range(num_attempts):
print(i)
Uc = U.copy()
Uc.backtrack(backtrack_height)
for i in range(num_mutations):
Uc = random_mutate(Uc)
Uc.simplify(mode='level')
if len(Uc) > 0:
return Uc
return None
def add_random_crossing(self,label):
tangle_copy = self.copy()
adj = tangle_copy.adjacent
adj[len(adj)/2:] = reversed(adj[len(adj)/2:])
new_crossing = spherogram.Crossing(label)
old_position = randint(0,len(adj)-1)
old_crossing, old_strand = adj.pop(old_position)
new_strand = randint(0,3)
old_crossing[old_strand]=new_crossing[new_strand]
for i in range(1,4):
adj.insert(old_position,(new_crossing,(new_strand-i)%4))
adj[len(adj)/2:] = reversed(adj[len(adj)/2:])
tangle_copy.crossings.append(new_crossing)
tangle_copy.n = self.n+1
return tangle_copy
v = Kc.exterior().volume() G = K.dual_graph() cycle = max(cycle_basis(G),key=len) T1, T2, gluings = tangle_neighborhood(Kc,c,1) print(gluings) """ v1 = T1.circular_sum(T1,0).exterior().volume() v2 = T2.circular_sum(T2,0).exterior().volume() avg_vol = v1/2+v2/2 tsums = T1.all_circular_sums(T2) vols = map(lambda x: x.exterior().volume(), tsums) print(v,avg_vol) """ a,b,c,d,e,f,g,h = [spherogram.Crossing(x) for x in 'abcdefgh'] a[0]=e[2] a[1]=b[3] a[3]=e[3] b[0]=f[2] b[1]=c[3] b[2]=c[2] c[0]=g[2] c[1]=d[3] d[0]=h[2] d[1]=h[1] e[1]=f[3] f[0]=g[0] f[1]=g[3] g[1]=h[3] crossings = [a,b,c,d,e,f,g,h]
def setUp(self):
# Trefoil
a = spherogram.Crossing('a')
b = spherogram.Crossing('b')
c = spherogram.Crossing('c')
a[2] = b[1]
b[3] = c[0]
c[2] = a[1]
a[3] = b[0]
b[2] = c[1]
c[3] = a[0]
self.Tref = spherogram.Link([a, b, c])
self.K3_1 = spherogram.Link('3_1')
self.K7_2 = spherogram.Link('7_2')
self.K8_3 = spherogram.Link('8_3')
self.K8_13 = spherogram.Link('8_13')
# Hopf Link
a = spherogram.Crossing('a')
b = spherogram.Crossing('b')
a[0] = b[1]
a[1] = b[0]
a[2] = b[3]
a[3] = b[2]
self.L2a1 = spherogram.Link([a, b])
# Borromean Link (3)
a = spherogram.Crossing('a')
b = spherogram.Crossing('b')
c = spherogram.Crossing('c')
d = spherogram.Crossing('d')
e = spherogram.Crossing('e')
f = spherogram.Crossing('f')
a[2] = f[1]
a[3] = e[0]
b[1] = a[0]
b[2] = e[3]
c[0] = a[1]
c[1] = b[0]
d[3] = c[2]
d[0] = b[3]
e[2] = d[1]
e[1] = f[0]
f[2] = c[3]
f[3] = d[2]
self.Borr = spherogram.Link([a, b, c, d, e, f])
self.L6a2 = spherogram.Link('L6a2')
self.L6a4 = spherogram.Link('L6a4')
self.L7a3 = spherogram.Link('L7a3')
self.L10n1 = spherogram.Link('L10n1')
self.knots = [self.K3_1, self.K7_2, self.K8_3, self.K8_13]
self.links = [self.L2a1, self.L6a4, self.L6a2, self.L7a3, self.L10n1]
self.all_links = self.knots + self.links