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amitjamadagni/gist:57b5de098efe11056efa

Created July 5, 2014 23:15
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good one
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gistfile1.py
def seifert_to_braid(self):
#x = self.final()
sc = self.final()[0]
regions = self.final()[1]
pd_code = self.final()[2]
sign = []
for i in pd_code:
if i[1] > i[3]:
sign.append('-')
elif i[1] < i[3]:
sign.append('+')
print sign
entering = []
leaving = []
for i in range(len(pd_code)):
t = []
q = []
if sign[i] == '-':
t.append(pd_code[i][0])
t.append(pd_code[i][3])
q.append(pd_code[i][1])
q.append(pd_code[i][2])
elif sign[i] == '+':
t.append(pd_code[i][0])
t.append(pd_code[i][1])
q.append(pd_code[i][2])
q.append(pd_code[i][3])
entering.append(t)
leaving.append(q)
print pd_code
print entering
print leaving
#making regions positive
for i in regions:
for j in range(len(i)):
if i[j] < 0:
i[j] = (-1)*i[j]
#finding which sc are same as regions
#r[0] is the first seifert cirlce and r[1] is the last one
#which coincides with a region and there are exactly two seifert
#circles here.
r = []
for i in sc:
for j in regions:
if set(i) == set(j):
r.append(i)
break
#here t stores the crossing information required to check which one
#is the next
t = [[None for i in range(2*len(sc[j]))] for j in range(len(sc))]
for i in range(len(sc)):
for j in range(len(sc[i])):
t[i][2*j] = sc[i][j] - 1
t[i][2*j+1] = sc[i][j] + 1
#print t
#here we find the order of the seifert circles
e = []
t1 = deepcopy(t)
a = r[0]
b = r[1]
del t[0]
i = 0
while True:
for i in range(len(t)):
if len(list(set(a).intersection(set(t[i])))) != 0:
r = t1.index(t[i])
e.append(a)
del t[i]
a = sc[r]
break
else:
e.append(b)
break
#braid numbering and matching the crossings
print e
t = []
flatentering = [a for b in entering for a in b]
for i in flatentering:
for k in e:
if i in k:
t.append(e.index(k))
print t
for i in range(len(entering)):
#if t[2*i] > t[2*i+1]:
if sign[i] == '-':
if t[2*i] > t[2*i+1]:
a = entering[i][0]
entering[i][0] = entering[i][1]
entering[i][1] = a
b = leaving[i][0]
leaving[i][0] = leaving[i][1]
leaving[i][1] = b
#elif sign[i] == '+':
#a = entering[i][0]
#entering[i][0] = entering[i][1]
#entering[i][1] = a
#elif sign[i] == '+':
#a = entering[i][
print entering
print leaving
bn = {}
for i in range(len(e)):
bn.update({i + 1 : e[i]})
print bn
crossingtoseifert = {}
for i in bn.iterkeys():
crossingtoseifert.update({i:[]})
for i in bn.iterkeys():
for k in pd_code:
if len(list(set(bn[i]).intersection(set(k)))) == 2:
crossingtoseifert[i].append(k)
print crossingtoseifert
crossingtoseifertcp = deepcopy(crossingtoseifert)
crossingtoseifertsign = {}
for i in crossingtoseifert.iterkeys():
crossingtoseifertsign.update({i:[]})
for i in crossingtoseifert.iterkeys():
for j in crossingtoseifert[i]:
if j[1] > j[3]:
crossingtoseifertsign[i].append(-1)
if j[1] < j[3]:
crossingtoseifertsign[i].append(1)
print crossingtoseifertsign
crossingtoseifertsigncp = deepcopy(crossingtoseifertsign)
tmp = []
reg = [0 for i in range(len(sc))]
if crossingtoseifertsign[1][0] == -1:
#reg[0] = crossingtoseifert[1][0][1]
#reg[1] = crossingtoseifert[1][0][2]
tmp.append(crossingtoseifert[1][0][1])
tmp.append(crossingtoseifert[1][0][2])
#leave.append(crossingtoseifert[1][0][1])
#leave.append(crossingtoseifert[1][0][2])
elif crossingtoseifertsign[1][0] == 1:
#reg[0] = crossingtoseifert[1][0][2]
#reg[1] = crossingtoseifert[1][0][3]
tmp.append(crossingtoseifert[1][0][2])
tmp.append(crossingtoseifert[1][0][3])
#leave.append(crossingtoseifert[1][0][2])
#leave.append(crossingtoseifert[1][0][3])
#print reg
#print tmp
for i in leaving:
if set(tmp) == set(i):
reg[0] = i[0]
reg[1] = i[1]
crossing = []
crossing.append(crossingtoseifert[1][0])
q = 0
while q < len(pd_code):
for val in zip(reg, reg[1:]):
#print val
for i in range(len(entering)):
if set(val) == set(entering[i]):
print val
#print entering[i]
crossing.append(pd_code[i])
#del pd_code[i]
if sign[i] == '-':
#reg[reg.index(val[0])] = pd_code[i][1]
#reg[reg.index(val[1])] = pd_code[i][2]
print leaving[i][0]
print leaving[i][1]
reg[reg.index(val[0])] = leaving[i][0]
reg[reg.index(val[1])] = leaving[i][1]
print reg
q = q + 1
break
elif sign[i] == '+':
print leaving[i][1]
print leaving[i][0]
if list(val) == entering[i]:
reg[reg.index(val[0])] = leaving[i][1]
reg[reg.index(val[1])] = leaving[i][0]
elif set(val) == set(entering[i]):
reg[reg.index(val[0])] = leaving[i][0]
reg[reg.index(val[1])] = leaving[i][1]
print reg
q = q + 1
break
#del pd_code[i]
if len(list(set(val).intersection(set(entering[i])))) == 1 and 0 in set(val):
crossing.append(pd_code[i])
#del pd_code[i]
if sign[i] == '-':
#reg[reg.index(val[0])+1] = pd_code[i][2]
#reg[reg.index(val[0])] = pd_code[i][1]
reg[reg.index(val[0])+1] = leaving[i][1]
reg[reg.index(val[0])] = leaving[i][0]
print reg
q = q + 1
break
#reg[reg.index(val[0])+1] = pd_code[i][2]
elif sign[i] == '+':
reg[reg.index(val[0])+1] = pd_code[i][2]
reg[reg.index(val[0])] = pd_code[i][3]
print reg
q = q + 1
break
#q = q + 1 #del pd_code[i]
#reg[reg.index(val[0])+1] = pd_code[i][3]
#print pd_code
del crossing[len(pd_code)]
print crossing
for i in range(1,len(sc)):
for j in crossingtoseifertcp[i]:
x = crossingtoseifertcp[i+1].index(j)
del crossingtoseifertcp[i+1][x]
del crossingtoseifertsigncp[i+1][x]
#print bn[i+1][x]
print crossingtoseifertcp
print crossingtoseifertsigncp
braid = []
for i in crossing:
for j,k in crossingtoseifertcp.items():
for l in k:
if i == l:
braid.append(j*crossingtoseifertsigncp[j][k.index(l)])
print braid
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