Seifert matrix

Major work without documentation

from sage.groups.free_group import FreeGroupElement
from sage.groups.braid import Braid

class Link:
	def __init__(self, input = None, gauss_code = None, dt_code = None):
		if type(input) == sage.groups.braid.Braid:
			self._braid = input
			self._gauss_code = None
			self._dt_code = None

		elif gauss_code != None:
			self._braid = None
			self._gauss_code = gauss_code
			self._dt_code = None

		elif dt_code != None:
			self._braid = None
			self._gauss_code = None
			self._dt_code = dt_code

		else:
			raise Exception("Invalid input")

	def braid(self):
		if self._braid != None:
			return self._braid

		elif self._gauss_code != None: 
			return "Not implemented Error"

		elif self._dt_code != None:
			return "Not Implemented Error"

	def gauss_code(self):
		if self._gauss_code != None:
			return self._gauss_code

		elif self._braid != None:
			return "Not Implemented Error"

		elif self._dt_code != None:
			return "Not Implemented Error"

	def dt_code(self):
		if self._dt_code != None:
			return self._dt_code

		elif self._braid != None:
			return "Not Implemented Error"

		elif self._gauss_code != None:
			return "Not Implemented Error"

	def braidcomponentsmatrix(self):
		b = self.braid()
		ml = list(b.Tietze())
		l = [abs(k) for k in ml]
		sorting1 = list(set(range(l[0],max(l)+1)) - set(l))
		sorting = list(set(range(l[0],max(l)+1)) - set(sorting1))
		missing = []
		difference = []
		difference.append(sorting[0] -1)
		for i in range(1, len(sorting)):
			difference.append(sorting[i] - sorting[i-1])
		missing = list(set(range(sorting[0],sorting[-1]+1)) - set(sorting))
		if len(missing) == 0:
			A = matrix(QQ,1,len(ml),ml)
			return A
		else:
			A = matrix(QQ, len(missing) + 1, len(l))
			for i in range(len(missing) + 1):
	        		k = 0
	        		for j in range(len(l)):
	        			if i == 0:
	        				if (abs(l[j]) < missing[i]):
	        					A[0, k] = ml[j]
	       						k = k + 1
	       				elif i>len(missing):
	       					if missing[i] < abs(x[j]):
	        					A[i, k] = ml[j]
	        					k = k + 1
	        			else:
	        				if(missing[i-1] < abs(l[j])):
	       						A[i, k] = ml[j]
	 	       					k = k + 1
	 	
	 		for i in range(len(missing) + 1):
					l1 = list(A.row(i))
	 				M = min(l1)
	 				if M == 0:
	 					a = min(n for n in l1 if n!=M)
	 					for j in range(len(l)):
	 						if(A[i,j] != a):
								A[i,j] = 0

			value = None
			for i in range(len(missing) + 1):
					for k in range(i+1, len(missing) + 1):
							if(A[i,0] == A[k,0]):
								value = 1
								A1 = A.delete_rows([k])
			return A1 if value == 1 else A				
			
	def braidwordcompenetsvector(self):
		A = self.braidcomponentsmatrix()
		if(A.nrows()>0):
			x2 = []
			for i in range(A.nrows()):
				for j in range(A.ncols()):
					x2.append(A[i,j])
					x3 = [value for value in x2 if value != 0]
			return x3
		else:
			x3 = A.row(1)
			return list(x3)
	
	def homology_generators(self):
		x4 = list(self.braid().Tietze())
		hom_gen = []
		for j in range(len(x4)-1):
			a = abs(x4[j])
			for i in range(j+1, len(x4)):
					if(a == abs(x4[i])):
						hom_gen.append(i)
						break
			else:
				hom_gen.append(0)
		return hom_gen

	def Seifert_Matrix(self):
		x5 = self.braidwordcompenetsvector()
		h = self.homology_generators()
		hl = len(h)
		A = matrix(QQ, hl, hl)
		for i in range(hl):
			if h[i] != 0:
				for j in range(i,hl):
						if i == j:
							A[i,j] = -cmp((x5[i] + x5[h[i]]),0)
						elif (h[i] > h[j]):
							A[i,j] = 0
							A[j,i] = 0
						elif (h[i] <  j):
							A[i,j] = 0
							A[j,i] = 0
						elif (h[i] == j):
							if(x5[j] > 0):
								A[i,j] = 0
								A[j,i] = 1
							else:
								A[i,j] = -1
								A[j,i] = 0
						elif abs(abs(x5[i]) - abs(x5[j])) > 1:
							A[i,j] =  0
						elif (abs(x5[i]) - abs(x5[j]) == 1):
							A[i,j] = 0
							A[j,i] = -1
						elif (abs(x5[j])- abs(x5[i]) == 1):
							A[i,j] = 1
							A[j,i] = 0
				else:
					A[i,j] = 2
					A[j,i] = 2
			else:
				for k in range(hl):
					A[k,i] = 0
					A[i,k] = 0
		k = []
		for i in range(hl):
				if h[i] == 0:
					k.append(i)
		for i in reversed(k):
				A = A.delete_rows([i])
				A = A.delete_columns([i])
		return A

	def link_number(self):
		count = 0
		b = self.braid().permutation()
		c = [0 for i in range(len(b))]
		for i in range(len(b)):
			if c[i] == 0:
				c[i] = 1
				k = b[i]
				#print k - 1 
				while((k-1) != i):
					c[(k-1)] = 1
					k = b[k-1]
				count = count + 1
		return count