A very initial implementation of Seifert Matrix.

seifert matrix

from sage.matrix.constructor import identity_matrix, matrix
def components(x):
	new = []
	for i in range(len(x)):
		a = abs(x[i])
		new.append(a)
	print new
	sorted = list(set(new))
	print sorted 
	'''sorting the absolute values of the braid word'''
	difference = []
	difference.append(sorted[0] - 1)
	for i in range(1,len(sorted)):
		difference.append(sorted[i]-sorted[i-1])
	print difference
	
	q=0
	missing = []
	for i in range(len(difference)):
		a = difference[i]-1
		for k in range(1,a+1):
			q = q + 1
			missing.append(sorted[i-1] + k)
	print missing

	h = []
	for j in range(len(new)):
		a = new[j]
		for i in range(j+1,len(new)):

			if(a == new[i]):
				h.append(i)
				break
		else:
			h.append(0)
	print h
	hlen=len(h)
	
	m = matrix(hlen)
	a = []
	a = m.columns()
	b = []

		
	for i in range(len(a)):
		b.append(list(a[i]))

	for i in range(len(x)-1):
		if((x[i]>0 and x[h[i]]<0) or (x[i]<0 and x[h[i]]>0)):
			b[i][i]=0
		if(x[i]>0 and x[h[i]]>0):
			b[i][i]=-1
		if(x[i]<0 and x[h[i]]<0):
                        b[i][i]=1
	for i in range(hlen):
		if(h[i]!=0):
			for j in range(hlen):
				if(i<j and h[i]>h[j]):
					b[i][j]=0
					b[j][i]=0
				if(i<j and h[i] < j):
					b[i][j]=0
					b[j][i]=0
				if(i<j and h[i]==j):
					if(x[j]>0):
						b[i][j]=0
						b[j][i]=1
					else:
						b[i][j]=-1
						b[j][i]=0
		else:
			if(abs(abs(x[i])-abs(x[j]))>1):
				b[i][j]=0
			if(abs(abs(x[i])-abs(x[j]))==1):
				b[i][j]=0
				b[i][j]=-1
			if(abs(abs(x[j])-abs(x[i]))==1):
				b[i][j]=1
				b[j][i]=0	
	print b	
	
x = [2,-2,-4,-2,3]
y = components(x)