# problems with gauss code for knots

I am generating Gauss-codes for knots, and I would like to compute some of their invariants (e.g. knot polynomials). However, I am running in some problems. For example:

```
A = Link([[[1, 2, -2, -1, -3, -4, 4, 3]], [1, 1, 1, 1]])
```

Is recognized as a knot (I can compute the fundamental group, the writhe and the Seifert circles, and tell if it is alternating), but If I try to compute the Alexander polynomial:

```
A.alexander_polynomial()
```

I get the following error:

```
ValueError ... Traceback (most recent call last)
in ()
1 A = Link([[[Integer(1),Integer(2),-Integer(2),-Integer(1),-Integer(3),-Integer(4),Integer(4),Integer(3)]],[Integer(1),Integer(1),Integer(1),Integer(1)]])
----> 2 A.alexander_polynomial()
/path/to/sagedir/local/lib/python2.7/site-packages/sage/knots/link.pyc in alexander_polynomial(self, var)
1792 R = LaurentPolynomialRing(ZZ, var)
1793 # The Alexander polynomial of disjoint links are defined to be 0
-> 1794 if len(self._braid_word_components()) > 1:
1795 return R.zero()
1796 t = R.gen()
/path/to/sagedir/local/lib/python2.7/site-packages/sage/knots/link.pyc in _braid_word_components(self)
1445 ([-2, 1, 1], [4, 4], [6])
1446 """
-> 1447 ml = list(self.braid().Tietze())
1448 if not ml:
1449 return tuple()
/path/to/sagedir/local/lib/python2.7/site-packages/sage/knots/link.pyc in braid(self)
666 C1 = newPD[newPD.index(heads[-a])]
667 C1[C1.index(-a)] = newedge + 1
--> 668 C2 = newPD[newPD.index(tails[-b])]
669 C2[C2.index(-b)] = newedge + 2
670 newPD.append([newedge + 2, newedge, newedge + 3, newedge + 1])
ValueError: [5, 8, 6, 1] is not in list
```

I think the problem is in the translation from Gauss code to an element in the braid group. Moreover, I get similar errors with other examples, also with really simple ones. Any idea on how to solve this? Thanks in Advance!

Welcome to Ask Sage! Thank you for your question!

Possibly related to:

I can observe the same error in Sage 8.2.beta8.

It seems that the braid function is not working properly

Yes, the issue can be reduced to: