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### 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() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in alexander_polynomial(self, var) 1780 R = LaurentPolynomialRing(ZZ, var) 1781 # The Alexander polynomial of disjoint links are defined to be 0 -> 1782 if len(self._braid_word_components()) > 1: 1783 return R.zero() 1784 t = R.gen() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in _braid_word_components(self) 1433 ([-2, 1, 1], [4, 4], [6]) 1434 """ -> 1435 ml = list(self.braid().Tietze()) 1436 if not ml: 1**437 return tuple() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in braid(self) 654 C1 = newPD[newPD.index(heads[-a])] 655 C1[C1.index(-a)] = newedge + 1 --> 656 C2 = newPD[newPD.index(tails[-b])] 657 C2[C2.index(-b)] = newedge + 2 658 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!

### 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]])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()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() A.alexander_polynomial() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in alexander_polynomial(self, var) 1780 R = LaurentPolynomialRing(ZZ, var) 1781 # The Alexander polynomial of disjoint links are defined to be 0 -> 1782 if len(self._braid_word_components()) > 1: 1783 return R.zero() 1784 t = R.gen() R.gen() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in _braid_word_components(self) 1433 ([-2, 1, 1], [4, 4], [6]) 1434 """ -> 1435 ml = list(self.braid().Tietze()) 1436 if not ml: 1**437 return tuple() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in braid(self) 654 C1 = newPD[newPD.index(heads[-a])] 655 C1[C1.index(-a)] = newedge + 1 --> 656 C2 = newPD[newPD.index(tails[-b])] 657 C2[C2.index(-b)] = newedge + 2 658 newPD.append([newedge + 2, newedge, newedge + 3, newedge + 1]) ValueError: [5, 8, 6, 1] is not in list**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!

 3 None slelievre 16999 ●21 ●151 ●335 http://carva.org/samue...

### 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]])
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()
A.alexander_polynomial()


I get the following error:

## ValueError ... Traceback (most recent call last) in () 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)]]) 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() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc A.alexander_polynomial() /path/to/sagedir/local/lib/python2.7/site-packages/sage/knots/link.pyc in alexander_polynomial(self, var) 1780 var) 1792 R = LaurentPolynomialRing(ZZ, var) 1781 var) 1793 # The Alexander polynomial of disjoint links are defined to be 0 0 -> 1782 1794 if len(self._braid_word_components()) > 1: 1783 1: 1795 return R.zero() 1784 R.zero() 1796 t = R.gen() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in _braid_word_components(self) 1433 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]) 1434 """ [6]) 1446 """ -> 1435 1447 ml = list(self.braid().Tietze()) 1436 list(self.braid().Tietze()) 1448 if not ml: 1**437 ml: 1449 return tuple() /home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/link.pyc in braid(self) 654 tuple() /path/to/sagedir/local/lib/python2.7/site-packages/sage/knots/link.pyc in braid(self) 666 C1 = newPD[newPD.index(heads[-a])] 655 newPD[newPD.index(heads[-a])] 667 C1[C1.index(-a)] = newedge + 1 1 --> 656 668 C2 = newPD[newPD.index(tails[-b])] 657 newPD[newPD.index(tails[-b])] 669 C2[C2.index(-b)] = newedge + 2 658 2 670 newPD.append([newedge + 2, newedge, newedge + 3, newedge + 1]) 1]) ValueError: [5, 8, 6, 1] is not in listlist 

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!