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Hi! I was trying to recursively construct connected sums of knots, but I seem to run in to some problems when connect summing a knot to itself more than two times:

B = BraidGroup(2)

trefoil = Knot(B([1,1,1]))

K = trefoil.connected_sum(trefoil)

L = K.connected_sum(trefoil)

This does not work:

ValueError                                Traceback (most recent call last)

ipython-input-1-7b977cf99468 in module()

 2 trefoil = Knot(B([Integer(1),Integer(1),Integer(1)]))

 3 K = trefoil.connected_sum(trefoil)

--> 4 L = K.connected_sum(trefoil)

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in connected_sum(self, other)

294         return Knot(B(list(b1.Tietze())

295                       + [(abs(i) + b2s) * Integer(i).sign() for i in b2.Tietze()]

--> 296                       + [b1s]))

 297 

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in __init__(self, data, check)

 104         if check:

 105             if self.number_of_components() != 1:

  --> 106                 raise ValueError("the input has more than 1 connected component")

  107 

  108     def __repr__(self):

 ValueError: the input has more than 1 connected component

Am I doing something wrong here? Thanks in advance!

Hi! I was trying to recursively construct connected sums of knots, but I seem to run in to some problems when connect summing a knot to itself more than two times:

B = BraidGroup(2)

trefoil = Knot(B([1,1,1]))

K = trefoil.connected_sum(trefoil)

L = K.connected_sum(trefoil)

This does not work:

ValueError                                Traceback (most recent call last)

ipython-input-1-7b977cf99468 in module()

 2 trefoil = Knot(B([Integer(1),Integer(1),Integer(1)]))

 3 K = trefoil.connected_sum(trefoil)

--> 4 L = K.connected_sum(trefoil)

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in connected_sum(self, other)

294         return Knot(B(list(b1.Tietze())

295                       + [(abs(i) + b2s) * Integer(i).sign() for i in b2.Tietze()]

--> 296                       + [b1s]))

 297 

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in __init__(self, data, check)

 104         if check:

 105             if self.number_of_components() != 1:

  --> 106                 raise ValueError("the input has more than 1 connected component")

  107 

  108     def __repr__(self):

 ValueError: the input has more than 1 connected component

Am I doing something wrong here? Thanks in advance!

Hi! I was trying to recursively construct connected sums of knots, but I seem to run in to some problems when connect summing a knot to itself more than two times:

B = BraidGroup(2)

trefoil = Knot(B([1,1,1]))

K = trefoil.connected_sum(trefoil)

L = K.connected_sum(trefoil)

This does not work:

ValueError                                Traceback (most recent call last)

ipython-input-1-7b977cf99468 in module()

 2 trefoil = Knot(B([Integer(1),Integer(1),Integer(1)]))

 3 K = trefoil.connected_sum(trefoil)

--> 4 L = K.connected_sum(trefoil)

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in connected_sum(self, other)

294         return Knot(B(list(b1.Tietze())

295                       + [(abs(i) + b2s) * Integer(i).sign() for i in b2.Tietze()]

--> 296                       + [b1s]))

 297 

/home/sc_serv/sage/local/lib/python2.7/site-packages/sage/knots/knot.pyc in __init__(self, data, check)

 104         if check:

 105             if self.number_of_components() != 1:

  --> 106                 raise ValueError("the input has more than 1 connected component")

  107 

  108     def __repr__(self):

 ValueError: the input has more than 1 connected component

Am I doing something wrong here? Thanks in advance!