I am currently working with SnapPy and I want to do the following: Given an oriented Knot K with a knot diagram and a specific crossing,I want to obtain the knot K', which is obtained by changing this crossing (meaning the strand going under becomes the strand going over and vice versa).
I tried to do the following: Using the function PD_code(), I get the PD-code of K. Now each crossing is an element of the PD_code represented by a list [a,b,c,d] where a,b,c,d are natural numbers (see here for PD-code notation https://knotinfo.math.indiana.edu/descriptions/pd_notation.html ) From this I know that 'a' labels the incoming lower edge. If the edge labeled by 'b' goes toward the edge labeled by 'd', then a change of crossing would make [a,b,c,d] into [b,c,d,a] and I would get the PD code of K' by replacing [a,b,c,d] by [b,c,d,a]. Unfortunately, this replacing method relies on knowing if the edge labeled by ('b' goes to 'd' or the other way around. Is there maybe some function which can determine the sign of a crossing? This would already solve my problem as this would determine whether 'b' goes to 'd' or if 'd' goes towards 'b'.