Computing the Arrow Polynomial

Determining if two knots are not equivalent in an efficient manner is important in the study of knots. The arrow polynomial, which is calculated from a virtual knot diagram and is invariant under the Reidemeister moves, can be used to determine if two knots are not equivalent and determine a lower bound on the virtual crossing number. In this paper, we present the necessary data structures and algorithms to represent a link diagram on a computer and calculate the arrow polynomial