虚拟链环的Kauffman尖括号多项式的Maple计算

Maple Calculation of the Kauffman Bracket Polynomial of Virtual Links

将Itik和Banks对经典链环的Kauffman尖括号多项式的计算方法推广到虚拟链环,算法使用了圈置换的方法计算虚拟链环投影图的每一种状态下的圈的个数.所谓虚拟链环投影图的状态是指对投影图中每个经典交叉进行Asmoothing或B-smoothing操作,而对虚拟交叉点采用直走的两条小弧线代替后所得的结果.利用Maple软件编写出了该算法的程序,可以实现任意一个虚拟链环的Kauffman尖括号多项式的计算.

We extend the computational method of the Kauffman bracket polynomial by Itik and Banks from classical links to virtual links.The algorithm uses cyclic permutations to count the number of circles of states obtained by the application of A-tybe or B-type smoothing to each classical crossing and the replacement of each virtual crossing with two arcs that they meet transversally.We show that our algorithm can be implemented easily by computer programs written in the Maple environment.