# A simple algorithm to compute link polynomials defined by using skein relations

## TL;DR

This paper introduces a straightforward algorithm for computing link polynomials via skein relations, utilizing a novel total order on braid representatives, and also derives a new complete link invariant.

## Contribution

The paper presents a simple, practical algorithm for link polynomial computation based on a new ordering of braid representatives, and introduces a new complete link invariant.

## Key findings

- Efficient computation of link polynomials using the new algorithm.
- Development of a new total order on braid representatives.
- Derivation of a new complete link invariant.

## Abstract

We give a simple and practical algorithm to compute the link polynomials, which are defined according to the skein relations. Our method is based on a new total order on the set of all braid representatives. As by-product a new complete link invariant are obtained.