Tangle equations for knots

We make a connection between "Tangle-valued 1-cocycles" and "Quantum equations" for knots.To each couple of knot diagrams we can associate linear systems of tangle-valued equations with integer coefficients. If one of the systems has no solution, than the knot diagrams represent different knots. In the opposit, each solution of a system gives a non-trivial restriction on the Reidemeister moves for each knot  isotopy which relates the two diagrams. This is an essential step for a solution of the most difficult problem in knot theory: given two diagrams, show in an efficient manner that they represent the same knot.