Research On The Primitive Representation Of Polynomial Invariants Of Rational Tangles With Palt Form

In this paper,we first give the base tuple of angle bracket polynomials of direction-al rational 3-tangle T in 6-plat form.On the basis,we discuss the coefficient relation theorem of angle bracket polynomials of T_i^*_j^?i=?_i^?_jⁱ·T under matrix algorithm,and give the Homfly polynomial expression theorem of link L after closed rational 3-tangle in 6-plat form.Secondly,the base tuple A_i(i=1,2,······,42)of angle bracket polynomials of the closed link L with the 10-plat form rational 5-tangle T is given.On the basis,the coefficient relation theorem of angle bracket polynomials of T_?i±1=?_i^±1·T under matrix algorithm is discussed,and the Jones polynomials expression theorem of closed link of 10-plat form rational 5-tangle is given.Finally,we give the base tuple of angle bracket polynomial and the matrix M(TD)about the base tuple of the tangle graph TD of rational 4-tangle T.On this basis,we give the theorem about the relationship between the matrix M(TD₁+TD₂)and M(TD_i)(i=1,2)corresponding to the rational 4-tangle graph TD₁and TD₂under the additive operation.We also give the matrix theorem under the equivalence class of rational 4-tangle graphs determined by the primitive representation of angle bracket polynomials and prove that the equivalence class[M^*(TD)]is a tangle invariant.