The potential energy function of CH2 has been derived from the many-body expansion theory.

Similarly,the harmonic frequency has been calculated and the analytic potential energy function of linear molecule N2O isomer is derived by many-body expansion theory for the first time.

For the ground state of GeH_2(X~1A_1),the analytic potential energy function has been derived by the many-body expansion theory,which is successfully described its configuration and the dissociation energy.

The notion of partitioned-parametric Grobner bases of a polynomial ideal with parameters is introduced and an algorithm for constructing the partitioned-parametric Grobner bases is given, the correctness and the termination of the algorithm are also proved.

In this paper, a new method of testing Hamilton path is given in simple digraph, via Grbner basis and polynomial ideal, which is simple, efficient and can be easily realized by mathematic software, such as Maple.

In this paper,an algorithm for linear programming basis iteration with continuous variable parameters is discussed,and the problem in expression in computerization of the rational polynomials appeared in the computing process is discussed.

Aiming at the problem of worse real-time in ordinary rendering fur linght effect method, a Lengyel fur real-time rendering method based on Polynomial Texture Maps(PTM) is proposed, which merges PTM into Lengyel rendering fur method.