The Term Orderings Which are Homogeneously Compatible with Composition
具有与多项式复合齐次相容的项序

Let Kx_1,x_2,...,x_n] e the polynomial ring over a field K in variables x_1,x_2,...,n. Let \Theta=(\theta_1,\theta_2,...\theta_n) be a list of n homogeneous polynomials in Kx_1,x_2,..., x_n]. Polynomial composition, denoted by \Theta, is the operation of replacing x_i by a polynomial by \theta_i. We say that composition \Theta is homogeneouly compatible with the term ordering > if for all terms p and q with p>q, deg p=deg q implies that p\circ lt(\Theta)> q \circ lt(\Theta) .It is very difficult to test the compatibility. At the end of the paper, a procedure for testing the compatibility is given.