THE TANGENT CONE ALGORITHM AND HOMOGENIZATION

Let S:= k[x(upsilon): upsilon is-an-element-of H] be a polynomial ring over the field k. For non-noetherian term orders there are essentially two ways to compute standard sets from a polynomial basis B of an ideal I subset-of S, one based on Mora's tangent cone algorithm, and was another one usign Lazard's homogenization approach. The former applies (in its original version) only to inflimited term orders. Encoupling ecart vector and term order we improve Mora's algorithm. The presented version applies to arbitrary term orders. It may increase also the power of existing implementations adding a new range of freedom. Moreover, the presented generalization is the connecting bridge between Mora's and Lazard's approaches. The insight obtained this way leads to an essential simplification of the termination proof in [8], the core of many results on standard bases. The algorithms are implemented in CALI [5], the author's REDUCE package for commutative algebra.