On the time-space complexity of geometric elimination procedures

In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation sy stem satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in thp introduction nf a innova tive point of this algorithmic concept consists in the introduction of a ne w geometric invariant, called the degree of the input system, and the proof that the most common elimination problems have time complexity which is po lynomial in this degree and the length of the input. In this paper we apply this algorithmic concept in order to exhibit an elimination procedure whos e space complexity is only quadratic and its time complexity is only cubic in the degree of the input system.