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 system satisfying a certain generic smoothness condition. The main innovative point of this algorithmic concept consists in thp introduction nf a innovative point of this algorithmic concept consists in the introduction of a new geometric invariant, called the degree of the input system, and the proof that the most common elimination problems have time complexity which is polynomial in this degree and the length of the input. In this paper we apply this algorithmic concept in order to exhibit an elimination procedure whose space complexity is only quadratic and its time complexity is only cubic in the degree of the input system.
time-space complexity algorithmic elimination theory polynomial equation solving symbolic computation algebraic complexity theory computation tree straight-line program