Irreducible zero decomposition

Abstract

Polynomial factorization is not required theoretically for the algorithms described in the previous two chapters. Nevertheless, available factoring programs have been efficient enough to be used to enhance the performance of elimination algorithms. It is a good strategy to incorporate polynomial factorization (even over algebraicextension fields) in the implementation of such algorithms. In this chapter, we elaborate how triangular systems can be further decomposed by making use of factorization in order to compute zero decompositions possessing better properties. For our exposition some of the material from Wu (1984; 1994, chap. 4) will be used without explicit mention.