Regeneration graphs for polynomial system solving.

Regeneration is a popular method for describing the solution set of a system of polynomial equations. In this paper we introduce regeneration graphs to solve polynomial systems. This translates the problem of solving a polynomial system to that of traversing a directed acyclic graph. Previous regeneration algorithms can be viewed in our context as breadth first traversal, and we formulate a depth first alternative which is useful in many applications because it quickly produces a subset of the solutions and is not ``all or nothing.''