Complexity of Triangular Representations of Algebraic Sets
  Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds. 
Eli Amzallag, Gleb Pogudin, Mengxiao Sun, Thieu N. Vo
math.AG math.AC