Erratum to "A new algorithm for discussing Gröbner bases with parameters" [J. Symbolic Comput. 33(1-2) (2002) 183-208]

In 2002, the third author has presented the algorithmDisPGB to compute a comprehensiveGröbner system for a parametric ideal in Montes (2002), and has implemented it in Maple. The first release (1.4 of 2002) contains some errors that were fixed in the second release (2.4 of 2004). The two first authors have also implemented this algorithm in Maple, and after testing on several examples, they have also found some other errors in the two sub-algorithms NewCond and NewVertex used in DisPGB. The NewCond algorithm receives, as input, a polynomial f and two sets of null and nonnull conditions, and it returns the whole set C of (irreducible) factors of the first non-null (w.r.t the given conditions) coefficient of f . But, this makes an error in the output of DisPGB algorithm. To fix this minor error, it shall return the first element of C . Now, if NewCond finds a new condition c , then Newvertex is called to create two newbranches by adding c = 0 and c ≠ 0 to the sets of null and nonnull conditions, respectively. In the latter case,Newvertex substitutes every polynomial g in the basis by the S-polynomial of f and g . But, if the leading coefficient of f has a non-decidable factor (w.r.t the given conditions), the output of DisPGBmay be false. Therefore, before performing this S-polynomial, using NewCond, we have to be sure the leading coefficient of f has no new condition.