The concepts of comprehensive Gröbner bases and Gröbner systems were introduced by Weispfenning in [13]. Montes in [9] has proposed DisPGB algorithm for computing Gröbner systems. But he has not explicitly used Buchberger’s criteria in his algorithm. In this paper, we show how to apply these criteria on Montes algorithm, and we propose an improved version of DisPGB.

In 1992, V. Weispfenning proved the existence of Comprehensive Gröbner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Gröbner Bases. Inspired in its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical Comp...

In 1992, V. Weispfenning proved the existence of Comprehensive Gröbner Bases (CGB) and gave an algorithm for computing one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Gröbner Bases. Inspired by its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical C...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.

In this paper we complete the algorithm DISPGB (Discussing Parametric Gröbner Basis) from the last paper by Montes, in order to obtain the Minimal Canonical Comprehensive Gröbner System (MCCGS). Given a parametric ideal, the MCCGS algorithm provides the minimal partition of the parameter space with associated Gröbner bases having the same type of solutions over each segment and provides a canon...

The concept of comprehensive Grobner bases was introduced by Weispfenning. Montes has proposed an efficient algorithm for computing these bases. But he has not explicitly used Buchberger's criteria in his algorithm. In this paper we prove that we can apply these criteria on Montes algorithm. We propose a modified version of Montes algorithm and evaluate its performance via some examples.

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 hav...

In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal f...