We introduce a new algorithm for computing comprehensive Gröbner systems. There exists the Suzuki-Sato algorithm for computing comprehensive Gröbner systems. The Suzuki-Sato algorithm often creates overmuch cells of the parameter space for comprehensive Gröbner systems. Therefore the computation becomes heavy. However, by using inequations ("not equal zero"), we can obtain different cells. In many cases, this number of cells of parameter space is smaller than that of Suzuki-Sato's. Therefore,

more »

... r new algorithm is more efficient than Suzuki-Sato's one, and outputs a nice comprehensive Gröbner system. Our new algorithm has been implemented in the computer algebra system Risa/Asir. We compare the runtime of our implementation with the Suzuki-Sato algorithm and find our algorithm superior in many cases. Notations LetĀ := {A 1 , . . . , A m } andX := {X 1 , . . . , X n } be finite sets of variables such thatĀ ∩X = ∅. K and L denote fields such that L is an extension of K. pp(X), pp(Ā) and pp(Ā,X) denote the sets of power products ofX,Ā andĀ ∪X, respectively. N, Q and C denote as the set of natural numbers with 0, the field of rational numbers and the field of complex numbers, respectively. In this paper, we define K[Ā,X] as a polynomial ring over a field K and K[Ā][X] := (K[Ā])[X] as a polynomial ring over a polynomial ring