Solving Detachability Problem for the Polynomial Ring by Signature-based Groebner Basis Algorithms

Signature-based algorithms are a popular kind of algorithms for computing Gröbner basis, including the famous F5 algorithm, F5C, extended F5, GV and the GVW algorithm. In this paper, an efficient method is proposed to solve the detachability problem. The new method only uses the outputs of signature-based algorithms, and no extra Gröbner basis computations are needed. When a Gröbner basis is obtained by signature-based algorithms, the detachability problem can be settled in polynomial time.