An efficient method for computing comprehensive Gröbner bases

An efficient method for computing comprehensive Gröbner bases

a r t i c l e i n f o a b s t r a c t A new approach is proposed for computing a comprehensive Gröb-ner basis of a parameterized polynomial system. The key new idea is not to simplify a polynomial under various specialization of its parameters, but rather keep track in the polynomial, of the power products whose coefficients vanish; this is achieved by partitioning the polynomial into two parts...

Computing inhomogeneous Gröbner bases

In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use a technique described in Section 2: the main tool ...

FGb: A Library for Computing Gröbner Bases

FGb is a high-performance, portable, C library for computing Gröbner bases over the integers and over finite fields. FGb provides high quality implementations of state-of-the-art algorithms (F4 and F5) for computing Gröbner bases. Currently, it is one of the best implementation of these algorithms, in terms of both speed and robustness. For instance, FGb has been used to break several cryptosys...

Modular algorithms for computing Gröbner bases

Intermediate coefficient swell is a well-known difficulty with Buchberger’s algorithm for computing Gröbner bases over the rational numbers. p-Adic and modular methods have been successful in limiting intermediate coefficient growth in other computations, and in particular in the Euclidian algorithm for computing the greatest common divisor (GCD) of polynomials in one variable. In this paper we...

Computing Gröbner bases for quasi-homogeneous systems