Parametric Greatest Common Divisors using Comprehensive Gröbner Systems
Kosaku Nagasaka · 2017
Computing the greatest common divisor (GCD) of polynomials can be done by computing the Grobner basis instead of the well-known Euclidean algorithm, studied by Gianni and Trager in 1985, and Sasaki and Suzuki in 1992. In this paper, we extend their theories to polynomials with parameters. That is the theory of parametric greatest common divisors by means of comprehensive Grobner systems (CGS). Moreover, this can be considered as an indirect extension of known parametric GCD algorithms to those for several multivariate polynomials with parameters.