This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The phenomenon of coefficient growth is described, and the history of… Expand

This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the sub resultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm.Expand

1 . Introduction . By an r-graph we mean a fixed set of vertices together with a class of unordered subsets of this fixed set, each subset containing exactly r elements and called an r-tuple . In the… Expand

This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm, with special atten- tion to the case of multivariate polynomials.Expand

Two earlier papers described the generalization of Euclid's algorithm to deal with the problem of computing the greatest common divisor (GCD) or the resultant of a pair of polynomials.Expand

One of the most controversial and least well defined of mathematical problems is the problem of simplification. The recent upsurge of interest in mechanized mathematics has lent new urgency to this… Expand