Degree reduction under specialization

[摘要] We examine the degree relationship between the elements of an ideal I subset of or equal to R[x] and the elements of phi (I) where phi: R --> R is a ring homomorphism. When R is a multivariate polynomial ring over a field, we use this relationship to show that the image of a Grobner basis remains a Grobner basis if we specialize all the variables but one, with no requirement on the dimension of I. As a corollary we obtain the GCD for a collection of parametric univariate polynomials. We also apply this result to solve parametric systems of polynomial equations and to reexamine the extension theorem for such systems. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-10-24

[效力级别]  Proceedings Paper