Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
We examine the degree relationship between the elements of an ideal I⊆R[x] and the elements of φ(I) where φ→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 Gröbner basis remains a Gröbner 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. © 2001 Elsevier Science B.V.
Zhihua Xiong, Yixin Xu, et al.
International Journal of Modelling, Identification and Control
Elizabeth A. Sholler, Frederick M. Meyer, et al.
SPIE AeroSense 1997
Ronen Feldman, Martin Charles Golumbic
Ann. Math. Artif. Intell.
John S. Lew
Mathematical Biosciences