Juliann Opitz, Robert D. Allen, et al.
Microlithography 1998
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.
Juliann Opitz, Robert D. Allen, et al.
Microlithography 1998
Shashanka Ubaru, Lior Horesh, et al.
Journal of Biomedical Informatics
Imran Nasim, Michael E. Henderson
Mathematics
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems