Isotropic treatment of EMF effects in advanced photomasks
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009
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.
Jaione Tirapu Azpiroz, Alan E. Rosenbluth, et al.
SPIE Photomask Technology + EUV Lithography 2009
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Nimrod Megiddo
Journal of Symbolic Computation
I.K. Pour, D.J. Krajnovich, et al.
SPIE Optical Materials for High Average Power Lasers 1992