Gröbner bases specialization through Hilbert functions
María José González López, Laureano González-Vega, Carlo Enrico Traverso, Alberto Zanoni · ACM SIGSAM Bulletin · 2000
This paper shows how to solve homogeneous polynomial systems that contain parameters. The Hilbert function is used to check that the specialization of a 'generic' Gröbner basis of the parametric homogeneous polynomial system (computed in a polynomial ring containing the parameters and the unknowns as variables) is a Gröbner basis of the specialized homogeneous polynomial system. A preliminary implementation of these algorithms in PoSSoLib is also reported.