Gröbner Bases Specialization through Hilbert Functions:
The Homogeneous Case

M.-J. Gonzalez-Lopez$^{*\dag }$ and L. Gonzalez-Vega^{1 2}
Dpto. Matemáticas, Estadística y Computación
Universidad de Cantabria, Santander, Spain - C. Traverso^* and A. Zanoni^*
Dipartimento di Matematica
Università di Pisa, Pisa, Italy

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Abstract:

In this paper it is shown how to deal with homogeneous polynomial system solving involving parameters by using the Hilbert function in order 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 into the PoSSoLib is also reported.