On reducing a system of equations to a single equation

Authors:
Gudmund S. Frandsen;Igor E. Shparlinski
Affiliations:
University of Aarhus, Denmark;Macquarie University, Australia
Venue:
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Year:
2004

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Abstract

For a system of polynomial equations over Q;p; we present an efficient construction of a single polynomial of quite small degree whose zero set over Q;p; coincides with the zero set over Q;p; of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity.The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.