On Reducing a System of Equations to a Single Equation

Gudmund Skovbjerg Frandsen
Igor E. Shparlinski

March 2004


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.

Available as PostScript, PDF, DVI.


Last modified: 2004-03-26 by webmaster.