Open AccessOn Reducing a System of Equations to a Single Equation
Author(s) -
Gudmund Skovbjerg Frandsen,
Igor E. Shparlinski
Publication year - 2004
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v11i6.21831
Subject(s) - mathematics , polynomial , zero (linguistics) , set (abstract data type) , degree (music) , line (geometry) , system of polynomial equations , discrete mathematics , combinatorics , mathematical analysis , computer science , geometry , physics , philosophy , linguistics , acoustics , programming language
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.