On the intrinsic complexity of elimination problems in effective Algebraic Geometry

Abstract

The representation of polynomials by arithmetic circuits evaluating them is an alternative data structure which allowed considerable progress in polynomial equation solving in the last fifteen years. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective algebraic geometry and show the intrinsically exponential complexity character of elimination in this complexity model.

37 pages. arXiv admin note: substantial text overlap with arXiv:1110.3030