Point searching in real singular complete intersection varieties – algorithms of intrinsic complexity

Bernd Bank , Marc Giusti , Joos Heintz

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2011-18

MSC 2000

68W30 Symbolic computation and algebraic computation

14P05 Real algebraic sets

14B05 Singularities

14B07 Deformations of singularities

68W10 Parallel algorithms

Abstract
Let X1 , . . . , Xn be indeterminates over Q and let X := (X1 , . . . , Xn ) . Let F1 , . . . , Fp be a regular sequence of polynomials in Q[X ] of degree at most d such that for each 1 ≤ k ≤ p the ideal (F1 , . . . , Fk ) is radical. Suppose that the variables X1 , . . . , Xn are in generic position with respect to F1 , . . . , Fp . Further suppose that the poly- nomials are given by an essentially division-free circuit β in Q[X ] of size L and non-scalar depth