A Separation Bound for Real Algebraic Expressions

Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking roots of polynomials whose coefficients are given by the values of subexpressions. We consider the sign computation of real algebraic expressions, a task vital for the implementation of geometric algorithms. We prove a new separation bound for real algebraic expressions and compare it analytically and experimentally with previous bounds. The bound is used in the sign test of the number type leda real.

• Type: Conference
• Year: 2001
• Where: ESA
• Authors: Christoph Burnikel, Stefan Funke, Kurt Mehlhorn, Stefan Schirra, Susanne Schmitt
• Keywords: Algorithms, ESA 2001, K-th Root Operations, Number Type Leda, Real Algebraic Expressions