A Separation Bound for Real Algebraic Expressions

Authors:
Christoph Burnikel;Stefan Funke;Kurt Mehlhorn;Stefan Schirra;Susanne Schmitt
Affiliations:
ENCOM GmbH, 66740, Saarlouis, Germany;Ernst-Moritz-Arndt Universität Greifswald, Institut für Mathematik und Informatik, 17487, Greifswald, Germany;MPI für Informatik, 66123, Saarbrücken, Germany;Otto-von-Guericke Universität Magdeburg, Fakultät für Informatik, Universitätsplatz 2, 39106, Magdeburg, Germany;MPI für Informatik, 66123, Saarbrücken, Germany
Venue:
Algorithmica
Year:
2009

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Abstract

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.