Adherence is better than adjacency: computing the Riemann index using CAD

Authors:
James C. Beaumont;Russell J. Bradford;James H. Davenport;Nalina Phisanbut
Affiliations:
University of Bath, Bath, England;University of Bath, Bath, England;University of Bath, Bath, England;University of Bath, Bath, England
Venue:
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Year:
2005

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Abstract

Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.