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

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’. Categories and Subject Descriptors

• Type: Conference
• Year: 2005
• Where: ISSAC
• Authors: James C. Beaumont, Russell J. Bradford, James H. Davenport, Nalina Phisanbut
• Keywords: Algebraic Branch Cuts, Branch Cuts, ISSAC 2005, Riemann Surface