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Abstract
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the singlevalued counterparts, the common approach to encoding multivalued functions in computer algebra systems. While the defining choices are usually simple (typically portions of either the real or imaginary axes) the cuts induced by the expression may be surprisingly complicated. We have made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple. We discuss the issues raised, classifying the different cuts produced. The techniques have been gathered in the BranchCuts package, along with tools for visualising the cuts. The package is included in Maple 17 as part of the FunctionAdvisor tool.
Original language  English 

Title of host publication  Intelligent Computer Mathematics 
Subtitle of host publication  MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 812, 2013. Proceedings 
Editors  Jacques Carette, David Aspinall, Christoph Lange, Petr Sojka, Wolfgang Windsteiger 
Place of Publication  Berlin 
Publisher  Springer 
Pages  136151 
Number of pages  16 
ISBN (Electronic)  9783642393204 
ISBN (Print)  9783642393198 
DOIs  
Publication status  Published  2013 
Event  Conferences on Intelligent Computer Mathematics: CICM 2013  Bath, UK United Kingdom Duration: 7 Jul 2013 → 11 Jul 2013 
Publication series
Name  Lecture Notes in Computer Science 

Publisher  Springer 
Volume  7961 
ISSN (Print)  03029743 
Conference
Conference  Conferences on Intelligent Computer Mathematics: CICM 2013 

Country/Territory  UK United Kingdom 
City  Bath 
Period  7/07/13 → 11/07/13 
Bibliographical note
The functionality described in the paper is built into Maple, version 17 and above, where it is used by default for queries to the FunctionAdvisor. The code provided here (in the .mpl file) offers users of earlier versions some of the functionality. It is designed for use in Maple 16 and may also work with those earlier versions which still contain the FunctionAdvisor.For information on working with the code see the Appendix of the paper, the help in Maple 17 and the introductory worksheet provided here (the .mw file).
Keywords
 branch cuts
 symbolic computation
 simplification
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 1 Finished

Real Geometry and Connectedness via Triangular Description
Davenport, J., Bradford, R., England, M. & Wilson, D.
Engineering and Physical Sciences Research Council
1/10/11 → 31/12/15
Project: Research council