Understanding branch cuts of expressions

Matthew England, Russell Bradford, James H. Davenport, David Wilson

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

10 Citations (Scopus)
10 Downloads (Pure)

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 single-valued counterparts, the common approach to encoding multi-valued 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 languageEnglish
Title of host publicationIntelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings
EditorsJacques Carette, David Aspinall, Christoph Lange, Petr Sojka, Wolfgang Windsteiger
Place of PublicationHeidelberg
PublisherSpringer
Pages136-151
Number of pages16
Volume7961 LNAI
ISBN (Electronic)9783642393204
ISBN (Print)9783642393198
DOIs
Publication statusPublished - 2013
Externally publishedYes
EventConference on Intelligent Computer Mathematics, CICM 2013, Co-located with the MKM 2013, Calculemus 2013, DML 2013, and Systems and Projects 2013 - Bath, United Kingdom
Duration: 8 Jul 201312 Jul 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7961 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

ConferenceConference on Intelligent Computer Mathematics, CICM 2013, Co-located with the MKM 2013, Calculemus 2013, DML 2013, and Systems and Projects 2013
CountryUnited Kingdom
CityBath
Period8/07/1312/07/13

Fingerprint

Branch
Algebra
Maple
Inverse trigonometric function
Addition formula
Multivalued Functions
Computer Algebra
Computer algebra system
Single valued
Encoding

Bibliographical note

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-39320-4_9


Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • branch cuts
  • simplification
  • symbolic computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

England, M., Bradford, R., Davenport, J. H., & Wilson, D. (2013). Understanding branch cuts of expressions. In J. Carette, D. Aspinall, C. Lange, P. Sojka, & W. Windsteiger (Eds.), Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings (Vol. 7961 LNAI, pp. 136-151). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7961 LNAI). Heidelberg: Springer. https://doi.org/10.1007/978-3-642-39320-4_9

Understanding branch cuts of expressions. / England, Matthew; Bradford, Russell; Davenport, James H.; Wilson, David.

Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings. ed. / Jacques Carette; David Aspinall; Christoph Lange; Petr Sojka; Wolfgang Windsteiger. Vol. 7961 LNAI Heidelberg : Springer, 2013. p. 136-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7961 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference proceeding

England, M, Bradford, R, Davenport, JH & Wilson, D 2013, Understanding branch cuts of expressions. in J Carette, D Aspinall, C Lange, P Sojka & W Windsteiger (eds), Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings. vol. 7961 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7961 LNAI, Springer, Heidelberg, pp. 136-151, Conference on Intelligent Computer Mathematics, CICM 2013, Co-located with the MKM 2013, Calculemus 2013, DML 2013, and Systems and Projects 2013, Bath, United Kingdom, 8/07/13. https://doi.org/10.1007/978-3-642-39320-4_9
England M, Bradford R, Davenport JH, Wilson D. Understanding branch cuts of expressions. In Carette J, Aspinall D, Lange C, Sojka P, Windsteiger W, editors, Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings. Vol. 7961 LNAI. Heidelberg: Springer. 2013. p. 136-151. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-39320-4_9
England, Matthew ; Bradford, Russell ; Davenport, James H. ; Wilson, David. / Understanding branch cuts of expressions. Intelligent Computer Mathematics - MKM, Calculemus, DML, and Systems and Projects 2013 - Held as Part of CICM 2013, Proceedings. editor / Jacques Carette ; David Aspinall ; Christoph Lange ; Petr Sojka ; Wolfgang Windsteiger. Vol. 7961 LNAI Heidelberg : Springer, 2013. pp. 136-151 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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