Understanding branch cuts of expressions

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

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

  • 9 Citations

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.
LanguageEnglish
Title of host publicationIntelligent Computer Mathematics
Subtitle of host publicationMKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8-12, 2013. Proceedings
EditorsJacques Carette, David Aspinall, Christoph Lange, Petr Sojka, Wolfgang Windsteiger
Place of PublicationBerlin
PublisherSpringer
Pages136-151
Number of pages16
ISBN (Electronic)9783642393204
ISBN (Print)9783642393198
DOIs
StatusPublished - 2013
EventConferences on Intelligent Computer Mathematics: CICM 2013 - Bath, UK United Kingdom
Duration: 7 Jul 201311 Jul 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume7961
ISSN (Print)0302-9743

Conference

ConferenceConferences on Intelligent Computer Mathematics: CICM 2013
CountryUK United Kingdom
CityBath
Period7/07/1311/07/13

Fingerprint

algebra
trigonometric functions
classifying
coding

Keywords

  • branch cuts
  • symbolic computation
  • simplification

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, Bath, UK, July 8-12, 2013. Proceedings (pp. 136-151). (Lecture Notes in Computer Science; Vol. 7961). Berlin: 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, Bath, UK, July 8-12, 2013. Proceedings. ed. / Jacques Carette; David Aspinall; Christoph Lange; Petr Sojka; Wolfgang Windsteiger. Berlin : Springer, 2013. p. 136-151 (Lecture Notes in Computer Science; Vol. 7961).

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

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, Bath, UK, July 8-12, 2013. Proceedings. Lecture Notes in Computer Science, vol. 7961, Springer, Berlin, pp. 136-151, Conferences on Intelligent Computer Mathematics: CICM 2013, Bath, UK United Kingdom, 7/07/13. 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, Bath, UK, July 8-12, 2013. Proceedings. Berlin: Springer. 2013. p. 136-151. (Lecture Notes in Computer Science). 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, Bath, UK, July 8-12, 2013. Proceedings. editor / Jacques Carette ; David Aspinall ; Christoph Lange ; Petr Sojka ; Wolfgang Windsteiger. Berlin : Springer, 2013. pp. 136-151 (Lecture Notes in Computer Science).
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