Research

Understanding branch cuts of expressions


Reference:

England, M., Bradford, R., Davenport, J. H. and Wilson, D., 2013. Understanding branch cuts of expressions. In: Carette, J., Aspinall, D., Lange, C., Sojka, P. and Windsteiger, W., eds. Intelligent Computer Mathematics. Berlin: Springer, pp. 136-151. (Lecture Notes in Computer Science; 7961)

Related documents:

[img]
Preview
PDF (Author's accepted version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (800kB) | Preview
    [img] Other (Branch_Cuts_Introduction.mw)
    Download (4MB)
      [img] Other (BranchCuts.mpl)
      Download (27kB)

        Official URL:

        http://dx.doi.org/10.1007/978-3-642-39320-4_9

        Related URLs:

        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.

        Details

        Item Type Book Sections
        CreatorsEngland, M., Bradford, R., Davenport, J. H. and Wilson, D.
        EditorsCarette, J., Aspinall, D., Lange, C., Sojka, P. and Windsteiger, W.
        DOI10.1007/978-3-642-39320-4_9
        Related URLs
        URLURL Type
        http://www.cicm-conference.org/2013/Organisation
        Uncontrolled Keywordsbranch cuts, symbolic computation, simplification
        DepartmentsFaculty of Science > Computer Science
        Publisher StatementBranchCuts.pdf: The final publication is available at link.springer.com
        StatusPublished
        ID Code32511
        Additional InformationThe 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).

        Export

        Actions (login required)

        View Item

        Document Downloads

        More statistics for this item...