Symbolic integration I: Transcendental functions
type: Item
instance of: scholarly article
title: Symbolic integration I: Transcendental functions
zbMATH Open document ID: 1059.12002
author: Manuel Bronstein
published in: Algorithms and Computation in Mathematics
publication date: 2004-12-14T00:00:00Z
review text: The second edition of Bronstein's excellent book [Algorithms and Computation in Mathematics. 1. (Berlin: Springer). (1997; Zbl 0880.12005)]; the second volume is still missing) contains a new chapter on parallel integration (also called the new Risch algorithm or the Risch-Norman algorithm) This alternative approach to integration attempts to avoid the highly recursive nature of the ``classical'' algorithms described in the first nine chapters. This method was introduced 1976 by \textit{R. Risch} and \textit{A. C. Norman} [Proc. 4th Int. Coll. Adv. Comput. Meth. Theor. Phys, Marseille (1977)] and is used in some computer algebra systems, mostly as a preprocessor for the complete integration algorithm: It is heuristic rather than algorithmic as in some cases it may fail to compute elementary antiderivatives. The first nine chapters of the book contain some improvements and a couple of additional exercises. Bronstein's book still presents the state of the art in the domain of integration of transcendental functions. Its unique blend of detailed mathematics and clear description of algorithms make it both a standard reference and a handbook for researchers and designers of computer algebra systems and a useful, easy to read textbook for teachers and students.
reviewed by: Friedrich Schwarz
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 12-02
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 28-04
zbMATH DE Number: 2122031
zbMATH Keywords: symbolic integration
zbMATH Keywords: integration in finite terms
zbMATH Keywords: transcendental functions
zbMATH Keywords: differential algebra
MaRDI profile type: Publication
full work available at URL: b138171
OpenAlex ID: W2477102943
DOI: 10.1007/B138171
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description: scientific article; zbMATH DE number 2122031