caa a22 4500 463202961 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s00200-007-0052-y doi (NATIONALLICENCE)springer-10.1007/s00200-007-0052-y Testing elementary function identities using CAD [Elektronische Daten] [James Beaumont, Russell Bradford, James Davenport, Nalina Phisanbut] One of the problems with manipulating function identities in computer algebra systems is that they often involve functions which are multivalued, whilst most users tend to work with single-valued functions. The problem is that many well-known identities may no longer be true everywhere in the complex plane when working with their single-valued counterparts. Conversely, we cannot ignore them, since in particular contexts they may be valid. We investigate the practicality of a method to verify such identities by means of an experiment; this is based on a set of test examples which one might realistically meet in practice. Essentially, the method works as follows. We decompose the complex plane via means of cylindrical algebraic decomposition into regions with respect to the branch cuts of the functions. We then test the identity numerically at a sample point in each region. The latter step is facilitated by the notion of the adherence of a branch cut, which was previously introduced by the authors. In addition to presenting the results of the experiment, we explain how adherence relates to the proposal of signed zeroes by W. Kahan, and develop this idea further in order to allow us to cover previously untreatable cases. Finally, we discuss other ways to improve upon our general methodology as well as topics for future research. Springer-Verlag, 2007 Elementary functions nationallicence Branch cuts nationallicence CAD nationallicence Beaumont James Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut Bradford Russell Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut Davenport James Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut Phisanbut Nalina Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/6(2007-12-01), 513-543 0938-1279 18:6<513 2007 18 200 https://doi.org/10.1007/s00200-007-0052-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-007-0052-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Beaumont James Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut NATIONALLICENCE 700 1- Bradford Russell Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut NATIONALLICENCE 700 1- Davenport James Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut NATIONALLICENCE 700 1- Phisanbut Nalina Department of Computer Science, University of Bath, BA2 7AY, Bath, England aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/6(2007-12-01), 513-543 0938-1279 18:6<513 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer