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Not seeing the roots for the branches: multivalued functions in computer algebra

Published: 01 September 2004 Publication History

Abstract

We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a cubic polynomial from the Cardano formulae, which contain fractional powers. We show that some definitions of these functions result in formulae that are correct only in the sense that they give candidates for solutions; these candidates must then be tested. Formulae that are based on single-valued functions, in contrast, are efficient and direct.

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cover image ACM SIGSAM Bulletin
ACM SIGSAM Bulletin  Volume 38, Issue 3
September 2004
51 pages
ISSN:0163-5824
DOI:10.1145/1040034
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2004
Published in SIGSAM Volume 38, Issue 3

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