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Zero Tests for Constants in Simple Scientific Computation

Zero Tests for Constants in Simple Scientific Computation It would be desirable to have an algorithm to decide equality among the constants which commonly occur in scientific computing. We do not yet know whether or not this is possible. It is known, however, that if the Schanuel conjecture is true, then equality is Turing decidable among the closed form numbers, that is, the complex numbers built up from the rationals using field operations, radicals, exponentials and logarithms. An algorithm based on the Schanuel conjecture is described in this article to decide equality among these numbers, presented as expressions. The algebraic part of this algorithm is simpler than those which have been given previously to solve related problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematics in Computer Science Springer Journals

Zero Tests for Constants in Simple Scientific Computation

Mathematics in Computer Science , Volume 1 (1) – Oct 23, 2007

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2007 by Springer
Subject
Mathematics; Computer Science, general ; Mathematics, general
ISSN
1661-8270
eISSN
1661-8289
DOI
10.1007/s11786-007-0002-x
Publisher site
See Article on Publisher Site

Abstract

It would be desirable to have an algorithm to decide equality among the constants which commonly occur in scientific computing. We do not yet know whether or not this is possible. It is known, however, that if the Schanuel conjecture is true, then equality is Turing decidable among the closed form numbers, that is, the complex numbers built up from the rationals using field operations, radicals, exponentials and logarithms. An algorithm based on the Schanuel conjecture is described in this article to decide equality among these numbers, presented as expressions. The algebraic part of this algorithm is simpler than those which have been given previously to solve related problems.

Journal

Mathematics in Computer ScienceSpringer Journals

Published: Oct 23, 2007

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