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Richardson's Theorem


Let R be the class of expressions generated by

1. The rational numbers and the two real numbers pi and ln2,

2. The variable x,

3. The operations of addition, multiplication, and composition, and

4. The sine, exponential, and absolute value functions.

Then if E in R, the predicate "E=0" is recursively undecidable.


See also

Constant Problem, Hidden Zero, Integer Relation, Integration Problem, Recursion, Recursively Undecidable, Rice's Theorem, Schanuel's Conjecture, Undecidable, Zero

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References

Caviness, B. F. "On Canonical Forms and Simplification." J. Assoc. Comp. Mach. 17, 385-396, 1970.Davenport, J. H. "Equality in Computer Algebra and Beyond." J. Symb. Comput. 34, 259-270, 2002.Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, 1996. http://www.cis.upenn.edu/~wilf/AeqB.html.Richardson, D. "Some Unsolvable Problems Involving Elementary Functions of a Real Variable." J. Symbolic Logic 33, 514-520, 1968.Richardson, D. "How to Recognize Zero." J. Symb. Comput. 24, 627-645, 1997.Richardson, D. "The Uniformity Conjecture." In Computability and Complexity in Analysis: 4th International Workshop, CCA 2000, Swansea, UK, September 17-19, 2000 (Ed. J. Blanck, V. Brattka, and P. Hertling). Berlin: Springer-Verlag, pp. 253-272, 2000.Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, 2005. http://www.mathematicaguidebooks.org/.

Referenced on Wolfram|Alpha

Richardson's Theorem

Cite this as:

Weisstein, Eric W. "Richardson's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RichardsonsTheorem.html

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