Denest nested radical expressions
Contributed by:
Swastik Banerjee (based on work by Corey Ziegler, Bill Gosper and Daniel Lichtblau)
Examples
Basic Examples (3)
Denest a nested radical:
Denest another:
Denest a third:
Scope (4)
Sometimes a denesting effort will only manage to reduce the degree of the radical without reducing the nesting depth:
Radicals under square roots and cube roots with arbitrary powers inside can be denested:
Options (2)
Some expressions cannot be denested within the default time constraint of five seconds:
Use the TimeConstraint option to allow more time. When the time constraint elapses, the most denested form found is returned:
Applications (2)
Many interesting denestings can be found:
The denestings given by Ramanujan et al., having no definite algorithm that does not involve the complex roots of unity, can be done heuristically using this function:
Possible Issues (1)
Since the methods used are heuristic, setting a high TimeConstraint still might not return a fully denested expression:
Publisher
Wolfram Summer School
Related Links
Version History
-
2.1.0
– 29 April 2024
-
2.0.1
– 06 March 2023
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2.0.0
– 06 December 2020
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1.0.0
– 02 October 2020
Related Resources
Author Notes
Much of the work was done by Corey Ziegler, Bill Gosper and Daniel Lichtblau. The current function implemented by Swastik Banerjee adds time constraints to different heuristic approaches, compares the nesting degrees of the denested expressions obtained from each such approach and returns the best denesting possible.