Abstract
The problem of simplification of nested radicals over arbitrary number fields was studied by many authors. The case of real radicals over real number fields is somewhat easier to study (at least, from theoretical point of view). In particular, an efficient (i.e., a polynomial-time) algorithm of simplification of at most doubly nested radicals is known. However, this algorithm does not guarantee complete simplification for the case of radicals with nesting depth more than two. In the paper, we give a detailed presentation of the theory that provides an algorithm which simplifies triply nested reals radicals over \(\mathbb {Q}\). Some examples of triply nested real radicals that cannot be simplified are also given.
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Acknowledgments
This work is supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement No. 075-02-2020-1534/1).
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Osipov, N.N., Kytmanov, A.A. (2021). Simplification of Nested Real Radicals Revisited. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2021. Lecture Notes in Computer Science(), vol 12865. Springer, Cham. https://doi.org/10.1007/978-3-030-85165-1_17
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DOI: https://doi.org/10.1007/978-3-030-85165-1_17
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