Abstract
Given a nested radical α involving only d th roots we show how to compute an optimal or near optimal depth denesting of α by a nested radical that only involves D th roots, where D is an arbitrary multiple of d. As a special case the algorithm computes denestings as in
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L. Babai, E. Luks, Á. Seress: Fast management of permutation groups. Proc. 29th Symposium on Foundations of Computer Science (1988) pp. 272–282.
J. Blömer: Computing Sums of Radicals in Polynomial Time. Proc. 32nd Symposium on Foundations of Computer Science (1991) pp. 670–677.
J. Blömer: Denesting Ramanujan's Nested Radicals. Proc. 33nd Symposium on Foundations of Computer Science (1992) pp. 447–456.
A. Borodin, R. Fagin, J. E. Hopcroft, M. Tompa: Decreasing the Nesting Depth of Expressions Involving Square Roots. Journal of Symbolic Computation 1 (1985) pp. 169–188.
B. Caviness, R. Fateman: Simplification of Radical Expressions. Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation (1976).
G. Horng, M.-D. Huang: Simplifying Nested Radicals and Solving Polynomials by Radicals in Minimum Depth. Proc. 31st Symposium on Foundations of Computer Science (1990) pp. 847–854.
S. Lang: Algebra, 3rd edition. (1993) Addison-Wesley.
S. Landau: Factoring polynomials over algebraic number fields. SIAM Journal on Computing 14(1) (1985) pp. 184–195.
S. Landau: Simplification of Nested Radicals. SIAM Journal on Computing 21(1) (1992) pp 85–110.
S. Landau: A Note on Zippel-Denesting. Journal of Symbolic Computation 13 (1992) pp. 41–46.
S. Landau: How to Tangle with a Nested Radical. Mathematical Intelligencer 16(2) (1994) pp. 49–55.
S. Landau, G. L. Miller: Solvability by Radicals is in Polynomial Time. Journal of Computer and System Sciences 30 (1985) pp. 179–208.
S. Ramanujan: Problems and Solutions, Collected Works of S. Ramanujan (1927) Cambridge University Press.
R. Zippel: Simplification of Expressions Involving Radicals. Journal of Symbolic Computation 1 (1985) pp. 189–210.
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© 1997 Springer-Verlag Berlin Heidelberg
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Blömer, J. (1997). Denesting by bounded degree radicals. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_5
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DOI: https://doi.org/10.1007/3-540-63397-9_5
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