The Mathematical Intelligencer

, Volume 16, Issue 2, pp 49–55 | Cite as

How to tangle with a nested radical

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References

  1. 1.
    E. Artin,Galois Theory, University of Notre Dame Press, Notre Dame, IN, 1942.Google Scholar
  2. 2.
    A. Besicovitch, On the linear independence of fractional powers of integers,J. London Math. Soc. 15 (1940), 3–6.CrossRefMathSciNetGoogle Scholar
  3. 3.
    A. Borodin, R. Fagin, J. Hopcroft, and M. Tompa, Decreasing the nesting depth of expressions involving square roots,J. Symb. Comput. 1 (1985), 169–188.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    J. Blömer, Computing sums of radicals in polynomial time,Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, 1991, pp. 670–677.Google Scholar
  5. 5.
    J. Blömer, How to denest Ramanujan’s nested radicals,Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, 1992, pp. 447–456.Google Scholar
  6. 6.
    B. Caviness and R. Fateman, Simplification of radical expressions,Proc. SYMSAC 77, pp. 329–338.Google Scholar
  7. 7.
    G. Horng and M. Huang, On simplifying nested radicals and solving polynomials by pure nested radicals of minimum depth,Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, 1990, pp. 847–854.Google Scholar
  8. 8.
    S. Landau, Simplification of nested radicals,SIAM J. Comput. 21 (1992), 85–109.CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    S. Landau, A Note on Zippel denesting,J. Symb. Comput. 13 (1992), 41–45.CrossRefMATHGoogle Scholar
  10. 10.
    S. Landau and G. Miller, Solvability by radicals is in polynomial time,J. Comput. Syst. Sci. 30 (1985), 179–208.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    S. Ramanujan,Problems and Solutions, Collected Works of S. Ramanujan, Cambridge University Press, Cambridge, 1927.Google Scholar
  12. 12.
    C. Siegel, Algebraische Abhängigkeit von Wurzeln,Acta Aritmetica 21 (1971), 59–64.Google Scholar
  13. 13.
    R. Zippel, Simplification of expressions involving radicals,J. Symb. Comput. 1 (1985), 189–210.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1994

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity of MassachusettsAmherstUSA

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