The Mathematical Intelligencer

, Volume 20, Issue 4, pp 55–60 | Cite as

√2 +√3: four different views

Article

Keywords

Galois Group Galois Theory Maximal Chain Splitting Field Irreducible Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. Berlekamp, Factoring polynomials over finite fields,Bell Syst. Tech. J. 46 (1967), 1853–1859.CrossRefMathSciNetGoogle Scholar
  2. [2]
    A. Borodin, R. Fagin, J. Hopcroft, and M. Tompa, Decreasing the nesting depth of expressions involving square roots,J. Symbol. Comput. 1 (1985), 169–188.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    D. Kozen and S. Landau, Polynomial decomposition algorithms,J. Symbol. Comput. 7 (1989), 445–456.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    S. Landau, How to tangle with a nested radical,Math. Intell. 16, no. 2 (1994), 49–55.CrossRefMATHGoogle Scholar
  5. [5]
    S. Landau, Simplification of nested radicals,SIAM J. Comput. 21 (1992), 85–110.CrossRefMATHMathSciNetGoogle Scholar
  6. [6]
    S. Landau and G. Miller, Solvability by radicals is in polynomial time,J. Comput. Syst. Sci. 30(2) (1985), 179–208.CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    H.W. Lenstra, Jr., Algorithms in algebraic number theory,Bull. AMS 26(2) (1992), 211–244.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    P. Pálfy, A polynomial bound for the orders of primitive solvable groups,J. Algebra 77 (1982), 127–137.CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    R. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public key cryptosystems,Communications of the ACM 21(1978), 120–126.CrossRefMATHMathSciNetGoogle Scholar
  10. [10]
    B.L. van der Waerden,Algebra, Frederick Ungar Publishing Co. (1977).Google Scholar
  11. [11]
    H. Zassenhaus, On Hensel factorization I,J. Number Theory 1 (1969), 291–311.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1998

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of MassachusettsAmherstUSA

Personalised recommendations