Analysis of the p-adic construction of multivariate correction coefficiencts in polynomial factorization: Iteration vs. recursion

  • Paul S. Wang
8. Algorithm Analysis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


In a recently published paper [4] the author described a new algorithm for multivariate polynomial factorization over the integers. One important feature of this algorithm is the variable-by-variable p-adic construction of all factors in parallel. To perform such p-adic construction of the factors, a second p-adic construction for multivariate "correction coefficients" is used. This second p-adic construction is in an "inner loop" of the construction process. Therefore its efficiency is of central importance to the entire factoring algorithm. In [4], an iterative algorithm is used for this second p-adic construction. A timing analysis of this iterative algorithm is included. A new recursive method for the p-adic construction of the correction coefficients is presented and analyzed.

Timing comparisons, both theoretical, and empirical are made of these two approaches. The recursive algorithm is shown to be much more efficient.


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  1. 1.
    D. E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Addison-Wesley, Reading, Mass., 1969. MR 44 #3531.Google Scholar
  2. 2.
    MACSYMA Reference Manual, The MATHLAB Group, Project MAC, M.I.T., Cambridge, Mass., May 1979.Google Scholar
  3. 3.
    M. Mignotte, "An inequality about factors of polynomials," Math. Comp., v. 28, 1974, pp. 1153–1157.Google Scholar
  4. 4.
    P. S. Wang, "An Improved Multivariate Polynomial Factoring Algorithm," Mathematics of Computation, Vol. 32, No. 144, Oct. 1978, pp. 1215–1231.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Paul S. Wang
    • 1
  1. 1.Department of MathematicsKent State UniversityKent

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