The Hensel Lemma in Algebraic Manipulation

Abstract

New and improved algorithms for computation in several fundamental polynomial operations are presented. The common basis for these algorithms are generalizations of the p-adic technique used in the constructive proof of the Hensel Lemma. Multivariate polynomial operations are stressed due to the special importance of the multivariate Hensel-type construction in replacing the modular evaluation-and-interpolation technique under certain conditions. Due to the availability of numerous methods for the computation of polynomial greatest common divisors (GCD), the EZGCD Algorithm is given special emphasis. Both theoretically and by actual computing data, this new algorithm demonstrates promising efficiencies by taking advantage of the sparseness of multivariate polynomials.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1974
Accession Number
ADA002737

Entities

People

  • David Y. Yun

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Computational Science
  • Computations
  • Computer Programming
  • Computer Science
  • Computers
  • Construction
  • Decomposition
  • Efficiency
  • Engineering
  • Integrals
  • Mathematics
  • Military Research
  • Numerical Analysis
  • Polynomials
  • Rational Functions
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computer Programming and Software Development.
  • Operations Research