This package contains classes for polynomials rings as unique
  factorization domains.  Provided methods with interface
  GreatestCommonDivisor are e.g. greatest common divisors
  gcd(), primitive part primitivePart() or
  coPrime().  The different classes implement variants of
  polynomial remainder sequences (PRS) and modular methods.  Interface
  Squarefree provides the greatest squarefree factor
  squarefreeFactor() and a complete squarefree
  decompostion can be obtained with method
  squarefreeFactors().  There is a
  Factorization interface with an
  FactorAbstract class with common codes.  Factorization
  of univariate polynomials exists for several coefficient rings:
  modulo primes in class FactorModular, over integers in
  class FactorInteger, over rational numbers in class
  FactorRational, over algebraic numbers in class
  FactorAlgebraic<C> and over rational functions in
  class FactorQuotient<C> (where for the last two
  classes C can be any other ring for which the
  FactorFactory. getImplementation returns an
  implementation).  Multivatiate polynomials over the integers (and
  rational numbers) are factored using the algorithm of P. Wang. For
  other coeffcients the multivatiate polynomials are reduced to
  univariate polynomials via Kronecker substitution.   The rational function class
  Quotient computes quotients of polynomials reduced to
  lowest terms.
  To choose the correct implementation always use the factory classes
  GCDFactory, SquarefreeFactory and
  FactorFactory with methods
  getImplementation() or getProxy().  These
  methods will take care of all possible (implemented) coefficient
  rings properties.  The polynomial coefficients must implement the
  GcdRingElem interface and so must allow greatest common
  divisor computations.  Greatest common divisor computation is
  completely generic and works for any implemented integral domain.
  If special, optimized implementations exist they will be used.
  Squarefree decomposition is also completely generic and works for
  any implemented integral domain. There are no special, optimized
  implementations.  Factorization is generic relative to the
  implemented ring constructions: algebraic field extensions and
  transcendent field extensions. Implemented base cases are modular
  coefficient, integer coefficients and rational number coefficients.
The implementation follows Geddes & Czapor & Labahn Algorithms for Computer Algebra and Cohen A Curse in Computational Algebraic Number Theory. See also Kaltofen Factorization of Polynomials in Computing Supplement, Springer, 1982, Davenport & Gianni & Trager Scratchpad's View of Algebra II: A Categorical View of Factorization in ISSAC'91 and the ALDES/SAC2 code as contained in MAS.
Last modified: Fri Sep 21 21:56:48 CEST 2012
$Id: package.html 4215 2012-09-21 21:56:08Z kredel $