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 $