| Interface | Description |
|---|---|
| Factorization<C extends GcdRingElem<C>> |
Factorization algorithms interface.
|
| GreatestCommonDivisor<C extends GcdRingElem<C>> |
Greatest common divisor algorithm interface.
|
| Squarefree<C extends GcdRingElem<C>> |
Squarefree decomposition interface.
|
| Class | Description |
|---|---|
| CycloUtil |
Cyclotomic polynomial utilities.
|
| Examples |
Examples for ufd and elementaty integration usage.
|
| ExamplesPartialFraction |
Examples related to partial fraction decomposition.
|
| FactorAbsolute<C extends GcdRingElem<C>> |
Absolute factorization algorithms class.
|
| FactorAbstract<C extends GcdRingElem<C>> |
Abstract factorization algorithms class.
|
| FactorAlgebraic<C extends GcdRingElem<C>> |
Algebraic number coefficients factorization algorithms.
|
| FactorAlgebraicTest |
Factor algebraic tests with JUnit.
|
| FactorComplex<C extends GcdRingElem<C>> |
Complex coefficients factorization algorithms.
|
| FactorComplexTest |
Factor complex via algebraic tests with JUnit.
|
| FactorFactory |
Factorization algorithms factory.
|
| FactorFraction<C extends GcdRingElem<C>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>> |
Fraction factorization algorithms.
|
| FactorFractionTest |
Factor fractions (of polynomial quotients) tests with JUnit.
|
| FactorGenericTest |
Factor rational tests with JUnit.
|
| FactorInteger<MOD extends GcdRingElem<MOD> & Modular> |
Integer coefficients factorization algorithms.
|
| FactorIntegerTest |
Factor tests with JUnit.
|
| FactorModular<MOD extends GcdRingElem<MOD> & Modular> |
Modular coefficients factorization algorithms.
|
| FactorModularTest |
Factor modular tests with JUnit.
|
| FactorMoreTest |
Factor tests with JUnit.
|
| FactorQuotient<C extends GcdRingElem<C>> |
Rational function coefficients factorization algorithms.
|
| FactorQuotientTest |
Factor quotient tests with JUnit.
|
| FactorRational |
Rational number coefficients factorization algorithms.
|
| FactorRationalTest |
Factor rational tests with JUnit.
|
| Factors<C extends GcdRingElem<C>> |
Container for the factors of absolute factorization.
|
| FactorsList<C extends GcdRingElem<C>> |
Container for the factors of a squarefree factorization.
|
| FactorsMap<C extends GcdRingElem<C>> |
Container for the factors of a eventually non-squarefree factorization.
|
| FactorTest |
Factor tests with JUnit.
|
| GCDFactory |
Greatest common divisor algorithms factory.
|
| GCDFactoryTest |
GreatestCommonDivisor factory tests with JUnit.
|
| GCDHenselTest |
GCD Hensel algorithm tests with JUnit.
|
| GCDModEvalTest |
GCD Modular Evaluation algorithm tests with JUnit.
|
| GCDModLongEvalTest |
GCD Modular Evaluation algorithm tests with JUnit.
|
| GCDModLongTest |
GCD Modular algorithm tests with JUnit.
|
| GCDModularTest |
GCD Modular algorithm tests with JUnit.
|
| GCDPartFracRatTest |
GCD partial fraction with rational coefficients algorithm tests with JUnit.
|
| GCDPrimitiveTest |
GCD Primitive PRS algorithm tests with JUnit.
|
| GCDProxy<C extends GcdRingElem<C>> |
Greatest common divisor parallel proxy.
|
| GCDProxyTest |
GreatestCommonDivisor proxy tests with JUnit.
|
| GCDSimpleTest |
GCD Simple PRS algorithm tests with JUnit.
|
| GCDSubresRatTest |
GCD Subres with rational coefficients algorithm tests with JUnit.
|
| GCDSubresTest |
GCD Subresultant PRS algorithm tests with JUnit.
|
| GCDTimingTest |
GreatestCommonDivisor timing tests with JUnit.
|
| GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> |
Greatest common divisor algorithms.
|
| GreatestCommonDivisorFake<C extends GcdRingElem<C>> |
Greatest common divisor algorithms with gcd always 1.
|
| GreatestCommonDivisorHensel<MOD extends GcdRingElem<MOD> & Modular> |
Greatest common divisor algorithms with subresultant polynomial remainder
sequence and univariate Hensel lifting.
|
| GreatestCommonDivisorModEval<MOD extends GcdRingElem<MOD> & Modular> |
Greatest common divisor algorithms with modular evaluation algorithm for
recursion.
|
| GreatestCommonDivisorModular<MOD extends GcdRingElem<MOD> & Modular> |
Greatest common divisor algorithms with modular computation and chinese
remainder algorithm.
|
| GreatestCommonDivisorPrimitive<C extends GcdRingElem<C>> |
Greatest common divisor algorithms with primitive polynomial remainder
sequence.
|
| GreatestCommonDivisorSimple<C extends GcdRingElem<C>> |
Greatest common divisor algorithms with monic polynomial remainder sequence.
|
| GreatestCommonDivisorSubres<C extends GcdRingElem<C>> |
Greatest common divisor algorithms with subresultant polynomial remainder
sequence.
|
| HenselApprox<MOD extends GcdRingElem<MOD> & Modular> |
Container for the approximation result from a Hensel algorithm.
|
| HenselMultUtil |
Hensel multivariate lifting utilities.
|
| HenselMultUtilTest |
HenselMultUtil tests with JUnit.
|
| HenselUtil |
Hensel utilities for ufd.
|
| HenselUtilTest |
HenselUtil tests with JUnit.
|
| PartialFraction<C extends GcdRingElem<C>> |
Container for the partial fraction decomposition of a squarefree denominator.
|
| PolyUfdUtil |
Polynomial ufd utilities.
|
| PolyUfdUtilTest |
PolyUfdUtil tests with JUnit.
|
| Quotient<C extends GcdRingElem<C>> |
Quotient, that is a rational function, based on GenPolynomial with RingElem
interface.
|
| QuotientIntTest |
Quotient over BigInteger GenPolynomial tests with JUnit.
|
| QuotientRatTest |
Quotient over BigRational GenPolynomial tests with JUnit.
|
| QuotientRing<C extends GcdRingElem<C>> |
Quotient ring factory based on GenPolynomial with RingElem interface.
|
| QuotIntPolynomialTest |
Quotient BigInteger coefficient GenPolynomial tests with JUnit.
|
| SquarefreeAbstract<C extends GcdRingElem<C>> |
Abstract squarefree decomposition class.
|
| SquarefreeAlgModTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeAlgQuotModTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeFactory |
Squarefree factorization algorithms factory.
|
| SquarefreeFieldChar0<C extends GcdRingElem<C>> |
Squarefree decomposition for coefficient fields of characteristic 0.
|
| SquarefreeFieldCharP<C extends GcdRingElem<C>> |
Squarefree decomposition for coefficient fields of characteristic p.
|
| SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>> |
Squarefree decomposition for finite coefficient fields of characteristic p.
|
| SquarefreeInfiniteAlgebraicFieldCharP<C extends GcdRingElem<C>> |
Squarefree decomposition for algebraic extensions of infinite coefficient
fields of characteristic p > 0.
|
| SquarefreeInfiniteFieldCharP<C extends GcdRingElem<C>> |
Squarefree decomposition for infinite coefficient fields of characteristic p.
|
| SquarefreeIntTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeModLongTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeModTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeQuotModTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeRatTest |
Squarefree factorization tests with JUnit.
|
| SquarefreeRingChar0<C extends GcdRingElem<C>> |
Squarefree decomposition for coefficient rings of characteristic 0.
|
| SquarefreeTest |
Squarefree Factory tests with JUnit.
|
| Exception | Description |
|---|---|
| NoLiftingException |
Non existing Hensel lifting.
|
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 $