Uses of Interface
edu.jas.structure.RingElem

Packages that use RingElem

Package	Description
edu.jas.application	Groebner base application package.
edu.jas.arith	Basic arithmetic package.
edu.jas.fd	Factorization domain package for solvable polynomial rings.
edu.jas.gb	Groebner bases package.
edu.jas.gbmod	Module Groebner base package.
edu.jas.gbufd	Groebner bases using unique factorization package.
edu.jas.poly	Generic coefficients polynomial package.
edu.jas.ps	Generic coefficients power series package.
edu.jas.root	Real and Complex Root Computation package.
edu.jas.structure	Basic structural interfaces.
edu.jas.ufd	Unique factorization domain package.
edu.jas.vector	Generic vector and matrix package.

Uses of RingElem in edu.jas.application

Classes in edu.jas.application with type parameters of type RingElem

Modifier and Type	Class	Description
class	ColorPolynomial<C extends RingElem<C>>	Colored Polynomials with green, red and white coefficients.
class	CPair<C extends RingElem<C>>	Serializable subclass to hold pairs of colored polynomials.
class	PolyUtilApp<C extends RingElem<C>>	Polynomial utilities for applications, for example conversion ExpVector to Product or zero dimensional ideal root computation.

Classes in edu.jas.application that implement RingElem

Modifier and Type	Class	Description
class	Local<C extends GcdRingElem<C>>	Local ring element based on GenPolynomial with RingElem interface.
class	LocalSolvablePolynomial<C extends GcdRingElem<C>>	LocalSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on bi-variate real algebraic numbers.
class	Residue<C extends GcdRingElem<C>>	Residue ring element based on GenPolynomial with RingElem interface.
class	ResidueSolvablePolynomial<C extends GcdRingElem<C>>	ResidueSolvablePolynomial generic solvable polynomials with solvable residue coefficients implementing RingElem.
class	ResidueSolvableWordPolynomial<C extends GcdRingElem<C>>	ResidueSolvableWordPolynomial solvable polynomials with WordResidue coefficients implementing RingElem.
class	SolvableLocal<C extends GcdRingElem<C>>	SolvableLocal ring element based on pairs of GenSolvablePolynomial with GcdRingElem interface.
class	SolvableLocalResidue<C extends GcdRingElem<C>>	SolvableLocalResidue, that is a (left) rational function, based on pairs of GenSolvablePolynomial with GcdRingElem interface.
class	SolvableResidue<C extends GcdRingElem<C>>	SolvableResidue ring element based on GenSolvablePolynomial with GcdRingElem interface.
class	WordResidue<C extends GcdRingElem<C>>	WordResidue ring element based on GenWordPolynomial with GcdRingElem interface.

Methods in edu.jas.application with type parameters of type RingElem

Modifier and Type	Method	Description
(package private) static <C extends RingElem<C>> GenPolynomial<C>	PolyUtilApp.convert(GenPolynomialRing<C> fac, GenPolynomial<C> p)
(package private) static <C extends RingElem<C>> GenPolynomial<Complex<C>>	PolyUtilApp.convertComplex(GenPolynomialRing<Complex<C>> fac, GenPolynomial<C> p)
(package private) static <C extends RingElem<C>> GenPolynomial<Complex<C>>	PolyUtilApp.convertComplexComplex(GenPolynomialRing<Complex<C>> fac, GenPolynomial<Complex<C>> p)

Uses of RingElem in edu.jas.arith

Classes in edu.jas.arith with type parameters of type RingElem

Modifier and Type	Interface	Description
interface	ModularRingFactory<C extends RingElem<C> & Modular>	Modular ring factory interface.
class	Product<C extends RingElem<C>>	Direct product element based on RingElem.
class	ProductRing<C extends RingElem<C>>	Direct product ring factory based on RingElem and RingFactory module.

Classes in edu.jas.arith that implement RingElem

Modifier and Type	Class	Description
final class	BigComplex	BigComplex class based on BigRational implementing the RingElem respectively the StarRingElem interface.
final class	BigDecimal	BigDecimal class to make java.math.BigDecimal available with RingElem interface.
final class	BigDecimalComplex	BigComplex class based on BigDecimal implementing the RingElem respectively the StarRingElem interface.
final class	BigInteger	BigInteger class to make java.math.BigInteger available with RingElem respectively the GcdRingElem interface.
final class	BigOctonion	BigOctonion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
class	BigQuaternion	BigQuaternion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
final class	BigQuaternionInteger	Integer BigQuaternion class based on BigRational implementing the RingElem interface and with the familiar MAS static method names.
final class	BigRational	Immutable arbitrary-precision rational numbers.
final class	ModInt	ModInt class with RingElem interface.
final class	ModInteger	ModInteger class with GcdRingElem interface.
final class	ModLong	ModLong class with RingElem interface.
class	Product<C extends RingElem<C>>	Direct product element based on RingElem.

Uses of RingElem in edu.jas.fd

Classes in edu.jas.fd that implement RingElem

Modifier and Type	Class	Description
class	QuotSolvablePolynomial<C extends GcdRingElem<C>>	QuotSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	SolvableQuotient<C extends GcdRingElem<C>>	SolvableQuotient, that is a (left) rational function, based on GenSolvablePolynomial with RingElem interface.

Uses of RingElem in edu.jas.gb

Classes in edu.jas.gb with type parameters of type RingElem

Modifier and Type	Class	Description
class	AbstractPair<C extends RingElem<C>>	Serializable abstract subclass to hold pairs of polynomials.
class	CriticalPair<C extends RingElem<C>>	Serializable subclass to hold critical pairs of polynomials.
class	CriticalPairComparator<C extends RingElem<C>>	Comparator for critical pairs of polynomials.
class	CriticalPairList<C extends RingElem<C>>	Critical pair list management.
class	DGroebnerBaseSeq<C extends RingElem<C>>	D-Groebner Base sequential algorithm.
interface	DReduction<C extends RingElem<C>>	Polynomial D Reduction interface.
class	DReductionSeq<C extends RingElem<C>>	Polynomial D-Reduction sequential use algorithm.
class	EGroebnerBaseSeq<C extends RingElem<C>>	E-Groebner Base sequential algorithm.
interface	EReduction<C extends RingElem<C>>	Polynomial E-Reduction interface.
class	EReductionSeq<C extends RingElem<C>>	Polynomial E-Reduction sequential use algorithm.
class	ExtendedGB<C extends RingElem<C>>	Container for a GB and transformation matrices.
(package private) class	GBClientSP<C extends RingElem<C>>	Objects of this class are to be send to a ExecutableServer.
class	GBDistSP<C extends RingElem<C>>	Deprecated. use RunGB or RunSGB for standalone execution
(package private) class	GBExerClient<C extends RingElem<C>>	Objects of this class are to be send to a ExecutableServer.
(package private) class	GBHybridExerClient<C extends RingElem<C>>	Objects of this class are to be send to a ExecutableServer.
(package private) class	GBSPTransportMessPair<C extends RingElem<C>>	Distributed GB transport message for pairs.
(package private) class	GBSPTransportMessPoly<C extends RingElem<C>>	Distributed GB transport message for polynomial.
(package private) final class	GBTransportMessPair<C extends RingElem<C>>	Distributed GB transport message for pairs.
(package private) final class	GBTransportMessPoly<C extends RingElem<C>>	Distributed GB transport message for polynomial.
interface	GroebnerBase<C extends RingElem<C>>	Groebner Bases interface.
class	GroebnerBaseAbstract<C extends RingElem<C>>	Groebner Bases abstract class.
class	GroebnerBaseArriSigSeqIter<C extends RingElem<C>>	Groebner Base Arri signature based sequential iterative algorithm.
class	GroebnerBaseDistributedEC<C extends RingElem<C>>	Groebner Base distributed algorithm.
class	GroebnerBaseDistributedHybridEC<C extends RingElem<C>>	Groebner Base distributed hybrid algorithm.
class	GroebnerBaseF5zSigSeqIter<C extends RingElem<C>>	Groebner Base F5z signature based sequential iterative algorithm.
class	GroebnerBaseGGVSigSeqIter<C extends RingElem<C>>	Groebner Base GGV signature based sequential iterative algorithm.
class	GroebnerBaseParallel<C extends RingElem<C>>	Groebner Base parallel algorithm.
class	GroebnerBaseParIter<C extends RingElem<C>>	Groebner Base parallel iterative algorithm.
class	GroebnerBaseSeq<C extends RingElem<C>>	Groebner Base sequential algorithm.
class	GroebnerBaseSeqIter<C extends RingElem<C>>	Groebner Base sequential iterative algorithm.
class	GroebnerBaseSeqPairDistributed<C extends RingElem<C>>	Deprecated. no direct alternative
class	GroebnerBaseSeqPairParallel<C extends RingElem<C>>	Groebner Base parallel algorithm.
class	GroebnerBaseSeqPairSeq<C extends RingElem<C>>	Groebner Base sequential algorithm.
class	GroebnerBaseSigSeqIter<C extends RingElem<C>>	Groebner Base signature based sequential iterative algorithm.
(package private) class	HybridReducerClientEC<C extends RingElem<C>>	Distributed clients reducing worker threads.
(package private) class	HybridReducerReceiverEC<C extends RingElem<C>>	Distributed server receiving worker thread.
(package private) class	HybridReducerServerEC<C extends RingElem<C>>	Distributed server reducing worker proxy threads.
(package private) class	LeftSolvableReducer<C extends RingElem<C>>	Reducing left worker threads.
(package private) class	LeftSolvableReducerSeqPair<C extends RingElem<C>>	Reducing left worker threads.
(package private) class	MiReducer<C extends RingElem<C>>	Reducing worker threads for minimal GB.
(package private) class	MiReducerClient<C extends RingElem<C>>	Distributed clients reducing worker threads for minimal GB.
(package private) class	MiReducerClientEC<C extends RingElem<C>>	Distributed clients reducing worker threads for minimal GB.
(package private) class	MiReducerClientSeqPair<C extends RingElem<C>>	Distributed clients reducing worker threads for minimal GB.
(package private) class	MiReducerIter<C extends RingElem<C>>	Reducing worker threads for minimal GB.
(package private) class	MiReducerSeqPair<C extends RingElem<C>>	Reducing worker threads for minimal GB.
(package private) class	MiReducerServer<C extends RingElem<C>>	Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.
(package private) class	MiReducerServerEC<C extends RingElem<C>>	Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.
(package private) class	MiReducerServerSeqPair<C extends RingElem<C>>	Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.
class	OrderedDPairlist<C extends RingElem<C>>	Pair list management for d-Groebner bases.
class	OrderedMinPairlist<C extends RingElem<C>>	Pair list management.
class	OrderedPairlist<C extends RingElem<C>>	Pair list management.
class	OrderedSyzPairlist<C extends RingElem<C>>	Pair list management.
class	OrderedWordPairlist<C extends RingElem<C>>	Pair list management of word polynomials.
class	Pair<C extends RingElem<C>>	Serializable subclass to hold pairs of polynomials.
interface	PairList<C extends RingElem<C>>	Pair list management interface.
(package private) class	Reducer<C extends RingElem<C>>	Reducing worker threads.
(package private) class	ReducerClientEC<C extends RingElem<C>>	Distributed clients reducing worker threads.
(package private) class	ReducerClientSeqPair<C extends RingElem<C>>	Distributed clients reducing worker threads.
(package private) class	ReducerIter<C extends RingElem<C>>	Reducing worker threads.
(package private) class	ReducerSeqPair<C extends RingElem<C>>	Reducing worker threads.
(package private) class	ReducerServerEC<C extends RingElem<C>>	Distributed server reducing worker threads.
(package private) class	ReducerServerSeqPair<C extends RingElem<C>>	Distributed server reducing worker threads.
interface	Reduction<C extends RingElem<C>>	Polynomial Reduction interface.
class	ReductionAbstract<C extends RingElem<C>>	Polynomial Reduction abstract class.
class	ReductionPar<C extends RingElem<C>>	Polynomial reduction parallel usable algorithm.
class	ReductionSeq<C extends RingElem<C>>	Polynomial reduction sequential use algorithm.
class	SigPair<C extends RingElem<C>>	Serializable subclass to hold pairs of polynomials.
class	SigPoly<C extends RingElem<C>>	Container for a polynomial and its signature.
interface	SigReduction<C extends RingElem<C>>	Polynomial SigReduction interface.
class	SigReductionSeq<C extends RingElem<C>>	Polynomial SigReduction class.
class	SolvableExtendedGB<C extends RingElem<C>>	Container for a GB and transformation matrices.
interface	SolvableGroebnerBase<C extends RingElem<C>>	Solvable Groebner Bases interface.
class	SolvableGroebnerBaseAbstract<C extends RingElem<C>>	Solvable Groebner Bases abstract class.
class	SolvableGroebnerBaseParallel<C extends RingElem<C>>	Solvable Groebner Base parallel algorithm.
class	SolvableGroebnerBaseSeq<C extends RingElem<C>>	Solvable Groebner bases sequential algorithms.
class	SolvableGroebnerBaseSeqPairParallel<C extends RingElem<C>>	Solvable Groebner Base parallel algorithm.
(package private) class	SolvableMiReducer<C extends RingElem<C>>	Reducing worker threads for minimal GB.
(package private) class	SolvableMiReducerSeqPair<C extends RingElem<C>>	Reducing worker threads for minimal GB.
interface	SolvableReduction<C extends RingElem<C>>	Solvable polynomial Reduction interface.
class	SolvableReductionAbstract<C extends RingElem<C>>	Solvable polynomial Reduction abstract class.
class	SolvableReductionPar<C extends RingElem<C>>	Solvable polynomial Reduction parallel usable algorithm.
class	SolvableReductionSeq<C extends RingElem<C>>	Solvable polynomial Reduction algorithm.
(package private) class	TwosidedSolvableReducer<C extends RingElem<C>>	Reducing twosided worker threads.
(package private) class	TwosidedSolvableReducerSeqPair<C extends RingElem<C>>	Reducing twosided worker threads.
interface	WordGroebnerBase<C extends RingElem<C>>	Non-commutative Groebner Bases interface for GenWordPolynomials.
class	WordGroebnerBaseAbstract<C extends RingElem<C>>	Non-commutative Groebner Bases abstract class.
class	WordGroebnerBaseSeq<C extends RingElem<C>>	Non-commutative word Groebner Base sequential algorithm.
class	WordPair<C extends RingElem<C>>	Serializable subclass to hold pairs of word polynomials.
interface	WordPairList<C extends RingElem<C>>	WordPair list management interface.
interface	WordReduction<C extends RingElem<C>>	Polynomial WordReduction interface.
class	WordReductionAbstract<C extends RingElem<C>>	Polynomial word reduction abstract class.
class	WordReductionSeq<C extends RingElem<C>>	Polynomial word reduction sequential use algorithm.

Methods in edu.jas.gb with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> void	GroebnerBaseDistributedEC.clientPart(String host, int port, int dhtport)	GB distributed client part.
static <C extends RingElem<C>> void	GroebnerBaseDistributedHybridEC.clientPart(String host, int threadsPerNode, int port, int dhtport)	GB distributed client part.

Uses of RingElem in edu.jas.gbmod

Classes in edu.jas.gbmod with type parameters of type RingElem

Modifier and Type	Interface	Description
interface	ModGroebnerBase<C extends RingElem<C>>	Deprecated. use respective methods from GroebnerBase
interface	ModSolvableGroebnerBase<C extends RingElem<C>>	Deprecated. use respective methods from SolvableGroebnerBase
class	ModSolvableGroebnerBaseAbstract<C extends RingElem<C>>	Deprecated. use respective methods from SolvableGroebnerBaseAbstract

Uses of RingElem in edu.jas.gbufd

Classes in edu.jas.gbufd with type parameters of type RingElem

Modifier and Type	Interface	Description
interface	PseudoReduction<C extends RingElem<C>>	Polynomial pseudo reduction interface.
class	PseudoReductionEntry<C extends RingElem<C>>	Polynomial reduction container.
class	PseudoReductionPar<C extends RingElem<C>>	Polynomial pseudo reduction sequential use algorithm.
class	PseudoReductionSeq<C extends RingElem<C>>	Polynomial pseudo reduction sequential use algorithm.
(package private) class	ResPart<C extends RingElem<C>>	Container for module resolution components.
(package private) class	ResPolPart<C extends RingElem<C>>	Container for polynomial resolution components.
interface	SolvablePseudoReduction<C extends RingElem<C>>	Polynomial pseudo reduction interface.
interface	SolvableSyzygy<C extends RingElem<C>>	Syzygy interface for solvable polynomials.
(package private) class	SolvResPart<C extends RingElem<C>>	Container for module resolution components.
(package private) class	SolvResPolPart<C extends RingElem<C>>	Container for polynomial resolution components.
interface	Syzygy<C extends RingElem<C>>	Syzygy interface.
interface	WordPseudoReduction<C extends RingElem<C>>	Polynomial pseudo reduction interface.
class	WordPseudoReductionEntry<C extends RingElem<C>>	Word polynomial reduction container.
class	WordPseudoReductionSeq<C extends RingElem<C>>	Polynomial word reduction sequential use algorithm.

Fields in edu.jas.gbufd declared as RingElem

Modifier and Type	Field	Description
final C	PseudoReductionEntry.multiplicator
final C	WordPseudoReductionEntry.multiplicator

Methods in edu.jas.gbufd with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<GenPolynomial<C>>>	PolyGBUtil.coefficientPseudoRemainder(GenPolynomial<GenPolynomial<GenPolynomial<C>>> P, GenPolynomial<GenPolynomial<C>> A)	Polynomial leading coefficient pseudo remainder.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyGBUtil.coefficientPseudoRemainderBase(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<C> A)	Polynomial leading coefficient pseudo remainder, base case.
static <C extends RingElem<C>> GroebnerBaseAbstract<Product<C>>	GBFactory.getImplementation(ProductRing<C> fac)	Determine suitable implementation of GB algorithms, case regular rings.
static <C extends RingElem<C>> GenPolynomial<C>	PolyGBUtil.topCoefficientPseudoRemainder(List<GenPolynomial<C>> A, GenPolynomial<C> P)	Top coefficient pseudo remainder of the leading coefficient of P wrt A in the main variables.
static <C extends RingElem<C>> GenPolynomial<C>	PolyGBUtil.topPseudoRemainder(List<GenPolynomial<C>> A, GenPolynomial<C> P)	Top pseudo reduction wrt the main variables.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyGBUtil.zeroDegrees(List<GenPolynomial<C>> A)	Extract polynomials with degree zero in the main variable.

Uses of RingElem in edu.jas.poly

Classes in edu.jas.poly with type parameters of type RingElem

Modifier and Type	Class	Description
class	AlgebraicNumber<C extends RingElem<C>>	Algebraic number class.
(package private) class	AlgebraicNumberIterator<C extends RingElem<C>>	Algebraic number iterator.
class	AlgebraicNumberRing<C extends RingElem<C>>	Algebraic number factory.
class	Complex<C extends RingElem<C>>	Generic Complex class implementing the RingElem interface.
class	ComplexRing<C extends RingElem<C>>	Generic Complex ring factory implementing the RingFactory interface.
(package private) class	CompRatToDec<C extends RingElem<C> & Rational>	Conversion of Complex Rational to Complex BigDecimal.
(package private) class	DistToRec<C extends RingElem<C>>	Conversion of distributive to recursive representation.
(package private) class	EvalAllPol<C extends RingElem<C>>	Evaluate all variable functor.
(package private) class	EvalMain<C extends RingElem<C>>	Evaluate main variable functor.
(package private) class	EvalMainPol<C extends RingElem<C>>	Evaluate main variable functor.
(package private) class	FromInteger<D extends RingElem<D>>	Conversion from BigInteger functor.
(package private) class	FromIntegerPoly<D extends RingElem<D>>	Conversion from GenPolynomial functor.
final class	GenExteriorPolynomial<C extends RingElem<C>>	GenExteriorPolynomial generic polynomials implementing RingElem.
final class	GenExteriorPolynomialRing<C extends RingElem<C>>	GenExteriorPolynomialRing generic antisymmetric polynomial factory implementing RingFactory; Factory for antisymmetric polynomials (in fact vectors) over C.
class	GenPolynomial<C extends RingElem<C>>	GenPolynomial generic polynomials implementing RingElem.
(package private) class	GenPolynomialIterator<C extends RingElem<C>>	Polynomial iterator.
(package private) class	GenPolynomialMonomialIterator<C extends RingElem<C>>	Polynomial monomial iterator.
class	GenPolynomialRing<C extends RingElem<C>>	GenPolynomialRing generic polynomial factory.
class	GenSolvablePolynomial<C extends RingElem<C>>	GenSolvablePolynomial generic solvable polynomials implementing RingElem.
class	GenSolvablePolynomialRing<C extends RingElem<C>>	GenSolvablePolynomialRing generic solvable polynomial factory implementing RingFactory and extending GenPolynomialRing factory.
final class	GenWordPolynomial<C extends RingElem<C>>	GenWordPolynomial generic polynomials implementing RingElem.
final class	GenWordPolynomialRing<C extends RingElem<C>>	GenWordPolynomialRing generic polynomial factory implementing RingFactory; Factory for non-commutative string polynomials over C.
(package private) class	ImagPartComplex<C extends RingElem<C>>	Imaginary part functor.
final class	IndexListMonomial<C extends RingElem<C>>	IndexListMonomial class.
class	IndexListPolyIterator<C extends RingElem<C>>	Iterator over monomials of a polynomial.
class	Local<C extends RingElem<C>>	Local element based on RingElem pairs.
class	LocalRing<C extends RingElem<C>>	Local ring factory based on RingElem principal ideal.
(package private) class	ModSymToInt<C extends RingElem<C> & Modular>	Conversion of symmetric ModInteger to BigInteger functor.
(package private) class	ModToInt<C extends RingElem<C> & Modular>	Conversion of ModInteger to BigInteger functor.
class	ModuleList<C extends RingElem<C>>	List of vectors of polynomials.
final class	Monomial<C extends RingElem<C>>	Monomial class.
class	OptimizedModuleList<C extends RingElem<C>>	Container for optimization results.
class	OptimizedPolynomialList<C extends RingElem<C>>	Container for optimization results.
class	OrderedModuleList<C extends RingElem<C>>	Ordered list of vectors of polynomials.
class	OrderedPolynomialList<C extends RingElem<C>>	Ordered list of polynomials.
class	PolyIterator<C extends RingElem<C>>	Iterator over monomials of a polynomial.
interface	Polynomial<C extends RingElem<C>>	Polynomial interface.
class	PolynomialComparator<C extends RingElem<C>>	Comparator for polynomials.
class	PolynomialList<C extends RingElem<C>>	List of polynomials.
interface	PolynomialRing<C extends RingElem<C>>	Polynomial factory interface.
class	PolySpliterator<C extends RingElem<C>>	Spliterator over monomials of a polynomial.
class	Quotient<C extends RingElem<C>>	Quotient element based on RingElem pairs.
class	QuotientRing<C extends RingElem<C>>	Quotient ring factory using RingElem and RingFactory.
(package private) class	RealPartComplex<C extends RingElem<C>>	Real part functor.
class	RecSolvablePolynomial<C extends RingElem<C>>	RecSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	RecSolvablePolynomialRing<C extends RingElem<C>>	RecSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
class	RecSolvableWordPolynomial<C extends RingElem<C>>	RecSolvableWordPolynomial generic recursive solvable polynomials implementing RingElem.
class	RecSolvableWordPolynomialRing<C extends RingElem<C>>	RecSolvableWordPolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
(package private) class	RecToDist<C extends RingElem<C>>	Conversion of recursive to distributive representation.
interface	RelationGenerator<C extends RingElem<C>>	Generate Relation Tables for solvable polynomial rings.
class	RelationTable<C extends RingElem<C>>	RelationTable for solvable polynomials.
class	Residue<C extends RingElem<C>>	Residue element based on RingElem residue.
class	ResidueRing<C extends RingElem<C>>	Residue ring factory based on RingElem and RingFactory module.
class	TableRelation<C extends RingElem<C>>	TableRelation container for storage and printing in RelationTable.
(package private) class	ToComplex<C extends RingElem<C>>	Rational to complex functor.
class	WeylRelations<C extends RingElem<C>>	Generate Relation Table for Weyl Algebras Adds the respective relations to the relation table of the given solvable ring factory.
class	WeylRelationsIterated<C extends RingElem<C>>	Generate Relation Table for Weyl Algebras Adds the respective relations to the relation table of the given solvable ring factory.
final class	WordMonomial<C extends RingElem<C>>	WordMonomial class.
class	WordPolyIterator<C extends RingElem<C>>	Iterator over monomials of a polynomial.

Subinterfaces of RingElem in edu.jas.poly

Modifier and Type	Interface	Description
interface	Polynomial<C extends RingElem<C>>	Polynomial interface.

Classes in edu.jas.poly that implement RingElem

Modifier and Type	Class	Description
class	AlgebraicNumber<C extends RingElem<C>>	Algebraic number class.
class	Complex<C extends RingElem<C>>	Generic Complex class implementing the RingElem interface.
final class	GenExteriorPolynomial<C extends RingElem<C>>	GenExteriorPolynomial generic polynomials implementing RingElem.
class	GenPolynomial<C extends RingElem<C>>	GenPolynomial generic polynomials implementing RingElem.
class	GenSolvablePolynomial<C extends RingElem<C>>	GenSolvablePolynomial generic solvable polynomials implementing RingElem.
final class	GenWordPolynomial<C extends RingElem<C>>	GenWordPolynomial generic polynomials implementing RingElem.
class	Local<C extends RingElem<C>>	Local element based on RingElem pairs.
class	QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>, D extends GcdRingElem<D>>	QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	Quotient<C extends RingElem<C>>	Quotient element based on RingElem pairs.
class	RecSolvablePolynomial<C extends RingElem<C>>	RecSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
class	RecSolvableWordPolynomial<C extends RingElem<C>>	RecSolvableWordPolynomial generic recursive solvable polynomials implementing RingElem.
class	Residue<C extends RingElem<C>>	Residue element based on RingElem residue.

Fields in edu.jas.poly declared as RingElem

Modifier and Type	Field	Description
(package private) final C	EvalMain.a
(package private) final C	EvalMainPol.a
final C	IndexListMonomial.c	Coefficient of monomial.
final C	Monomial.c	Coefficient of monomial.
final C	WordMonomial.c	Coefficient of monomial.
protected final C	Local.den	Denominator part of the element data structure.
final C	Quotient.den	Denominator part of the element data structure.
protected final C	LocalRing.ideal	Ideal generator for localization.
protected final C	Complex.im	Imaginary part of the data structure.
protected final C	ResidueRing.modul	Ring element for reduction.
protected final C	Local.num	Numerator part of the element data structure.
final C	Quotient.num	Numerator part of the element data structure.
protected final C	Complex.re	Real part of the data structure.
protected final C	Residue.val	Value part of the element data structure.

Methods in edu.jas.poly with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> C	PolyUtil.absNorm(GenPolynomial<C> p)	Absolute norm.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseDensePseudoQuotient(GenPolynomial<C> P, GenPolynomial<C> S)	GenPolynomial dense pseudo quotient.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseDensePseudoRemainder(GenPolynomial<C> P, GenPolynomial<C> S)	GenPolynomial dense pseudo remainder.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseDerivative(GenPolynomial<C> P)	GenPolynomial polynomial derivative main variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseDerivative(GenPolynomial<C> P, int r)	GenPolynomial polynomial partial derivative variable r.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseIntegral(GenPolynomial<C> P)	GenPolynomial polynomial integral main variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.basePseudoDivide(GenPolynomial<C> P, GenPolynomial<C> S)	GenPolynomial sparse pseudo divide.
static <C extends RingElem<C>> GenPolynomial<C>[]	PolyUtil.basePseudoQuotientRemainder(GenPolynomial<C> P, GenPolynomial<C> S)	GenPolynomial sparse pseudo quotient and remainder.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.basePseudoRemainder(GenPolynomial<C> P, GenPolynomial<C> S)	Deprecated. (forRemoval=true) Use PolyUtil.baseSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.baseRecursiveDivide(GenPolynomial<GenPolynomial<C>> P, C s)	GenPolynomial base divide.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseRemainderPoly(GenPolynomial<C> P, C s)	GenPolynomial coefficient wise remainder.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.baseSparsePseudoRemainder(GenPolynomial<C> P, GenPolynomial<C> S)	GenPolynomial sparse pseudo remainder.
static <C extends RingElem<C>> List<List<GenPolynomial<C>>>	ModuleList.castToList(List<List<GenSolvablePolynomial<C>>> slist)	Get a solvable polynomials list as List of GenPolynomials.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolynomialList.castToList(List<? extends GenPolynomial<C>> slist)	Get list of extensions of polynomials as List of GenPolynomials.
static <C extends RingElem<C>> List<List<GenPolynomial<C>>>	PolynomialList.castToMatrix(List<List<? extends GenPolynomial<C>>> slist)	Get list of list of extensions of polynomials as List of List of GenPolynomials.
static <C extends RingElem<C>> List<GenSolvablePolynomial<C>>	PolynomialList.castToSolvableList(List<GenPolynomial<C>> list)	Get list as List of GenSolvablePolynomials.
static <C extends RingElem<C>> List<List<GenSolvablePolynomial<C>>>	PolynomialList.castToSolvableMatrix(List<List<GenPolynomial<C>>> list)	Get list of list as List of List of GenSolvablePolynomials.
static <C extends RingElem<C> & Modular> GenPolynomial<C>	PolyUtil.chineseRemainder(GenPolynomialRing<C> fac, GenPolynomial<C> A, C mi, GenPolynomial<C> B)	ModInteger chinese remainder algorithm on coefficients.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.coefficientBasePseudoDivide(GenPolynomial<C> P, C s)	GenPolynomial pseudo divide.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.coefficientPseudoDivide(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<C> s)	GenPolynomial pseudo divide.
static <C extends RingElem<C>> long	PolyUtil.coeffMaxDegree(GenPolynomial<GenPolynomial<C>> A)	Maximal degree in the coefficient polynomials.
static <C extends RingElem<C> & Rational> GenPolynomial<Complex<BigDecimal>>	PolyUtil.complexDecimalFromRational(GenPolynomialRing<Complex<BigDecimal>> fac, GenPolynomial<Complex<C>> A)	Convert to complex decimal coefficients.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.conjugateCoeff(GenPolynomial<C> A)	Conjugate coefficients.
static <C extends RingElem<C> & Rational> GenPolynomial<BigDecimal>	PolyUtil.decimalFromRational(GenPolynomialRing<BigDecimal> fac, GenPolynomial<C> A)	Convert to decimal coefficients.
static <C extends RingElem<C>> List<GenPolynomial<BigInteger>>	TermOrderOptimization.degreeMatrix(GenPolynomial<C> A)	Degree matrix.
static <C extends RingElem<C>> List<GenPolynomial<BigInteger>>	TermOrderOptimization.degreeMatrix(Collection<GenPolynomial<C>> L)	Degree matrix.
static <C extends RingElem<C>> List<GenPolynomial<BigInteger>>	TermOrderOptimization.degreeMatrixOfCoefficients(GenPolynomial<GenPolynomial<C>> A)	Degree matrix of coefficient polynomials.
static <C extends RingElem<C>> List<GenPolynomial<BigInteger>>	TermOrderOptimization.degreeMatrixOfCoefficients(Collection<GenPolynomial<GenPolynomial<C>>> L)	Degree matrix of coefficient polynomials.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.distribute(GenPolynomialRing<C> dfac, GenPolynomial<GenPolynomial<C>> B)	Distribute a recursive polynomial to a generic polynomial.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.distribute(GenPolynomialRing<C> dfac, List<GenPolynomial<GenPolynomial<C>>> L)	Distribute a recursive polynomial list to a generic polynomial list.
static <C extends RingElem<C>> GenSolvablePolynomialRing<C>	RecSolvablePolynomialRing.distribute(RecSolvablePolynomialRing<C> rf)	Distributive representation as polynomial with all main variables.
<C extends RingElem<C>> C	ExpVector.evaluate(RingFactory<C> cf, List<C> a)	Evaluate.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.evaluate(GenPolynomialRing<C> cfac, GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomialRing<GenPolynomial<C>> nfac, GenPolynomialRing<C> dfac, GenPolynomial<C> A, C a)	Evaluate at k-th variable.
static <C extends RingElem<C>> C	PolyUtil.evaluateAll(RingFactory<C> cfac, GenPolynomial<C> A, List<C> a)	Evaluate all variables.
static <C extends RingElem<C>> List<C>	PolyUtil.evaluateAll(RingFactory<C> cfac, List<GenPolynomial<C>> L, List<C> a)	Evaluate all variables.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.evaluateFirst(GenPolynomialRing<C> cfac, GenPolynomialRing<C> dfac, GenPolynomial<C> A, C a)	Evaluate at first (lowest) variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.evaluateFirstRec(GenPolynomialRing<C> cfac, GenPolynomialRing<C> dfac, GenPolynomial<GenPolynomial<C>> A, C a)	Evaluate at first (lowest) variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.evaluateMain(GenPolynomialRing<C> cfac, GenPolynomial<C> A, C a)	Evaluate at main variable.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.evaluateMain(GenPolynomialRing<C> cfac, List<GenPolynomial<C>> L, C a)	Evaluate at main variable.
static <C extends RingElem<C>> C	PolyUtil.evaluateMain(RingFactory<C> cfac, GenPolynomial<C> A, C a)	Evaluate at main variable.
static <C extends RingElem<C>> List<C>	PolyUtil.evaluateMain(RingFactory<C> cfac, List<GenPolynomial<C>> L, C a)	Evaluate at main variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.evaluateMainRecursive(GenPolynomialRing<C> cfac, GenPolynomial<GenPolynomial<C>> A, C a)	Evaluate at main variable.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.extendCoefficients(GenPolynomialRing<GenPolynomial<C>> pfac, GenPolynomial<GenPolynomial<C>> A, int j, long k)	Extend coefficient variables.
static <C extends RingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>	PolyUtil.extendCoefficients(GenSolvablePolynomialRing<GenPolynomial<C>> pfac, GenSolvablePolynomial<GenPolynomial<C>> A, int j, long k)	Extend coefficient variables.
static <C extends RingElem<C>> GenExteriorPolynomial<C>	PolyUtil.exteriorDerivative(GenExteriorPolynomial<C> P)	GenExteriorPolynomial polynomial exterior derivative.
static <C extends RingElem<C>> GenExteriorPolynomial<GenPolynomial<C>>	PolyUtil.exteriorDerivativePoly(GenExteriorPolynomial<GenPolynomial<C>> P)	GenExteriorPolynomial over polynomial exterior derivative.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.fromIntegerCoefficients(GenPolynomialRing<C> fac, GenPolynomial<BigInteger> A)	From BigInteger coefficients.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.fromIntegerCoefficients(GenPolynomialRing<C> fac, List<GenPolynomial<BigInteger>> L)	From BigInteger coefficients.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.imaginaryPartFromComplex(GenPolynomialRing<C> fac, GenPolynomial<Complex<C>> A)	Imaginary part.
static <C extends RingElem<C> & Modular> GenPolynomial<BigInteger>	PolyUtil.integerFromModularCoefficients(GenPolynomialRing<BigInteger> fac, GenPolynomial<C> A)	BigInteger from ModInteger coefficients, symmetric.
static <C extends RingElem<C> & Modular> List<GenPolynomial<BigInteger>>	PolyUtil.integerFromModularCoefficients(GenPolynomialRing<BigInteger> fac, List<GenPolynomial<C>> L)	BigInteger from ModInteger coefficients, symmetric.
static <C extends RingElem<C> & Modular> GenPolynomial<BigInteger>	PolyUtil.integerFromModularCoefficientsPositive(GenPolynomialRing<BigInteger> fac, GenPolynomial<C> A)	BigInteger from ModInteger coefficients, positive.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.interpolate(GenPolynomialRing<C> fac, GenPolynomial<C> A, GenPolynomial<C> M, C mi, C a, C am)	Univariate polynomial interpolation.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.interpolate(GenPolynomialRing<GenPolynomial<C>> fac, GenPolynomial<GenPolynomial<C>> A, GenPolynomial<C> M, C mi, GenPolynomial<C> B, C am)	ModInteger interpolate on first variable.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.intersect(GenPolynomialRing<C> R, List<GenPolynomial<C>> F)	Intersection.
static <C extends RingElem<C>> List<GenSolvablePolynomial<C>>	PolyUtil.intersect(GenSolvablePolynomialRing<C> R, List<GenSolvablePolynomial<C>> F)	Intersection.
static <C extends RingElem<C>> List<GenWordPolynomial<C>>	PolyUtil.intersect(GenWordPolynomialRing<C> R, List<GenWordPolynomial<C>> F)	Intersection.
static <C extends RingElem<C>> boolean	PolyUtil.isBasePseudoQuotientRemainder(GenPolynomial<C> P, GenPolynomial<C> S, GenPolynomial<C> q, GenPolynomial<C> r)	Is GenPolynomial pseudo quotient and remainder.
static <C extends RingElem<C>> boolean	PolyUtil.isRecursivePseudoQuotientRemainder(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S, GenPolynomial<GenPolynomial<C>> q, GenPolynomial<GenPolynomial<C>> r)	Is recursive GenPolynomial pseudo quotient and remainder.
static <C extends RingElem<C>> List<ExpVector>	PolyUtil.leadingExpVector(List<GenPolynomial<C>> L)	Polynomial list leading exponent vectors.
static <C extends RingElem<C>, D extends RingElem<D>> GenPolynomial<D>	PolyUtil.map(GenPolynomialRing<D> ring, GenPolynomial<C> p, UnaryFunctor<C,D> f)	Map a unary function to the coefficients.
static <C extends RingElem<C>, D extends RingElem<D>> GenPolynomial<D>	PolyUtil.map(GenPolynomialRing<D> ring, GenPolynomial<C> p, UnaryFunctor<C,D> f)	Map a unary function to the coefficients.
static <C extends RingElem<C>> long	PolyUtil.maxDegree(List<GenPolynomial<C>> P)	Maximal degree of polynomial list.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.monic(GenPolynomial<GenPolynomial<C>> p)	GenPolynomial monic, i.e.
static <C extends RingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>	PolyUtil.monic(GenSolvablePolynomial<GenPolynomial<C>> p)	GenSolvablePolynomial monic, i.e.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.monic(List<GenPolynomial<C>> L)	Polynomial list monic.
static <C extends RingElem<C>> List<GenPolynomial<GenPolynomial<C>>>	PolyUtil.monicRec(List<GenPolynomial<GenPolynomial<C>>> L)	Recursive polynomial list monic.
static <C extends RingElem<C>> OptimizedPolynomialList<C>	TermOrderOptimization.optimizeTermOrder(GenPolynomialRing<C> R, List<GenPolynomial<C>> L)	Optimize variable order.
static <C extends RingElem<C>> OptimizedModuleList<C>	TermOrderOptimization.optimizeTermOrder(ModuleList<C> P)	Optimize variable order.
static <C extends RingElem<C>> OptimizedPolynomialList<C>	TermOrderOptimization.optimizeTermOrder(PolynomialList<C> P)	Optimize variable order.
static <C extends RingElem<C>> OptimizedModuleList<C>	TermOrderOptimization.optimizeTermOrderModule(GenPolynomialRing<C> R, List<List<GenPolynomial<C>>> L)	Optimize variable order.
static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>>	TermOrderOptimization.optimizeTermOrderOnCoefficients(GenPolynomialRing<GenPolynomial<C>> ring, List<GenPolynomial<GenPolynomial<C>>> L)	Optimize variable order on coefficients.
static <C extends RingElem<C>> OptimizedModuleList<GenPolynomial<C>>	TermOrderOptimization.optimizeTermOrderOnCoefficients(ModuleList<GenPolynomial<C>> P)	Optimize variable order on coefficients.
static <C extends RingElem<C>> OptimizedPolynomialList<GenPolynomial<C>>	TermOrderOptimization.optimizeTermOrderOnCoefficients(PolynomialList<GenPolynomial<C>> P)	Optimize variable order on coefficients.
static <C extends RingElem<C>> List<List<GenPolynomial<C>>>	ModuleList.padCols(GenPolynomialRing<C> ring, List<List<GenPolynomial<C>>> l)	Pad columns and remove zero rows.
static <C extends RingElem<C>> GenPolynomialRing<C>	TermOrderOptimization.permutation(List<Integer> P, GenPolynomialRing<C> R)	Permutation of polynomial ring variables.
static <C extends RingElem<C>> GenPolynomial<C>	TermOrderOptimization.permutation(List<Integer> P, GenPolynomialRing<C> R, GenPolynomial<C> A)	Permutation of polynomial exponent vectors.
static <C extends RingElem<C>> List<GenPolynomial<C>>	TermOrderOptimization.permutation(List<Integer> P, GenPolynomialRing<C> R, List<GenPolynomial<C>> L)	Permutation of polynomial exponent vectors.
static <C extends RingElem<C>> List<GenSolvablePolynomial<C>>	TermOrderOptimization.permutation(List<Integer> P, GenSolvablePolynomialRing<C> R, List<GenSolvablePolynomial<C>> L)	Permutation of solvable polynomial exponent vectors.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	TermOrderOptimization.permutationOnCoefficients(List<Integer> P, GenPolynomialRing<GenPolynomial<C>> R, GenPolynomial<GenPolynomial<C>> A)	Permutation of polynomial exponent vectors of coefficient polynomials.
static <C extends RingElem<C>> List<GenPolynomial<GenPolynomial<C>>>	TermOrderOptimization.permutationOnCoefficients(List<Integer> P, GenPolynomialRing<GenPolynomial<C>> R, List<GenPolynomial<GenPolynomial<C>>> L)	Permutation of polynomial exponent vectors of coefficients.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.realPartFromComplex(GenPolynomialRing<C> fac, GenPolynomial<Complex<C>> A)	Real part.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.reciprocalTransformation(GenPolynomial<C> A)	Polynomial reciprocal transformation.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.reciprocalTransformation(GenPolynomial<C> A, int i)	Polynomial reciprocal transformation.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursive(GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomial<C> A)	Recursive representation.
static <C extends RingElem<C>> List<GenPolynomial<GenPolynomial<C>>>	PolyUtil.recursive(GenPolynomialRing<GenPolynomial<C>> rfac, List<GenPolynomial<C>> L)	Recursive representation.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursiveDensePseudoRemainder(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S)	GenPolynomial dense pseudo remainder.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursiveDerivative(GenPolynomial<GenPolynomial<C>> P)	GenPolynomial recursive polynomial derivative main variable.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursiveDivide(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<C> s)	GenPolynomial divide.
static <C extends RingElem<C>> GenWordPolynomial<GenPolynomial<C>>	PolyUtil.recursiveDivide(GenWordPolynomial<GenPolynomial<C>> P, GenPolynomial<C> s)	GenPolynomial divide.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursivePseudoDivide(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S)	GenPolynomial recursive pseudo divide.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursivePseudoRemainder(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S)	Deprecated. (forRemoval=true) Use PolyUtil.recursiveSparsePseudoRemainder(edu.jas.poly.GenPolynomial,edu.jas.poly.GenPolynomial) instead
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.recursiveSparsePseudoRemainder(GenPolynomial<GenPolynomial<C>> P, GenPolynomial<GenPolynomial<C>> S)	GenPolynomial sparse pseudo remainder.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.removeUnusedLowerVariables(GenPolynomial<C> p)	Remove all lower variables which do not occur in polynomial.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.removeUnusedMiddleVariables(GenPolynomial<C> p)	Remove upper block of middle variables which do not occur in polynomial.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.removeUnusedUpperVariables(GenPolynomial<C> p)	Remove all upper variables which do not occur in polynomial.
static <C extends RingElem<C>> List<GenPolynomial<C>>	PolyUtil.rightMonic(List<GenPolynomial<C>> L)	Solvable polynomial list right monic.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.selectWithVariable(List<GenPolynomial<C>> P, int i)	Select polynomial with univariate leading term in variable i.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.seriesOfTaylor(GenPolynomial<C> f, C a)	Taylor series for polynomial.
static <C extends RingElem<C>> List<List<GenPolynomial<C>>>	OrderedModuleList.sort(GenPolynomialRing<C> r, List<List<GenPolynomial<C>>> l)	Sort a list of vectors of polynomials with respect to the ascending order of the leading Exponent vectors of the first column.
static <C extends RingElem<C>> List<GenPolynomial<C>>	OrderedPolynomialList.sort(GenPolynomialRing<C> r, List<GenPolynomial<C>> L)	Sort a list of polynomials with respect to the ascending order of the leading Exponent vectors.
static <C extends RingElem<C>> List<GenPolynomial<C>>	OrderedPolynomialList.sort(List<GenPolynomial<C>> L)	Sort a list of polynomials with respect to the ascending order of the leading Exponent vectors.
static <C extends RingElem<C>> List<GenPolynomial<C>>	OrderedPolynomialList.sortDegree(List<GenPolynomial<C>> L)	Sort a list of polynomials with respect to the ascending order of the degree.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.substituteMain(GenPolynomial<C> A, GenPolynomial<C> s)	Substitute main variable.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.substituteUnivariate(GenPolynomial<C> f, GenPolynomial<C> t)	Substitute univariate polynomial.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.substituteUnivariateMult(GenPolynomial<C> f, GenPolynomial<C> t)	Substitute univariate polynomial with multivariate coefficients.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.switchVariables(GenPolynomial<GenPolynomial<C>> P)	Recursive GenPolynomial switch variable blocks.
static <C extends RingElem<C>> GenPolynomial<Complex<C>>	PolyUtil.toComplex(GenPolynomialRing<Complex<C>> fac, GenPolynomial<C> A)	Complex from real polynomial.
static <C extends RingElem<C>> Product<GenPolynomial<C>>	PolyUtil.toProduct(ProductRing<GenPolynomial<C>> pfac, C c, ExpVector e)	Product representation.
static <C extends RingElem<C>> Product<GenPolynomial<C>>	PolyUtil.toProduct(ProductRing<GenPolynomial<C>> pfac, GenPolynomial<C> A)	Product representation.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.toRecursive(GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomial<C> A)	To recursive representation.
static <C extends RingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>	PolyUtil.toRecursive(GenSolvablePolynomialRing<GenPolynomial<C>> rfac, GenSolvablePolynomial<C> A)	To recursive representation.
static <C extends RingElem<C>> long	PolyUtil.totalDegree(List<GenPolynomial<C>> P)	Total degree of polynomial list.
static <C extends RingElem<C>> long	PolyUtil.totalDegreeLeadingTerm(List<GenPolynomial<C>> P)	Maximal degree of leading terms of a polynomial list.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.translation(GenPolynomial<C> A, List<C> H)	Polynomial translation, all variables.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.translation1(GenPolynomial<C> A, List<C> H)	Polynomial translation, r-1 variables.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.translationBase(GenPolynomial<C> A, C h)	Polynomial translation, base univariate.
static <C extends RingElem<C>> GenPolynomial<C>	PolyUtil.translationMain(GenPolynomial<C> A, C h)	Polynomial translation, main variable.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUtil.translationMainRecursive(GenPolynomial<GenPolynomial<C>> A, C h)	Polynomial translation, main variable.
static <C extends RingElem<C>> List<List<GenPolynomial<C>>>	ModuleList.vecToList(List<GenVector<GenPolynomial<C>>> vlist)	Get a list of vectors as List of list of GenPolynomials.
static <C extends RingElem<C>> List<GenWordPolynomial<C>>	PolyUtil.wordMonic(List<GenWordPolynomial<C>> L)	Word polynomial list monic.

Uses of RingElem in edu.jas.ps

Classes in edu.jas.ps with type parameters of type RingElem

Modifier and Type	Class	Description
class	Coefficients<C extends RingElem<C>>	Abstract class for generating functions for coefficients of power series.
(package private) static class	Examples.Odds<C extends RingElem<C>>
(package private) static class	Examples.Sum<C extends RingElem<C>>
(package private) class	Multiply<C extends RingElem<C>>	Internal scalar multiplication functor.
class	MultiVarCoefficients<C extends RingElem<C>>	Abstract class for generating functions for coefficients of multivariate power series.
class	MultiVarPowerSeries<C extends RingElem<C>>	Multivariate power series implementation.
interface	MultiVarPowerSeriesMap<C extends RingElem<C>>	Multivariate power series map interface.
class	MultiVarPowerSeriesRing<C extends RingElem<C>>	Multivariate power series ring implementation.
(package private) class	Negate<C extends RingElem<C>>	Internal negation functor.
class	OrderedPairlist<C extends RingElem<C>>	Pair list management.
class	Pair<C extends RingElem<C>>	Serializable subclass to hold pairs of power series.
class	PolynomialTaylorFunction<C extends RingElem<C>>	Polynomial functions capable for Taylor series expansion.
class	ReductionSeq<C extends RingElem<C>>	Multivariate power series reduction sequential use algorithm.
class	StandardBaseSeq<C extends RingElem<C>>	Standard Base sequential algorithm.
(package private) class	Subtract<C extends RingElem<C>>	Internal subtraction functor.
(package private) class	Sum<C extends RingElem<C>>	Internal summation functor.
interface	TaylorFunction<C extends RingElem<C>>	Interface for functions capable for Taylor series expansion.
class	TaylorFunctionAdapter<C extends RingElem<C>>	Adapter for functions capable for Taylor series expansion.
class	UnivPowerSeries<C extends RingElem<C>>	Univariate power series implementation.
interface	UnivPowerSeriesMap<C extends RingElem<C>>	Univariate power series map interface.
class	UnivPowerSeriesRing<C extends RingElem<C>>	Univariate power series ring implementation.

Classes in edu.jas.ps that implement RingElem

Modifier and Type	Class	Description
class	MultiVarPowerSeries<C extends RingElem<C>>	Multivariate power series implementation.
class	UnivPowerSeries<C extends RingElem<C>>	Univariate power series implementation.

Fields in edu.jas.ps declared as RingElem

Modifier and Type	Field	Description
(package private) C	Examples.Odds.two
(package private) C	Multiply.x

Methods in edu.jas.ps with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> List<MultiVarPowerSeries<C>>	PSUtil.monic(List<MultiVarPowerSeries<C>> L)	Power series list monic.
static <C extends RingElem<C>> List<UnivPowerSeries<C>>	PSUtil.monicUniv(List<UnivPowerSeries<C>> L)	Univariate power series list monic.
<C2 extends RingElem<C2>> UnivPowerSeries<C>	UnivPowerSeries.zip(BinaryFunctor<? super C, ? super C2, C> f, UnivPowerSeries<C2> ps)	Map a binary function to this and another power series.

Uses of RingElem in edu.jas.root

Classes in edu.jas.root with type parameters of type RingElem

Modifier and Type	Class	Description
class	Boundary<C extends RingElem<C> & Rational>	Boundary determined by a rectangle and a polynomial.
interface	ComplexRoots<C extends RingElem<C> & Rational>	Complex roots interface.
class	ComplexRootsAbstract<C extends RingElem<C> & Rational>	Complex roots abstract class.
class	ComplexRootsSturm<C extends RingElem<C> & Rational>	Complex roots implemented by Sturm sequences.
class	Interval<C extends RingElem<C> & Rational>	Interval.
interface	RealRoots<C extends RingElem<C> & Rational>	Real roots interface.
class	RealRootsAbstract<C extends RingElem<C> & Rational>	Real roots abstract class.
class	RealRootsSturm<C extends RingElem<C> & Rational>	Real root isolation using Sturm sequences.
class	Rectangle<C extends RingElem<C> & Rational>	Rectangle.

Classes in edu.jas.root that implement RingElem

Modifier and Type	Class	Description
class	ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on AlgebraicNumber.
class	RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Real algebraic number class based on AlgebraicNumber.

Fields in edu.jas.root declared as RingElem

Modifier and Type	Field	Description
final C	Interval.left	left interval border.
final C	Interval.right	right interval border.

Methods in edu.jas.root with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C> & Rational> Interval<C>	RootUtil.parseInterval(RingFactory<C> fac, String s)	Parse interval for a real root from String.
static <C extends RingElem<C> & Rational> Rectangle<C>	RootUtil.parseRectangle(RingFactory<Complex<C>> fac, String s)	Parse rectangle for a complex root from String.
static <C extends RingElem<C>> long	RootUtil.signVar(List<C> L)	Count changes in sign.

Uses of RingElem in edu.jas.structure

Classes in edu.jas.structure with type parameters of type RingElem

Modifier and Type	Interface	Description
interface	AlgebraElem<A extends AlgebraElem<A,C>, C extends RingElem<C>>	Algabra element interface.
interface	AlgebraFactory<A extends AlgebraElem<A,C>, C extends RingElem<C>>	Algebra factory interface.
interface	FieldFactory<C extends RingElem<C>>	Field factory interface.
interface	ModulElem<M extends ModulElem<M,C>, C extends RingElem<C>>	Module element interface.
interface	ModulFactory<M extends ModulElem<M,C>, C extends RingElem<C>>	Module factory interface.
class	Power<C extends RingElem<C>>	Power class to compute powers of RingElem.
interface	QuotPair<C extends RingElem<C>>	Quotient pair interface.
interface	QuotPairFactory<C extends RingElem<C>, D extends RingElem<D>>	Quotient pair factory interface.
interface	QuotPairFactory<C extends RingElem<C>, D extends RingElem<D>>	Quotient pair factory interface.
interface	RingElem<C extends RingElem<C>>	Ring element interface.
interface	RingFactory<C extends RingElem<C>>	Ring factory interface.
interface	Selector<C extends RingElem<C>>	Selector interface.
interface	Value<C extends RingElem<C>>	Value interface.
interface	ValueFactory<C extends RingElem<C>, D extends RingElem<D>>	Value factory interface.
interface	ValueFactory<C extends RingElem<C>, D extends RingElem<D>>	Value factory interface.

Subinterfaces of RingElem in edu.jas.structure

Modifier and Type	Interface	Description
interface	AlgebraElem<A extends AlgebraElem<A,C>, C extends RingElem<C>>	Algabra element interface.
interface	FieldElem<C extends FieldElem<C>>	Field element interface.
interface	GcdRingElem<C extends GcdRingElem<C>>	Gcd ring element interface.
interface	NoncomRingElem<C extends NoncomRingElem<C>>	Non-commutative ring element interface.
interface	RegularRingElem<C extends RegularRingElem<C>>	Regular ring element interface.
interface	StarRingElem<C extends StarRingElem<C>>	Star ring element interface.

Methods in edu.jas.structure with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> long	Power.logarithm(long p, long a)	Logarithm.
static <C extends RingElem<C>> long	Power.logarithm(C p, C a)	Logarithm.
static <C extends RingElem<C>> C	Power.modPositivePower(C a, long n, C m)	power of a to the n-th, n positive, modulo m.
static <C extends RingElem<C>> C	Power.modPositivePower(C a, BigInteger n, C m)	power of a to the n-th, n positive, modulo m.
static <C extends RingElem<C>> C	Power.multiply(RingFactory<C> fac, List<C> A)	Multiply elements in list.
static <C extends RingElem<C>> C	Power.positivePower(C a, long n)	power of a to the n-th, n positive.
static <C extends RingElem<C>> C	Power.positivePower(C a, BigInteger n)	power of a to the n-th, n positive.
static <C extends RingElem<C>> C	Power.power(RingFactory<C> fac, C a, long n)	power of a to the n-th.
static <C extends RingElem<C>> C	Power.sum(RingFactory<C> fac, List<C> A)	Sum elements in list.

Methods in edu.jas.structure that return RingElem

Modifier and Type	Method	Description
C[]	RingElem.egcd(C b)	Extended greatest common divisor.

Uses of RingElem in edu.jas.ufd

Classes in edu.jas.ufd with type parameters of type RingElem

Modifier and Type	Class	Description
class	EvalPoints<C extends RingElem<C>>	Container for the evaluation points of a polynomial.

Classes in edu.jas.ufd that implement RingElem

Modifier and Type	Class	Description
class	Quotient<C extends GcdRingElem<C>>	Quotient, that is a rational function, based on GenPolynomial with RingElem interface.

Methods in edu.jas.ufd with type parameters of type RingElem

Modifier and Type	Method	Description
static <C extends RingElem<C>> long	FactorInteger.degreeSum(List<GenPolynomial<C>> L)	Sum of all degrees.
static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>>	PolyUfdUtil.fromIntegerCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, GenPolynomial<GenPolynomial<BigInteger>> A)	From BigInteger coefficients.
static <C extends RingElem<C>> List<GenPolynomial<GenPolynomial<C>>>	PolyUfdUtil.fromIntegerCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, List<GenPolynomial<GenPolynomial<BigInteger>>> L)	From BigInteger coefficients.

Uses of RingElem in edu.jas.vector

Classes in edu.jas.vector with type parameters of type RingElem

Modifier and Type	Class	Description
class	BasicLinAlg<C extends RingElem<C>>	Basic linear algebra methods.
class	GenMatrix<C extends RingElem<C>>	GenMatrix implements a generic matrix algebra over RingElem entries.
class	GenMatrixRing<C extends RingElem<C>>	GenMatrixRing implements a generic matrix algebra factory with RingFactory.
class	GenVector<C extends RingElem<C>>	GenVector implements generic vectors with RingElem entries.
class	GenVectorModul<C extends RingElem<C>>	GenVectorModul implements a generic vector factory with RingElem entries.
class	LinAlg<C extends RingElem<C>>	Linear algebra methods.

Classes in edu.jas.vector that implement RingElem

Modifier and Type	Class	Description
class	GenMatrix<C extends RingElem<C>>	GenMatrix implements a generic matrix algebra over RingElem entries.

Constructors in edu.jas.vector with parameters of type RingElem

Modifier	Constructor	Description
	GenMatrix(GenMatrixRing<C> r, C[][] m)	Constructor for GenMatrix.
	GenVector(GenVectorModul<C> m, C[] v)	Constructor for GenVector.