Uses of Interface edu.jas.structure.GcdRingElem

Packages that use GcdRingElem
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.integrate	Elementary Integration package.
edu.jas.poly	Generic coefficients polynomial 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.ufdroot	Unique Factorization Domain and Roots package.

Uses of GcdRingElem in edu.jas.application

Classes in edu.jas.application with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`AlgebraicRootsPrimElem<C extends GcdRingElem<C> & Rational>`	Container for the real and complex algebraic roots of a univariate polynomial together with primitive element.
`(package private) class`	`CoeffConvertAlg<C extends GcdRingElem<C>>`	Coefficient to convert algebriac functor.
`(package private) class`	`CoeffRecConvertAlg<C extends GcdRingElem<C>>`	Coefficient recursive to convert algebriac functor.
`(package private) class`	`CoeffToComplexReal<C extends GcdRingElem<C> & Rational>`	Coefficient to complex real algebriac functor.
`class`	`ColoredSystem<C extends GcdRingElem<C>>`	Container for a condition, a corresponding colored polynomial list and a Groebner base pair list.
`class`	`ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>`	Comprehensive Groebner Base sequential algorithm.
`class`	`Condition<C extends GcdRingElem<C>>`	Condition.
`class`	`CReductionSeq<C extends GcdRingElem<C>>`	Polynomial parametric ring reduction sequential use algorithm.
`(package private) class`	`EvaluateToComplexReal<C extends GcdRingElem<C> & Rational>`	Polynomial coefficient to complex real algebriac evaluation functor.
`class`	`FactorAlgebraicPrim<C extends GcdRingElem<C>>`	Algebraic number coefficients factorization algorithms.
`class`	`FactorRealReal<C extends GcdRingElem<C> & Rational>`	Real algebraic number coefficients factorization algorithms.
`class`	`GBAlgorithmBuilder<C extends GcdRingElem<C>>`	Builder for commutative Gröbner bases algorithm implementations.
`class`	`GroebnerSystem<C extends GcdRingElem<C>>`	Container for a Groebner system.
`class`	`Ideal<C extends GcdRingElem<C>>`	Ideal implements some methods for ideal arithmetic, for example intersection, quotient and zero and positive dimensional ideal decomposition.
`class`	`IdealWithComplexAlgebraicRoots<D extends GcdRingElem<D> & Rational>`	Container for Ideals together with univariate polynomials and complex algebraic roots.
`(package private) class`	`IdealWithComplexRoots<C extends GcdRingElem<C>>`	Container for Ideals together with univariate polynomials and complex roots.
`class`	`IdealWithRealAlgebraicRoots<D extends GcdRingElem<D> & Rational>`	Container for Ideals together with univariate polynomials and real algebraic roots.
`class`	`IdealWithRealRoots<C extends GcdRingElem<C>>`	Container for Ideals together with univariate polynomials and real roots.
`class`	`IdealWithUniv<C extends GcdRingElem<C>>`	Container for Ideals together with univariate polynomials.
`class`	`Local<C extends GcdRingElem<C>>`	Local ring element based on GenPolynomial with RingElem interface.
`class`	`LocalRing<C extends GcdRingElem<C>>`	Local ring class based on GenPolynomial with RingElem interface.
`class`	`LocalSolvablePolynomial<C extends GcdRingElem<C>>`	LocalSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
`class`	`LocalSolvablePolynomialRing<C extends GcdRingElem<C>>`	LocalSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
`class`	`OrderedCPairlist<C extends GcdRingElem<C>>`	Pair list management.
`class`	`PrimaryComponent<C extends GcdRingElem<C>>`	Container for primary components of ideals.
`class`	`PrimitiveElement<C extends GcdRingElem<C>>`	Container for primitive elements.
`class`	`RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>`	Complex algebraic number class based on bi-variate real algebraic numbers.
`class`	`RealAlgebraicRing<C extends GcdRingElem<C> & Rational>`	Real algebraic number factory class based on bi-variate real algebraic numbers.
`(package private) class`	`RealFromReAlgCoeff<C extends GcdRingElem<C> & Rational>`	Coefficient to real algebriac from algebraic functor.
`(package private) class`	`ReAlgFromRealCoeff<C extends GcdRingElem<C> & Rational>`	Coefficient to real algebriac from real algebraic functor.
`class`	`Residue<C extends GcdRingElem<C>>`	Residue ring element based on GenPolynomial with RingElem interface.
`class`	`ResidueRing<C extends GcdRingElem<C>>`	Residue ring factory based on GenPolynomial with RingFactory interface.
`class`	`ResidueSolvablePolynomial<C extends GcdRingElem<C>>`	ResidueSolvablePolynomial generic solvable polynomials with solvable residue coefficients implementing RingElem.
`class`	`ResidueSolvablePolynomialRing<C extends GcdRingElem<C>>`	ResidueSolvablePolynomialRing generic solvable polynomial with residue coefficients factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
`class`	`ResidueSolvableWordPolynomial<C extends GcdRingElem<C>>`	ResidueSolvableWordPolynomial solvable polynomials with WordResidue coefficients implementing RingElem.
`class`	`ResidueSolvableWordPolynomialRing<C extends GcdRingElem<C>>`	ResidueSolvableWordPolynomialRing solvable polynomial with word residue coefficients factory.
`class`	`SolvableIdeal<C extends GcdRingElem<C>>`	Solvable Ideal implements some methods for ideal arithmetic, for example sum, intersection, quotient.
`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`	`SolvableLocalResidueRing<C extends GcdRingElem<C>>`	SolvableLocalResidue ring factory for SolvableLocalResidue based on GenSolvablePolynomial with GcdRingElem interface.
`class`	`SolvableLocalRing<C extends GcdRingElem<C>>`	SolvableLocal ring factory for SolvableLocal with GcdRingElem interface.
`class`	`SolvableResidue<C extends GcdRingElem<C>>`	SolvableResidue ring element based on GenSolvablePolynomial with GcdRingElem interface.
`class`	`SolvableResidueRing<C extends GcdRingElem<C>>`	SolvableResidue ring factory based on GenSolvablePolynomialRing with GcdRingFactory interface.
`class`	`WordIdeal<C extends GcdRingElem<C>>`	Word Ideal implements some methods for ideal arithmetic, for example containment, sum or product.
`class`	`WordResidue<C extends GcdRingElem<C>>`	WordResidue ring element based on GenWordPolynomial with GcdRingElem interface.
`class`	`WordResidueRing<C extends GcdRingElem<C>>`	WordResidue ring factory based on GenWordPolynomialRing with GcdRingFactory interface.

Classes in edu.jas.application that implement GcdRingElem
Modifier and Type	Class	Description
`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`	`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 GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C>> java.util.List<Ideal<C>>`	IdealWithUniv.`asListOfIdeals(java.util.List<IdealWithUniv<C>> Bl)`	Get list of ideals from list of ideals with univariates.
`static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>>`	RootFactoryApp.`complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)`	Complex algebraic number roots.
`static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>>`	RootFactoryApp.`complexAlgebraicNumbersSquarefree(GenPolynomial<Complex<C>> f)`	Complex algebraic number roots.
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithComplexAlgebraicRoots<D>>`	PolyUtilApp.`complexAlgebraicRoots(Ideal<D> I)`	Construct exact set of complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> IdealWithComplexAlgebraicRoots<D>`	PolyUtilApp.`complexAlgebraicRoots(IdealWithUniv<D> I)`	Construct complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithComplexAlgebraicRoots<D>>`	PolyUtilApp.`complexAlgebraicRoots(java.util.List<IdealWithUniv<D>> I)`	Construct complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithComplexRoots<D>>`	PolyUtilApp.`complexRoots(Ideal<D> G, BigRational eps)`	Construct superset of complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<Complex<BigDecimal>>>`	PolyUtilApp.`complexRoots(Ideal<D> I, java.util.List<GenPolynomial<D>> univs, BigRational eps)`	Construct superset of complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithComplexRoots<D>>`	PolyUtilApp.`complexRoots(java.util.List<IdealWithUniv<D>> Il, BigRational eps)`	Construct superset of complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<Complex<BigDecimal>>>`	PolyUtilApp.`complexRootTuples(Ideal<D> I, BigRational eps)`	Construct superset of complex roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<Complex<BigDecimal>>>`	PolyUtilApp.`complexRootTuples(java.util.List<IdealWithUniv<D>> Il, BigRational eps)`	Construct superset of complex roots for zero dimensional ideal(G).
`static <C extends GcdRingElem<C>> IdealWithUniv<C>`	Ideal.`contraction(IdealWithUniv<Quotient<C>> eid)`	Ideal contraction.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<Complex<RealAlgebraicNumber<C>>>`	PolyUtilApp.`convertToComplexRealCoefficients(GenPolynomialRing<Complex<RealAlgebraicNumber<C>>> pfac, GenPolynomial<Complex<C>> A)`	Convert to Complex<RealAlgebraicNumber> coefficients.
`static <C extends GcdRingElem<C>> AlgebraicNumber<C>`	PolyUtilApp.`convertToPrimitiveElem(AlgebraicNumberRing<C> cfac, AlgebraicNumber<C> A, AlgebraicNumber<C> a)`	Convert to primitive element ring.
`static <C extends GcdRingElem<C>> AlgebraicNumber<C>`	PolyUtilApp.`convertToPrimitiveElem(AlgebraicNumberRing<C> cfac, AlgebraicNumber<C> A, AlgebraicNumber<C> B, AlgebraicNumber<AlgebraicNumber<C>> a)`	Convert to primitive element ring.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtilApp.`convertToPrimitiveElem(AlgebraicNumberRing<C> cfac, AlgebraicNumber<C> A, AlgebraicNumber<C> B, GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> a)`	Convert to primitive element ring.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtilApp.`convertToPrimitiveElem(AlgebraicNumberRing<C> cfac, AlgebraicNumber<C> A, GenPolynomial<AlgebraicNumber<C>> a)`	Convert coefficients to primitive element ring.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<Complex<RealAlgebraicNumber<C>>>`	PolyUtilApp.`evaluateToComplexRealCoefficients(GenPolynomialRing<Complex<RealAlgebraicNumber<C>>> pfac, GenPolynomial<GenPolynomial<Complex<C>>> A, Complex<RealAlgebraicNumber<C>> r)`	Evaluate to Complex<RealAlgebraicNumber> coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>`	PolyUtilApp.`fromProduct(GenPolynomialRing<GenPolynomial<C>> pfac, GenPolynomial<Product<Residue<C>>> P, int i)`	From product representation.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<GenPolynomial<C>>>`	PolyUtilApp.`fromProduct(GenPolynomialRing<GenPolynomial<C>> pfac, java.util.List<GenPolynomial<Product<Residue<C>>>> L, int i)`	From product representation.
`static <C extends GcdRingElem<C> & Rational> FactorAbstract<RealAlgebraicNumber<C>>`	FactorFactory.`getImplementation(RealAlgebraicRing<C> fac)`	Determine suitable implementation of factorization algorithms, case RealAlgebraicNumber<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<AlgebraicNumber<C>>`	FactorFactory.`getImplementation(AlgebraicNumberRing<C> fac)`	Determine suitable implementation of factorization algorithms, case AlgebraicNumber<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<Complex<C>>`	FactorFactory.`getImplementation(ComplexRing<C> fac)`	Determine suitable implementation of factorization algorithms, case Complex<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<C>`	FactorFactory.`getImplementation(GenPolynomialRing<C> fac)`	Determine suitable implementation of factorization algorithms, case recursive GenPolynomial<C>.
`static <C extends GcdRingElem<C> & Rational> FactorAbstract<RealAlgebraicNumber<C>>`	FactorFactory.`getImplementation(RealAlgebraicRing<C> fac)`	Determine suitable implementation of factorization algorithms, case RealAlgebraicNumber<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<C>`	FactorFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of factorization algorithms, other cases.
`static <C extends GcdRingElem<C>> FactorAbstract<Quotient<C>>`	FactorFactory.`getImplementation(QuotientRing<C> fac)`	Determine suitable implementation of factorization algorithms, case Quotient<C>.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactoryApp.`isRoot(GenPolynomial<Complex<C>> f, Complex<RealAlgebraicNumber<C>> r)`	Is complex algebraic number a root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactoryApp.`isRoot(GenPolynomial<Complex<C>> f, java.util.List<Complex<RealAlgebraicNumber<C>>> R)`	Is complex algebraic number a root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactoryApp.`isRootRealCoeff(GenPolynomial<C> f, Complex<RealAlgebraicNumber<C>> r)`	Is complex algebraic number a root of a polynomial.
`static <C extends GcdRingElem<C>> IdealWithUniv<C>`	Ideal.`permutation(GenPolynomialRing<C> oring, IdealWithUniv<C> Cont)`	Ideal permutation.
`static <C extends GcdRingElem<C>> GBAlgorithmBuilder<C>`	GBAlgorithmBuilder.`polynomialRing(GenPolynomialRing<C> fac)`	Define polynomial ring.
`static <C extends GcdRingElem<C>> PrimitiveElement<C>`	PolyUtilApp.`primitiveElement(AlgebraicNumberRing<C> a, AlgebraicNumberRing<C> b)`	Construct primitive element for double field extension.
`static <C extends GcdRingElem<C>> PrimitiveElement<C>`	PolyUtilApp.`primitiveElement(AlgebraicNumberRing<AlgebraicNumber<C>> b)`	Construct primitive element for double field extension.
`static <C extends GcdRingElem<C>> java.util.Map<Ideal<C>,PolynomialList<GenPolynomial<C>>>`	PolyUtilApp.`productSlice(PolynomialList<Product<Residue<C>>> L)`	Product slice.
`static <C extends GcdRingElem<C>> PolynomialList<GenPolynomial<C>>`	PolyUtilApp.`productSlice(PolynomialList<Product<Residue<C>>> L, int i)`	Product slice at i.
`static <C extends GcdRingElem<C>> java.lang.String`	PolyUtilApp.`productSliceToString(java.util.Map<Ideal<C>,PolynomialList<GenPolynomial<C>>> L)`	Product slice to String.
`static <C extends GcdRingElem<C>> java.lang.String`	PolyUtilApp.`productToString(PolynomialList<Product<Residue<C>>> L)`	Product slice to String.
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithRealAlgebraicRoots<D>>`	PolyUtilApp.`realAlgebraicRoots(Ideal<D> I)`	Construct exact set of real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> IdealWithRealAlgebraicRoots<D>`	PolyUtilApp.`realAlgebraicRoots(IdealWithUniv<D> I)`	Construct real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithRealAlgebraicRoots<D>>`	PolyUtilApp.`realAlgebraicRoots(java.util.List<IdealWithUniv<D>> I)`	Construct real roots for zero dimensional ideal(G).
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilApp.`realAlgFromRealCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> afac, GenPolynomial<RealAlgebraicNumber<C>> A)`	Convert to RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilApp.`realFromRealAlgCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> rfac, GenPolynomial<RealAlgebraicNumber<C>> A)`	Convert to RealAlgebraicNumber coefficients.
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithRealRoots<D>>`	PolyUtilApp.`realRoots(Ideal<D> G, BigRational eps)`	Construct superset of real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<BigDecimal>>`	PolyUtilApp.`realRoots(Ideal<D> I, java.util.List<GenPolynomial<D>> univs, BigRational eps)`	Construct superset of real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<IdealWithRealRoots<D>>`	PolyUtilApp.`realRoots(java.util.List<IdealWithUniv<D>> Il, BigRational eps)`	Construct superset of real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<BigDecimal>>`	PolyUtilApp.`realRootTuples(Ideal<D> I, BigRational eps)`	Construct superset of real roots for zero dimensional ideal(G).
`static <D extends GcdRingElem<D> & Rational> java.util.List<java.util.List<BigDecimal>>`	PolyUtilApp.`realRootTuples(java.util.List<IdealWithUniv<D>> Il, BigRational eps)`	Construct superset of real roots for zero dimensional ideal(G).
`static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>`	RootFactoryApp.`rootReduce(AlgebraicNumberRing<C> a, AlgebraicNumberRing<C> b)`	Root reduce of real and complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>`	RootFactoryApp.`rootReduce(GenPolynomial<C> a, GenPolynomial<C> b)`	Root reduce of real and complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>`	RootFactoryApp.`rootReduce(AlgebraicRoots<C> a, AlgebraicRoots<C> b)`	Root reduce of real and complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>`	RootFactoryApp.`rootsOfUnity(AlgebraicRootsPrimElem<C> ar)`	Roots of unity of real and complex algebraic numbers.
`static <C extends GcdRingElem<C>> Product<Residue<C>>`	PolyUtilApp.`toProductRes(ProductRing<Residue<C>> pfac, GenPolynomial<C> c)`	Product representation.
`static <C extends GcdRingElem<C>> GenPolynomial<Product<Residue<C>>>`	PolyUtilApp.`toProductRes(GenPolynomialRing<Product<Residue<C>>> pfac, GenPolynomial<GenPolynomial<C>> A)`	Product representation.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Product<Residue<C>>>>`	PolyUtilApp.`toProductRes(GenPolynomialRing<Product<Residue<C>>> pfac, java.util.List<GenPolynomial<GenPolynomial<C>>> L)`	Product representation.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Product<Residue<C>>>>`	PolyUtilApp.`toProductRes(java.util.List<ColoredSystem<C>> CS)`	Product residue representation.
`static <C extends GcdRingElem<C>> GenPolynomial<Residue<C>>`	PolyUtilApp.`toResidue(GenPolynomialRing<Residue<C>> pfac, GenPolynomial<GenPolynomial<C>> A)`	Residue coefficient representation.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Residue<C>>>`	PolyUtilApp.`toResidue(GenPolynomialRing<Residue<C>> pfac, java.util.List<GenPolynomial<GenPolynomial<C>>> L)`	Residue coefficient representation.
`static <D extends GcdRingElem<D> & Rational> java.lang.String`	PolyUtilApp.`toString(Complex<RealAlgebraicNumber<D>> c)`	String representation of a deximal approximation of a complex number.
`static <D extends GcdRingElem<D> & Rational> java.lang.String`	PolyUtilApp.`toString1(Complex<D> c)`	String representation of a deximal approximation of a complex number.

Uses of GcdRingElem in edu.jas.arith

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

Fields in edu.jas.arith declared as GcdRingElem
Modifier and Type	Field	Description
`GcdRingElem`	ModularNotInvertibleException.`f`
`GcdRingElem`	ModularNotInvertibleException.`f1`
`GcdRingElem`	ModularNotInvertibleException.`f2`

Constructors in edu.jas.arith with parameters of type GcdRingElem
Constructor	Description
`ModularNotInvertibleException(GcdRingElem f, GcdRingElem f1, GcdRingElem f2)`	Constructor.
`ModularNotInvertibleException(java.lang.String c, GcdRingElem f, GcdRingElem f1, GcdRingElem f2)`	Constructor.
`ModularNotInvertibleException(java.lang.String c, java.lang.Throwable t, GcdRingElem f, GcdRingElem f1, GcdRingElem f2)`	Constructor.
`ModularNotInvertibleException(java.lang.Throwable t, GcdRingElem f, GcdRingElem f1, GcdRingElem f2)`	Constructor.

Uses of GcdRingElem in edu.jas.fd

Classes in edu.jas.fd with type parameters of type GcdRingElem
Modifier and Type	Interface	Description
`interface`	`GreatestCommonDivisor<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor algorithm interface.
`class`	`GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor common algorithms.
`class`	`GreatestCommonDivisorFake<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor common algorithms with monic polynomial remainder sequence.
`class`	`GreatestCommonDivisorPrimitive<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor common algorithms with primitive polynomial remainder sequence.
`class`	`GreatestCommonDivisorSimple<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor common algorithms with monic polynomial remainder sequence.
`class`	`GreatestCommonDivisorSyzygy<C extends GcdRingElem<C>>`	(Non-unique) factorization domain greatest common divisor common algorithms with syzygy computation.
`class`	`QuotSolvablePolynomial<C extends GcdRingElem<C>>`	QuotSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
`class`	`QuotSolvablePolynomialRing<C extends GcdRingElem<C>>`	QuotSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
`class`	`SGCDParallelProxy<C extends GcdRingElem<C>>`	Solvable greatest common divisor parallel proxy.
`class`	`SolvableQuotient<C extends GcdRingElem<C>>`	SolvableQuotient, that is a (left) rational function, based on GenSolvablePolynomial with RingElem interface.
`class`	`SolvableQuotientRing<C extends GcdRingElem<C>>`	SolvableQuotient ring factory based on GenPolynomial with RingElem interface.

Classes in edu.jas.fd that implement GcdRingElem
Modifier and Type	Class	Description
`class`	`SolvableQuotient<C extends GcdRingElem<C>>`	SolvableQuotient, that is a (left) rational function, based on GenSolvablePolynomial with RingElem interface.

Methods in edu.jas.fd with type parameters of type GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	FDUtil.`basePseudoLeftDivide(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial sparse pseudo divide.
`(package private) static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`experimentalRecursiveLeftDivide(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<C> s)`
`static <C extends GcdRingElem<C>> GreatestCommonDivisorAbstract<C>`	SGCDFactory.`getFakeImplementation(RingFactory<C> fac)`	Determine fake implementation of gcd algorithms, other cases.
`static <C extends GcdRingElem<C>> GreatestCommonDivisorAbstract<C>`	SGCDFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of gcd algorithms, other cases.
`static <C extends GcdRingElem<C>> GreatestCommonDivisorAbstract<C>`	SGCDFactory.`getProxy(RingFactory<C> fac)`	Determine suitable proxy for gcd algorithms, other cases.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`integralFromQuotientCoefficients(GenSolvablePolynomialRing<GenPolynomial<C>> fac, GenSolvablePolynomial<SolvableQuotient<C>> A)`	Integral solvable polynomial from solvable rational function coefficients.
`static <C extends GcdRingElem<C>> java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>`	FDUtil.`integralFromQuotientCoefficients(GenSolvablePolynomialRing<GenPolynomial<C>> fac, java.util.Collection<GenSolvablePolynomial<SolvableQuotient<C>>> L)`	Integral solvable polynomial from solvable rational function coefficients.
`static <C extends GcdRingElem<C>> boolean`	FDUtil.`isLeftBasePseudoQuotientRemainder(GenPolynomial<C> P, GenPolynomial<C> S, GenPolynomial<C> q, GenPolynomial<C> r)`	Is GenSolvablePolynomial left base pseudo quotient and remainder.
`static <C extends GcdRingElem<C>> boolean`	FDUtil.`isRecursivePseudoQuotientRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S, GenSolvablePolynomial<GenPolynomial<C>> q, GenSolvablePolynomial<GenPolynomial<C>> r)`	Is recursive GenSolvablePolynomial pseudo quotient and remainder.
`static <C extends GcdRingElem<C>> boolean`	FDUtil.`isRecursiveRightPseudoQuotientRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S, GenSolvablePolynomial<GenPolynomial<C>> q, GenSolvablePolynomial<GenPolynomial<C>> r)`	Is recursive GenSolvablePolynomial right pseudo quotient and remainder.
`static <C extends GcdRingElem<C>> boolean`	FDUtil.`isRightBasePseudoQuotientRemainder(GenPolynomial<C> P, GenPolynomial<C> S, GenPolynomial<C> q, GenPolynomial<C> r)`	Is GenSolvablePolynomial right base pseudo quotient and remainder.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	FDUtil.`leftBasePseudoQuotient(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial sparse pseudo quotient for univariate polynomials or exact division.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[]`	FDUtil.`leftBasePseudoQuotientRemainder(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial sparse pseudo quotient and remainder for univariate polynomials or exact division.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	FDUtil.`leftBaseSparsePseudoRemainder(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial sparse pseudo remainder for univariate polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<SolvableQuotient<C>>`	FDUtil.`quotientFromIntegralCoefficients(GenSolvablePolynomialRing<SolvableQuotient<C>> fac, GenSolvablePolynomial<GenPolynomial<C>> A)`	Solvable rational function from integral solvable polynomial coefficients.
`static <C extends GcdRingElem<C>> java.util.List<GenSolvablePolynomial<SolvableQuotient<C>>>`	FDUtil.`quotientFromIntegralCoefficients(GenSolvablePolynomialRing<SolvableQuotient<C>> fac, java.util.Collection<GenSolvablePolynomial<GenPolynomial<C>>> L)`	Solvable rational function from integral solvable polynomial coefficients.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveDivide(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<C> s)`	GenSolvablePolynomial left recursive quotient for recursive polynomials and exact division by coefficient ring element.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveDivideRightEval(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<C> s)`	GenSolvablePolynomial recursive quotient for recursive polynomials and exact division by coefficient ring element.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveLeftDivide(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<C> s)`	GenSolvablePolynomial recursive quotient for recursive polynomials and partial left exact division by coefficient ring element.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursivePseudoQuotient(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial recursive pseudo quotient for recursive polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>[]`	FDUtil.`recursivePseudoQuotientRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial recursive pseudo quotient and remainder for recursive polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveRightDivide(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<C> s)`	GenSolvablePolynomial recursive quotient for recursive polynomials and partial right exact division by coefficient ring element.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveRightPseudoQuotient(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial recursive right pseudo quotient for recursive polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>[]`	FDUtil.`recursiveRightPseudoQuotientRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial right sparse pseudo quotient and remainder for recursive solvable polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveRightSparsePseudoRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial right sparse pseudo remainder for recursive solvable polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<GenPolynomial<C>>`	FDUtil.`recursiveSparsePseudoRemainder(GenSolvablePolynomial<GenPolynomial<C>> P, GenSolvablePolynomial<GenPolynomial<C>> S)`	GenSolvablePolynomial sparse pseudo remainder for recursive solvable polynomials.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	FDUtil.`rightBasePseudoQuotient(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial right sparse pseudo quotient for univariate polynomials or exact division.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[]`	FDUtil.`rightBasePseudoQuotientRemainder(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial right sparse pseudo quotient and remainder for univariate polynomials or exact division.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	FDUtil.`rightBaseSparsePseudoRemainder(GenSolvablePolynomial<C> P, GenSolvablePolynomial<C> S)`	GenSolvablePolynomial sparse right pseudo remainder for univariate polynomials.

Methods in edu.jas.fd that return GcdRingElem
Modifier and Type	Method	Description
`C[]`	GreatestCommonDivisorAbstract.`leftOreCond(C a, C b)`	Coefficient left Ore condition.
`C[]`	GreatestCommonDivisorAbstract.`rightOreCond(C a, C b)`	Coefficient right Ore condition.

Uses of GcdRingElem in edu.jas.gb

Classes in edu.jas.gb with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`GBOptimized<C extends GcdRingElem<C>>`	Groebner bases via optimized variable and term order.
`class`	`GBProxy<C extends GcdRingElem<C>>`	Groebner bases parallel proxy.
`class`	`SGBProxy<C extends GcdRingElem<C>>`	Groebner bases parallel proxy.

Uses of GcdRingElem in edu.jas.gbmod

Classes in edu.jas.gbmod with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`ModGroebnerBaseAbstract<C extends GcdRingElem<C>>`	Deprecated. use respective methods from GroebnerBaseAbstract
`class`	`ModGroebnerBasePar<C extends GcdRingElem<C>>`	Deprecated. use respective methods from GroebnerBaseParallel
`class`	`ModGroebnerBaseSeq<C extends GcdRingElem<C>>`	Deprecated. use respective methods from GroebnerBaseSeq
`class`	`ModSolvableGroebnerBasePar<C extends GcdRingElem<C>>`	Deprecated. use respective methods from SolvableGroebnerBaseParallel
`class`	`ModSolvableGroebnerBaseSeq<C extends GcdRingElem<C>>`	Deprecated. use respective methods from SolvableGroebnerBaseSeq

Uses of GcdRingElem in edu.jas.gbufd

Classes in edu.jas.gbufd with type parameters of type GcdRingElem
Modifier and Type	Interface	Description
`interface`	`CharacteristicSet<C extends GcdRingElem<C>>`	Characteristic Set interface.
`class`	`CharacteristicSetSimple<C extends GcdRingElem<C>>`	Characteristic Set class according to the simple algorithm, where the leading coefficients are not rereduced.
`class`	`CharacteristicSetWu<C extends GcdRingElem<C>>`	Characteristic Set class according to Wu.
`class`	`GroebnerBaseFGLM<C extends GcdRingElem<C>>`	Groebner Base sequential FGLM algorithm.
`class`	`GroebnerBasePartial<C extends GcdRingElem<C>>`	Partial Groebner Bases for subsets of variables.
`class`	`GroebnerBasePseudoParallel<C extends GcdRingElem<C>>`	Groebner Base with pseudo reduction multi-threaded parallel algorithm.
`class`	`GroebnerBasePseudoRecParallel<C extends GcdRingElem<C>>`	Groebner Base with recursive pseudo reduction multi-threaded parallel algorithm.
`class`	`GroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>`	Groebner Base with pseudo reduction sequential algorithm for integral function coefficients.
`class`	`GroebnerBasePseudoSeq<C extends GcdRingElem<C>>`	Groebner Base with pseudo reduction sequential algorithm.
`class`	`GroebnerBaseQuotient<C extends GcdRingElem<C>>`	Groebner Base sequential algorithm for rational function coefficients, fraction free computation.
`class`	`GroebnerBaseWalk<C extends GcdRingElem<C>>`	Groebner Base sequential Groebner Walk algorithm.
`class`	`MultiplicativeSet<C extends GcdRingElem<C>>`	Multiplicative set of polynomials.
`class`	`MultiplicativeSetCoPrime<C extends GcdRingElem<C>>`	Multiplicative set of co-prime polynomials.
`class`	`MultiplicativeSetFactors<C extends GcdRingElem<C>>`	Multiplicative set of irreducible polynomials.
`class`	`MultiplicativeSetSquarefree<C extends GcdRingElem<C>>`	Multiplicative set of squarefree and co-prime polynomials.
`(package private) class`	`PseudoMiReducer<C extends GcdRingElem<C>>`	Pseudo Reducing worker threads for minimal GB.
`(package private) class`	`PseudoMiReducerRec<C extends GcdRingElem<C>>`	Pseudo Reducing worker threads for minimal GB.
`(package private) class`	`PseudoReducer<C extends GcdRingElem<C>>`	Pseudo GB Reducing worker threads.
`(package private) class`	`PseudoReducerRec<C extends GcdRingElem<C>>`	Pseudo GB Reducing worker threads.
`class`	`SolvableGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>`	Solvable Groebner Base with pseudo reduction sequential algorithm.
`class`	`SolvableGroebnerBasePseudoSeq<C extends GcdRingElem<C>>`	Solvable Groebner Base with pseudo reduction sequential algorithm.
`class`	`SolvablePseudoReductionSeq<C extends GcdRingElem<C>>`	Polynomial pseudo reduction sequential use algorithm.
`class`	`SolvableSyzygyAbstract<C extends GcdRingElem<C>>`	Syzygy abstract class for solvable polynomials.
`class`	`SolvableSyzygySeq<C extends GcdRingElem<C>>`	Syzygy sequential class for solvable polynomials.
`class`	`SyzygyAbstract<C extends GcdRingElem<C>>`	SyzygyAbstract class.
`class`	`SyzygySeq<C extends GcdRingElem<C>>`	SyzygySeq class.
`class`	`WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>`	Non-commutative word Groebner Base sequential algorithm.
`class`	`WordGroebnerBasePseudoSeq<C extends GcdRingElem<C>>`	Non-commutative word Groebner Base sequential algorithm.

Methods in edu.jas.gbufd with type parameters of type GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyGBUtil.`chineseRemainderTheorem(java.util.List<java.util.List<GenPolynomial<C>>> F, java.util.List<GenPolynomial<C>> A)`	Chinese remainder theorem.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyGBUtil.`CRTInterpolation(GenPolynomialRing<C> fac, java.util.List<java.util.List<C>> E, java.util.List<C> V)`	Chinese remainder theorem, interpolation.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<C>`	GBFactory.`getImplementation()`	Determine suitable implementation of GB algorithms, no factory case.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<GenPolynomial<C>>`	GBFactory.`getImplementation(GenPolynomialRing<C> fac)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<GenPolynomial<C>>`	GBFactory.`getImplementation(GenPolynomialRing<C> fac, PairList<GenPolynomial<C>> pl)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<GenPolynomial<C>>`	GBFactory.`getImplementation(GenPolynomialRing<C> fac, GBFactory.Algo a)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<GenPolynomial<C>>`	GBFactory.`getImplementation(GenPolynomialRing<C> fac, GBFactory.Algo a, PairList<GenPolynomial<C>> pl)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<C>`	GBFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of GB algorithms, other cases.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<C>`	GBFactory.`getImplementation(RingFactory<C> fac, PairList<C> pl)`	Determine suitable implementation of GB algorithms, other cases.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>`	GBFactory.`getImplementation(QuotientRing<C> fac)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>`	GBFactory.`getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>`	GBFactory.`getImplementation(QuotientRing<C> fac, GBFactory.Algo a)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<Quotient<C>>`	GBFactory.`getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<C>`	SGBFactory.`getImplementation()`	Determine suitable implementation of GB algorithms, no factory case.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<GenPolynomial<C>>`	SGBFactory.`getImplementation(GenPolynomialRing<C> fac)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<GenPolynomial<C>>`	SGBFactory.`getImplementation(GenPolynomialRing<C> fac, PairList<GenPolynomial<C>> pl)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<GenPolynomial<C>>`	SGBFactory.`getImplementation(GenPolynomialRing<C> fac, GBFactory.Algo a)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<GenPolynomial<C>>`	SGBFactory.`getImplementation(GenPolynomialRing<C> fac, GBFactory.Algo a, PairList<GenPolynomial<C>> pl)`	Determine suitable implementation of GB algorithms, case (recursive) polynomial.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<C>`	SGBFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of GB algorithms, other cases.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<C>`	SGBFactory.`getImplementation(RingFactory<C> fac, PairList<C> pl)`	Determine suitable implementation of GB algorithms, other cases.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>`	SGBFactory.`getImplementation(QuotientRing<C> fac)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>`	SGBFactory.`getImplementation(QuotientRing<C> fac, PairList<Quotient<C>> pl)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>`	SGBFactory.`getImplementation(QuotientRing<C> fac, GBFactory.Algo a)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<Quotient<C>>`	SGBFactory.`getImplementation(QuotientRing<C> fac, GBFactory.Algo a, PairList<Quotient<C>> pl)`	Determine suitable implementation of GB algorithms, case Quotient coefficients.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<GenPolynomial<C>>`	GBFactory.`getProxy(GenPolynomialRing<C> fac)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<C>`	GBFactory.`getProxy(RingFactory<C> fac)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> GroebnerBaseAbstract<C>`	GBFactory.`getProxy(RingFactory<C> fac, PairList<C> pl)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<GenPolynomial<C>>`	SGBFactory.`getProxy(GenPolynomialRing<C> fac)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<C>`	SGBFactory.`getProxy(RingFactory<C> fac)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> SolvableGroebnerBaseAbstract<C>`	SGBFactory.`getProxy(RingFactory<C> fac, PairList<C> pl)`	Determine suitable parallel/concurrent implementation of GB algorithms if possible.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<C>>`	PolyGBUtil.`intersect(GenPolynomialRing<C> pfac, java.util.List<GenPolynomial<C>> A, java.util.List<GenPolynomial<C>> B)`	Intersection.
`static <C extends GcdRingElem<C>> java.util.List<GenSolvablePolynomial<C>>`	PolyGBUtil.`intersect(GenSolvablePolynomialRing<C> pfac, java.util.List<GenSolvablePolynomial<C>> A, java.util.List<GenSolvablePolynomial<C>> B)`	Intersection.
`static <C extends GcdRingElem<C>> java.util.List<GenWordPolynomial<C>>`	PolyGBUtil.`intersect(GenWordPolynomialRing<C> pfac, java.util.List<GenWordPolynomial<C>> A, java.util.List<GenWordPolynomial<C>> B)`	Intersection.
`static <C extends GcdRingElem<C>> java.util.List<GenWordPolynomial<C>>`	PolyGBUtil.`intersect(GenWordPolynomialRing<C> pfac, java.util.List<GenWordPolynomial<C>> A, java.util.List<GenWordPolynomial<C>> B, WordGroebnerBaseAbstract<C> bb)`	Intersection.
`static <C extends GcdRingElem<C>> boolean`	PolyGBUtil.`isChineseRemainder(java.util.List<java.util.List<GenPolynomial<C>>> F, java.util.List<GenPolynomial<C>> A, GenPolynomial<C> h)`	Is Chinese remainder.
`static <C extends GcdRingElem<C>> boolean`	PolyGBUtil.`isResultant(GenPolynomial<C> A, GenPolynomial<C> B, GenPolynomial<C> r)`	Test for resultant.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[]`	PolyGBUtil.`quotientRemainder(GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Solvable quotient and remainder via reduction.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<C>>`	PolyGBUtil.`subRing(java.util.List<GenPolynomial<C>> A)`	Subring generators.
`static <C extends GcdRingElem<C>> boolean`	PolyGBUtil.`subRingAndMember(java.util.List<GenPolynomial<C>> A, GenPolynomial<C> g)`	Subring and membership test.
`static <C extends GcdRingElem<C>> boolean`	PolyGBUtil.`subRingMember(java.util.List<GenPolynomial<C>> A, GenPolynomial<C> g)`	Subring membership.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyModUtil.`syzGcd(GenPolynomialRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d)`	Greatest common divisor.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	PolyModUtil.`syzGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Greatest common divisor via least common multiple.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>[]`	PolyModUtil.`syzGcdCofactors(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Greatest common divisor and cofactors via least common multiple and reduction.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyModUtil.`syzLcm(GenPolynomialRing<C> r, GenPolynomial<C> n, GenPolynomial<C> d)`	Least common multiple.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	PolyModUtil.`syzLcm(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Least common multiple via ideal intersection.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	PolyModUtil.`syzLeftGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Left greatest common divisor via least common multiple.
`static <C extends GcdRingElem<C>> GenSolvablePolynomial<C>`	PolyModUtil.`syzRightGcd(GenSolvablePolynomialRing<C> r, GenSolvablePolynomial<C> n, GenSolvablePolynomial<C> d)`	Right greatest common divisor via least common multiple.

Uses of GcdRingElem in edu.jas.integrate

Classes in edu.jas.integrate with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`ElementaryIntegration<C extends GcdRingElem<C>>`	Methods related to elementary integration.
`class`	`ElementaryIntegrationBernoulli<C extends GcdRingElem<C>>`	Methods related to the Bernoulli algorithm for elementary integration.
`class`	`ElementaryIntegrationCzichowski<C extends GcdRingElem<C>>`	Method related to elementary integration.
`class`	`ElementaryIntegrationLazard<C extends GcdRingElem<C>>`	Method related to elementary integration.
`class`	`Integral<C extends GcdRingElem<C>>`	Container for a rational function integral, polynomial version.
`class`	`LogIntegral<C extends GcdRingElem<C>>`	Container for the logarithmic part of a rational function integral.
`class`	`QuotIntegral<C extends GcdRingElem<C>>`	Container for a rational function integral, quotient version .

Uses of GcdRingElem in edu.jas.poly

Classes in edu.jas.poly with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`(package private) class`	`AlgebToCompl<C extends GcdRingElem<C>>`	Algebraic to generic complex functor.
`(package private) class`	`AlgToPoly<C extends GcdRingElem<C>>`	Algebraic to polynomial functor.
`(package private) class`	`AnyToComplex<C extends GcdRingElem<C>>`	Any ring element to generic complex functor.
`(package private) class`	`CoeffToAlg<C extends GcdRingElem<C>>`	Coefficient to algebriac functor.
`(package private) class`	`CoeffToRecAlg<C extends GcdRingElem<C>>`	Coefficient to recursive algebriac functor.
`(package private) class`	`ComplToAlgeb<C extends GcdRingElem<C>>`	Ceneric complex to algebraic number functor.
`(package private) class`	`PolyToAlg<C extends GcdRingElem<C>>`	Polynomial to algebriac functor.
`class`	`QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>`	QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
`class`	`QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>`	QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
`class`	`QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>`	QLRSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
`class`	`QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>`	QLRSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.

Classes in edu.jas.poly that implement GcdRingElem
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.

Methods in edu.jas.poly with type parameters of type GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtil.`algebraicFromComplex(GenPolynomialRing<AlgebraicNumber<C>> fac, GenPolynomial<Complex<C>> A)`	AlgebraicNumber from complex coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<Complex<C>>`	PolyUtil.`complexFromAlgebraic(GenPolynomialRing<Complex<C>> fac, GenPolynomial<AlgebraicNumber<C>> A)`	Complex from algebraic coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<Complex<C>>`	PolyUtil.`complexFromAny(GenPolynomialRing<Complex<C>> fac, GenPolynomial<C> A)`	Complex from ring element coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtil.`convertRecursiveToAlgebraicCoefficients(GenPolynomialRing<AlgebraicNumber<C>> pfac, GenPolynomial<GenPolynomial<C>> A)`	Convert to AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtil.`convertToAlgebraicCoefficients(GenPolynomialRing<AlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUtil.`convertToRecAlgebraicCoefficients(int depth, GenPolynomialRing<AlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to recursive AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>`	PolyUtil.`fromAlgebraicCoefficients(GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomial<AlgebraicNumber<C>> A)`	From AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> Product<C>`	PolyUtil.`toProductGen(ProductRing<C> pfac, C c)`	Product representation.
`static <C extends GcdRingElem<C>> GenPolynomial<Product<C>>`	PolyUtil.`toProductGen(GenPolynomialRing<Product<C>> pfac, GenPolynomial<C> A)`	Product representation.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Product<C>>>`	PolyUtil.`toProductGen(GenPolynomialRing<Product<C>> pfac, java.util.List<GenPolynomial<C>> L)`	Product representation.

Uses of GcdRingElem in edu.jas.root

Classes in edu.jas.root with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`AlgebraicRoots<C extends GcdRingElem<C> & Rational>`	Container for the real and complex algebraic roots of a univariate polynomial.
`(package private) class`	`AlgFromRealCoeff<C extends GcdRingElem<C> & Rational>`	Coefficient to algebraic from real algebraic functor.
`(package private) class`	`CoeffToComplex<C extends GcdRingElem<C> & Rational>`	Coefficient to complex algebraic functor.
`(package private) class`	`CoeffToComplexFromComplex<C extends GcdRingElem<C> & Rational>`	Coefficient to complex algebraic from complex functor.
`(package private) class`	`CoeffToReal<C extends GcdRingElem<C> & Rational>`	Coefficient to real algebraic functor.
`(package private) class`	`CoeffToReAlg<C extends GcdRingElem<C> & Rational>`	Coefficient to algebraic functor.
`(package private) class`	`CoeffToRecReAlg<C extends GcdRingElem<C> & Rational>`	Coefficient to recursive algebraic functor.
`class`	`ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>`	Complex algebraic number class based on AlgebraicNumber.
`class`	`ComplexAlgebraicRing<C extends GcdRingElem<C> & Rational>`	Complex algebraic number factory class based on AlgebraicNumberRing with RingFactory interface.
`class`	`DecimalRoots<C extends GcdRingElem<C> & Rational>`	Container for the real and complex algebraic roots of a univariate polynomial.
`(package private) class`	`PolyToReAlg<C extends GcdRingElem<C> & Rational>`	Polynomial to algebraic functor.
`class`	`RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>`	Real algebraic number class based on AlgebraicNumber.
`class`	`RealAlgebraicRing<C extends GcdRingElem<C> & Rational>`	Real algebraic number factory class based on AlgebraicNumberRing with RingFactory interface.
`(package private) class`	`RealFromAlgCoeff<C extends GcdRingElem<C> & Rational>`	Coefficient to real algebriac from algebraic functor.
`class`	`RealRootTuple<C extends GcdRingElem<C> & Rational>`	RealAlgebraicNumber root tuple.

Classes in edu.jas.root that implement GcdRingElem
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.

Methods in edu.jas.root with type parameters of type GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<AlgebraicNumber<C>>`	PolyUtilRoot.`algebraicFromRealCoefficients(GenPolynomialRing<AlgebraicNumber<C>> afac, GenPolynomial<RealAlgebraicNumber<C>> A)`	Convert to AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> AlgebraicRoots<C>`	RootFactory.`algebraicRoots(GenPolynomial<C> f)`	Roots as real and complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>`	RootFactory.`complexAlgebraicNumbers(GenPolynomial<C> f)`	Complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>`	RootFactory.`complexAlgebraicNumbers(GenPolynomial<C> f, BigRational eps)`	Complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>`	RootFactory.`complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)`	Complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>`	RootFactory.`complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f, BigRational eps)`	Complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<Complex<C>>`	PolyUtilRoot.`complexFromAny(GenPolynomial<C> f)`	Convert to Complex coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilRoot.`convertRecursiveToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<GenPolynomial<C>> A)`	Convert to RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilRoot.`convertToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>>`	PolyUtilRoot.`convertToComplexCoefficients(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to ComplexAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>>`	PolyUtilRoot.`convertToComplexCoefficientsFromComplex(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac, GenPolynomial<Complex<C>> A)`	Convert to ComplexAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilRoot.`convertToRealCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilRoot.`convertToRecAlgebraicCoefficients(int depth, GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)`	Convert to recursive RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> DecimalRoots<C>`	RootFactory.`decimalRoots(GenPolynomial<C> f, BigRational eps)`	Roots as real and complex decimal numbers.
`static <C extends GcdRingElem<C> & Rational> DecimalRoots<C>`	RootFactory.`decimalRoots(AlgebraicRoots<C> ar, BigRational eps)`	Roots as real and complex decimal numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<BigDecimal>>`	RootFactory.`filterOutRealRoots(GenPolynomial<C> f, java.util.List<Complex<BigDecimal>> c, java.util.List<BigDecimal> r, BigRational eps)`	Filter real roots from complex roots.
`static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>`	RootFactory.`filterOutRealRoots(GenPolynomial<C> f, java.util.List<ComplexAlgebraicNumber<C>> c, java.util.List<RealAlgebraicNumber<C>> r)`	Filter real roots from complex roots.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactory.`isRealRoot(GenPolynomial<C> f, Complex<BigDecimal> c, BigDecimal r, BigRational eps)`	Is complex decimal number a real root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactory.`isRealRoot(GenPolynomial<C> f, ComplexAlgebraicNumber<C> c, RealAlgebraicNumber<C> r)`	Is complex algebraic number a real root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactory.`isRoot(GenPolynomial<C> f, ComplexAlgebraicNumber<C> r)`	Is complex algebraic number a root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactory.`isRoot(GenPolynomial<C> f, RealAlgebraicNumber<C> r)`	Is real algebraic number a root of a polynomial.
`static <C extends GcdRingElem<C> & Rational> boolean`	RootFactory.`isRootComplex(GenPolynomial<Complex<C>> f, ComplexAlgebraicNumber<C> r)`	Is complex algebraic number a root of a complex polynomial.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbers(GenPolynomial<C> f)`	Real algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbers(GenPolynomial<C> f, BigRational eps)`	Real algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbersField(GenPolynomial<C> f)`	Real algebraic numbers from a field.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbersField(GenPolynomial<C> f, BigRational eps)`	Real algebraic numbers from a field.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbersIrred(GenPolynomial<C> f)`	Real algebraic numbers from a irreducible polynomial.
`static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>`	RootFactory.`realAlgebraicNumbersIrred(GenPolynomial<C> f, BigRational eps)`	Real algebraic numbers from a irreducible polynomial.
`static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>`	PolyUtilRoot.`realFromAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> rfac, GenPolynomial<AlgebraicNumber<C>> A)`	Convert to RealAlgebraicNumber coefficients.
`static <C extends GcdRingElem<C> & Rational> void`	RootFactory.`rootRefine(AlgebraicRoots<C> a, BigRational eps)`	Root refinement of real and complex algebraic numbers.
`static <C extends GcdRingElem<C> & Rational> AlgebraicRoots<C>`	RootFactory.`rootsOfUnity(AlgebraicRoots<C> ar)`	Roots of unity of real and complex algebraic numbers.

Uses of GcdRingElem in edu.jas.structure

Classes in edu.jas.structure with type parameters of type GcdRingElem
Modifier and Type Interface Description

interface GcdRingElem<C extends GcdRingElem<C>>
Gcd ring element interface.

Subinterfaces of GcdRingElem in edu.jas.structure
Modifier and Type Interface Description

interface RegularRingElem<C extends RegularRingElem<C>>
Regular ring element interface.

Classes in edu.jas.structure with type parameters of type GcdRingElem
Modifier and Type	Interface	Description
`interface`	`GcdRingElem<C extends GcdRingElem<C>>`	Gcd ring element interface.

Subinterfaces of GcdRingElem in edu.jas.structure
Modifier and Type	Interface	Description
`interface`	`RegularRingElem<C extends RegularRingElem<C>>`	Regular ring element interface.

Uses of GcdRingElem in edu.jas.ufd

Classes in edu.jas.ufd with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`(package private) class`	`BackSubstKronecker<C extends GcdRingElem<C>>`	Kronecker back substitutuion functor.
`class`	`FactorAbsolute<C extends GcdRingElem<C>>`	Absolute factorization algorithms class.
`class`	`FactorAbstract<C extends GcdRingElem<C>>`	Abstract factorization algorithms class.
`class`	`FactorAlgebraic<C extends GcdRingElem<C>>`	Algebraic number coefficients factorization algorithms.
`class`	`FactorComplex<C extends GcdRingElem<C>>`	Complex coefficients factorization algorithms.
`class`	`FactorFraction<C extends GcdRingElem<C>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>>`	Fraction factorization algorithms.
`class`	`FactorFraction<C extends GcdRingElem<C>,D extends GcdRingElem<D> & QuotPair<GenPolynomial<C>>>`	Fraction factorization algorithms.
`class`	`FactorInteger<MOD extends GcdRingElem<MOD> & Modular>`	Integer coefficients factorization algorithms.
`interface`	`Factorization<C extends GcdRingElem<C>>`	Factorization algorithms interface.
`class`	`FactorModular<MOD extends GcdRingElem<MOD> & Modular>`	Modular coefficients factorization algorithms.
`class`	`FactorModularBerlekamp<MOD extends GcdRingElem<MOD>>`	Modular coefficients Berlekamp factorization algorithms.
`class`	`FactorQuotient<C extends GcdRingElem<C>>`	Rational function coefficients factorization algorithms.
`class`	`Factors<C extends GcdRingElem<C>>`	Container for the factors of absolute factorization.
`class`	`FactorsList<C extends GcdRingElem<C>>`	Container for the factors of a squarefree factorization.
`class`	`FactorsMap<C extends GcdRingElem<C>>`	Container for the factors of a eventually non-squarefree factorization.
`class`	`GCDProxy<C extends GcdRingElem<C>>`	Greatest common divisor parallel proxy.
`interface`	`GreatestCommonDivisor<C extends GcdRingElem<C>>`	Greatest common divisor algorithm interface.
`class`	`GreatestCommonDivisorAbstract<C extends GcdRingElem<C>>`	Greatest common divisor algorithms.
`class`	`GreatestCommonDivisorFake<C extends GcdRingElem<C>>`	Greatest common divisor algorithms with gcd always 1.
`class`	`GreatestCommonDivisorHensel<MOD extends GcdRingElem<MOD> & Modular>`	Greatest common divisor algorithms with subresultant polynomial remainder sequence and univariate Hensel lifting.
`class`	`GreatestCommonDivisorModEval<MOD extends GcdRingElem<MOD> & Modular>`	Greatest common divisor algorithms with modular evaluation algorithm for recursion.
`class`	`GreatestCommonDivisorModular<MOD extends GcdRingElem<MOD> & Modular>`	Greatest common divisor algorithms with modular computation and Chinese remainder algorithm.
`class`	`GreatestCommonDivisorPrimitive<C extends GcdRingElem<C>>`	Greatest common divisor algorithms with primitive polynomial remainder sequence.
`class`	`GreatestCommonDivisorSimple<C extends GcdRingElem<C>>`	Greatest common divisor algorithms with monic polynomial remainder sequence.
`class`	`GreatestCommonDivisorSubres<C extends GcdRingElem<C>>`	Greatest common divisor algorithms with subresultant polynomial remainder sequence.
`class`	`HenselApprox<MOD extends GcdRingElem<MOD> & Modular>`	Container for the approximation result from a Hensel algorithm.
`class`	`PartialFraction<C extends GcdRingElem<C>>`	Container for the partial fraction decomposition of a squarefree denominator.
`class`	`Quotient<C extends GcdRingElem<C>>`	Quotient, that is a rational function, based on GenPolynomial with RingElem interface.
`class`	`QuotientRing<C extends GcdRingElem<C>>`	Quotient ring factory based on GenPolynomial with RingElem interface.
`class`	`QuotientTaylorFunction<C extends GcdRingElem<C>>`	Polynomial quotient functions capable for Taylor series expansion.
`interface`	`Squarefree<C extends GcdRingElem<C>>`	Squarefree decomposition interface.
`class`	`SquarefreeAbstract<C extends GcdRingElem<C>>`	Abstract squarefree decomposition class.
`class`	`SquarefreeFieldChar0<C extends GcdRingElem<C>>`	Squarefree decomposition for coefficient fields of characteristic 0.
`class`	`SquarefreeFieldChar0Yun<C extends GcdRingElem<C>>`	Squarefree decomposition for coefficient fields of characteristic 0, algorithm of Yun.
`class`	`SquarefreeFieldCharP<C extends GcdRingElem<C>>`	Squarefree decomposition for coefficient fields of characteristic p.
`class`	`SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>>`	Squarefree decomposition for finite coefficient fields of characteristic p.
`class`	`SquarefreeInfiniteAlgebraicFieldCharP<C extends GcdRingElem<C>>`	Squarefree decomposition for algebraic extensions of infinite coefficient fields of characteristic p > 0.
`class`	`SquarefreeInfiniteFieldCharP<C extends GcdRingElem<C>>`	Squarefree decomposition for infinite coefficient fields of characteristic p.
`class`	`SquarefreeRingChar0<C extends GcdRingElem<C>>`	Squarefree decomposition for coefficient rings of characteristic 0.
`(package private) class`	`SubstKronecker<C extends GcdRingElem<C>>`	Kronecker substitutuion functor.

Classes in edu.jas.ufd that implement GcdRingElem
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 GcdRingElem
Modifier and Type	Method	Description
`static <C extends GcdRingElem<C>> GenPolynomial<C>[]`	PolyUfdUtil.`agcd(GenPolynomial<C> R, GenPolynomial<C> S, int n)`	GenPolynomial approximate common divisor.
`static <C extends GcdRingElem<C>> AlgebraicNumberRing<C>`	PolyUfdUtil.`algebraicNumberField(GenPolynomialRing<C> ring, int degree)`	Construct an algebraic number field of degree d.
`static <C extends GcdRingElem<C>> AlgebraicNumberRing<C>`	PolyUfdUtil.`algebraicNumberField(RingFactory<C> cfac, int degree)`	Construct an algebraic number field of degree d.
`static <C extends GcdRingElem<C>> Quotient<C>`	PolyUfdUtil.`approximantOfPade(UnivPowerSeriesRing<C> upr, TaylorFunction<C> f, C a, int m, int n)`	Pade approximant [m/n] of function f.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`backSubstituteKronecker(GenPolynomialRing<C> fac, GenPolynomial<C> A, long d)`	Kronecker back substitution.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<C>>`	PolyUfdUtil.`backSubstituteKronecker(GenPolynomialRing<C> fac, java.util.List<GenPolynomial<C>> A, long d)`	Kronecker back substitution.
`static <C extends GcdRingElem<C>> java.util.ArrayList<java.util.ArrayList<C>>`	PolyUfdUtil.`constructQmatrix(GenPolynomial<C> A)`	Construct Berlekamp Q matrix.
`static <C extends GcdRingElem<C>> Quotient<C>`	PolyUfdUtil.`derivative(Quotient<C> r)`	Derivation of a univariate rational function.
`static <C extends GcdRingElem<C>> Quotient<C>`	PolyUfdUtil.`derivative(Quotient<C> Q, int r)`	Polynomial quotient partial derivative variable r.
`static <C extends GcdRingElem<C>> void`	PolyUfdUtil.`ensureFieldProperty(AlgebraicNumberRing<C> afac)`	Ensure that the field property is determined.
`static <C extends GcdRingElem<C>> C`	PolyUfdUtil.`evaluateAll(RingFactory<C> cfac, Quotient<C> A, java.util.List<C> a)`	Evaluate all variables.
`static <C extends GcdRingElem<C>> C`	PolyUfdUtil.`evaluateMain(RingFactory<C> cfac, Quotient<C> A, C a)`	Evaluate at main variable.
`static <C extends GcdRingElem<C>> EvalPoints<C>`	PolyUfdUtil.`evaluationPoints(GenPolynomial<C> A)`	Polynomial suitable evaluation points.
`static <C extends GcdRingElem<C>> GenExteriorPolynomial<Quotient<C>>`	PolyUfdUtil.`exteriorDerivativeQuot(GenExteriorPolynomial<Quotient<C>> P)`	GenExteriorPolynomial over polynomial quotient exterior derivative.
`static <C extends GcdRingElem<C>> java.util.SortedMap<Quotient<C>,java.lang.Long>`	PolyUfdUtil.`factors(Quotient<C> A)`	Factors of Quotient rational function.
`static <C extends GcdRingElem<C>> FactorAbstract<AlgebraicNumber<C>>`	FactorFactory.`getImplementation(AlgebraicNumberRing<C> fac)`	Determine suitable implementation of factorization algorithms, case AlgebraicNumber<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<Complex<C>>`	FactorFactory.`getImplementation(ComplexRing<C> fac)`	Determine suitable implementation of factorization algorithms, case Complex<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<C>`	FactorFactory.`getImplementation(GenPolynomialRing<C> fac)`	Determine suitable implementation of factorization algorithms, case recursive GenPolynomial<C>.
`static <C extends GcdRingElem<C>> FactorAbstract<C>`	FactorFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of factorization algorithms, other cases.
`static <C extends GcdRingElem<C>> FactorAbstract<Quotient<C>>`	FactorFactory.`getImplementation(QuotientRing<C> fac)`	Determine suitable implementation of factorization algorithms, case Quotient<C>.
`static <C extends GcdRingElem<C>> GreatestCommonDivisorAbstract<C>`	GCDFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of gcd algorithms, other cases.
`static <C extends GcdRingElem<C>> SquarefreeAbstract<AlgebraicNumber<C>>`	SquarefreeFactory.`getImplementation(AlgebraicNumberRing<C> fac)`	Determine suitable implementation of squarefree factorization algorithms, case AlgebraicNumber<C>.
`static <C extends GcdRingElem<C>> SquarefreeAbstract<C>`	SquarefreeFactory.`getImplementation(GenPolynomialRing<C> fac)`	Determine suitable implementation of squarefree factorization algorithms, case GenPolynomial<C>.
`static <C extends GcdRingElem<C>> SquarefreeAbstract<C>`	SquarefreeFactory.`getImplementation(RingFactory<C> fac)`	Determine suitable implementation of squarefree factorization algorithms, other cases.
`static <C extends GcdRingElem<C>> SquarefreeAbstract<Quotient<C>>`	SquarefreeFactory.`getImplementation(QuotientRing<C> fac)`	Determine suitable implementation of squarefree factorization algorithms, case Quotient<C>.
`protected static <C extends GcdRingElem<C>> SquarefreeAbstract<C>`	SquarefreeFactory.`getImplementationPoly(GenPolynomialRing<C> fac)`
`static <C extends GcdRingElem<C>> GreatestCommonDivisorAbstract<C>`	GCDFactory.`getProxy(RingFactory<C> fac)`	Determine suitable proxy for gcd algorithms, other cases.
`static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>`	PolyUfdUtil.`integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, GenPolynomial<Quotient<C>> A)`	Integral polynomial from rational function coefficients.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<GenPolynomial<C>>>`	PolyUfdUtil.`integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac, java.util.Collection<GenPolynomial<Quotient<C>>> L)`	Integral polynomial from rational function coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>`	PolyUfdUtil.`introduceLowerVariable(GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomial<C> A)`	Introduce lower variable.
`static <MOD extends GcdRingElem<MOD> & Modular> boolean`	HenselUtil.`isDiophantLift(GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> S1, GenPolynomial<MOD> S2, GenPolynomial<MOD> C)`	Modular Diophant relation lifting test.
`static <MOD extends GcdRingElem<MOD> & Modular> boolean`	HenselUtil.`isDiophantLift(java.util.List<GenPolynomial<MOD>> A, java.util.List<GenPolynomial<MOD>> S, GenPolynomial<MOD> C)`	Modular Diophant relation lifting test.
`static <MOD extends GcdRingElem<MOD> & Modular> boolean`	HenselUtil.`isExtendedEuclideanLift(java.util.List<GenPolynomial<MOD>> A, java.util.List<GenPolynomial<MOD>> S)`	Modular extended Euclidean relation lifting test.
`static <C extends GcdRingElem<C>> boolean`	PolyUfdUtil.`isFactorization(Quotient<C> P, java.util.SortedMap<Quotient<C>,java.lang.Long> F)`	Quotient is (squarefree) factorization.
`static <MOD extends GcdRingElem<MOD> & Modular> boolean`	HenselMultUtil.`isHenselLift(GenPolynomial<BigInteger> C, GenPolynomial<MOD> Cp, java.util.List<GenPolynomial<MOD>> F, java.util.List<GenPolynomial<MOD>> L)`	Modular Hensel lifting algorithm on coefficients test.
`static <MOD extends GcdRingElem<MOD> & Modular> boolean`	HenselUtil.`isHenselLift(GenPolynomial<BigInteger> C, BigInteger M, BigInteger p, HenselApprox<MOD> Ha)`	Modular Hensel lifting test.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselMultUtil.`liftDiophant(GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> C, java.util.List<MOD> V, long d, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselMultUtil.`liftDiophant(java.util.List<GenPolynomial<MOD>> A, GenPolynomial<MOD> C, java.util.List<MOD> V, long d, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftDiophant(GenPolynomial<MOD> A, GenPolynomial<MOD> B, long e, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftDiophant(GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> C, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftDiophant(java.util.List<GenPolynomial<MOD>> A, long e, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftDiophant(java.util.List<GenPolynomial<MOD>> A, GenPolynomial<MOD> C, long k)`	Modular diophantine equation solution and lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> GenPolynomial<MOD>[]`	HenselUtil.`liftExtendedEuclidean(GenPolynomial<MOD> A, GenPolynomial<MOD> B, long k)`	Constructing and lifting algorithm for extended Euclidean relation.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftExtendedEuclidean(java.util.List<GenPolynomial<MOD>> A, long k)`	Constructing and lifting algorithm for extended Euclidean relation.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselMultUtil.`liftHensel(GenPolynomial<BigInteger> C, GenPolynomial<MOD> Cp, java.util.List<GenPolynomial<MOD>> F, java.util.List<BigInteger> V, long k, java.util.List<GenPolynomial<BigInteger>> G)`	Modular Hensel lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHensel(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B)`	Modular Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHensel(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> S, GenPolynomial<MOD> T)`	Modular Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftHensel(GenPolynomial<BigInteger> C, java.util.List<GenPolynomial<MOD>> F, long k, BigInteger g)`	Modular Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselMultUtil.`liftHenselFull(GenPolynomial<BigInteger> C, java.util.List<GenPolynomial<MOD>> F, java.util.List<BigInteger> V, long k, java.util.List<GenPolynomial<BigInteger>> G)`	Modular Hensel full lifting algorithm.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselMultUtil.`liftHenselMonic(GenPolynomial<BigInteger> C, GenPolynomial<MOD> Cp, java.util.List<GenPolynomial<MOD>> F, java.util.List<BigInteger> V, long k)`	Modular Hensel lifting algorithm, monic case.
`static <MOD extends GcdRingElem<MOD> & Modular> java.util.List<GenPolynomial<MOD>>`	HenselUtil.`liftHenselMonic(GenPolynomial<BigInteger> C, java.util.List<GenPolynomial<MOD>> F, long k)`	Modular Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHenselQuadratic(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B)`	Modular quadratic Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHenselQuadratic(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> S, GenPolynomial<MOD> T)`	Modular quadratic Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHenselQuadraticFac(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B)`	Modular Hensel lifting algorithm on coefficients.
`static <MOD extends GcdRingElem<MOD> & Modular> HenselApprox<MOD>`	HenselUtil.`liftHenselQuadraticFac(GenPolynomial<BigInteger> C, BigInteger M, GenPolynomial<MOD> A, GenPolynomial<MOD> B, GenPolynomial<MOD> S, GenPolynomial<MOD> T)`	Modular Hensel lifting algorithm on coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`norm(GenPolynomial<AlgebraicNumber<C>> A)`	Norm of a polynomial with AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`norm(GenPolynomial<AlgebraicNumber<C>> A, long k)`	Norm of a polynomial with AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<Quotient<C>>`	PolyUfdUtil.`quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, GenPolynomial<GenPolynomial<C>> A)`	Rational function from integral polynomial coefficients.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<Quotient<C>>>`	PolyUfdUtil.`quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac, java.util.Collection<GenPolynomial<GenPolynomial<C>>> L)`	Rational function from integral polynomial coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`randomIrreduciblePolynomial(GenPolynomialRing<C> ring, int degree)`	Construct a random irreducible univariate polynomial of degree d.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`randomIrreduciblePolynomial(RingFactory<C> cfac, int degree)`	Construct a random irreducible univariate polynomial of degree d.
`static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>>`	PolyUfdUtil.`substituteConvertToAlgebraicCoefficients(GenPolynomialRing<AlgebraicNumber<C>> pfac, GenPolynomial<C> A, long k)`	Convert to AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>>`	PolyUfdUtil.`substituteFromAlgebraicCoefficients(GenPolynomialRing<GenPolynomial<C>> rfac, GenPolynomial<AlgebraicNumber<C>> A, long k)`	From AlgebraicNumber coefficients.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`substituteKronecker(GenPolynomial<C> A)`	Kronecker substitution.
`static <C extends GcdRingElem<C>> GenPolynomial<C>`	PolyUfdUtil.`substituteKronecker(GenPolynomial<C> A, long d)`	Kronecker substitution.
`static <C extends GcdRingElem<C>> java.util.List<GenPolynomial<C>>`	PolyUfdUtil.`substituteKronecker(java.util.List<GenPolynomial<C>> A, int d)`	Kronecker substitution.

Uses of GcdRingElem in edu.jas.ufdroot

Classes in edu.jas.ufdroot with type parameters of type GcdRingElem
Modifier and Type	Class	Description
`class`	`FactorRealAlgebraic<C extends GcdRingElem<C> & Rational>`	Real algebraic number coefficients factorization algorithms.

Uses of Interfaceedu.jas.structure.GcdRingElem

Uses of GcdRingElem in edu.jas.application

Uses of GcdRingElem in edu.jas.arith

Uses of GcdRingElem in edu.jas.fd

Uses of GcdRingElem in edu.jas.gb

Uses of GcdRingElem in edu.jas.gbmod

Uses of GcdRingElem in edu.jas.gbufd

Uses of GcdRingElem in edu.jas.integrate

Uses of GcdRingElem in edu.jas.poly

Uses of GcdRingElem in edu.jas.root

Uses of GcdRingElem in edu.jas.structure

Uses of GcdRingElem in edu.jas.ufd

Uses of GcdRingElem in edu.jas.ufdroot

Uses of Interface
edu.jas.structure.GcdRingElem