Uses of Interface
edu.jas.arith.Rational

Packages that use Rational

Package	Description
edu.jas.application	Groebner base application package.
edu.jas.arith	Basic arithmetic package.
edu.jas.poly	Generic coefficients polynomial package.
edu.jas.root	Real and Complex Root Computation package.
edu.jas.ufdroot	Unique Factorization Domain and Roots package.

Uses of Rational in edu.jas.application

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

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	CoeffToComplexReal<C extends GcdRingElem<C> & Rational>	Coefficient to complex real algebriac functor.
(package private) class	EvaluateToComplexReal<C extends GcdRingElem<C> & Rational>	Polynomial coefficient to complex real algebriac evaluation functor.
class	FactorRealReal<C extends GcdRingElem<C> & Rational>	Real algebraic number coefficients factorization algorithms.
class	IdealWithComplexAlgebraicRoots<D extends GcdRingElem<D> & Rational>	Container for Ideals together with univariate polynomials and complex algebraic roots.
class	IdealWithRealAlgebraicRoots<D extends GcdRingElem<D> & Rational>	Container for Ideals together with univariate polynomials and real algebraic roots.
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.

Classes in edu.jas.application that implement Rational

Modifier and Type	Class	Description
class	RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on bi-variate real algebraic numbers.

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

Modifier and Type	Method	Description
static <C extends GcdRingElem<C> & Rational> List<Complex<RealAlgebraicNumber<C>>>	RootFactoryApp.complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)	Complex algebraic number roots.
static <C extends GcdRingElem<C> & Rational> List<Complex<RealAlgebraicNumber<C>>>	RootFactoryApp.complexAlgebraicNumbersSquarefree(GenPolynomial<Complex<C>> f)	Complex algebraic number roots.
static <D extends GcdRingElem<D> & Rational> 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> List<IdealWithComplexAlgebraicRoots<D>>	PolyUtilApp.complexAlgebraicRoots(List<IdealWithUniv<D>> I)	Construct complex roots for zero dimensional ideal(G).
static <D extends GcdRingElem<D> & Rational> 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> List<List<Complex<BigDecimal>>>	PolyUtilApp.complexRoots(Ideal<D> I, List<GenPolynomial<D>> univs, BigRational eps)	Construct superset of complex roots for zero dimensional ideal(G).
static <D extends GcdRingElem<D> & Rational> List<IdealWithComplexRoots<D>>	PolyUtilApp.complexRoots(List<IdealWithUniv<D>> Il, BigRational eps)	Construct superset of complex roots for zero dimensional ideal(G).
static <D extends GcdRingElem<D> & Rational> List<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> List<List<Complex<BigDecimal>>>	PolyUtilApp.complexRootTuples(List<IdealWithUniv<D>> Il, BigRational eps)	Construct superset of complex roots for zero dimensional ideal(G).
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> & 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> & Rational> FactorAbstract<RealAlgebraicNumber<C>>	FactorFactory.getImplementation(RealAlgebraicRing<C> fac)	Determine suitable implementation of factorization algorithms, case RealAlgebraicNumber<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> & 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, 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 <D extends GcdRingElem<D> & Rational> 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> List<IdealWithRealAlgebraicRoots<D>>	PolyUtilApp.realAlgebraicRoots(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> 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> List<List<BigDecimal>>	PolyUtilApp.realRoots(Ideal<D> I, List<GenPolynomial<D>> univs, BigRational eps)	Construct superset of real roots for zero dimensional ideal(G).
static <D extends GcdRingElem<D> & Rational> List<IdealWithRealRoots<D>>	PolyUtilApp.realRoots(List<IdealWithUniv<D>> Il, BigRational eps)	Construct superset of real roots for zero dimensional ideal(G).
static <D extends GcdRingElem<D> & Rational> List<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> List<List<BigDecimal>>	PolyUtilApp.realRootTuples(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 <D extends GcdRingElem<D> & Rational> String	PolyUtilApp.toString(Complex<RealAlgebraicNumber<D>> c)	String representation of a deximal approximation of a complex number.
static <D extends GcdRingElem<D> & Rational> String	PolyUtilApp.toString1(Complex<D> c)	String representation of a deximal approximation of a complex number.

Uses of Rational in edu.jas.arith

Classes in edu.jas.arith that implement Rational

Modifier and Type	Class	Description
final class	BigDecimal	BigDecimal class to make java.math.BigDecimal available with RingElem interface.
final class	BigInteger	BigInteger class to make java.math.BigInteger available with RingElem respectively the GcdRingElem interface.
final class	BigRational	Immutable arbitrary-precision rational numbers.

Uses of Rational in edu.jas.poly

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

Modifier and Type	Class	Description
(package private) class	CompRatToDec<C extends RingElem<C> & Rational>	Conversion of Complex Rational to Complex BigDecimal.
(package private) class	RatToDec<C extends Element<C> & Rational>	Conversion of Rational to BigDecimal.

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

Modifier and Type	Method	Description
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> & Rational> GenPolynomial<BigDecimal>	PolyUtil.decimalFromRational(GenPolynomialRing<BigDecimal> fac, GenPolynomial<C> A)	Convert to decimal coefficients.

Uses of Rational in edu.jas.root

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

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.
class	Boundary<C extends RingElem<C> & Rational>	Boundary determined by a rectangle and a polynomial.
(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.
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	DecimalRoots<C extends GcdRingElem<C> & Rational>	Container for the real and complex algebraic roots of a univariate polynomial.
class	Interval<C extends RingElem<C> & Rational>	Interval.
(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.
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	RealRootTuple<C extends GcdRingElem<C> & Rational>	RealAlgebraicNumber root tuple.
class	Rectangle<C extends RingElem<C> & Rational>	Rectangle.

Classes in edu.jas.root that implement Rational

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

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

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> List<ComplexAlgebraicNumber<C>>	RootFactory.complexAlgebraicNumbers(GenPolynomial<C> f)	Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> List<ComplexAlgebraicNumber<C>>	RootFactory.complexAlgebraicNumbers(GenPolynomial<C> f, BigRational eps)	Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> List<ComplexAlgebraicNumber<C>>	RootFactory.complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)	Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> 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> List<Complex<BigDecimal>>	RootFactory.filterOutRealRoots(GenPolynomial<C> f, List<Complex<BigDecimal>> c, List<BigDecimal> r, BigRational eps)	Filter real roots from complex roots.
static <C extends GcdRingElem<C> & Rational> List<ComplexAlgebraicNumber<C>>	RootFactory.filterOutRealRoots(GenPolynomial<C> f, List<ComplexAlgebraicNumber<C>> c, 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 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 GcdRingElem<C> & Rational> List<RealAlgebraicNumber<C>>	RootFactory.realAlgebraicNumbers(GenPolynomial<C> f)	Real algebraic numbers.
static <C extends GcdRingElem<C> & Rational> List<RealAlgebraicNumber<C>>	RootFactory.realAlgebraicNumbers(GenPolynomial<C> f, BigRational eps)	Real algebraic numbers.
static <C extends GcdRingElem<C> & Rational> List<RealAlgebraicNumber<C>>	RootFactory.realAlgebraicNumbersField(GenPolynomial<C> f)	Real algebraic numbers from a field.
static <C extends GcdRingElem<C> & Rational> List<RealAlgebraicNumber<C>>	RootFactory.realAlgebraicNumbersField(GenPolynomial<C> f, BigRational eps)	Real algebraic numbers from a field.
static <C extends GcdRingElem<C> & Rational> List<RealAlgebraicNumber<C>>	RootFactory.realAlgebraicNumbersIrred(GenPolynomial<C> f)	Real algebraic numbers from a irreducible polynomial.
static <C extends GcdRingElem<C> & Rational> 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 Rational in edu.jas.ufdroot

Classes in edu.jas.ufdroot with type parameters of type Rational

Modifier and Type	Class	Description
class	FactorRealAlgebraic<C extends GcdRingElem<C> & Rational>	Real algebraic number coefficients factorization algorithms.