Uses of Class
edu.jas.application.Ideal

Packages that use Ideal

Package	Description
edu.jas.application	Groebner base application package.

Uses of Ideal in edu.jas.application

Classes in edu.jas.application that implement interfaces with type arguments of type Ideal

Modifier and Type	Class	Description
class	Ideal<C extends GcdRingElem<C>>	Ideal implements some methods for ideal arithmetic, for example intersection, quotient and zero and positive dimensional ideal decomposition.

Fields in edu.jas.application declared as Ideal

Modifier and Type	Field	Description
(package private) Ideal<BigInteger>	IntegerProgram.GB
(package private) Ideal<BigInteger>	IntegerProgram.I
final Ideal<C>	IdealWithUniv.ideal	The ideal.
final Ideal<C>	LocalRing.ideal	Polynomial ideal for localization.
final Ideal<C>	ResidueRing.ideal	Polynomial ideal for the reduction.
final Ideal<C>	PrimaryComponent.primary	The primary ideal.
final Ideal<C>	Condition.zero	Data structure for condition zero.

Methods in edu.jas.application that return Ideal

Modifier and Type	Method	Description
Ideal<C>	Ideal.annihilator(Ideal<C> H)	Annihilator for ideal modulo this ideal.
Ideal<C>	Ideal.annihilator(GenPolynomial<C> h)	Annihilator for element modulo this ideal.
Ideal<C>	Ideal.copy()	Clone this.
Ideal<C>	Ideal.eliminate(GenPolynomialRing<C> R)	Eliminate.
Ideal<C>	Ideal.eliminate(String... ename)	Eliminate.
Ideal<C>	Ideal.GB()	Groebner Base.
Ideal<C>	Ideal.getONE()	Get the one ideal.
Ideal<C>	Ideal.getZERO()	Get the zero ideal.
Ideal<C>	Ideal.infiniteQuotient(Ideal<C> H)	Infinite Quotient.
Ideal<C>	Ideal.infiniteQuotient(GenPolynomial<C> h)	Infinite quotient.
Ideal<C>	Ideal.infiniteQuotientOld(GenPolynomial<C> h)	Infinite quotient.
Ideal<C>	Ideal.infiniteQuotientRab(Ideal<C> H)	Infinite Quotient.
Ideal<C>	Ideal.infiniteQuotientRab(GenPolynomial<C> h)	Infinite quotient.
Ideal<C>	Ideal.intersect(Ideal<C> B)	Intersection.
Ideal<C>	Ideal.intersect(GenPolynomialRing<C> R)	Intersection.
Ideal<C>	Ideal.intersect(List<Ideal<C>> Bl)	Intersection.
Ideal<C>	Ideal.power(int d)	Power.
Ideal<C>	Ideal.primaryIdeal(Ideal<C> P)	Zero dimensional ideal associated primary ideal.
Ideal<C>	Ideal.product(Ideal<C> B)	Product.
Ideal<C>	Ideal.product(GenPolynomial<C> b)	Product.
Ideal<C>	Ideal.quotient(Ideal<C> H)	Quotient.
Ideal<C>	Ideal.quotient(GenPolynomial<C> h)	Quotient.
Ideal<C>	Ideal.radical()	Ideal radical.
Ideal<C>	Ideal.squarefree()	Radical approximation.
Ideal<C>	Ideal.sum(Ideal<C> B)	Summation.
Ideal<C>	Ideal.sum(GenPolynomial<C> b)	Summation.
Ideal<C>	Ideal.sum(List<GenPolynomial<C>> L)	Summation.

Methods in edu.jas.application that return types with arguments of type Ideal

Modifier and Type	Method	Description
static <C extends GcdRingElem<C>> List<Ideal<C>>	IdealWithUniv.asListOfIdeals(List<IdealWithUniv<C>> Bl)	Get list of ideals from list of ideals with univariates.
static <C extends GcdRingElem<C>> Map<Ideal<C>, PolynomialList<GenPolynomial<C>>>	PolyUtilApp.productSlice(PolynomialList<Product<Residue<C>>> L)	Product slice.

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

Modifier and Type	Method	Description
Ideal<C>	Ideal.annihilator(Ideal<C> H)	Annihilator for ideal modulo this ideal.
int	Ideal.compareTo(Ideal<C> L)	Ideal list comparison.
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> 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<List<Complex<BigDecimal>>>	PolyUtilApp.complexRootTuples(Ideal<D> I, BigRational eps)	Construct superset of complex roots for zero dimensional ideal(G).
boolean	Ideal.contains(Ideal<C> B)	Ideal containment.
Ideal<C>	Ideal.infiniteQuotient(Ideal<C> H)	Infinite Quotient.
int	Ideal.infiniteQuotientExponent(GenPolynomial<C> h, Ideal<C> Q)	Infinite quotient exponent.
Ideal<C>	Ideal.infiniteQuotientRab(Ideal<C> H)	Infinite Quotient.
Ideal<C>	Ideal.intersect(Ideal<C> B)	Intersection.
boolean	Ideal.isAnnihilator(Ideal<C> H, Ideal<C> A)	Test for annihilator of ideal modulo this ideal.
boolean	Ideal.isAnnihilator(GenPolynomial<C> h, Ideal<C> A)	Test for annihilator of element modulo this ideal.
Ideal<C>	Ideal.primaryIdeal(Ideal<C> P)	Zero dimensional ideal associated primary ideal.
Ideal<C>	Ideal.product(Ideal<C> B)	Product.
Ideal<C>	Ideal.quotient(Ideal<C> H)	Quotient.
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> 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<List<BigDecimal>>	PolyUtilApp.realRootTuples(Ideal<D> I, BigRational eps)	Construct superset of real roots for zero dimensional ideal(G).
Ideal<C>	Ideal.sum(Ideal<C> B)	Summation.

Method parameters in edu.jas.application with type arguments of type Ideal

Modifier and Type	Method	Description
Ideal<C>	Ideal.intersect(List<Ideal<C>> Bl)	Intersection.
static <C extends GcdRingElem<C>> String	PolyUtilApp.productSliceToString(Map<Ideal<C>, PolynomialList<GenPolynomial<C>>> L)	Product slice to String.

Constructors in edu.jas.application with parameters of type Ideal

Modifier	Constructor	Description
	Condition(Ideal<C> z)	Condition constructor.
	Condition(Ideal<C> z, MultiplicativeSet<C> nz)	Condition constructor.
	IdealWithComplexAlgebraicRoots(Ideal<D> id, List<GenPolynomial<D>> up, List<List<Complex<RealAlgebraicNumber<D>>>> cr)	Constructor.
	IdealWithComplexRoots(Ideal<C> id, List<GenPolynomial<C>> up, List<List<Complex<BigDecimal>>> cr)	Constructor.
	IdealWithRealAlgebraicRoots(Ideal<D> id, List<GenPolynomial<D>> up, List<List<RealAlgebraicNumber<D>>> rr)	Constructor.
	IdealWithRealRoots(Ideal<C> id, List<GenPolynomial<C>> up, List<List<BigDecimal>> rr)	Constructor.
protected	IdealWithUniv(Ideal<C> id, List<GenPolynomial<C>> up)	Constructor.
protected	IdealWithUniv(Ideal<C> id, List<GenPolynomial<C>> up, List<GenPolynomial<C>> og)	Constructor.
	LocalRing(Ideal<C> i)	The constructor creates a LocalRing object from an Ideal.
protected	PrimaryComponent(Ideal<C> q, IdealWithUniv<C> p)	Constructor.
protected	PrimaryComponent(Ideal<C> q, IdealWithUniv<C> p, int e)	Constructor.
	ResidueRing(Ideal<C> i)	The constructor creates a ResidueRing object from an Ideal.
	ResidueRing(Ideal<C> i, boolean isMaximal)	The constructor creates a ResidueRing object from an Ideal.