Package edu.jas.application

Groebner base application package.

See: Description

Class Summary

Class	Description
ColoredSystem<C extends GcdRingElem<C>>	Container for a condition, a corresponding colored polynomial list and a Groebner base pair list.
ColorPolynomial<C extends RingElem<C>>	Colored Polynomials with green, red and white coefficients.
ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>	Comprehensive Groebner Base sequential algorithm.
Condition<C extends GcdRingElem<C>>	Condition.
CPair<C extends RingElem<C>>	Serializable subclass to hold pairs of colored polynomials.
CReductionSeq<C extends GcdRingElem<C>>	Polynomial parametric ring reduction sequential use algorithm.
Dimension	Container for dimension parameters.
Examples	Examples for application usage.
ExamplesGeoTheorems	ExamplesGeoTheorems for Groebner base usage.
ExtensionFieldBuilder	Builder for extension field towers.
FactorAlgebraicPrim<C extends GcdRingElem<C>>	Algebraic number coefficients factorization algorithms.
FactorFactory	Factorization algorithms factory.
FactorRealReal<C extends GcdRingElem<C> & Rational>	Real algebraic number coefficients factorization algorithms.
GBAlgorithmBuilder<C extends GcdRingElem<C>>	Builder for commutative Gröbner bases algorithm implementations.
GroebnerSystem<C extends GcdRingElem<C>>	Container for a Groebner system.
Ideal<C extends GcdRingElem<C>>	Ideal implements some methods for ideal arithmetic, for example intersection, quotient and zero and positive dimensional ideal decomposition.
IdealWithComplexAlgebraicRoots<D extends GcdRingElem<D> & Rational>	Container for Ideals together with univariate polynomials and complex algebraic roots.
IdealWithRealAlgebraicRoots<D extends GcdRingElem<D> & Rational>	Container for Ideals together with univariate polynomials and real algebraic roots.
IdealWithRealRoots<C extends GcdRingElem<C>>	Container for Ideals together with univariate polynomials and real roots.
IdealWithUniv<C extends GcdRingElem<C>>	Container for Ideals together with univariate polynomials.
Local<C extends GcdRingElem<C>>	Local ring element based on GenPolynomial with RingElem interface.
LocalRing<C extends GcdRingElem<C>>	Local ring class based on GenPolynomial with RingElem interface.
LocalSolvablePolynomial<C extends GcdRingElem<C>>	LocalSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
LocalSolvablePolynomialRing<C extends GcdRingElem<C>>	LocalSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
OrderedCPairlist<C extends GcdRingElem<C>>	Pair list management.
PolyUtilApp<C extends RingElem<C>>	Polynomial utilities for applications, for example conversion ExpVector to Product or zero dimensional ideal root computation.
PrimaryComponent<C extends GcdRingElem<C>>	Container for primary components of ideals.
PrimitiveElement<C extends GcdRingElem<C>>	Container for primitive elements.
QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>	QLRSolvablePolynomial generic recursive solvable polynomials implementing RingElem.
QLRSolvablePolynomialRing<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>,D extends GcdRingElem<D>>	QLRSolvablePolynomialRing generic recursive solvable polynomial factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>	Complex algebraic number class based on bi-variate real algebraic numbers.
RealAlgebraicRing<C extends GcdRingElem<C> & Rational>	Real algebraic number factory class based on bi-variate real algebraic numbers.
Residue<C extends GcdRingElem<C>>	Residue ring element based on GenPolynomial with RingElem interface.
ResidueRing<C extends GcdRingElem<C>>	Residue ring factory based on GenPolynomial with RingFactory interface.
ResidueSolvablePolynomial<C extends GcdRingElem<C>>	ResidueSolvablePolynomial generic solvable polynomials with solvable residue coefficients implementing RingElem.
ResidueSolvablePolynomialRing<C extends GcdRingElem<C>>	ResidueSolvablePolynomialRing generic solvable polynomial with residue coefficients factory implementing RingFactory and extending GenSolvablePolynomialRing factory.
RingFactoryTokenizer	RingFactory Tokenizer.
RootFactory	Roots factory.
RunGB	Simple setup to run a GB example.
RunSGB	Simple setup to run a solvable GB example.
SolvableIdeal<C extends GcdRingElem<C>>	Solvable Ideal implements some methods for ideal arithmetic, for example sum, intersection, quotient.
SolvableLocal<C extends GcdRingElem<C>>	SolvableLocal ring element based on GenSolvablePolynomial with GcdRingElem interface.
SolvableLocalResidue<C extends GcdRingElem<C>>	SolvableLocalResidue, that is a (left) rational function, based on SolvableResidue and GenSolvablePolynomial with RingElem interface.
SolvableLocalResidueRing<C extends GcdRingElem<C>>	SolvableLocalResidue ring factory based on SolvableResidue and GenSolvablePolynomial with RingElem interface.
SolvableLocalRing<C extends GcdRingElem<C>>	SolvableLocal ring class based on GenSolvablePolynomial with RingElem interface.
SolvableResidue<C extends GcdRingElem<C>>	SolvableResidue ring element based on GenSolvablePolynomial with RingElem interface.
SolvableResidueRing<C extends GcdRingElem<C>>	SolvableResidue ring factory based on GenSolvablePolynomial with RingFactory interface.

Enum Summary

Enum	Description
Condition.Color	Colors.

Package edu.jas.application Description

Groebner base application package.

This package contains classes with applications of Groebner bases such as ideal intersections, ideal quotients or ideal dimension are implemented in Ideal and SolvableIdeal. Class Residue provides polynomials residues modulo an ideal defined in ResidueRing. Comprehensive Groebner bases for polynomial rings over parameter rings are implemented in ComprehensiveGroebnerBaseSeq.

Heinz Kredel

Last modified: Fri Dec 24 15:00:18 CET 2010

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