Package edu.jas.application
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.
Method rootReduce() from class RootFactoryApp
computes a primitive element of two algebraic roots.
Heinz Kredel
Last modified: Wed Aug 17 23:35:02 CEST 2016
$Id$
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Class Summary Class Description AlgebraicRootsPrimElem<C extends GcdRingElem<C> & Rational> Container for the real and complex algebraic roots of a univariate polynomial together with primitive element.CoeffConvertAlg<C extends GcdRingElem<C>> Coefficient to convert algebriac functor.CoeffRecConvertAlg<C extends GcdRingElem<C>> Coefficient recursive to convert algebriac functor.CoeffToComplexReal<C extends GcdRingElem<C> & Rational> Coefficient to complex real algebriac functor.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.EvaluateToComplexReal<C extends GcdRingElem<C> & Rational> Polynomial coefficient to complex real algebriac evaluation functor.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.IdealWithComplexRoots<C extends GcdRingElem<C>> Container for Ideals together with univariate polynomials and complex 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.IntegerProgram Solution of Integer Programming problems using Groebner bases.IntegerProgramExamples Examples for Integer Programming.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.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.RealFromReAlgCoeff<C extends GcdRingElem<C> & Rational> Coefficient to real algebriac from algebraic functor.ReAlgFromRealCoeff<C extends GcdRingElem<C> & Rational> Coefficient to real algebriac from real algebraic functor.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.ResidueSolvableWordPolynomial<C extends GcdRingElem<C>> ResidueSolvableWordPolynomial solvable polynomials with WordResidue coefficients implementing RingElem.ResidueSolvableWordPolynomialRing<C extends GcdRingElem<C>> ResidueSolvableWordPolynomialRing solvable polynomial with word residue coefficients factory.RingFactoryTokenizer RingFactory Tokenizer.RootFactoryApp 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 pairs of GenSolvablePolynomial with GcdRingElem interface.SolvableLocalResidue<C extends GcdRingElem<C>> SolvableLocalResidue, that is a (left) rational function, based on pairs of GenSolvablePolynomial with GcdRingElem interface.SolvableLocalResidueRing<C extends GcdRingElem<C>> SolvableLocalResidue ring factory for SolvableLocalResidue based on GenSolvablePolynomial with GcdRingElem interface.SolvableLocalRing<C extends GcdRingElem<C>> SolvableLocal ring factory for SolvableLocal with GcdRingElem interface.SolvableResidue<C extends GcdRingElem<C>> SolvableResidue ring element based on GenSolvablePolynomial with GcdRingElem interface.SolvableResidueRing<C extends GcdRingElem<C>> SolvableResidue ring factory based on GenSolvablePolynomialRing with GcdRingFactory interface.WordIdeal<C extends GcdRingElem<C>> Word Ideal implements some methods for ideal arithmetic, for example containment, sum or product.WordResidue<C extends GcdRingElem<C>> WordResidue ring element based on GenWordPolynomial with GcdRingElem interface.WordResidueRing<C extends GcdRingElem<C>> WordResidue ring factory based on GenWordPolynomialRing with GcdRingFactory interface. -
Enum Summary Enum Description Condition.Color Colors.RingFactoryTokenizer.coeffType RingFactoryTokenizer.polyType SolvableIdeal.Side Side variant of ideal.