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.