Uses of Class
cc.redberry.rings.poly.multivar.AMultivariatePolynomial

Packages that use AMultivariatePolynomial

Package	Description
cc.redberry.rings
cc.redberry.rings.io
cc.redberry.rings.poly
cc.redberry.rings.poly.multivar
cc.redberry.rings.poly.univar

Uses of AMultivariatePolynomial in cc.redberry.rings

Methods in cc.redberry.rings with type parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	Rings.MultipleFieldExtension(sPoly... minimalPolynomials) Multiple field extension generated by given algebraic elements represented by their minimal polynomials (not tested that they are irreducible)
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> MultivariateRing<Poly>	Rings.MultivariateRing(Poly factory) Ring of multivariate polynomials with specified factory
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> QuotientRing<Term,Poly>	Rings.QuotientRing(MultivariateRing<Poly> baseRing, Ideal<Term,Poly> ideal) Quotient ring baseRing/<ideal>
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	Rings.SplittingField(sPoly polynomial) Splitting field of a given polynomial.

Uses of AMultivariatePolynomial in cc.redberry.rings.io

Classes in cc.redberry.rings.io with type parameters of type AMultivariatePolynomial

Modifier and Type	Class and Description
class	Coder<Element,Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> High-level parser and stringifier of ring elements.

Methods in cc.redberry.rings.io with type parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
static <Element,Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Coder<Element,Term,Poly>	Coder.mkCoder(Ring<Element> baseRing, Map<String,Element> eVariables, MultivariateRing<Poly> polyRing, Map<String,Poly> pVariables, SerializableFunction<Poly,Element> polyToElement)
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> Coder<mPoly,?,?>	Coder.mkMultipleExtensionCoder(MultipleFieldExtension<Term,mPoly,sPoly> field, Map<String,mPoly> variables) Create coder for multiple field extension
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> Coder<mPoly,?,?>	Coder.mkMultipleExtensionCoder(MultipleFieldExtension<Term,mPoly,sPoly> field, String... variables) Create coder for multiple field extension
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Coder<Poly,Term,Poly>	Coder.mkMultivariateCoder(MultivariateRing<Poly> ring, Map<String,Poly> variables) Create coder for multivariate polynomial rings
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Coder<Poly,Term,Poly>	Coder.mkMultivariateCoder(MultivariateRing<Poly> ring, String... variables) Create coder for multivariate polynomial rings

Uses of AMultivariatePolynomial in cc.redberry.rings.poly

Classes in cc.redberry.rings.poly with type parameters of type AMultivariatePolynomial

Modifier and Type	Class and Description
class	MultipleFieldExtension<Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> Multiple field extension F(α_1, α_2, ..., α_N).
class	MultivariateRing<Poly extends AMultivariatePolynomial<?,Poly>> Ring of multivariate polynomials.
class	QuotientRing<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Multivariate quotient ring

Methods in cc.redberry.rings.poly with type parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
<Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>> MultipleFieldExtension<Term,mPoly,E>	SimpleFieldExtension.asMultipleExtension() Returns a view of this as a multiple field extension
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	MultipleFieldExtension.mkMultipleExtension(SimpleFieldExtension<sPoly> ext)
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	MultipleFieldExtension.mkMultipleExtension(sPoly... minimalPolynomials) Creates multiple field extension F(α_1, α_2, ..., α_i) where α_i are specified by their minimal polynomials over F.
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	MultipleFieldExtension.mkMultipleExtension(sPoly a)
static <Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>> MultipleFieldExtension<Term,mPoly,sPoly>	MultipleFieldExtension.mkSplittingField(sPoly poly) Constructs splitting field for a given polynomial.
<MPoly extends AMultivariatePolynomial> MPoly	SimpleFieldExtension.normOfPolynomial(MultivariatePolynomial<E> poly) Gives the norm of multivariate polynomial over this field extension, which is always a polynomial with the coefficients from the base field.

Methods in cc.redberry.rings.poly that return AMultivariatePolynomial

Modifier and Type	Method and Description
Poly[]	QuotientRing.divideAndRemainder(Poly dividend, Poly divider)
Poly[]	MultivariateRing.divideAndRemainder(Poly dividend, Poly divider)
mPoly[]	MultipleFieldExtension.extendedGCD(mPoly a, mPoly b)

Methods in cc.redberry.rings.poly with parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
mPoly	MultipleFieldExtension.gcd(mPoly... elements)
Poly	MultivariateRing.gcd(Poly[] elements)

Uses of AMultivariatePolynomial in cc.redberry.rings.poly.multivar

Classes in cc.redberry.rings.poly.multivar with type parameters of type AMultivariatePolynomial

Modifier and Type	Class and Description
class	AMultivariatePolynomial<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Parent class for multivariate polynomials.
static class	AMultivariatePolynomial.PolynomialCollector<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Collector which collects stream of element to a UnivariatePolynomial
class	Ideal<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal represented by its Groebner basis.
class	PairedIterator<Term1 extends AMonomial<Term1>,Poly1 extends AMultivariatePolynomial<Term1,Poly1>,Term2 extends AMonomial<Term2>,Poly2 extends AMultivariatePolynomial<Term2,Poly2>> Iterator over a pair of polynomials
class	PairedIterator<Term1 extends AMonomial<Term1>,Poly1 extends AMultivariatePolynomial<Term1,Poly1>,Term2 extends AMonomial<Term2>,Poly2 extends AMultivariatePolynomial<Term2,Poly2>> Iterator over a pair of polynomials

Subclasses of AMultivariatePolynomial in cc.redberry.rings.poly.multivar

Modifier and Type	Class and Description
class	MultivariatePolynomial<E>
class	MultivariatePolynomialZp64 Multivariate polynomial over Zp ring with the modulus in the range (0, 2^62) (see MachineArithmetic.MAX_SUPPORTED_MODULUS).

Methods in cc.redberry.rings.poly.multivar with type parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
static <Poly extends AMultivariatePolynomial> boolean	GroebnerMethods.algebraicallyDependentQ(List<Poly> sys) Returns true if a given set of polynomials is algebraically dependent or false otherwise.
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.algebraicRelations(List<Poly> polys) Gives a list of algebraic relations (annihilating polynomials) for the given list of polynomials
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	AMultivariatePolynomial.asMultivariate(IUnivariatePolynomial poly, int nVariables, int variable, Comparator<DegreeVector> ordering) Converts univariate polynomial to multivariate.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	AMultivariatePolynomial.asMultivariate(UnivariatePolynomial<Poly> uPoly, int variable) Convert univariate polynomial over multivariate polynomials to a normal multivariate poly
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	AMultivariatePolynomial.asMultivariate(UnivariatePolynomial<Poly> univariate, int uVariable, boolean join)
static <Poly extends AMultivariatePolynomial<?,Poly>> UnivariateRing<UnivariatePolynomial<Poly>>	MultivariateConversions.asUnivariate(IPolynomialRing<Poly> ring, int variable) Given poly in R[x1,x2,...,xN] converts to poly in R[other_variables][variable]
static <Poly extends AMultivariatePolynomial<?,Poly>> UnivariatePolynomial<Poly>	MultivariateConversions.asUnivariate(Poly poly, int variable) Given poly in R[x1,x2,...,xN] converts to poly in R[other_variables][variable]
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>,uPoly extends IUnivariatePolynomial<uPoly>> void	HenselLifting.bivariateLiftNoLCCorrection0(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation, int degreeBound) Fast bivariate Hensel lifting which uses dense representation for bivariate polynomials
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.BuchbergerGB(List<Poly> generators, Comparator<DegreeVector> monomialOrder) Computes minimized and reduced Groebner basis of a given ideal via Buchberger algorithm.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.BuchbergerGB(List<Poly> generators, Comparator<DegreeVector> monomialOrder, Comparator<GroebnerBases.SyzygyPair> strategy) Computes minimized and reduced Groebner basis of a given ideal via Buchberger algorithm.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateResultants.ClassicalResultant(Poly a, Poly b, int variable) Computes resultant via subresultant sequences
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.ConvertBasis(List<Poly> generators, Comparator<DegreeVector> desiredOrder) Converts basis into a basis for desired monomial order
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.create(List<Poly> generators) Creates ideal given by a list of generators.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.create(List<Poly> generators, Comparator<DegreeVector> monomialOrder) Creates ideal given by a list of generators.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.create(Poly... generators) Creates ideal given by a list of generators.
static <Poly extends AMultivariatePolynomial> Poly	MultivariateResultants.Discriminant(Poly a, int variable) Computes discriminant of polynomial
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	MultivariateDivision.divideAndRemainder(Poly dividend, Poly... dividers) Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	MultivariateDivision.divideAndRemainder(Poly dividend, Poly divider) Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.divideExact(Poly dividend, Poly divider) Divides dividend by divider or throws exception if exact division is not possible
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.divideOrNull(Poly dividend, Poly divider) Divides dividend by divider or returns null if exact division is not possible
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	MultivariateDivision.dividesQ(Poly dividend, Poly divider) Tests whether divisor is a divisor of poly
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateGCD.EEZGCD(Poly a, Poly b) Calculates GCD of two multivariate polynomials over Zp using enhanced EZ algorithm
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.eliminate(List<Poly> ideal, int... variables) Eliminates specified variables from the given ideal.
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.eliminate(List<Poly> ideal, int variable) Eliminates specified variables from the given ideal.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.empty(Poly factory) Creates empty ideal
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.empty(Poly factory, Comparator<DegreeVector> monomialOrder) Creates empty ideal
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.F4GB(List<Poly> generators, Comparator<DegreeVector> monomialOrder) Computes minimized and reduced Groebner basis of a given ideal via Faugère's F4 F4 algorithm.
static <Poly extends AMultivariatePolynomial<?,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateFactorization.Factor(Poly poly) Factors multivariate polynomial
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateFactorization.FactorInGF(Poly polynomial) Factors multivariate polynomial over finite field
static <Poly extends AMultivariatePolynomial<?,Poly>> IPolynomialRing<Poly>	MultivariateConversions.fromUnivariate(IPolynomialRing<UnivariatePolynomial<Poly>> ring, int variable) Given poly in R[variables][other_variables] converts it to poly in R[x1,x2,...,xN]
static <Poly extends AMultivariatePolynomial<?,Poly>> Poly	MultivariateConversions.fromUnivariate(UnivariatePolynomial<Poly> poly, int variable) Given poly in R[variables][other_variables] converts it to poly in R[x1,x2,...,xN]
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.GroebnerBasis(List<Poly> generators, Comparator<DegreeVector> monomialOrder) Computes Groebner basis (minimized and reduced) of a given ideal represented by a list of generators.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.GroebnerBasisInGF(List<Poly> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries) Computes Groebner basis (minimized and reduced) of a given ideal over finite filed represented by a list of generators.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.GroebnerBasisRegardingGrevLexWithPermutation(List<Poly> ideal, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm<Term,Poly> baseAlgorithm, MonomialOrder.GrevLexWithPermutation order) computes Groebner basis in GREVLEX with shuffled variables
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.GroebnerBasisWithOptimizedGradedOrder(List<Poly> ideal) computes Groebner basis in GREVLEX with shuffled variables
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.GroebnerBasisWithOptimizedGradedOrder(List<Poly> ideal, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm<Term,Poly> baseAlgorithm) computes Groebner basis in GREVLEX with shuffled variables
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.HilbertConvertBasis(List<Poly> groebnerBasis, Comparator<DegreeVector> desiredOrdering) Converts Groebner basis to a given monomial order using Hilbert-driven algorithm
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.HilbertGB(List<Poly> generators, Comparator<DegreeVector> monomialOrder) Hilbert-driven algorithm for Groebner basis computation
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.HilbertGB(List<Poly> generators, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm<Term,Poly> baseAlgorithm) Hilbert-driven algorithm for Groebner basis computation.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Term,Poly>	GroebnerBases.HilbertGB(List<Poly> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries) Hilbert-driven algorithm for Groebner basis computation
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	GroebnerBases.isGroebnerBasis(List<Poly> ideal, List<Poly> generators, Comparator<DegreeVector> monomialOrder) Check whether specified generators form Groebner basis of given ideal
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	MultivariateSquareFreeFactorization.isSquareFree(Poly poly) Tests whether the given poly is square free.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[][]	GroebnerMethods.JacobianMatrix(List<Poly> sys) Creates a Jacobian matrix of a given list of polynomials
static <Poly extends AMultivariatePolynomial> List<Rational<Poly>>	GroebnerMethods.LeinartasDecomposition(Rational<Poly> fraction) Computes Leinartas's decomposition of given rational expression (see https://arxiv.org/abs/1206.4740)
static <Poly extends AMultivariatePolynomial<?,Poly>> MultivariateRing<Poly>	MultivariateConversions.merge(IPolynomialRing<MultivariatePolynomial<Poly>> ring, int... variables) Given poly in R[x1,x2,...,xN] converts to poly in R[variables][other_variables]
static <Poly extends AMultivariatePolynomial<?,Poly>> Poly	MultivariateConversions.merge(MultivariatePolynomial<Poly> poly, int... variables) Given poly in R[variables][other_variables] converts it to poly in R[x1,x2,...,xN]
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	GroebnerBases.minimizeGroebnerBases(List<Poly> basis) Minimizes Groebner basis.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	HenselLifting.multivariateLiftAutomaticLC(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation) Multivariate lift with automatic leading coefficient correction
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	HenselLifting.multivariateLiftAutomaticLC(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation, int from) Multivariate lift with automatic leading coefficient correction
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> boolean	MultivariateDivision.nontrivialQuotientQ(Poly dividend, Poly divider) Tests whether there is nontrivial quotient dividend / divider
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.NullstellensatzCertificate(List<Poly> polynomials) Computes Nullstellensatz certificate for a given list of polynomials assuming that they have no common zeros (or equivalently assuming that the ideal formed by the list is trivial).
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.NullstellensatzCertificate(List<Poly> polynomials, boolean boundTotalDeg) Computes Nullstellensatz certificate for a given list of polynomials assuming that they have no common zeros (or equivalently assuming that the ideal formed by the list is trivial).
static <Poly extends AMultivariatePolynomial> List<Poly>	GroebnerMethods.NullstellensatzSolver(List<Poly> polynomials, Poly rhs, boolean boundTotalDeg) Tries to find solution of the equation {@code S_1 * f_1 + ...
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Comparator<DegreeVector>	GroebnerBases.optimalOrder(List<Poly> ideal) Deduce the optimal order for GB algorithms
static <Poly extends AMultivariatePolynomial> Poly	MultivariateGCD.PolynomialGCD(Iterable<Poly> arr) Calculates greatest common divisor of the array of polynomials
static <Poly extends AMultivariatePolynomial> Poly	MultivariateGCD.PolynomialGCD(Poly... arr) Calculates greatest common divisor of the array of polynomials
static <Poly extends AMultivariatePolynomial> Poly	MultivariateGCD.PolynomialGCD(Poly a, Poly b) Calculates greatest common divisor of two multivariate polynomials
static <Poly extends AMultivariatePolynomial> Poly	MultivariateGCD.PolynomialGCDinGF(Poly a, Poly b) Calculates greatest common divisor of two multivariate polynomials over finite fields
static <Poly extends AMultivariatePolynomial> boolean	GroebnerMethods.probablyAlgebraicallyDependentQ(List<Poly> sys) Returns true if a given set of polynomials is probably algebraically dependent or false otherwise (which means that the given set is certainly independent).
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.pseudoRemainder(Poly dividend, Collection<Poly> dividers) Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.pseudoRemainder(Poly dividend, Poly... dividers) Performs multivariate pseudo division with remainder and returns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.pseudoRemainder(Poly dividend, Poly divider) Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	RandomMultivariatePolynomials.randomPolynomial(Poly factory, int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd) Generates random multivariate polynomial
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.remainder(Poly dividend, Collection<Poly> dividers) Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.remainder(Poly dividend, Poly... dividers) Performs multivariate division with remainder and returns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.remainder(Poly dividend, Poly divider) Performs multivariate division with remainder and rerurns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	GroebnerBases.removeRedundant(List<Poly> basis) Computes reduced Groebner basis
static <T extends AMonomial<T>,P extends AMultivariatePolynomial<T,P>> P	AMultivariatePolynomial.renameVariables(P poly, int[] newVariables) Rename variables from [0,1,...N] to [newVariables[0], newVariables[1], ..., newVariables[N]] (new instance created)
static <T extends AMonomial<T>,P extends AMultivariatePolynomial<T,P>> P	AMultivariatePolynomial.renameVariables(P poly, int[] newVariables, Comparator<DegreeVector> newOrdering) Rename variables from [0,1,...N] to [newVariables[0], newVariables[1], ..., newVariables[N]] (new instance created)
static <Poly extends AMultivariatePolynomial> Poly	MultivariateResultants.Resultant(Poly a, Poly b, int variable) Calculates polynomial resultant of two given polynomials with respect to specified variable
static <Poly extends AMultivariatePolynomial> Poly	MultivariateResultants.ResultantInGF(Poly a, Poly b, int variable) Computes polynomial resultant of two polynomials over finite field
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateResultants.ResultantInSmallCharacteristic(Poly a, Poly b, int variable) Resultant in small characteristic
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>,uPoly extends IUnivariatePolynomial<uPoly>> UnivariatePolynomial<uPoly>	HenselLifting.seriesExpansionDense(Ring<uPoly> ring, Poly poly, int variable, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluate) Generates a power series expansion for poly about the point specified by variable and evaluation
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> List<Poly>	GroebnerBases.solveGB(List<Poly> generators, List<Collection<DegreeVector>> gbSkeleton, Comparator<DegreeVector> monomialOrder) Sparse Groebner basis via "linear lifting".
static <Poly extends AMultivariatePolynomial<?,Poly>> MultivariateRing<MultivariatePolynomial<Poly>>	MultivariateConversions.split(IPolynomialRing<Poly> ring, int... variables) Given poly in R[x1,x2,...,xN] converts to poly in R[variables][other_variables]
static <Poly extends AMultivariatePolynomial<?,Poly>> MultivariatePolynomial<Poly>	MultivariateConversions.split(Poly poly, int... variables) Given poly in R[x1,x2,...,xN] converts to poly in R[variables][other_variables]
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateSquareFreeFactorization.SquareFreeFactorization(Poly poly) Performs square-free factorization of a {@code poly.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateSquareFreeFactorization.SquareFreeFactorizationMusser(Poly poly) Performs square-free factorization of a poly which coefficient ring has any characteristic using Musser's algorithm.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateSquareFreeFactorization.SquareFreeFactorizationMusserZeroCharacteristics(Poly poly) Performs square-free factorization of a poly which coefficient ring has zero characteristic using Musser's algorithm.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> PolynomialFactorDecomposition<Poly>	MultivariateSquareFreeFactorization.SquareFreeFactorizationYunZeroCharacteristics(Poly poly) Performs square-free factorization of a poly which coefficient ring has zero characteristic using Yun's algorithm.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateSquareFreeFactorization.SquareFreePart(Poly poly) Returns square-free part of the poly
static <T extends AMonomial<T>,P extends AMultivariatePolynomial<T,P>> P	AMultivariatePolynomial.swapVariables(P poly, int i, int j) Renames variable i to j and j to i (new instance created)
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	GroebnerBases.syzygy(GroebnerBases.SyzygyPair<Term,Poly> sPair) Computes syzygy of given polynomials
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	GroebnerBases.syzygy(Poly a, Poly b) Computes syzygy of given polynomials
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.trivial(Poly factory) Creates trivial ideal (ideal = ring)
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.trivial(Poly factory, Comparator<DegreeVector> monomialOrder) Creates trivial ideal (ideal = ring)

Methods in cc.redberry.rings.poly.multivar that return AMultivariatePolynomial

Modifier and Type	Method and Description
Poly[]	AMultivariatePolynomial.derivative() Gives the derivative vector
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	MultivariateDivision.divideAndRemainder(Poly dividend, Poly... dividers) Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	MultivariateDivision.divideAndRemainder(Poly dividend, Poly divider) Performs multivariate division with remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[][]	GroebnerMethods.JacobianMatrix(List<Poly> sys) Creates a Jacobian matrix of a given list of polynomials
AMultivariatePolynomial	MultivariatePolynomialZp64.toSparseRecursiveForm() Gives a recursive sparse univariate representation of this poly.
AMultivariatePolynomial	MultivariatePolynomial.toSparseRecursiveForm() Gives a recursive sparse univariate representation of this poly.

Methods in cc.redberry.rings.poly.multivar with parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>,uPoly extends IUnivariatePolynomial<uPoly>> void	HenselLifting.bivariateLiftNoLCCorrection0(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation, int degreeBound) Fast bivariate Hensel lifting which uses dense representation for bivariate polynomials
Poly	AMultivariatePolynomial.composition(int[] variables, Poly[] values) Substitutes given polynomial instead of specified variable (that is this(x_1, ..., value, ..., x_N), where value is on the place of specified variable)
Poly	AMultivariatePolynomial.composition(Poly... values) Substitutes given polynomials instead of variables of this (that is this(values_1, ..., values_N))
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Ideal<Term,Poly>	Ideal.create(Poly... generators) Creates ideal given by a list of generators.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly[]	MultivariateDivision.divideAndRemainder(Poly dividend, Poly... dividers) Performs multivariate division with remainder.
static <E> E	MultivariatePolynomial.evaluateSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, E[] values) Evaluates polynomial given in a sparse recursive form at a given points
static long	MultivariatePolynomialZp64.evaluateSparseRecursiveForm(AMultivariatePolynomial recForm, long[] values) Evaluates polynomial given in a sparse recursive form at a given points
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.fromSparseRecursiveForm(AMultivariatePolynomial recForm, Comparator<DegreeVector> ordering) Converts poly from a sparse recursive univariate representation.
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.fromSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering) Converts poly from a recursive univariate representation.
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.fromSparseRecursiveForm(AMultivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering) Converts poly from a recursive univariate representation.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	HenselLifting.multivariateLiftAutomaticLC(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation) Multivariate lift with automatic leading coefficient correction
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> void	HenselLifting.multivariateLiftAutomaticLC(Poly base, Poly[] factors, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluation, int from) Multivariate lift with automatic leading coefficient correction
static <Poly extends AMultivariatePolynomial> Poly	MultivariateGCD.PolynomialGCD(Poly... arr) Calculates greatest common divisor of the array of polynomials
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.pseudoRemainder(Poly dividend, Poly... dividers) Performs multivariate pseudo division with remainder and returns the remainder.
static <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Poly	MultivariateDivision.remainder(Poly dividend, Poly... dividers) Performs multivariate division with remainder and returns the remainder.
boolean	AMultivariatePolynomial.sameSkeletonExceptQ(AMultivariatePolynomial oth, int... variables) Tests whether this and oth have the same skeleton with respect all except specified variables
boolean	AMultivariatePolynomial.sameSkeletonQ(AMultivariatePolynomial oth) Tests whether this and oth have the same skeleton
boolean	AMultivariatePolynomial.sameSkeletonQ(AMultivariatePolynomial oth, int... variables) Tests whether this and oth have the same skeleton with respect to specified variables

Method parameters in cc.redberry.rings.poly.multivar with type arguments of type AMultivariatePolynomial

Modifier and Type	Method and Description
static GroebnerBases.HilbertSeries	GroebnerBases.HilbertSeriesOfLeadingTermsSet(List<? extends AMultivariatePolynomial> ideal) Computes Hilbert-Poincare series of specified ideal given by its Groebner basis
static boolean	GroebnerBases.isHomogeneousIdeal(List<? extends AMultivariatePolynomial> ideal) Check whether ideal is homogeneous
static boolean	GroebnerBases.isMonomialIdeal(List<? extends AMultivariatePolynomial> ideal) Check whether all specified generators are monomials
static List<DegreeVector>	GroebnerBases.leadTermsSet(List<? extends AMultivariatePolynomial> ideal) List of lead terms of generators

Uses of AMultivariatePolynomial in cc.redberry.rings.poly.univar

Methods in cc.redberry.rings.poly.univar that return AMultivariatePolynomial

Modifier and Type	Method and Description
default AMultivariatePolynomial	IUnivariatePolynomial.asMultivariate() Convert to multivariate polynomial
AMultivariatePolynomial	UnivariatePolynomialZ64.asMultivariate(Comparator<DegreeVector> ordering)
AMultivariatePolynomial	IUnivariatePolynomial.asMultivariate(Comparator<DegreeVector> ordering) Convert to multivariate polynomial
AMultivariatePolynomial	UnivariatePolynomialZ64.composition(AMultivariatePolynomial value)
AMultivariatePolynomial	IUnivariatePolynomial.composition(AMultivariatePolynomial value) Calculates the composition of this(oth)

Methods in cc.redberry.rings.poly.univar with parameters of type AMultivariatePolynomial

Modifier and Type	Method and Description
MultivariatePolynomialZp64	UnivariatePolynomialZp64.composition(AMultivariatePolynomial value)
AMultivariatePolynomial	UnivariatePolynomialZ64.composition(AMultivariatePolynomial value)
MultivariatePolynomial<E>	UnivariatePolynomial.composition(AMultivariatePolynomial value)
AMultivariatePolynomial	IUnivariatePolynomial.composition(AMultivariatePolynomial value) Calculates the composition of this(oth)