Uses of Interface
cc.redberry.rings.poly.univar.IUnivariatePolynomial

Packages that use IUnivariatePolynomial

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 IUnivariatePolynomial in cc.redberry.rings

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

Modifier and Type	Method and Description
static <Poly extends IUnivariatePolynomial<Poly>> AlgebraicNumberField<Poly>	Rings.AlgebraicNumberField(Poly minimalPoly) Algebraic number field generated by the specified minimal polynomial
static <Poly extends IUnivariatePolynomial<Poly>> FiniteField<Poly>	Rings.GF(Poly irreducible) Galois field with the specified minimal polynomial.
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 <Poly extends IUnivariatePolynomial<Poly>> Poly[]	RationalReconstruction.reconstruct(Poly n, Poly modulus, int numeratorBound, int denominatorBound) Performs a rational number reconstruction.
static <uPoly extends IUnivariatePolynomial<uPoly>> SimpleFieldExtension<uPoly>	Rings.SimpleFieldExtension(uPoly minimalPolynomial) Returns a simple field extension generated by given minimal polynomial
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.
static <uPoly extends IUnivariatePolynomial<uPoly>> SimpleFieldExtension<uPoly>	Rings.UnivariateQuotientRing(uPoly modulus) Deprecated. Use either Rings.GF(IUnivariatePolynomial) or Rings.AlgebraicNumberField(IUnivariatePolynomial)
static <Poly extends IUnivariatePolynomial<Poly>> UnivariateRing<Poly>	Rings.UnivariateRing(Poly factory) Ring of univariate polynomials with specified factory

Methods in cc.redberry.rings that return IUnivariatePolynomial

Modifier and Type	Method and Description
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	RationalReconstruction.reconstruct(Poly n, Poly modulus, int numeratorBound, int denominatorBound) Performs a rational number reconstruction.

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

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)

Uses of IUnivariatePolynomial in cc.redberry.rings.io

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

Modifier and Type	Method and Description
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 <Poly extends IUnivariatePolynomial<Poly>> Coder<Poly,?,?>	Coder.mkUnivariateCoder(IPolynomialRing<Poly> ring, Map<String,Poly> variables) Create coder for univariate polynomial rings
static <Poly extends IUnivariatePolynomial<Poly>> Coder<Poly,?,?>	Coder.mkUnivariateCoder(IPolynomialRing<Poly> ring, String variable) Create coder for univariate polynomial rings

Uses of IUnivariatePolynomial in cc.redberry.rings.poly

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

Modifier and Type	Class and Description
class	AlgebraicNumberField<E extends IUnivariatePolynomial<E>> Algebraic number field F(α) represented as a simple field extension, for details see SimpleFieldExtension.
class	FiniteField<E extends IUnivariatePolynomial<E>> Galois field GF(p, q).
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	SimpleFieldExtension<E extends IUnivariatePolynomial<E>> A simple field extension F(α) represented as a univariate quotient ring F[x]/<m(x)> where m(x) is the minimal polynomial of α.
class	UnivariateRing<Poly extends IUnivariatePolynomial<Poly>> Ring of univariate polynomials.

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

Modifier and Type	Method and Description
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.
static <T extends IUnivariatePolynomial<T>> T[]	PolynomialMethods.PolynomialExtendedGCD(T a, T b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).

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

Modifier and Type	Method and Description
E[]	SimpleFieldExtension.createArray(int length)
E[][]	SimpleFieldExtension.createArray2d(int length)
E[][]	SimpleFieldExtension.createArray2d(int m, int n)
E[]	FiniteField.divideAndRemainder(E a, E b)
E[]	AlgebraicNumberField.divideAndRemainder(E a, E b)
Poly[]	UnivariateRing.divideAndRemainder(Poly a, Poly b)
Poly[]	UnivariateRing.extendedGCD(Poly a, Poly b)
Poly[]	UnivariateRing.firstBezoutCoefficient(Poly a, Poly b)
sPoly[]	MultipleFieldExtension.getGeneratorReps() Returns representation of generators as elements of simple field extension generated by primitive element MultipleFieldExtension.getPrimitiveElement()
static <T extends IUnivariatePolynomial<T>> T[]	PolynomialMethods.PolynomialExtendedGCD(T a, T b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).

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

Modifier and Type	Method and Description
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.

Constructors in cc.redberry.rings.poly with parameters of type IUnivariatePolynomial

Constructor and Description
MultipleFieldExtension(MultipleFieldExtension<Term,mPoly,sPoly>[] tower, UnivariatePolynomial<mPoly>[] minimalPolynomialsOfGenerators, mPoly primitiveElement, sPoly[] generatorsReps, SimpleFieldExtension<sPoly> simpleExtension)

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

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

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
<sPoly extends IUnivariatePolynomial<sPoly>> sPoly	AMultivariatePolynomial.composition(Ring<sPoly> uRing, sPoly... values) Substitutes given polynomials instead of variables of this (that is this(values_1, ..., values_N))
<sPoly extends IUnivariatePolynomial<sPoly>> sPoly	AMultivariatePolynomial.composition(sPoly... 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>,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

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

Modifier and Type	Method and Description
abstract IUnivariatePolynomial	AMultivariatePolynomial.asUnivariate() Converts this to univariate polynomial or throws exception if conversion is impossible (more than one variable have non zero exponents)
abstract IUnivariatePolynomial	AMultivariatePolynomial.contentUnivariate(int variable) Gives the content of this considered as R[variable][other_variables]
IUnivariatePolynomial	MultivariatePolynomialZp64.toDenseRecursiveForm() Gives a recursive univariate representation of this poly.

Methods in cc.redberry.rings.poly.multivar that return types with arguments of type IUnivariatePolynomial

Modifier and Type	Method and Description
abstract MultivariatePolynomial<? extends IUnivariatePolynomial>	AMultivariatePolynomial.asOverUnivariate(int variable) Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable
abstract MultivariatePolynomial<? extends IUnivariatePolynomial>	AMultivariatePolynomial.asOverUnivariateEliminate(int variable) Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable, the resulting polynomial have (nVariable - 1) multivariate variables (specified variable is eliminated)

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

Modifier and Type	Method and Description
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.
<sPoly extends IUnivariatePolynomial<sPoly>> sPoly	AMultivariatePolynomial.composition(Ring<sPoly> uRing, sPoly... values) Substitutes given polynomials instead of variables of this (that is this(values_1, ..., values_N))
<sPoly extends IUnivariatePolynomial<sPoly>> sPoly	AMultivariatePolynomial.composition(sPoly... values) Substitutes given polynomials instead of variables of this (that is this(values_1, ..., values_N))
static long	MultivariatePolynomialZp64.evaluateDenseRecursiveForm(IUnivariatePolynomial recForm, long[] values) Evaluates polynomial given in a dense recursive form at a given points
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.fromDenseRecursiveForm(IUnivariatePolynomial recForm, Comparator<DegreeVector> ordering) Converts poly from a recursive univariate representation.
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.fromDenseRecursiveForm(IUnivariatePolynomial recForm, int nVariables, Comparator<DegreeVector> ordering) Converts poly from a recursive univariate representation.

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

Classes in cc.redberry.rings.poly.univar with type parameters of type IUnivariatePolynomial

Modifier and Type	Class and Description
static class	DiophantineEquations.DiophantineSolver<Poly extends IUnivariatePolynomial<Poly>> Solves a1 * x1 + a2 * x2 + ...
static interface	HenselLifting.LiftableQuintet<PolyZp extends IUnivariatePolynomial<PolyZp>> Liftable quintet.
interface	IUnivariatePolynomial<Poly extends IUnivariatePolynomial<Poly>> Parent interface for univariate polynomials.
static class	UnivariateDivision.InverseModMonomial<Poly extends IUnivariatePolynomial<Poly>> Holds poly^(-1) mod x^i
static class	UnivariateResultants.APolynomialRemainderSequence<Poly extends IUnivariatePolynomial<Poly>> Polynomial remainder sequence (PRS).

Classes in cc.redberry.rings.poly.univar that implement IUnivariatePolynomial

Modifier and Type	Class and Description
class	UnivariatePolynomial<E> Univariate polynomial over generic ring.
class	UnivariatePolynomialZ64 Univariate polynomial over machine integers in range [-2^63, 2^63].
class	UnivariatePolynomialZp64 Univariate polynomial over Zp ring with modulus in the range of [2, 2^62) (the last value is specified by MachineArithmetic.MAX_SUPPORTED_MODULUS_BITS.

Fields in cc.redberry.rings.poly.univar declared as IUnivariatePolynomial

Modifier and Type	Field and Description
Poly	UnivariateResultants.APolynomialRemainderSequence.a Initial polynomials
Poly	UnivariateResultants.APolynomialRemainderSequence.b Initial polynomials

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

Modifier and Type	Method and Description
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	EqualDegreeFactorization.CantorZassenhaus(Poly input, int d) Plain Cantor-Zassenhaus algorithm implementation
static <T extends IUnivariatePolynomial<T>> T	ModularComposition.composition(T poly, T point, T polyModulus) Returns modular composition poly(point) mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	ModularComposition.composition(T poly, T point, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod) Returns modular composition poly(point) mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	ModularComposition.compositionBrentKung(T poly, ArrayList<T> pointPowers, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, int tBrentKung) Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.
static <T extends IUnivariatePolynomial<T>> T	ModularComposition.compositionBrentKung(T poly, T point, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod) Returns modular composition poly(point) mod polyModulus calculated using Brent & Kung algorithm for modular composition.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.createMonomialMod(BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod) Creates x^exponent mod polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.createMonomialMod(long exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod) Creates x^exponent mod polyModulus.
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateResultants.DiscriminantAsPoly(Poly a) Computes discriminant of polynomial and returns the result as a constant poly
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	DistinctDegreeFactorization.DistinctDegreeFactorization(Poly poly) Performs distinct-degree factorization for square-free polynomial poly.
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	DistinctDegreeFactorization.DistinctDegreeFactorizationShoup(Poly poly) Performs distinct-degree factorization for square-free polynomial poly using Victor Shoup's baby step / giant step algorithm.
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainder(Poly dividend, Poly divider, boolean copy) Returns {quotient, remainder} of dividend and divider or null if the division is not possible.
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainderFast(Poly dividend, Poly divider, UnivariateDivision.InverseModMonomial<Poly> invMod, boolean copy) Returns {quotient, remainder} of dividend and divider
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainderFast0(Poly dividend, Poly divider, UnivariateDivision.InverseModMonomial<Poly> invRevMod, boolean copy) fast division implementation
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateDivision.divideExact(Poly dividend, Poly divider, boolean copy) Divides dividend by divider or throws ArithmeticException if exact division is not possible
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateDivision.divideOrNull(Poly dividend, Poly divider, boolean copy) Divides dividend by divider or returns null if exact division is not possible
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.EuclidFirstBezoutCoefficient(T a, T b) Returns array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.EuclidGCD(T a, T b) Returns the GCD calculated with Euclidean algorithm.
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.ExtendedEuclidGCD(T a, T b) Runs extended Euclidean algorithm to compute [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.ExtendedHalfGCD(T a, T b) Runs extended Half-GCD algorithm to compute [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateFactorization.Factor(Poly poly) Factors univariate poly.
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateFactorization.FactorInGF(Poly poly) Factors polynomial over finite field
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateFactorization.FactorInZ(Poly poly) Factors polynomial in Z[x].
static <T extends IUnivariatePolynomial<T>> PolynomialFactorDecomposition<T>	UnivariateFactorization.FactorSquareFreeInGF(T poly) Factors square-free polynomial over finite field
static <PolyZ extends IUnivariatePolynomial<PolyZ>> PolynomialFactorDecomposition<PolyZ>	UnivariateFactorization.FactorSquareFreeInZ(PolyZ poly)
static <Poly extends IUnivariatePolynomial<Poly>> UnivariateDivision.InverseModMonomial<Poly>	UnivariateDivision.fastDivisionPreConditioning(Poly divider) Prepares rev(divider)^(-1) mod x^i for fast division.
static <Poly extends IUnivariatePolynomial<Poly>> UnivariateDivision.InverseModMonomial<Poly>	UnivariateDivision.fastDivisionPreConditioningWithLCCorrection(Poly divider) Prepares rev(divider)^(-1) mod x^i for fast division.
static <Poly extends IUnivariatePolynomial<Poly>> boolean	IrreduciblePolynomials.finiteFieldIrreducibleBenOr(Poly poly) Tests whether poly is irreducible over the finite field
static <Poly extends IUnivariatePolynomial<Poly>> boolean	IrreduciblePolynomials.finiteFieldIrreducibleQ(Poly poly) Tests whether poly is irreducible over the finite field
static <Poly extends IUnivariatePolynomial<Poly>> boolean	IrreduciblePolynomials.finiteFieldIrreducibleViaModularComposition(Poly poly) Tests whether poly is irreducible over the finite field
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.HalfGCD(T a, T b) Half-GCD algorithm.
static <Poly extends IUnivariatePolynomial<Poly>> boolean	IrreduciblePolynomials.irreducibleQ(Poly poly) Tests whether poly is irreducible
static <T extends IUnivariatePolynomial<T>> boolean	UnivariateSquareFreeFactorization.isSquareFree(T poly) Returns true if poly is square-free and false otherwise
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	DiophantineEquations.monicExtendedEuclid(Poly a, Poly b) runs xgcd for coprime polynomials ensuring that gcd is 1 (not another constant)
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyAddMod(T m1, T m2, T polyModulus, boolean copy) Returns the remainder of the sum (m1 + m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyAddMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns the remainder of the sum (m1 + m2) and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyMod(T dividend, T polyModulus, boolean copy) Returns the remainder of dividend and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyMod(T dividend, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns the remainder of dividend and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyMultiplyMod(T m1, T m2, T polyModulus, boolean copy) Returns the remainder of the product (m1 * m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyMultiplyMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns the remainder of the product (m1 * m2) and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyNegateMod(T m1, T polyModulus, boolean copy) Returns the remainder of the negated poly -m1 and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyNegateMod(T m1, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns the remainder of the negated poly -m1 and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.PolynomialExtendedGCD(T a, T b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.PolynomialFirstBezoutCoefficient(T a, T b) Returns array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.PolynomialGCD(Iterable<T> polynomials) Returns GCD of a list of polynomials.
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.PolynomialGCD(T... polynomials) Returns GCD of a list of polynomials.
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.PolynomialGCD(T a, T b) Calculates the GCD of two polynomials.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyPow(T base, long exponent, boolean copy) Returns base in a power of non-negative exponent
static <T extends IUnivariatePolynomial<T>> ArrayList<T>	ModularComposition.polyPowers(T poly, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, int nIterations) Returns poly^{i} mod polyModulus for i in [0...nIterations]
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyPowMod(T base, BigInteger exponent, T polyModulus, boolean copy) Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyPowMod(T base, BigInteger exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyPowMod(T base, long exponent, T polyModulus, boolean copy) Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polyPowMod(T base, long exponent, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns base in a power of non-negative exponent modulo polyModulus
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polySubtractMod(T m1, T m2, T polyModulus, boolean copy) Returns the remainder of the difference (m1 - m2) and polyModulus.
static <T extends IUnivariatePolynomial<T>> T	UnivariatePolynomialArithmetic.polySubtractMod(T m1, T m2, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, boolean copy) Returns the remainder of the difference (m1 - m2) and polyModulus using fast algorithm for pre-conditioned modulus.
static <T extends IUnivariatePolynomial<T>> T	ModularComposition.powModulusMod(T poly, T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod, ArrayList<T> xPowers) Returns poly^modulus mod polyModulus using precomputed monomial powers x^{i*modulus} mod polyModulus for i in [0...degree(poly)]
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.pseudoDivideAndRemainder(Poly dividend, Poly divider, boolean copy) Returns quotient and remainder of dividend and divider using pseudo division.
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateDivision.quotient(Poly dividend, Poly divider, boolean copy) Returns quotient dividend/ divider or null if exact division o
static <Poly extends IUnivariatePolynomial<Poly>> Poly	IrreduciblePolynomials.randomIrreduciblePolynomial(Poly factory, int degree, org.apache.commons.math3.random.RandomGenerator rnd) Generated random irreducible polynomial of degree degree
static <Poly extends IUnivariatePolynomial<Poly>> Poly	RandomUnivariatePolynomials.randomPoly(Poly factory, int degree, org.apache.commons.math3.random.RandomGenerator rnd) Creates random polynomial of specified degree.
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateDivision.remainder(Poly dividend, Poly divider, boolean copy) Returns remainder of dividend and divider.
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateDivision.remainderFast(Poly dividend, Poly divider, UnivariateDivision.InverseModMonomial<Poly> invMod, boolean copy) Fast remainder using Newton's iteration with switch to classical remainder for small polynomials.
static <T extends IUnivariatePolynomial<T>> T	UnivariateDivision.remainderMonomial(T dividend, int xDegree, boolean copy) Returns the remainder of dividend and monomial x^xDegree
static <Poly extends IUnivariatePolynomial<Poly>> Poly	UnivariateResultants.ResultantAsPoly(Poly a, Poly b) Computes resultant of two polynomials and returns the result as a constant poly
static <T extends IUnivariatePolynomial<T>> PolynomialFactorDecomposition<T>	UnivariateSquareFreeFactorization.SquareFreeFactorization(T poly) Performs square-free factorization of a poly.
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateSquareFreeFactorization.SquareFreeFactorizationMusser(Poly poly) Performs square-free factorization of a poly using Musser's algorithm (both zero and non-zero characteristic of coefficient ring allowed).
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateSquareFreeFactorization.SquareFreeFactorizationMusserZeroCharacteristics(Poly poly) Performs square-free factorization of a poly which coefficient ring has zero characteristic using Musser's algorithm.
static <Poly extends IUnivariatePolynomial<Poly>> PolynomialFactorDecomposition<Poly>	UnivariateSquareFreeFactorization.SquareFreeFactorizationYunZeroCharacteristics(Poly poly) Performs square-free factorization of a poly which coefficient ring has zero characteristic using Yun's algorithm.
static <T extends IUnivariatePolynomial<T>> T	UnivariateSquareFreeFactorization.SquareFreePart(T poly) Returns square-free part of the poly
static <T extends IUnivariatePolynomial<T>> ArrayList<T>	ModularComposition.xPowers(T polyModulus, UnivariateDivision.InverseModMonomial<T> invMod) Returns x^{i*modulus} mod polyModulus for i in [0...degree], where degree is polyModulus degree.

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

Modifier and Type	Method and Description
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainder(Poly dividend, Poly divider, boolean copy) Returns {quotient, remainder} of dividend and divider or null if the division is not possible.
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainderFast(Poly dividend, Poly divider, UnivariateDivision.InverseModMonomial<Poly> invMod, boolean copy) Returns {quotient, remainder} of dividend and divider
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.divideAndRemainderFast0(Poly dividend, Poly divider, UnivariateDivision.InverseModMonomial<Poly> invRevMod, boolean copy) fast division implementation
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.EuclidFirstBezoutCoefficient(T a, T b) Returns array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.ExtendedEuclidGCD(T a, T b) Runs extended Euclidean algorithm to compute [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.ExtendedHalfGCD(T a, T b) Runs extended Half-GCD algorithm to compute [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	DiophantineEquations.monicExtendedEuclid(Poly a, Poly b) runs xgcd for coprime polynomials ensuring that gcd is 1 (not another constant)
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.PolynomialExtendedGCD(T a, T b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static <T extends IUnivariatePolynomial<T>> T[]	UnivariateGCD.PolynomialFirstBezoutCoefficient(T a, T b) Returns array of [gcd(a,b), s] such that s * a + t * b = gcd(a, b)
static <Poly extends IUnivariatePolynomial<Poly>> Poly[]	UnivariateDivision.pseudoDivideAndRemainder(Poly dividend, Poly divider, boolean copy) Returns quotient and remainder of dividend and divider using pseudo division.
Poly[]	DiophantineEquations.DiophantineSolver.solve(Poly rhs)

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

Modifier and Type	Method and Description
static <T extends IUnivariatePolynomial<T>> T	UnivariateGCD.PolynomialGCD(T... polynomials) Returns GCD of a list of polynomials.

Constructors in cc.redberry.rings.poly.univar with parameters of type IUnivariatePolynomial

Constructor and Description
DiophantineSolver(Poly[] factors)