Uses of Class
cc.redberry.rings.Rational

Packages that use Rational

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 Rational in cc.redberry.rings

Fields in cc.redberry.rings with type parameters of type Rational

Modifier and Type	Field and Description
static AlgebraicNumberField<UnivariatePolynomial<Rational<BigInteger>>>	Rings.GaussianRationals Field of Gaussian rationals (rational complex numbers).
static UnivariateRing<UnivariatePolynomial<Rational<BigInteger>>>	Rings.UnivariateRingQ Ring of univariate polynomials over rationals (Q[x])

Methods in cc.redberry.rings that return Rational

Modifier and Type	Method and Description
Rational<E>	Rational.abs() Returns the absolute value of this Rational.
Rational<E>	Rational.add(E that) Add that to this
Rational<E>	Rational.add(Rational<E> that) Add that to this
Rational<E>	Rationals.add(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.copy(Rational<E> element)
Rational<E>[]	Rationals.createArray(int length)
Rational<E>[][]	Rationals.createArray2d(int length)
Rational<E>[][]	Rationals.createArray2d(int m, int n)
Rational<E>	Rational.divide(E oth) Divide this by oth
Rational<E>	Rational.divide(Rational<E> oth) Divide this by oth
Rational<E>[]	Rationals.divideAndRemainder(Rational<E> dividend, Rational<E> divider)
Rational<E>	Rationals.gcd(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.getNegativeOne()
Rational<E>	Rationals.getOne()
Rational<E>	Rationals.getZero()
Rational<E>	Rational.map(Function<E,E> function) Maps rational
<O> Rational<O>	Rational.map(Ring<O> ring, Function<E,O> function) Maps rational to a new ring
Rational<E>	Rationals.mk(E num, E den) Gives rational with a given numerator and denominator
Rational<E>	Rationals.mk(long num, long den) Gives rational with a given numerator and denominator
Rational<E>	Rationals.mkDenominator(E den) Gives rational with a given denominator and unit numerator
Rational<E>	Rationals.mkDenominator(long den) Gives rational with a given denominator and unit numerator
Rational<E>	Rationals.mkNumerator(E num) Gives rational with a given numerator and unit denominator
Rational<E>	Rationals.mkNumerator(long num) Gives rational with a given numerator and unit denominator
Rational<E>	Rational.multiply(E oth) Multiply this by oth
Rational<E>	Rational.multiply(Rational<E> oth) Multiply this by oth
Rational<E>	Rationals.multiply(Rational<E> a, Rational<E> b)
Rational<E>	Rational.negate() Negate this fraction
Rational<E>	Rationals.negate(Rational<E> element)
Rational<E>[]	Rational.normal() Reduces this rational to normal form by doing division with remainder, that is if numerator = div * denominator + rem then the array (div, rem/denominator) will be returned.
static <E> Rational<E>	Rational.one(Ring<E> ring) Constructs one
Rational<E>	Rational.pow(BigInteger exponent) Raise this in a power exponent
Rational<E>	Rational.pow(int exponent) Raise this in a power exponent
Rational<E>	Rational.pow(long exponent) Raise this in a power exponent
Rational<E>	Rationals.randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
Rational<E>	Rationals.randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)
Rational<E>	Rational.reciprocal() Reciprocal of this
Rational<E>	Rationals.reciprocal(Rational<E> element)
Rational<E>	Rational.subtract(E that) Subtract that from this
Rational<E>	Rational.subtract(Rational<E> that) Add that to this
Rational<E>	Rationals.subtract(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.valueOf(long val)
Rational<E>	Rationals.valueOf(Rational<E> val)
Rational<E>	Rationals.valueOfBigInteger(BigInteger val)
static <E> Rational<E>	Rational.zero(Ring<E> ring) Constructs zero

Methods in cc.redberry.rings that return types with arguments of type Rational

Modifier and Type	Method and Description
FactorDecomposition<Rational<E>>	Rationals.factor(Rational<E> element)
FactorDecomposition<Rational<E>>	Rationals.factorSquareFree(Rational<E> element)
Iterator<Rational<E>>	Rationals.iterator()
static MultivariateRing<MultivariatePolynomial<Rational<BigInteger>>>	Rings.MultivariateRingQ(int nVariables) Ring of multivariate polynomials over rationals (Q[x1, x2, ...])

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

Modifier and Type	Method and Description
Rational<E>	Rational.add(Rational<E> that) Add that to this
Rational<E>	Rationals.add(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.add(Rational<E> a, Rational<E> b)
int	Rationals.compare(Rational<E> o1, Rational<E> o2)
int	Rationals.compare(Rational<E> o1, Rational<E> o2)
int	Rational.compareTo(Rational<E> object)
Rational<E>	Rationals.copy(Rational<E> element)
Rational<E>	Rational.divide(Rational<E> oth) Divide this by oth
Rational<E>[]	Rationals.divideAndRemainder(Rational<E> dividend, Rational<E> divider)
Rational<E>[]	Rationals.divideAndRemainder(Rational<E> dividend, Rational<E> divider)
FactorDecomposition<Rational<E>>	Rationals.factor(Rational<E> element)
FactorDecomposition<Rational<E>>	Rationals.factorSquareFree(Rational<E> element)
Rational<E>	Rationals.gcd(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.gcd(Rational<E> a, Rational<E> b)
boolean	Rationals.isOne(Rational<E> element)
boolean	Rationals.isUnit(Rational<E> element)
boolean	Rationals.isZero(Rational<E> element)
Rational<E>	Rational.multiply(Rational<E> oth) Multiply this by oth
Rational<E>	Rationals.multiply(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.multiply(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.negate(Rational<E> element)
Rational<E>	Rationals.reciprocal(Rational<E> element)
int	Rationals.signum(Rational<E> element)
Rational<E>	Rational.subtract(Rational<E> that) Add that to this
Rational<E>	Rationals.subtract(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.subtract(Rational<E> a, Rational<E> b)
Rational<E>	Rationals.valueOf(Rational<E> val)

Method parameters in cc.redberry.rings with type arguments of type Rational

Modifier and Type	Method and Description
String	Rationals.toString(IStringifier<Rational<E>> stringifier)
String	Rational.toString(IStringifier<Rational<E>> stringifier)
String	Rational.toStringFactors(IStringifier<Rational<E>> stringifier)

Uses of Rational in cc.redberry.rings.io

Methods in cc.redberry.rings.io that return types with arguments of type Rational

Modifier and Type	Method and Description
static <E> Coder<Rational<E>,?,?>	Coder.mkRationalsCoder(Rationals<E> ring, Coder<E,?,?> elementsCoder) Create coder for rational elements

Uses of Rational in cc.redberry.rings.poly

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

Modifier and Type	Method and Description
static <E> MultivariatePolynomial<Rational<E>>	Util.asOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly)
static <E> UnivariatePolynomial<Rational<E>>	Util.asOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly)
static <E> MultivariatePolynomial<Rational<E>>	Util.divideOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly, E denominator)
static <E> UnivariatePolynomial<Rational<E>>	Util.divideOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly, E denominator)

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

Modifier and Type	Method and Description
static <E> MultivariatePolynomial<Rational<E>>	Util.asOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly)
static <E> UnivariatePolynomial<Rational<E>>	Util.asOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly)
static <E> E	Util.commonDenominator(MultivariatePolynomial<Rational<E>> poly) Returns a common denominator of given poly
static <E> E	Util.commonDenominator(UnivariatePolynomial<Rational<E>> poly) Returns a common denominator of given poly
static <E> MultivariatePolynomial<Rational<E>>	Util.divideOverRationals(Ring<Rational<E>> field, MultivariatePolynomial<E> poly, E denominator)
static <E> UnivariatePolynomial<Rational<E>>	Util.divideOverRationals(Ring<Rational<E>> field, UnivariatePolynomial<E> poly, E denominator)
static <E> Util.Tuple2<MultivariatePolynomial<E>,E>	Util.toCommonDenominator(MultivariatePolynomial<Rational<E>> poly) Brings polynomial with rational coefficients to common denominator
static <E> Util.Tuple2<UnivariatePolynomial<E>,E>	Util.toCommonDenominator(UnivariatePolynomial<Rational<E>> poly) Brings polynomial with rational coefficients to common denominator

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

Fields in cc.redberry.rings.poly.multivar with type parameters of type Rational

Modifier and Type	Field and Description
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.initialNumerator Initial numerator (numerator and denominator may have nontrivial GCD)
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.numerator Reduced numerator (GCD is cancelled)

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

Modifier and Type	Method and Description
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.cyclic(int n)
static PolynomialFactorDecomposition<MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	MultivariateFactorization.FactorInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> polynomial) Factors multivariate polynomial over simple number field via Trager's algorithm
static <E> PolynomialFactorDecomposition<MultivariatePolynomial<Rational<E>>>	MultivariateFactorization.FactorInQ(MultivariatePolynomial<Rational<E>> polynomial) Factors multivariate polynomial over Q
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBases.GroebnerBasisInQ(List<MultivariatePolynomial<Rational<BigInteger>>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular) Computes Groebner basis (minimized and reduced) of a given ideal over Q represented by a list of generators.
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.hilbertPolynomial() Hilbert polynomial
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.hilbertPolynomialZ() Integral Hilbert polynomial (i.e.
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.integralPart() Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura(int i)
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura10()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura11()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura12()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura13()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura14()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura2()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura3()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura4()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura5()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura6()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura7()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura8()
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBasesData.katsura9()
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 MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateResultants.ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable) Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Calculates greatest common divisor of two multivariate polynomials over Z
UnivariatePolynomial<Rational<BigInteger>>	GroebnerBases.HilbertSeries.remainderNumerator() Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result

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

Modifier and Type	Method and Description
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)

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

Modifier and Type	Method and Description
static PolynomialFactorDecomposition<MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	MultivariateFactorization.FactorInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> polynomial) Factors multivariate polynomial over simple number field via Trager's algorithm
static <E> PolynomialFactorDecomposition<MultivariatePolynomial<Rational<E>>>	MultivariateFactorization.FactorInQ(MultivariatePolynomial<Rational<E>> polynomial) Factors multivariate polynomial over Q
static List<MultivariatePolynomial<Rational<BigInteger>>>	GroebnerBases.GroebnerBasisInQ(List<MultivariatePolynomial<Rational<BigInteger>>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular) Computes Groebner basis (minimized and reduced) of a given ideal over Q represented by a list of generators.
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ModularGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, BiFunction<MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>,MultivariatePolynomial<UnivariatePolynomialZp64>> modularAlgorithm) Modular interpolation algorithm for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateResultants.ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable) Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateResultants.ModularResultantInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b, int variable) Modular resultant in simple number field
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.PolynomialGCDinNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaLangemyrMcCallum(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for computing GCD associate for polynomials over simple field extensions with the use of Langemyr & McCallum approach to avoid rational reconstruction
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result
static MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	MultivariateGCD.ZippelGCDInNumberFieldViaRationalReconstruction(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Zippel's sparse modular interpolation algorithm for polynomials over simple field extensions with the use of rational reconstruction to reconstruct the result

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

Methods in cc.redberry.rings.poly.univar that return types with arguments of type Rational

Modifier and Type	Method and Description
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly) Factors polynomial in Q(alpha)[x] via Trager's algorithm
static <E> PolynomialFactorDecomposition<UnivariatePolynomial<Rational<E>>>	UnivariateFactorization.FactorInQ(UnivariatePolynomial<Rational<E>> poly) Factors polynomial over Q
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly) Factors polynomial in Q(alpha)[x] via Trager's algorithm
static UnivariatePolynomial<Rational<BigInteger>>	UnivariateResultants.ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Modular resultant in simple number field
static UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	UnivariateGCD.PolynomialGCDInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Computes GCD via Langemyr & Mccallum modular algorithm over algebraic number field

Method parameters in cc.redberry.rings.poly.univar with type arguments of type Rational

Modifier and Type	Method and Description
static UnivariatePolynomialZp64	UnivariatePolynomial.asOverZp64Q(UnivariatePolynomial<Rational<BigInteger>> poly, IntegersZp64 ring) Converts Zp[x] poly over rationals to machine-sized polynomial in Zp
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly) Factors polynomial in Q(alpha)[x] via Trager's algorithm
static <E> PolynomialFactorDecomposition<UnivariatePolynomial<Rational<E>>>	UnivariateFactorization.FactorInQ(UnivariatePolynomial<Rational<E>> poly) Factors polynomial over Q
static PolynomialFactorDecomposition<UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>>	UnivariateFactorization.FactorSquareFreeInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> poly) Factors polynomial in Q(alpha)[x] via Trager's algorithm
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedRationalGCD(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b) Computes [gcd(a,b), s, t] such that s * a + t * b = gcd(a, b).
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedResultantGCDInQ(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b) Modular extended GCD algorithm for polynomials over Q with the use of resultants.
static UnivariatePolynomial<Rational<BigInteger>>[]	UnivariateGCD.ModularExtendedResultantGCDInQ(UnivariatePolynomial<Rational<BigInteger>> a, UnivariatePolynomial<Rational<BigInteger>> b) Modular extended GCD algorithm for polynomials over Q with the use of resultants.
static UnivariatePolynomial<Rational<BigInteger>>	UnivariateResultants.ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Modular resultant in simple number field
static UnivariatePolynomial<Rational<BigInteger>>	UnivariateResultants.ModularResultantInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Modular resultant in simple number field
static UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	UnivariateGCD.PolynomialGCDInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Computes GCD via Langemyr & Mccallum modular algorithm over algebraic number field
static UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>	UnivariateGCD.PolynomialGCDInNumberField(UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> a, UnivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> b) Computes GCD via Langemyr & Mccallum modular algorithm over algebraic number field