static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.cyclic(int n) |
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static PolynomialFactorDecomposition<MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>>> |
MultivariateFactorization.FactorInNumberField(MultivariatePolynomial<UnivariatePolynomial<Rational<BigInteger>>> polynomial) |
Factors multivariate polynomial over simple number field via Trager's algorithm
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static <E> PolynomialFactorDecomposition<MultivariatePolynomial<Rational<E>>> |
MultivariateFactorization.FactorInQ(MultivariatePolynomial<Rational<E>> polynomial) |
Factors multivariate polynomial over Q
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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.
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UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBases.HilbertSeries.hilbertPolynomial() |
Hilbert polynomial
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UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBases.HilbertSeries.hilbertPolynomialZ() |
Integral Hilbert polynomial (i.e.
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UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBases.HilbertSeries.integralPart() |
Integral part I(t) of HPS(t): HPS(t) = I(t) + Q(t)/(1-t)^m
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura(int i) |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura10() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura11() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura12() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura13() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura14() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura2() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura3() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura4() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura5() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura6() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura7() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura8() |
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static List<MultivariatePolynomial<Rational<BigInteger>>> |
GroebnerBasesData.katsura9() |
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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)
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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
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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
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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
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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
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UnivariatePolynomial<Rational<BigInteger>> |
GroebnerBases.HilbertSeries.remainderNumerator() |
Remainder part R(t) of HPS(t): HPS(t) = I(t) + R(t)/(1-t)^m
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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
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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
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