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

Packages that use MultivariatePolynomial

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 MultivariatePolynomial in cc.redberry.rings

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

Modifier and Type	Method and Description
static <E> MultivariateRing<MultivariatePolynomial<E>>	Rings.MultivariateRing(int nVariables, Ring<E> coefficientRing) Ring of multivariate polynomials with specified number of variables over specified coefficient ring
static <E> MultivariateRing<MultivariatePolynomial<E>>	Rings.MultivariateRing(int nVariables, Ring<E> coefficientRing, Comparator<DegreeVector> monomialOrder) Ring of multivariate polynomials with specified number of variables over specified coefficient ring
static MultivariateRing<MultivariatePolynomial<Rational<BigInteger>>>	Rings.MultivariateRingQ(int nVariables) Ring of multivariate polynomials over rationals (Q[x1, x2, ...])
static MultivariateRing<MultivariatePolynomial<BigInteger>>	Rings.MultivariateRingZ(int nVariables) Ring of multivariate polynomials over integers (Z[x1, x2, ...])
static MultivariateRing<MultivariatePolynomial<BigInteger>>	Rings.MultivariateRingZp(int nVariables, BigInteger modulus) Ring of multivariate polynomials over Zp integers (Zp[x1, x2, ...]) with arbitrary large modulus

Uses of MultivariatePolynomial in cc.redberry.rings.io

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

Modifier and Type	Method and Description
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, Map<String,MultivariatePolynomial<E>> variables) Create coder for multivariate polynomial rings
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, Map<String,MultivariatePolynomial<E>> variables) Create coder for multivariate polynomial rings
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, String... variables) Create parser for multivariate polynomial rings
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, String... variables) Create parser for multivariate polynomial rings

Method parameters in cc.redberry.rings.io with type arguments of type MultivariatePolynomial

Modifier and Type	Method and Description
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, Map<String,MultivariatePolynomial<E>> variables) Create coder for multivariate polynomial rings
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, Map<String,MultivariatePolynomial<E>> variables) Create coder for multivariate polynomial rings
static <E> Coder<MultivariatePolynomial<E>,Monomial<E>,MultivariatePolynomial<E>>	Coder.mkMultivariateCoder(MultivariateRing<MultivariatePolynomial<E>> ring, Coder<E,?,?> cfCoder, String... variables) Create parser for multivariate polynomial rings

Uses of MultivariatePolynomial in cc.redberry.rings.poly

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

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

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

Modifier and Type	Method and Description
static <E> Util.Tuple2<MultivariatePolynomial<E>,E>	Util.toCommonDenominator(MultivariatePolynomial<Rational<E>> poly) Brings polynomial with rational coefficients to common denominator

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

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

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

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

Modifier and Type	Method and Description
MultivariatePolynomial<E>	MultivariatePolynomial.add(E oth) Adds oth to this polynomial
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asMultivariate(UnivariatePolynomial<E> poly, int nVariables, int variable, Comparator<DegreeVector> ordering) Converts univariate polynomial to multivariate.
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly, int[] coefficientVariables, int[] mainVariables) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomial<E>> poly, int variable) Converts multivariate polynomial over univariate polynomial ring (R[variable][other_variables]) to a multivariate polynomial over coefficient ring (R[variables])
MultivariatePolynomial<MultivariatePolynomialZp64>	MultivariatePolynomialZp64.asOverMultivariate(int... variables)
MultivariatePolynomial<MultivariatePolynomial<E>>	MultivariatePolynomial.asOverMultivariate(int... variables)
abstract MultivariatePolynomial<Poly>	AMultivariatePolynomial.asOverMultivariate(int... variables) Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
MultivariatePolynomial<Poly>	AMultivariatePolynomial.asOverMultivariateEliminate(int... variables) Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
MultivariatePolynomial<MultivariatePolynomialZp64>	MultivariatePolynomialZp64.asOverMultivariateEliminate(int[] variables, Comparator<DegreeVector> ordering)
MultivariatePolynomial<MultivariatePolynomial<E>>	MultivariatePolynomial.asOverMultivariateEliminate(int[] variables, Comparator<DegreeVector> ordering)
abstract MultivariatePolynomial<Poly>	AMultivariatePolynomial.asOverMultivariateEliminate(int[] variables, Comparator<DegreeVector> ordering) Converts this to a multivariate polynomial with coefficients being multivariate polynomials polynomials over variables that is polynomial in R[variables][other_variables]
MultivariatePolynomial<Poly>	AMultivariatePolynomial.asOverPoly(Poly factory) Consider coefficients of this as constant polynomials of the same type as a given factory polynomial
MultivariatePolynomial<UnivariatePolynomialZp64>	MultivariatePolynomialZp64.asOverUnivariate(int variable)
MultivariatePolynomial<UnivariatePolynomial<E>>	MultivariatePolynomial.asOverUnivariate(int variable)
abstract MultivariatePolynomial<? extends IUnivariatePolynomial>	AMultivariatePolynomial.asOverUnivariate(int variable) Converts this to a multivariate polynomial with coefficients being univariate polynomials over variable
MultivariatePolynomial<UnivariatePolynomialZp64>	MultivariatePolynomialZp64.asOverUnivariateEliminate(int variable)
MultivariatePolynomial<UnivariatePolynomial<E>>	MultivariatePolynomial.asOverUnivariateEliminate(int 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)
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.asPolyZ() Returns polynomial over Z formed from the coefficients of this
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZ(MultivariatePolynomial<BigInteger> poly, boolean copy) Returns Z[X] polynomial formed from the coefficients of the poly.
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.asPolyZSymmetric() Returns polynomial over Z formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly) Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
static <E> MultivariatePolynomial<E>	MultivariateGCD.BrownGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Brown's algorithm with dense interpolation.
static <E> MultivariatePolynomial<E>	MultivariateResultants.BrownResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Brown's algorithm for resultant with dense interpolation
MultivariatePolynomial<E>	MultivariatePolynomial.ccAsPoly()
MultivariatePolynomial<E>	MultivariatePolynomial.clone()
MultivariatePolynomial<E>	MultivariatePolynomial.contentAsPoly()
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.create(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering, Iterable<Monomial<E>> terms) Creates multivariate polynomial from a list of monomial terms
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.create(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering, Monomial<E>... terms) Creates multivariate polynomial from a list of monomial terms
MultivariatePolynomial<E>[]	MultivariatePolynomial.createArray(int length)
MultivariatePolynomial<E>[][]	MultivariatePolynomial.createArray2d(int length)
MultivariatePolynomial<E>[][]	MultivariatePolynomial.createArray2d(int length1, int length2)
MultivariatePolynomial<E>	MultivariatePolynomial.createConstant(E val) Creates constant polynomial with specified value
MultivariatePolynomial<E>	MultivariatePolynomial.createConstantFromTerm(Monomial<E> monomial)
MultivariatePolynomial<E>	MultivariatePolynomial.createLinear(int variable, E cc, E lc) Creates linear polynomial of the form cc + lc * variable
MultivariatePolynomial<E>	MultivariatePolynomial.createOne()
MultivariatePolynomial<E>	MultivariatePolynomial.createZero()
MultivariatePolynomial<E>	MultivariatePolynomial.decrement()
MultivariatePolynomial<E>	MultivariatePolynomial.derivative(int variable, int order)
MultivariatePolynomial<E>	MultivariatePolynomial.divideByLC(MultivariatePolynomial<E> other)
MultivariatePolynomial<E>	MultivariatePolynomial.divideExact(E factor) Divides this polynomial by a factor or throws exception if exact division is not possible
MultivariatePolynomial<E>	MultivariatePolynomial.divideOrNull(E factor) Divides this polynomial by a factor or returns null (causing loss of internal data) if some of the elements can't be exactly divided by the factor.
MultivariatePolynomial<E>	MultivariatePolynomial.divideOrNull(Monomial<E> monomial)
MultivariatePolynomial<E>	MultivariatePolynomial.eliminate(int[] variables, E[] values) Returns a copy of this with values substituted for variables
MultivariatePolynomial<E>	MultivariatePolynomial.eliminate(int variable, E value) Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
MultivariatePolynomial<E>	MultivariatePolynomial.eliminate(int variable, long value) Substitutes value for variable and eliminates variable from the list of variables so that the resulting polynomial has result.nVariables = this.nVariables - 1.
MultivariatePolynomial<E>	MultivariatePolynomial.HornerForm.evaluate(E[] values) Substitute given values for evaluation variables (for example, if this is in R[x1,x2,x3,x4] and evaluation variables are x2 and x4, the result will be a poly in R[x1,x3]).
MultivariatePolynomial<E>	MultivariatePolynomial.evaluate(int[] variables, E[] values) Returns a copy of this with values substituted for variables.
MultivariatePolynomial<E>[]	MultivariatePolynomial.evaluate(int variable, E... values) Evaluates this polynomial at specified points
MultivariatePolynomial<E>	MultivariatePolynomial.evaluate(int variable, E value) Returns a copy of this with value substituted for variable.
MultivariatePolynomial<E>	MultivariatePolynomial.evaluate(int variable, long value) Returns a copy of this with value substituted for variable.
MultivariatePolynomial<E>	MultivariatePolynomial.evaluateAtRandom(int variable, org.apache.commons.math3.random.RandomGenerator rnd)
MultivariatePolynomial<E>	MultivariatePolynomial.evaluateAtRandomPreservingSkeleton(int variable, org.apache.commons.math3.random.RandomGenerator rnd)
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.fromDenseRecursiveForm(UnivariatePolynomial 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.
MultivariatePolynomial<E>	MultivariateInterpolation.Interpolation.getInterpolatingPolynomial() Returns resulting interpolating polynomial
MultivariatePolynomial<E>	MultivariatePolynomial.increment()
static <E> MultivariatePolynomial<E>	MultivariateInterpolation.interpolateNewton(int variable, E[] points, MultivariatePolynomial<E>[] values) Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganEEZModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganSparseModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
MultivariatePolynomial<E>	MultivariatePolynomial.lcAsPoly()
MultivariatePolynomial<E>	MultivariatePolynomial.lcAsPoly(Comparator<DegreeVector> ordering)
<T> MultivariatePolynomial<T>	MultivariatePolynomial.mapCoefficients(Ring<T> newRing, Function<E,T> mapper) Maps coefficients of this using specified mapping function
<T> MultivariatePolynomial<T>	MultivariatePolynomialZp64.mapCoefficients(Ring<T> newRing, LongFunction<T> mapper) Maps coefficients of this using specified mapping function
<E> MultivariatePolynomial<E>	MultivariatePolynomialZp64.mapCoefficientsAsPolys(Ring<E> ring, Function<MultivariatePolynomialZp64,E> mapper)
abstract <E> MultivariatePolynomial<E>	AMultivariatePolynomial.mapCoefficientsAsPolys(Ring<E> ring, Function<Poly,E> mapper)
<T> MultivariatePolynomial<T>	MultivariatePolynomial.mapCoefficientsAsPolys(Ring<T> ring, Function<MultivariatePolynomial<E>,T> mapper)
<T> MultivariatePolynomial<T>	MultivariatePolynomial.mapTerms(Ring<T> newRing, Function<Monomial<E>,Monomial<T>> mapper) Maps terms of this using specified mapping function
<T> MultivariatePolynomial<T>	MultivariatePolynomialZp64.mapTerms(Ring<T> newRing, Function<MonomialZp64,Monomial<T>> mapper) Maps terms of this using specified mapping function
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<BigInteger>	MultivariateGCD.ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp) Modular GCD algorithm for polynomials over Z.
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<BigInteger>>	MultivariateResultants.ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over Z
MultivariatePolynomial<E>	MultivariatePolynomial.monic() Makes this polynomial monic if possible, if not -- destroys this and returns null
MultivariatePolynomial<E>	MultivariatePolynomial.monic(Comparator<DegreeVector> ordering)
MultivariatePolynomial<E>	MultivariatePolynomial.monic(Comparator<DegreeVector> ordering, E factor) Sets this to its monic part (with respect to given ordering) multiplied by the given factor;
MultivariatePolynomial<E>	MultivariatePolynomial.monic(E factor) Sets this to its monic part multiplied by the factor modulo modulus (that is monic(modulus).multiply(factor) ).
MultivariatePolynomial<E>	MultivariatePolynomial.monicWithLC(Comparator<DegreeVector> ordering, MultivariatePolynomial<E> other)
MultivariatePolynomial<E>	MultivariatePolynomial.monicWithLC(MultivariatePolynomial<E> other)
MultivariatePolynomial<E>	MultivariatePolynomial.multiply(E factor) Multiplies this by the factor
MultivariatePolynomial<E>	MultivariatePolynomial.multiply(long factor)
MultivariatePolynomial<E>	MultivariatePolynomial.multiply(Monomial<E> monomial)
MultivariatePolynomial<E>	MultivariatePolynomial.multiply(MultivariatePolynomial<E> oth)
MultivariatePolynomial<E>	MultivariatePolynomial.multiplyByBigInteger(BigInteger factor)
MultivariatePolynomial<E>	MultivariatePolynomial.multiplyByLC(MultivariatePolynomial<E> other)
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.one(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering) Creates unit polynomial.
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string) Deprecated. use #parse(string, ring, ordering, variables)
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, Comparator<DegreeVector> ordering) Deprecated. use #parse(string, ring, ordering, variables)
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, Comparator<DegreeVector> ordering, String... variables) Parse multivariate Z[X] polynomial from string.
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.parse(String string, Ring<E> ring) Deprecated. use #parse(string, ring, ordering, variables)
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.parse(String string, Ring<E> ring, Comparator<DegreeVector> ordering) Deprecated. use #parse(string, ring, ordering, variables)
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.parse(String string, Ring<E> ring, Comparator<DegreeVector> ordering, String... variables) Parse multivariate polynomial from string.
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.parse(String string, Ring<E> ring, String... variables) Parse multivariate polynomial from string.
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.parse(String string, String... variables) Parse multivariate Z[X] polynomial from string.
MultivariatePolynomial<E>	MultivariatePolynomial.parsePoly(String string) Deprecated.
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<BigInteger>>	MultivariateGCD.PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateGCD.PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Calculates greatest common divisor of two multivariate polynomials over Z
MultivariatePolynomial<E>	MultivariatePolynomial.primitivePart()
MultivariatePolynomial<E>	MultivariatePolynomial.primitivePart(int variable)
MultivariatePolynomial<E>	MultivariatePolynomial.primitivePartSameSign()
static MultivariatePolynomial<BigInteger>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, BigInteger bound, Comparator<DegreeVector> ordering, org.apache.commons.math3.random.RandomGenerator rnd) Generates random Z[X] polynomial with coefficients bounded by bound
static <E> MultivariatePolynomial<E>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int minDegree, int maxDegree, int size, Ring<E> ring, Comparator<DegreeVector> ordering, Function<org.apache.commons.math3.random.RandomGenerator,E> method, org.apache.commons.math3.random.RandomGenerator rnd) Generates random polynomial
static MultivariatePolynomial<BigInteger>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, org.apache.commons.math3.random.RandomGenerator rnd) Generates random Z[X] polynomial
static <E> MultivariatePolynomial<E>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, Ring<E> ring, Comparator<DegreeVector> ordering, Function<org.apache.commons.math3.random.RandomGenerator,E> method, org.apache.commons.math3.random.RandomGenerator rnd) Generates random polynomial
static <E> MultivariatePolynomial<E>	RandomMultivariatePolynomials.randomPolynomial(int nVars, int degree, int size, Ring<E> ring, Comparator<DegreeVector> ordering, org.apache.commons.math3.random.RandomGenerator rnd) Generates random polynomial
static <E> MultivariatePolynomial<E>	RandomMultivariatePolynomials.randomSharpPolynomial(int nVars, int degree, int size, Ring<E> ring, Comparator<DegreeVector> ordering, Function<org.apache.commons.math3.random.RandomGenerator,E> rndCoefficients, org.apache.commons.math3.random.RandomGenerator rnd) Generates random Zp[X] polynomial over machine integers
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Computes polynomial resultant of two polynomials over Z
MultivariatePolynomial<E>	MultivariatePolynomial.seriesCoefficient(int variable, int order)
MultivariatePolynomial<E>	MultivariatePolynomial.setCoefficientRingFrom(MultivariatePolynomial<E> poly)
MultivariatePolynomial<E>	MultivariatePolynomial.setLC(E val) Sets the leading coefficient to the specified value
MultivariatePolynomial<E>	MultivariatePolynomial.setRing(Ring<E> newRing) Returns a copy of this with coefficient reduced to a newRing
<E> MultivariatePolynomial<E>	MultivariatePolynomialZp64.setRing(Ring<E> newRing) Switches to another ring specified by newRing
MultivariatePolynomial<E>	MultivariatePolynomial.setRingUnsafe(Ring<E> newRing) internal API
MultivariatePolynomial<E>	MultivariatePolynomial.shift(int[] variables, E[] shifts) Returns a copy of this with variables -> variables + shifts
MultivariatePolynomial<E>	MultivariatePolynomial.shift(int variable, E shift) Returns a copy of this with variable -> variable + shift
MultivariatePolynomial<E>	MultivariatePolynomial.shift(int variable, long shift) Returns a copy of this with variable -> variable + shift
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]
MultivariatePolynomial<E>	MultivariatePolynomial.square()
MultivariatePolynomial<E>	MultivariatePolynomial.substitute(int variable, MultivariatePolynomial<E> poly) Returns a copy of this with poly substituted for variable.
MultivariatePolynomial<E>	MultivariatePolynomial.subtract(E oth) Subtracts oth from this polynomial
MultivariatePolynomial<BigInteger>	MultivariatePolynomialZp64.toBigPoly() Returns polynomial over Z formed from the coefficients of this
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.zero(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering) Creates zero polynomial.
static <E> MultivariatePolynomial<E>	MultivariateGCD.ZippelGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Zippel's algorithm with sparse interpolation.
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<BigInteger>	MultivariateGCD.ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Sparse modular GCD algorithm for polynomials over Z.
static <E> MultivariatePolynomial<E>	MultivariateResultants.ZippelResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Zippel's algorithm for resultant with sparse interpolation

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

Modifier and Type	Method and Description
MultivariatePolynomial<MultivariatePolynomial<E>>	MultivariatePolynomial.asOverMultivariate(int... variables)
MultivariatePolynomial<MultivariatePolynomial<E>>	MultivariatePolynomial.asOverMultivariateEliminate(int[] variables, Comparator<DegreeVector> ordering)
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 PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>	MultivariateFactorization.FactorInZ(MultivariatePolynomial<BigInteger> polynomial) Factors multivariate polynomial over Z
List<MultivariatePolynomial<E>>	MultivariateInterpolation.Interpolation.getValues() Returns the list of polynomial values at interpolation points
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 cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.GroebnerBasisInZ(List<MultivariatePolynomial<BigInteger>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular) Computes Groebner basis (minimized and reduced) of a given ideal over Z represented by a list of generators.
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 cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse) Modular Groebner basis algorithm.
static <E> Ideal<Monomial<E>,MultivariatePolynomial<E>>	Ideal.parse(String[] generators, Ring<E> field, Comparator<DegreeVector> monomialOrder, String[] variables) Shortcut for parse
static <E> Ideal<Monomial<E>,MultivariatePolynomial<E>>	Ideal.parse(String[] generators, Ring<E> field, String[] variables) Shortcut for parse
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]

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

Modifier and Type	Method and Description
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly, int[] coefficientVariables, int[] mainVariables) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> poly) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomialZp64> poly, int[] coefficientVariables, int[] mainVariables) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomial<E>> poly, int variable) Converts multivariate polynomial over univariate polynomial ring (R[variable][other_variables]) to a multivariate polynomial over coefficient ring (R[variables])
static MultivariatePolynomialZp64	MultivariatePolynomialZp64.asNormalMultivariate(MultivariatePolynomial<UnivariatePolynomialZp64> poly, int variable) Converts multivariate polynomial over univariate polynomial ring (Zp[variable][other_variables]) to a multivariate polynomial over coefficient ring (Zp[all_variables])
static MultivariatePolynomialZp64	MultivariatePolynomial.asOverZp64(MultivariatePolynomial<BigInteger> poly) Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomialZp64	MultivariatePolynomial.asOverZp64(MultivariatePolynomial<BigInteger> poly, IntegersZp64 ring) Converts multivariate polynomial over BigIntegers to multivariate polynomial over machine modular integers
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZ(MultivariatePolynomial<BigInteger> poly, boolean copy) Returns Z[X] polynomial formed from the coefficients of the poly.
static MultivariatePolynomial<BigInteger>	MultivariatePolynomial.asPolyZSymmetric(MultivariatePolynomial<BigInteger> poly) Converts Zp[x] polynomial to Z[x] polynomial formed from the coefficients of this represented in symmetric modular form (-modulus/2 <= cfx <= modulus/2).
static <E> MultivariatePolynomial<E>	MultivariateGCD.BrownGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Brown's algorithm with dense interpolation.
static <E> MultivariatePolynomial<E>	MultivariateGCD.BrownGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Brown's algorithm with dense interpolation.
static <E> MultivariatePolynomial<E>	MultivariateResultants.BrownResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Brown's algorithm for resultant with dense interpolation
static <E> MultivariatePolynomial<E>	MultivariateResultants.BrownResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Brown's algorithm for resultant with dense interpolation
int	MultivariatePolynomial.compareTo(MultivariatePolynomial<E> oth)
MultivariatePolynomial<E>	MultivariatePolynomial.divideByLC(MultivariatePolynomial<E> other)
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 PolynomialFactorDecomposition<MultivariatePolynomial<BigInteger>>	MultivariateFactorization.FactorInZ(MultivariatePolynomial<BigInteger> polynomial) Factors multivariate polynomial over Z
static <E> MultivariatePolynomial<E>	MultivariateInterpolation.interpolateNewton(int variable, E[] points, MultivariatePolynomial<E>[] values) Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganEEZModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganEEZModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganSparseModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
static <E> MultivariatePolynomial<E>	MultivariateGCD.KaltofenMonaganSparseModularGCDInGF(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Modular GCD algorithm for polynomials over finite fields of small cardinality.
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 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<BigInteger>	MultivariateGCD.ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp) Modular GCD algorithm for polynomials over Z.
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ModularGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, BiFunction<MultivariatePolynomialZp64,MultivariatePolynomialZp64,MultivariatePolynomialZp64> gcdInZp) Modular GCD algorithm for polynomials over Z.
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<BigInteger>>	MultivariateResultants.ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateResultants.ModularResultantInRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over rings of integers
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over Z
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ModularResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Modular algorithm with Zippel sparse interpolation for resultant over Z
MultivariatePolynomial<E>	MultivariatePolynomial.monicWithLC(Comparator<DegreeVector> ordering, MultivariatePolynomial<E> other)
MultivariatePolynomial<E>	MultivariatePolynomial.monicWithLC(MultivariatePolynomial<E> other)
MultivariatePolynomial<E>	MultivariatePolynomial.multiply(MultivariatePolynomial<E> oth)
MultivariatePolynomial<E>	MultivariatePolynomial.multiplyByLC(MultivariatePolynomial<E> other)
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<BigInteger>>	MultivariateGCD.PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<UnivariatePolynomial<BigInteger>>	MultivariateGCD.PolynomialGCDinRingOfIntegersOfNumberField(MultivariatePolynomial<UnivariatePolynomial<BigInteger>> a, MultivariatePolynomial<UnivariatePolynomial<BigInteger>> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateGCD.PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateGCD.PolynomialGCDinZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Calculates greatest common divisor of two multivariate polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Computes polynomial resultant of two polynomials over Z
static MultivariatePolynomial<BigInteger>	MultivariateResultants.ResultantInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b, int variable) Computes polynomial resultant of two polynomials over Z
boolean	MultivariatePolynomial.sameCoefficientRingWith(MultivariatePolynomial<E> oth)
MultivariatePolynomial<E>	MultivariatePolynomial.setCoefficientRingFrom(MultivariatePolynomial<E> poly)
MultivariatePolynomial<E>	MultivariatePolynomial.substitute(int variable, MultivariatePolynomial<E> poly) Returns a copy of this with poly substituted for variable.
MultivariateInterpolation.Interpolation<E>	MultivariateInterpolation.Interpolation.update(E[] points, MultivariatePolynomial<E>[] values) Updates interpolation, so that interpolating polynomial satisfies interpolation[point] = value
MultivariateInterpolation.Interpolation<E>	MultivariateInterpolation.Interpolation.update(E point, MultivariatePolynomial<E> value) Updates interpolation, so that interpolating polynomial satisfies interpolation[point] = value
static <E> MultivariatePolynomial<E>	MultivariateGCD.ZippelGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Zippel's algorithm with sparse interpolation.
static <E> MultivariatePolynomial<E>	MultivariateGCD.ZippelGCD(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b) Calculates GCD of two multivariate polynomials over Zp using Zippel's algorithm with sparse interpolation.
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
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Sparse modular GCD algorithm for polynomials over Z.
static MultivariatePolynomial<BigInteger>	MultivariateGCD.ZippelGCDInZ(MultivariatePolynomial<BigInteger> a, MultivariatePolynomial<BigInteger> b) Sparse modular GCD algorithm for polynomials over Z.
static <E> MultivariatePolynomial<E>	MultivariateResultants.ZippelResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Zippel's algorithm for resultant with sparse interpolation
static <E> MultivariatePolynomial<E>	MultivariateResultants.ZippelResultant(MultivariatePolynomial<E> a, MultivariatePolynomial<E> b, int variable) Zippel's algorithm for resultant with sparse interpolation

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

Modifier and Type	Method and Description
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.asNormalMultivariate(MultivariatePolynomial<MultivariatePolynomial<E>> poly, int[] coefficientVariables, int[] mainVariables) Converts multivariate polynomial over multivariate polynomial ring to a multivariate polynomial over coefficient ring
String	MultivariatePolynomial.coefficientRingToString(IStringifier<MultivariatePolynomial<E>> stringifier)
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 cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.GroebnerBasisInZ(List<MultivariatePolynomial<BigInteger>> generators, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean tryModular) Computes Groebner basis (minimized and reduced) of a given ideal over Z represented by a list of generators.
<T> MultivariatePolynomial<T>	MultivariatePolynomial.mapCoefficientsAsPolys(Ring<T> ring, Function<MultivariatePolynomial<E>,T> mapper)
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 cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm modularAlgorithm, cc.redberry.rings.poly.multivar.GroebnerBases.GroebnerAlgorithm defaultAlgorithm, BigInteger firstPrime, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries) Modular Groebner basis algorithm.
static cc.redberry.rings.poly.multivar.GroebnerBases.GBResult<Monomial<BigInteger>,MultivariatePolynomial<BigInteger>>	GroebnerBases.ModularGB(List<MultivariatePolynomial<BigInteger>> ideal, Comparator<DegreeVector> monomialOrder, GroebnerBases.HilbertSeries hilbertSeries, boolean trySparse) Modular Groebner basis algorithm.
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.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>>>	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
String	MultivariatePolynomial.toString(IStringifier<MultivariatePolynomial<E>> stringifier)

Constructors in cc.redberry.rings.poly.multivar with parameters of type MultivariatePolynomial

Constructor and Description
Interpolation(int variable, E point, MultivariatePolynomial<E> value) Start new interpolation with interpolation[variable = point] = value
Interpolation(int variable, MultivariatePolynomial<E> factory) Start new interpolation

Constructor parameters in cc.redberry.rings.poly.multivar with type arguments of type MultivariatePolynomial

Constructor and Description
Interpolation(int variable, IPolynomialRing<MultivariatePolynomial<E>> factory) Start new interpolation

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

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

Modifier and Type	Method and Description
MultivariatePolynomial<E>	UnivariatePolynomial.asMultivariate()
MultivariatePolynomial<E>	UnivariatePolynomial.asMultivariate(Comparator<DegreeVector> ordering)
MultivariatePolynomial<E>	UnivariatePolynomial.composition(AMultivariatePolynomial value)