Uses of Interface
cc.redberry.rings.Ring

Packages that use Ring

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

Uses of Ring in cc.redberry.rings

Classes in cc.redberry.rings that implement Ring

Modifier and Type	Class	Description
class	ARing<E>	Abstract ring which holds perfect power decomposition of its cardinality.
class	ImageRing<F,I>	A ring obtained via isomorphism specified by ImageRing.image(Object) and ImageRing.inverse(Object) functions.
class	Integers	The ring of integers (Z).
class	IntegersZp	Ring of integers modulo some modulus.
class	Rationals<E>	The ring of rationals (Q).

Fields in cc.redberry.rings declared as Ring

Modifier and Type	Field	Description
Ring<E>	FactorDecomposition.ring	The ring
Ring<F>	ImageRing.ring	the ring
Ring<E>	Rational.ring	The ring.
Ring<E>	Rationals.ring	Ring that numerator and denominator belongs to

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

Modifier and Type	Method	Description
static <E> E	ChineseRemainders.ChineseRemainders(Ring<E> ring, ChineseRemainders.ChineseRemaindersMagic<E> magic, E remainder1, E remainder2)	Runs Chinese Remainders algorithm using the precomputed magic (speed's up computation when several invocations with the same magic performed)
static <E> E	ChineseRemainders.ChineseRemainders(Ring<E> ring, E[] primes, E[] remainders)	Runs Chinese Remainders algorithm
static <E> E	ChineseRemainders.ChineseRemainders(Ring<E> ring, E prime1, E prime2, E remainder1, E remainder2)	Runs Chinese Remainders algorithm
static <E> ChineseRemainders.ChineseRemaindersMagic<E>	ChineseRemainders.createMagic(Ring<E> ring, E prime1, E prime2)	Magic for fast repeated Chinese Remainders
static <E> FactorDecomposition<E>	FactorDecomposition.empty(Ring<E> ring)	Empty factorization
static <E> Rationals<E>	Rings.Frac(Ring<E> ring)	Ring of rational functions over specified ring
static <E> AlgebraicNumberField<UnivariatePolynomial<E>>	Rings.GaussianNumbers(Ring<E> ring)	Gaussian numbers for a given ring (that is ring adjoined with imaginary unit)
<O> Rational<O>	Rational.map(Ring<O> ring, Function<E,O> function)	Maps rational to a new ring
<R> FactorDecomposition<R>	FactorDecomposition.mapTo(Ring<R> othRing, Function<E,R> mapper)
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 <E> FactorDecomposition<E>	FactorDecomposition.of(Ring<E> ring, E... factors)	Factor decomposition with specified factors and exponents
static <E> FactorDecomposition<E>	FactorDecomposition.of(Ring<E> ring, E unit, List<E> factors, gnu.trove.list.array.TIntArrayList exponents)	Factor decomposition with specified factors and exponents
static <E> FactorDecomposition<E>	FactorDecomposition.of(Ring<E> ring, Collection<E> factors)	Factor decomposition with specified factors and exponents
static <E> Rational<E>	Rational.one(Ring<E> ring)	Constructs one
static <E> FactorDecomposition<E>	FactorDecomposition.unit(Ring<E> ring, E unit)	Unit factorization
static <E> UnivariateRing<UnivariatePolynomial<E>>	Rings.UnivariateRing(Ring<E> coefficientRing)	Ring of univariate polynomials over specified coefficient ring
static <E> Rational<E>	Rational.zero(Ring<E> ring)	Constructs zero

Constructors in cc.redberry.rings with parameters of type Ring

Constructor	Description
FactorDecomposition(Ring<E> ring, E unit, List<E> factors, gnu.trove.list.array.TIntArrayList exponents)
ImageRing(Ring<F> ring, Function<I,F> inverseFunc, Function<F,I> imageFunc)
Rational(Ring<E> ring, E numerator)
Rational(Ring<E> ring, E numerator, E denominator)
Rationals(Ring<E> ring)

Uses of Ring in cc.redberry.rings.io

Fields in cc.redberry.rings.io declared as Ring

Modifier and Type	Field	Description
protected Ring<Element>	Coder.baseRing	the base ring

Fields in cc.redberry.rings.io with type parameters of type Ring

Modifier and Type	Field	Description
protected Map<Ring<?>,Coder<?,?,?>>	Coder.subcoders	inner coders
Map<Ring,IStringifier>	IStringifier.SimpleStringifier.substringifiers

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

Modifier and Type	Method	Description
<Oth> Coder<Oth,?,?>	Coder.map(Ring<Oth> ring, Function<Element,Oth> func)	Maps this coder to a given type via mapper func which just applies to each parsed element as well as to bindings (for IStringifier.stringify(Object)).
static <E> Coder<E,?,?>	Coder.mkCoder(Ring<E> ring)	Create coder for generic ring
static <E> Coder<E,?,?>	Coder.mkCoder(Ring<E> ring, Map<String,E> variables)	Create coder for generic rings
static <Element,Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>> Coder<Element,Term,Poly>	Coder.mkCoder(Ring<Element> baseRing, Map<String,Element> eVariables, MultivariateRing<Poly> polyRing, Map<String,Poly> pVariables, SerializableFunction<Poly,Element> polyToElement)
static <E,I> Coder<E,?,?>	Coder.mkNestedCoder(Ring<E> ring, Map<String,E> variables, Coder<I,?,?> innerCoder, SerializableFunction<I,E> imageFunc)	Create coder for nested rings (e.g.
<K> IStringifier<K>	Coder.substringifier(Ring<K> ring)
<U> IStringifier<U>	IStringifier.SimpleStringifier.substringifier(Ring<U> ring)
<UnderlyingElement> IStringifier<UnderlyingElement>	IStringifier.substringifier(Ring<UnderlyingElement> ring)	Get stringifier for the specified ring of some underlying elements, should never give null (use dummy() for absent stringifier)

Uses of Ring in cc.redberry.rings.linear

Methods in cc.redberry.rings.linear with parameters of type Ring

Modifier and Type	Method	Description
static <E> void	LinearSolver.reducedRowEchelonForm(Ring<E> ring, E[][] lhs, E[] rhs)	Gives the reduced row echelon form of the linear system lhs.x = rhs from a given row echelon form.
static <E> int	LinearSolver.rowEchelonForm(Ring<E> ring, E[][] matrix)	Gives the row echelon form of the matrix
static <E> int	LinearSolver.rowEchelonForm(Ring<E> ring, E[][] matrix, boolean reduce)	Gives the row echelon form of the matrix
static <E> int	LinearSolver.rowEchelonForm(Ring<E> ring, E[][] lhs, E[] rhs)	Gives the row echelon form of the linear system lhs.x = rhs.
static <E> int	LinearSolver.rowEchelonForm(Ring<E> ring, E[][] lhs, E[] rhs, boolean reduce, boolean breakOnUnderDetermined)	Gives the row echelon form of the linear system lhs.x = rhs.
static <E> E[]	LinearSolver.solve(Ring<E> ring, E[][] lhs, E[] rhs)	Solves linear system lhs.x = rhs and reduces lhs to row echelon form.
static <E> LinearSolver.SystemInfo	LinearSolver.solve(Ring<E> ring, E[][] lhs, E[] rhs, E[] result)	Solves linear system lhs.x = rhs and reduces the lhs to row echelon form.
static <E> LinearSolver.SystemInfo	LinearSolver.solve(Ring<E> ring, E[][] lhs, E[] rhs, E[] result, boolean solveIfUnderDetermined)	Solves linear system lhs.x = rhs and reduces the lhs to row echelon form.
static <E> LinearSolver.SystemInfo	LinearSolver.solve(Ring<E> ring, ArrayList<E[]> lhs, ArrayList<E> rhs, E[] result)	Solves linear system lhs.x = rhs and stores the result in result (which should be of the enough length).
static <E> E[]	LinearSolver.solveVandermonde(Ring<E> ring, E[] row, E[] rhs)	Solves Vandermonde linear system (that is with i-th equation of the form row[i]^0 * x0 + row[i]^1 * x1 + ... row[i]^N * xN = rhs[i] ).
static <E> LinearSolver.SystemInfo	LinearSolver.solveVandermonde(Ring<E> ring, E[] row, E[] rhs, E[] result)	Solves Vandermonde linear system (that is with i-th equation of the form row[i]^0 * x0 + row[i]^1 * x1 + ... row[i]^N * xN = rhs[i] ) and stores the result in result (which should be of the enough length).
static <E> E[]	LinearSolver.solveVandermondeT(Ring<E> ring, E[] row, E[] rhs)	Solves transposed Vandermonde linear system (that is with i-th equation of the form row[0]^i * x0 + row[1]^i * x1 + ... row[N]^i * xN = rhs[i] ).
static <E> LinearSolver.SystemInfo	LinearSolver.solveVandermondeT(Ring<E> ring, E[] row, E[] rhs, E[] result)	Solves transposed Vandermonde linear system (that is with i-th equation of the form row[0]^i * x0 + row[1]^i * x1 + ... row[N]^i * xN = rhs[i] ) and stores the result in result (which should be of the enough length).

Uses of Ring in cc.redberry.rings.poly

Subinterfaces of Ring in cc.redberry.rings.poly

Modifier and Type	Interface	Description
interface	IPolynomialRing<Poly extends IPolynomial<Poly>>	Polynomial ring.

Classes in cc.redberry.rings.poly that implement Ring

Modifier and Type	Class	Description
class	AlgebraicNumberField<E extends IUnivariatePolynomial<E>>	Algebraic number field F(α) represented as a simple field extension, for details see SimpleFieldExtension.
class	FiniteField<E extends IUnivariatePolynomial<E>>	Galois field GF(p, q).
class	MultipleFieldExtension<Term extends AMonomial<Term>,mPoly extends AMultivariatePolynomial<Term,mPoly>,sPoly extends IUnivariatePolynomial<sPoly>>	Multiple field extension F(α_1, α_2, ..., α_N).
class	MultivariateRing<Poly extends AMultivariatePolynomial<?,Poly>>	Ring of multivariate polynomials.
class	QuotientRing<Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>>	Multivariate quotient ring
class	SimpleFieldExtension<E extends IUnivariatePolynomial<E>>	A simple field extension F(α) represented as a univariate quotient ring F[x]/<m(x)> where m(x) is the minimal polynomial of α.
class	UnivariateRing<Poly extends IUnivariatePolynomial<Poly>>	Ring of univariate polynomials.

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

Modifier and Type	Method	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)

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

Fields in cc.redberry.rings.poly.multivar declared as Ring

Modifier and Type	Field	Description
Ring<E>	IMonomialAlgebra.MonomialAlgebra.ring
Ring<E>	MultivariatePolynomial.ring	The coefficient ring

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

Modifier and Type	Method	Description
<sPoly extends IUnivariatePolynomial<sPoly>> sPoly	AMultivariatePolynomial.composition(Ring<sPoly> uRing, sPoly... values)	Substitutes given polynomials instead of variables of this (that is this(values_1, ..., values_N))
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
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
<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
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)
<E> MultivariatePolynomial<E>	MultivariatePolynomialZp64.mapCoefficientsAsPolys(Ring<E> ring, Function<MultivariatePolynomialZp64,E> 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 <E> MultivariatePolynomial.PrecomputedPowersHolder<E>	MultivariatePolynomial.mkPrecomputedPowers(int nVariables, Ring<E> ring, int[] variables, E[] values)
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.one(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering)	Creates unit polynomial.
static <E> Ideal<Monomial<E>,MultivariatePolynomial<E>>	Ideal.parse(String[] generators, Ring<E> field, String[] variables)	Shortcut for parse
static <E> Ideal<Monomial<E>,MultivariatePolynomial<E>>	Ideal.parse(String[] generators, Ring<E> field, Comparator<DegreeVector> monomialOrder, String[] variables)	Shortcut for parse
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, String... variables)	Parse multivariate polynomial from string.
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>	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 <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 <Term extends AMonomial<Term>,Poly extends AMultivariatePolynomial<Term,Poly>,uPoly extends IUnivariatePolynomial<uPoly>> UnivariatePolynomial<uPoly>	HenselLifting.seriesExpansionDense(Ring<uPoly> ring, Poly poly, int variable, cc.redberry.rings.poly.multivar.HenselLifting.IEvaluation<Term,Poly> evaluate)	Generates a power series expansion for poly about the point specified by variable and evaluation
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
static <E> MultivariatePolynomial<E>	MultivariatePolynomial.zero(int nVariables, Ring<E> ring, Comparator<DegreeVector> ordering)	Creates zero polynomial.

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

Constructor	Description
MonomialAlgebra(Ring<E> ring)
PrecomputedPowersHolder(Ring<E> ring, cc.redberry.rings.poly.multivar.MultivariatePolynomial.PrecomputedPowers<E>[] powers)

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

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

Modifier and Type	Field	Description
Ring<E>	UnivariatePolynomial.ring	The coefficient ring

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

Modifier and Type	Method	Description
default Poly	IUnivariatePolynomial.composition(Ring<Poly> ring, Poly value)	Calculates the composition of this(oth) (new instance, so the content of this is not changed))
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.constant(Ring<E> ring, E constant)	Creates constant polynomial over specified ring
static UnivariatePolynomial<BigInteger>	UnivariatePolynomial.create(Ring<BigInteger> ring, long... data)	Creates univariate polynomial over specified ring (with integer elements) with the specified coefficients
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.create(Ring<E> ring, E... data)	Creates new univariate polynomial over specified ring with the specified coefficients.
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.createUnsafe(Ring<E> ring, E[] data)	skips ring.setToValueOf(data)
static <E> UnivariatePolynomial<E>	UnivariateInterpolation.interpolateLagrange(Ring<E> ring, E[] points, E[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
static <E> UnivariatePolynomial<E>	UnivariateInterpolation.interpolateNewton(Ring<E> ring, E[] points, E[] values)	Constructs an interpolating polynomial which values at points[i] are exactly values[i].
<T> UnivariatePolynomial<T>	UnivariatePolynomial.mapCoefficients(Ring<T> ring, Function<E,T> mapper)	Applies transformation function to this and returns the result.
default <E> UnivariatePolynomial<E>	IUnivariatePolynomial.mapCoefficientsAsPolys(Ring<E> ring, Function<Poly,E> mapper)
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.one(Ring<E> ring)	Creates unit polynomial over specified ring
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.parse(String string, Ring<E> ring)	Deprecated. use UnivariatePolynomial.parse(String, Ring, String)
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.parse(String string, Ring<E> ring, String var)	Parse string into polynomial
static <E> E[]	RandomUnivariatePolynomials.randomArray(int degree, Ring<E> ring, Function<org.apache.commons.math3.random.RandomGenerator,E> method, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements from the specified ring
static <E> E[]	RandomUnivariatePolynomials.randomArray(int degree, Ring<E> ring, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random array of length degree + 1 with elements from the specified ring
static <E> UnivariatePolynomial<E>	IrreduciblePolynomials.randomIrreduciblePolynomial(Ring<E> ring, int degree, org.apache.commons.math3.random.RandomGenerator rnd)	Generated random irreducible polynomial over specified ring of degree degree
static <E> UnivariatePolynomial<E>	RandomUnivariatePolynomials.randomMonicPoly(int degree, Ring<E> ring, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree.
static <E> UnivariatePolynomial<E>	RandomUnivariatePolynomials.randomPoly(int degree, Ring<E> ring, Function<org.apache.commons.math3.random.RandomGenerator,E> method, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree with elements from specified ring
static <E> UnivariatePolynomial<E>	RandomUnivariatePolynomials.randomPoly(int degree, Ring<E> ring, org.apache.commons.math3.random.RandomGenerator rnd)	Creates random polynomial of specified degree with elements from specified ring
UnivariatePolynomial<E>	UnivariatePolynomial.setRing(Ring<E> newRing)	Returns a copy of this with elements reduced to a new coefficient ring
UnivariatePolynomial<E>	UnivariatePolynomial.setRingUnsafe(Ring<E> newRing)	internal API
static <E> UnivariatePolynomial<E>	UnivariatePolynomial.zero(Ring<E> ring)	Creates zero polynomial over specified ring

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

Constructor	Description
Interpolation(Ring<E> ring)	Start new interpolation with interpolation[point] = value
PolynomialCollector(Ring<E> ring)