All Classes and Interfaces

Class	Description
AbstractModule<V,S,R extends Ring<S>>
AbstractVectorSpace<V,S,F extends Field<S>>
AdditiveGroup<E>	An additive group is like a Group but where the operation is commutative and is called add.
AffinePoint<E>
AKS	Implementation of the AKS deterministic primality test.
AlgebraicFieldExtension<E,F extends Field<E>>
ArgMax<A extends Comparable<A>>
ArrayUtils
BarrettReduction	Barrett reduction is a fast method for computing x mod m for large x and m.
BaseMatrix<E>	This class represents a matrix of elements of type E.
BaseVector<E>
BatchPolynomialEvaluation<E>	Batch polynomial evaluation using the Moenck–Borodin algorithm.
BellPolynomials	This demo computes the first 16 Bell polynomials.
BerlekampRabinAlgorithm	Find a root of a polynomial over a prime field using the probabilistic Berlekamp-Rabin algorithm.
BigElement<E>
BigElements<E>
BigFiniteField
BigIntegers
BigIntegersModuloN	This class is an implementation of ℤ / nℤ, e.g.
BigLegendreSymbol	Compute the Legendre symbol of a number a modulo a prime p.
BigPrimeField
BigRationals
BigTonelliShanks
BinaryGCD
BinaryTree<L>	This represents a labeled binary tree where the label of an internal node is the result of an operation on the labels of its children.
BinaryTree.SubproductTree<E>	A binary tree where the leafs are x-l_i for a set of constants (l_0, ..., l_{n-1}) and internal nodes are the product of their children.
BitLength<E>	Compute the bit length of an element in a ring assuming access to a bit shift operation.
BLS12381
BLS12381	Implementation of the BLS12-381 pairing-friendly elliptic curve construction.
BN254	Implementation of the BN254 (aka BN128) pairing-friendly elliptic curve construction.
Calculator<E>
CauchyMatrix
CharacteristicPolynomial<E>
ChineseRemainderTheorem<E>	Compute the solution to a system of congruences using the Chinese Remainder Theorem.
ClassGroup	This implements the ideal class group for a negative discriminant.
CommutativeMonoid<E>	A commutative monoid is a set with an associative and commutative addition operation.
ComplexCoordinateSpace
ComplexNumber
ComplexNumbers
ConcreteVector<E>
CongruenceSolver
Constants
ConstructiveReal
ConstructiveReals	The real numbers represented as constructive reals, e.g.
ConstructiveRealsDemo	A demo of using constructive reals for various computations.
ConstructiveVector<E>
Curve25519
DataConversionPrimitives
Determinant<E>	Calculate the determinant of a matrix.
DeterminantFormula	Compute a closed formula for the determinant of a 6x6 matrix
DiscreteFourierTransform<E>	Compute the Discrete Fourier Transform over a ring.
DotProduct<E>	Compute the dot product of two vectors over a ring.
ECMDemo	Implementation of the elliptic-curve factorization method (ECM).
EdwardsCurve<E,F extends Field<E>>	Instances of this class represents a curve over a field over elements of type E satisfying the equation x2 + y2 = 1 + d x2 y2.
EdwardsPoint<E>	Instances of this class represents a point on an Edwards Curve over a field with elements of type E.
EncodingUtils
EuclideanAlgorithm<E>	Implementation of the Euclidean algorithm for computing the greatest common divisor of two elements in a Euclidean domain.
EuclideanAlgorithm.ExtendedResult<E>
EuclideanAlgorithm.Result<E>
EuclideanDomain<E>	A Euclidean domain is a ring with Euclidean division.
EulersTotientFunction
EvaluationException
Evaluator<NumberT>	This class can evaluate expressions parsed to reverse polish notation using the Parser class.
Factorize
FastDivision<E>	Algorthm 9.5 from Modern Computer Algebra.
Field<E>	A field is a commutative ring where every non-zero element has a multiplicative inverse.
FieldOfFractions<E>
FiniteField
Fraction<E>	A fraction.
GaussianElimination<E>	Perform Gaussian elimination on a matrix.
GaussianRationals
GeneralLinearGroup<E,F extends Field<E>>	This class represents the general linear group GL(n, F) of invertible n × n matrices over a field F.
GradedLexicographicalOrdering
GramMatrix<E>	Compute the Gram matrix for a given matrix.
GramSchmidt<V,S,F extends Field<S>>	Gram-Schmidt orthogonalization.
GramSchmidtOverRing<E>	Gram-Schmidt orthogonalization over a ring.
GröbnerBasis<E>
Group<E>	A group is a set with an operation and an inverse operation.
HadamardMatrix	Find an Hadamard Matrix of order 92 using Williamson's method as presented in J.S.
InnerProductSpace<V,S,F extends Field<S>>	A group is a set with an associative addition operation and an inverse operation.
IntBinaryFunction<E>
IntegerPolynomial
IntegerRingEmbedding<E>	This function computes the canonical embedding of the integers into any ring by mapping an integer n to the identity element added to itself n times.
Integers
IntegersModuloN	This class is an implementation of ℤ / nℤ, e.g.
InvalidParametersException
InverseDiscreteFourierTransform<E>	Compute the Inverse Discrete Fourier Transform over a ring, assuming that n has an inverse over the ring.
Inversion<E>	Assuming f(0) = 1, this computes g such that fg = 1 (mod x^l).
JacobianPoint<E>
JacobiSymbol	Compute the Jacobi symbol of a number a modulo an odd number n.
KaratsubaAlgorithm<E>	The Karatsuba algorithm for multiplying two polynomials.
KroneckerProduct<E>	Compute the Kronecker product of two matrices.
LagrangePolynomial<E>	Compute the Lagrange interpolation polynomial which is the polynomial of the lowest degree which assumes a given set of points.
LexicographicalOrdering
MathUtils
Matrix<E>	A representation of a matrix taking entries of type E.
MatrixAddition<E>	Compute the sum of two matrices.
MatrixIndex
MatrixInversion<E>	Compute the inverse of a matrix.
MatrixMultiplication<E>	This function computes the product of two matrices.
MatrixRing<E>	This class represents a ring of n × n matrices over a base ring.
MillersAlgorithm<E>	Given two points P and Q of order m on an elliptic curve, this algorithm computes f(Q) where div(f) = [m]P - m[O].
ModularSquareRoot
Module<V,S,R extends Ring<S>>	A module over a ring R is an additive group V together with a scalar multiplication.
Monoid<E>	A monoid is a set with an associative operation.
Monomial
MonomialOrdering
MontgomeryCurve<E,F extends Field<E>>	Curve on Montgomery form By2 = x3 + Ax2 + x.
MultiDimensionalArray<T>	A multi-dimensional array is a data collection where entries are indexed by a fixed length vector (the length equals the dimension of the array).
MultiOperator<T>
MultiOperator<E>	Instances of this class allows for easy repeated application of a binary operator on many operands.
Multiply<E>	Compute e a for and integer e and an element from an additive group, a.
MultivariatePolynomial<E>
MultivariatePolynomial.Builder<S>
MultivariatePolynomialDivision<E>
MultivariatePolynomialRing<E>	This class implements the ring of polynomials K[x] over a field K.
MultivariatePolynomialRingOverRing<E>	This class implements the ring of polynomials K[x] over a field K.
MultivariatePolynomials
MutableMatrix<E>	Instances of this class represents a mutable matrix.
NormedVectorSpace<V,S,F extends Field<S>>	An inner product space is a vector space with an inner product.
NotASquareException
NotInvertibleException
NullSafeRing<E>	This class wraps a ring but operations will treat null operands as if they were zero.
NumberParser<T>
OptimalAtePairing<E1,E2,ET>	Compute the optimal Ate pairing.
OrderedSet<E>	A set with an ordering.
Pair<E,F>
Parser<NumberT>	This class parses arithmetic expressions into reverse polish notation which makes them easy to evaluate.
PerformanceLoggingField<E>	Wrapper for the ring class which logs the number of operations performed in this ring.
PerformanceLoggingRing<E>	Wrapper for the ring class which logs the number of operations performed in this ring.
Permutation
PermutationUtils
PollardRho
Polynomial<E>
Polynomial<S>
Polynomial.Builder<S>
PolynomialInterpolation<E>
PolynomialMultiplication
PolynomialRing<E>	This class implements the ring of polynomials K[x] over a field K.
PolynomialRingFFT<E>	This class implements the ring of polynomials K[x] over a field K.
PolynomialRingKaratsuba<E>	This class implements the ring of polynomials K[x] over a field K.
PolynomialRingOverRing<E>
Poseidon
Poseidon.PoseidonHash<E>
Power<E>	Compute ae for a BigInteger e.
PrimeField
Product<E>	Compute the product of a list of elements over a monoid.
Projection<V,S,F extends Field<S>>	Compute the projection of a vector v onto another vector u in the given vector space.
ProjectivePoint<E>
QRDecomposition<E,F extends Field<E>>	Compute the QR decomposition of a matrix.
QuadraticEquation<E,F extends Field<E>>	Solve a quadratic equation of the form ax^2 + bx + c = 0 over a field of characteristic != 2.
QuadraticField
QuadraticForm<E,R extends EuclideanDomain<E> & OrderedSet<E>>
QuotientRing<E>
RandomDerangement
Rationals
RealCoordinateSpace
RealNumbers	Real numbers represented by Doubles.
Ring<E>	A ring is a set with an associative and commutative addition operation and an associative multiplication operation.
RungeKutta<V>	Numerical integration using the Runge-Kutta method.
SamePair<E>
SamplingUtils
Semigroup<E>	A semigroup is a set with an associative multiplication operation.
SemiRing<E>	A semiring is a set with an associative and commutative addition operation and an associative multiplication operation.
Serialization
Serialization.Group
Set<E>	A set is a collection of elements.
ShortWeierstrassCurveAffine<E,F extends Field<E>>
ShortWeierstrassCurveProjective<E>
SparseMatrix<E>	This class represents a sparse matrix by only storing the non-zero entries.
SparseMatrix.Builder<F>
StrassenDemo	Compute the product of two 8x8 matrices using the traditional algorithm and Strassen's algorithm and compare the number of operations used for each.
StrassenMultiplication<E>	This function computes the product of two square matrices using the Strassen algorithm.
StreamUtils
StringUtils
Sum<E>	Compute the sum of a list of elements over an additive group.
SymmetricGroup
TernaryOperator<A>
TestUtils
TestUtils.TestBigIntegers
TestUtils.TestField
TestUtils.TestIntegers
Token	Instances of this class represents a token in an arithmetic expression.
Token.Type
TonelliShanks
TriFunction<A,B,C,D>
Triple<E,F,G>
Vector<E>
VectorGroup<E>
VectorSpace<V,S,F extends Field<S>>	A vector space is a module over a field.
VectorSpaceOverField<E,F extends Field<E>>
WeilPairing<E>	Compute the Weil pairing of two points on an elliptic curve.
WeilPairingDemo