Uses of Class
org.episteme.core.mathematics.numbers.integers.Natural

Packages that use Natural

Package	Description
org.episteme.core.mathematics.algebra.intervals
org.episteme.core.mathematics.analysis.series
org.episteme.core.mathematics.discrete.generators
org.episteme.core.mathematics.numbers.integers
org.episteme.core.mathematics.numbertheory
org.episteme.core.mathematics.random
org.episteme.core.mathematics.sets
org.episteme.core.mathematics.topology
org.episteme.social.history.time	Temporal coordinate and interval support for historical analysis.

Uses of Natural in org.episteme.core.mathematics.algebra.intervals

Methods in org.episteme.core.mathematics.algebra.intervals that return types with arguments of type Natural

Modifier and Type	Method	Description
static RingIntervalND<Natural>	NaturalInterval.closed(long min, long max)	Creates a closed interval [min, max] from long values.
static RingIntervalND<Natural>	NaturalInterval.closed(Natural min, Natural max)	Creates a closed interval [min, max] over Natural numbers.
static RingIntervalND<Natural>	NaturalInterval.closedOpen(long min, long max)	Creates a half-open interval [min, max) from long values.
static RingIntervalND<Natural>	NaturalInterval.closedOpen(Natural min, Natural max)	Creates a half-open interval [min, max) over Natural numbers.
static Iterator<Natural>	NaturalInterval.iterator(Interval<Natural> interval)	Returns an iterator over all Natural numbers in the interval.
static RingIntervalND<Natural>	NaturalInterval.open(long min, long max)	Creates an open interval (min, max) from long values.
static RingIntervalND<Natural>	NaturalInterval.open(Natural min, Natural max)	Creates an open interval (min, max) over Natural numbers.
static RingIntervalND<Natural>	NaturalInterval.singleton(long value)	Creates an interval containing a single Natural number from a long.
static RingIntervalND<Natural>	NaturalInterval.singleton(Natural value)	Creates an interval containing a single Natural number.
static Stream<Natural>	NaturalInterval.stream(Interval<Natural> interval)	Returns a stream of all Natural numbers in the interval.

Methods in org.episteme.core.mathematics.algebra.intervals with parameters of type Natural

Modifier and Type	Method	Description
static RingIntervalND<Natural>	NaturalInterval.closed(Natural min, Natural max)	Creates a closed interval [min, max] over Natural numbers.
static RingIntervalND<Natural>	NaturalInterval.closedOpen(Natural min, Natural max)	Creates a half-open interval [min, max) over Natural numbers.
static RingIntervalND<Natural>	NaturalInterval.open(Natural min, Natural max)	Creates an open interval (min, max) over Natural numbers.
static RingIntervalND<Natural>	NaturalInterval.singleton(Natural value)	Creates an interval containing a single Natural number.

Method parameters in org.episteme.core.mathematics.algebra.intervals with type arguments of type Natural

Modifier and Type	Method	Description
static boolean	NaturalInterval.isEmpty(Interval<Natural> interval)	Returns whether the interval is empty.
static Iterator<Natural>	NaturalInterval.iterator(Interval<Natural> interval)	Returns an iterator over all Natural numbers in the interval.
static long	NaturalInterval.size(Interval<Natural> interval)	Returns the number of Natural numbers in the interval.
static Stream<Natural>	NaturalInterval.stream(Interval<Natural> interval)	Returns a stream of all Natural numbers in the interval.

Uses of Natural in org.episteme.core.mathematics.analysis.series

Subinterfaces with type arguments of type Natural in org.episteme.core.mathematics.analysis.series

Modifier and Type	Interface	Description
interface	Sequence<T>	A mathematical sequence a(n) for n ≥ 0.

Methods in org.episteme.core.mathematics.analysis.series with parameters of type Natural

Modifier and Type	Method	Description
default T	Sequence.apply(Natural n)	Function interface implementation - delegates to get(Natural).
default T	Sequence.evaluate(Natural n)	Function interface implementation - delegates to get(Natural).
Integer	BellSequence.get(Natural n)
Integer	CatalanSequence.get(Natural n)
Integer	FactorialSequence.get(Natural n)
Integer	FibonacciSequence.get(Natural n)
Integer	PrimePiSequence.get(Natural n)
Integer	PrimeSequence.get(Natural n)
T	Sequence.get(Natural n)	Returns the n-th term of the sequence (0-indexed).
Integer	SquareSequence.get(Natural n)
Integer	TriangularSequence.get(Natural n)
default long	IntegerSequence.getLong(Natural n)	Convenience method to get value as long using Natural index.

Uses of Natural in org.episteme.core.mathematics.discrete.generators

Methods in org.episteme.core.mathematics.discrete.generators that return types with arguments of type Natural

Modifier and Type	Method	Description
static Graph<Natural>	ScaleFreeGenerator.generate(int n, int m0, int m)	Generates a scale-free network.
static Graph<Natural>	SmallWorldGenerator.generate(int n, int k, double beta)	Generates a small-world network.

Uses of Natural in org.episteme.core.mathematics.numbers.integers

Classes in org.episteme.core.mathematics.numbers.integers that implement interfaces with type arguments of type Natural

Modifier and Type	Class	Description
class	Natural	Abstract base class for natural numbers (â„• = {0, 1, 2, ...}).
class	Natural	Abstract base class for natural numbers (â„• = {0, 1, 2, ...}).

Fields in org.episteme.core.mathematics.numbers.integers declared as Natural

Modifier and Type	Field	Description
static final Natural	Natural.ONE	The natural number 1
static final Natural	Natural.ZERO	The natural number 0

Methods in org.episteme.core.mathematics.numbers.integers that return Natural

Modifier and Type	Method	Description
abstract Natural	Natural.add(Natural other)	Adds another natural number.
abstract Natural	Natural.divide(Natural other)	Divides by another natural number (integer division).
abstract Natural	Natural.modulo(Natural other)	Computes this modulo another natural number.
abstract Natural	Natural.multiply(Natural other)	Multiplies by another natural number.
static Natural	Natural.of(int value)	Creates a natural number from an int value.
static Natural	Natural.of(long value)	Creates a natural number from a long value.
static Natural	Natural.of(BigInteger value)	Creates a natural number from a BigInteger.
abstract Natural	Natural.subtract(Natural other)	Subtracts another natural number.

Methods in org.episteme.core.mathematics.numbers.integers with parameters of type Natural

Modifier and Type	Method	Description
abstract Natural	Natural.add(Natural other)	Adds another natural number.
abstract int	Natural.compareTo(Natural other)
abstract Natural	Natural.divide(Natural other)	Divides by another natural number (integer division).
abstract Natural	Natural.modulo(Natural other)	Computes this modulo another natural number.
abstract Natural	Natural.multiply(Natural other)	Multiplies by another natural number.
abstract Natural	Natural.subtract(Natural other)	Subtracts another natural number.

Uses of Natural in org.episteme.core.mathematics.numbertheory

Methods in org.episteme.core.mathematics.numbertheory that return Natural

Modifier and Type	Method	Description
static Natural	NumberTheory.eulerTotient(Natural n)	Euler's totient function φ(n): count of numbers ≤ n coprime to n.
static Natural	NumberTheory.gcd(Natural a, Natural b)	Euclidean algorithm for GCD.
static Natural	NumberTheory.lcm(Natural a, Natural b)	Least common multiple.
static Natural	NumberTheory.modInverse(Natural a, Natural m)	Modular inverse: finds x such that (a * x) ≡ 1 (mod m).
static Natural	NumberTheory.modPow(Natural base, Natural exp, Natural m)	Modular exponentiation: (base^exp) mod m.

Methods in org.episteme.core.mathematics.numbertheory with parameters of type Natural

Modifier and Type	Method	Description
static Natural	NumberTheory.eulerTotient(Natural n)	Euler's totient function φ(n): count of numbers ≤ n coprime to n.
static Natural	NumberTheory.gcd(Natural a, Natural b)	Euclidean algorithm for GCD.
static boolean	NumberTheory.isProbablePrime(Natural n, int certainty)	Probabilistic primality test using Miller-Rabin.
static Natural	NumberTheory.lcm(Natural a, Natural b)	Least common multiple.
static Natural	NumberTheory.modInverse(Natural a, Natural m)	Modular inverse: finds x such that (a * x) ≡ 1 (mod m).
static Natural	NumberTheory.modPow(Natural base, Natural exp, Natural m)	Modular exponentiation: (base^exp) mod m.

Uses of Natural in org.episteme.core.mathematics.random

Methods in org.episteme.core.mathematics.random that return Natural

Modifier and Type	Method	Description
Natural	RandomGenerator.nextNatural(int bound)	Returns random Natural in [0, bound).

Uses of Natural in org.episteme.core.mathematics.sets

Classes in org.episteme.core.mathematics.sets that implement interfaces with type arguments of type Natural

Modifier and Type	Class	Description
final class	Naturals	The structure of natural numbers (â„• = {0, 1, 2, 3, ...}).
final class	Naturals	The structure of natural numbers (â„• = {0, 1, 2, 3, ...}).

Methods in org.episteme.core.mathematics.sets that return Natural

Modifier and Type	Method	Description
Natural	Naturals.add(Natural a, Natural b)
Natural	Naturals.multiply(Natural a, Natural b)
Natural	Naturals.one()
Natural	Naturals.operate(Natural a, Natural b)
Natural	Naturals.zero()

Methods in org.episteme.core.mathematics.sets that return types with arguments of type Natural

Modifier and Type	Method	Description
Stream<Natural>	Naturals.stream(int count)	Returns a stream of the first n natural numbers.

Methods in org.episteme.core.mathematics.sets with parameters of type Natural

Modifier and Type	Method	Description
Natural	Naturals.add(Natural a, Natural b)
boolean	Naturals.contains(Natural element)
Natural	Naturals.multiply(Natural a, Natural b)
Natural	Naturals.operate(Natural a, Natural b)

Uses of Natural in org.episteme.core.mathematics.topology

Methods in org.episteme.core.mathematics.topology that return types with arguments of type Natural

Modifier and Type	Method	Description
Set<Natural>	Simplex.getVertices()	Returns the vertices of this simplex.

Constructors in org.episteme.core.mathematics.topology with parameters of type Natural

Modifier	Constructor	Description
	Simplex(Natural... verts)	Creates a simplex from a list of Natural vertex IDs.

Constructor parameters in org.episteme.core.mathematics.topology with type arguments of type Natural

Modifier	Constructor	Description
	Simplex(Set<Natural> verts)	Creates a simplex from a set of vertex IDs.

Uses of Natural in org.episteme.social.history.time

Methods in org.episteme.social.history.time that return Natural

Modifier and Type	Method	Description
Natural	FuzzyTimePoint.getYear()