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

Packages that use Integer

Package	Description
org.episteme.core.mathematics.algebra.groups
org.episteme.core.mathematics.algebra.intervals
org.episteme.core.mathematics.algebra.polynomials
org.episteme.core.mathematics.analysis.series
org.episteme.core.mathematics.loaders.mathml	Provides the invalid reference org.episteme.core.ml.mathml module.
org.episteme.core.mathematics.numbers.integers
org.episteme.core.mathematics.numbers.rationals
org.episteme.core.mathematics.numbertheory
org.episteme.core.mathematics.random
org.episteme.core.mathematics.sequences
org.episteme.core.mathematics.sets

Uses of Integer in org.episteme.core.mathematics.algebra.groups

Classes in org.episteme.core.mathematics.algebra.groups that implement interfaces with type arguments of type Integer

Modifier and Type	Class	Description
class	CyclicGroup	Represents a Cyclic Group of order n (Z_n).

Methods in org.episteme.core.mathematics.algebra.groups that return Integer

Modifier and Type	Method	Description
Integer	CyclicGroup.getOrder()	Returns the order of this group.
Integer	CyclicGroup.identity()
Integer	CyclicGroup.inverse(Integer element)
Integer	CyclicGroup.operate(Integer a, Integer b)

Methods in org.episteme.core.mathematics.algebra.groups with parameters of type Integer

Modifier and Type	Method	Description
boolean	CyclicGroup.contains(Integer element)
Integer	CyclicGroup.inverse(Integer element)
Integer	CyclicGroup.operate(Integer a, Integer b)

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

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

Modifier and Type	Method	Description
static RingIntervalND<Integer>	IntegerInterval.closed(long min, long max)	Creates a closed interval [min, max] from long values.
static RingIntervalND<Integer>	IntegerInterval.closed(Integer min, Integer max)	Creates a closed interval [min, max] over Integer numbers.
static RingIntervalND<Integer>	IntegerInterval.closedOpen(long min, long max)	Creates a half-open interval [min, max) from long values.
static RingIntervalND<Integer>	IntegerInterval.closedOpen(Integer min, Integer max)	Creates a half-open interval [min, max) over Integer numbers.
static Iterator<Integer>	IntegerInterval.iterator(Interval<Integer> interval)	Returns an iterator over all Integer numbers in the interval.
static RingIntervalND<Integer>	IntegerInterval.open(long min, long max)	Creates an open interval (min, max) from long values.
static RingIntervalND<Integer>	IntegerInterval.open(Integer min, Integer max)	Creates an open interval (min, max) over Integer numbers.
static RingIntervalND<Integer>	IntegerInterval.range(long n)	Creates a range from 0 to n-1 (useful for array indexing).
static RingIntervalND<Integer>	IntegerInterval.range(long start, long end)	Creates a range from start to end-1 (Python-style range).
static RingIntervalND<Integer>	IntegerInterval.singleton(long value)	Creates an interval containing a single Integer number from a long.
static RingIntervalND<Integer>	IntegerInterval.singleton(Integer value)	Creates an interval containing a single Integer number.
static Stream<Integer>	IntegerInterval.stream(Interval<Integer> interval)	Returns a stream of all Integer numbers in the interval.

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

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

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

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

Uses of Integer in org.episteme.core.mathematics.algebra.polynomials

Fields in org.episteme.core.mathematics.algebra.polynomials declared as Integer

Modifier and Type	Field	Description
final Integer	PolynomialFactorization.Factorization.content

Fields in org.episteme.core.mathematics.algebra.polynomials with type parameters of type Integer

Modifier and Type	Field	Description
final List<Polynomial<Integer>>	PolynomialFactorization.Factorization.factors
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.gcd
final List<Integer>	PolynomialFactorization.Factorization.multiplicities
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.s
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.t

Methods in org.episteme.core.mathematics.algebra.polynomials that return Integer

Modifier and Type	Method	Description
static Integer	PolynomialAlgebra.content(Polynomial<Integer> p)	Content of polynomial (GCD of all coefficients).
static Integer	PolynomialAlgebra.discriminant(Polynomial<Integer> p)	Discriminant of polynomial.
static Integer	PolynomialAlgebra.resultant(Polynomial<Integer> a, Polynomial<Integer> b)	Resultant of two polynomials.

Methods in org.episteme.core.mathematics.algebra.polynomials that return types with arguments of type Integer

Modifier and Type	Method	Description
static Polynomial<Integer>	PolynomialAlgebra.derivative(Polynomial<Integer> p)	Computes derivative of polynomial.
static Polynomial<Integer>	PolynomialAlgebra.derivative(Polynomial<Integer> p, int n)	Computes nth derivative.
static PolynomialDivision.DivisionResult<Integer>	PolynomialDivision.divide(Polynomial<Integer> dividend, Polynomial<Integer> divisor)	Performs polynomial division of dividend by divisor.
static List<Polynomial<Integer>>	PolynomialFactorization.factorQuadratic(Integer a, Integer b, Integer c)	Factors quadratic ax² + bx + c.
static Polynomial<Integer>	PolynomialAlgebra.gcd(Polynomial<Integer> a, Polynomial<Integer> b)	Euclidean algorithm for polynomial GCD.
static Polynomial<Integer>	PolynomialAlgebra.primitivePart(Polynomial<Integer> p)	Primitive part: polynomial / content
static List<Polynomial<Integer>>	PolynomialAlgebra.squareFreeFactorization(Polynomial<Integer> f)	Square-free factorization: f = ∏ f_i^i

Methods in org.episteme.core.mathematics.algebra.polynomials with parameters of type Integer

Modifier and Type	Method	Description
static List<Polynomial<Integer>>	PolynomialFactorization.factorQuadratic(Integer a, Integer b, Integer c)	Factors quadratic ax² + bx + c.

Method parameters in org.episteme.core.mathematics.algebra.polynomials with type arguments of type Integer

Modifier and Type	Method	Description
static Integer	PolynomialAlgebra.content(Polynomial<Integer> p)	Content of polynomial (GCD of all coefficients).
static Polynomial<Integer>	PolynomialAlgebra.derivative(Polynomial<Integer> p)	Computes derivative of polynomial.
static Polynomial<Integer>	PolynomialAlgebra.derivative(Polynomial<Integer> p, int n)	Computes nth derivative.
static Integer	PolynomialAlgebra.discriminant(Polynomial<Integer> p)	Discriminant of polynomial.
static PolynomialDivision.DivisionResult<Integer>	PolynomialDivision.divide(Polynomial<Integer> dividend, Polynomial<Integer> divisor)	Performs polynomial division of dividend by divisor.
static PolynomialFactorization.Factorization	PolynomialFactorization.factor(Polynomial<Integer> p)	Factors polynomial completely over integers.
static Polynomial<Integer>	PolynomialAlgebra.gcd(Polynomial<Integer> a, Polynomial<Integer> b)	Euclidean algorithm for polynomial GCD.
static boolean	PolynomialAlgebra.isIrreducible(Polynomial<Integer> p)	Checks if polynomial is irreducible.
static Polynomial<Integer>	PolynomialAlgebra.primitivePart(Polynomial<Integer> p)	Primitive part: polynomial / content
static Integer	PolynomialAlgebra.resultant(Polynomial<Integer> a, Polynomial<Integer> b)	Resultant of two polynomials.
static List<Polynomial<Integer>>	PolynomialAlgebra.squareFreeFactorization(Polynomial<Integer> f)	Square-free factorization: f = ∏ f_i^i

Constructors in org.episteme.core.mathematics.algebra.polynomials with parameters of type Integer

Modifier	Constructor	Description
	Factorization(Integer content, List<Polynomial<Integer>> factors, List<Integer> multiplicities)

Constructor parameters in org.episteme.core.mathematics.algebra.polynomials with type arguments of type Integer

Modifier	Constructor	Description
	ExtendedGCDResult(Polynomial<Integer> gcd, Polynomial<Integer> s, Polynomial<Integer> t)
	Factorization(Integer content, List<Polynomial<Integer>> factors, List<Integer> multiplicities)

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

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

Modifier and Type	Interface	Description
interface	IntegerSequence	A sequence of integers (ℤ).

Methods in org.episteme.core.mathematics.analysis.series that return Integer

Modifier and Type	Method	Description
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(int n)	Convenience method using primitive int.
Integer	PrimeSequence.get(Natural n)
Integer	SquareSequence.get(Natural n)
Integer	TriangularSequence.get(Natural n)

Uses of Integer in org.episteme.core.mathematics.loaders.mathml

Method parameters in org.episteme.core.mathematics.loaders.mathml with type arguments of type Integer

Modifier and Type	Method	Description
Element	MathMLDocumentEpistemeImpl.createIntegerMatrix(DenseMatrix<Integer> m)
Element	MathMLDocumentEpistemeImpl.createIntegerVector(DenseVector<Integer> v)

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

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

Modifier and Type	Class	Description
class	Integer	Abstract base class for integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
class	Integer	Abstract base class for integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
class	Integer	Abstract base class for integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).

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

Modifier and Type	Field	Description
static final Integer	Integer.MINUS_ONE	The integer -1
static final Integer	Integer.ONE	The integer 1
static final Integer	Integer.ZERO	The integer 0

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

Modifier and Type	Method	Description
abstract Integer	Integer.abs()	Returns the absolute value of this integer.
abstract Integer	Integer.add(Integer other)	Adds another integer.
abstract Integer	Integer.divide(Integer other)	Divides by another integer (integer division).
Integer	Integer.gcd(Integer other)	Returns the greatest common divisor of absolute value of this integer and absolute value of other integer.
abstract Integer	Integer.mod(Integer divisor)	Returns the remainder of the division of this integer by the specified integer.
abstract Integer	Integer.multiply(Integer other)	Multiplies by another integer.
abstract Integer	Integer.negate()	Returns the negation of this integer.
static Integer	Integer.of(int value)	Creates an integer from an int value.
static Integer	Integer.of(long value)	Creates an integer from a long value.
static Integer	Integer.of(BigInteger value)	Creates an integer from a BigInteger.
Integer	Integer.one()
abstract Integer	Integer.remainder(Integer other)	Computes the remainder of division.
abstract Integer	Integer.subtract(Integer other)	Subtracts another integer.
static Integer	Integer.valueOf(String value)	Creates an integer from a String representation.
Integer	Integer.zero()

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

Modifier and Type	Method	Description
abstract Integer	Integer.add(Integer other)	Adds another integer.
abstract int	Integer.compareTo(Integer other)
abstract Integer	Integer.divide(Integer other)	Divides by another integer (integer division).
Integer	Integer.gcd(Integer other)	Returns the greatest common divisor of absolute value of this integer and absolute value of other integer.
abstract Integer	Integer.mod(Integer divisor)	Returns the remainder of the division of this integer by the specified integer.
abstract Integer	Integer.multiply(Integer other)	Multiplies by another integer.
abstract Integer	Integer.remainder(Integer other)	Computes the remainder of division.
abstract Integer	Integer.subtract(Integer other)	Subtracts another integer.

Uses of Integer in org.episteme.core.mathematics.numbers.rationals

Methods in org.episteme.core.mathematics.numbers.rationals that return Integer

Modifier and Type	Method	Description
Integer	Rational.ceil()
Integer	Rational.floor()
Integer	Rational.getDenominator()
Integer	Rational.getNumerator()

Methods in org.episteme.core.mathematics.numbers.rationals with parameters of type Integer

Modifier and Type	Method	Description
static Rational	Rational.of(Integer numerator, Integer denominator)

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

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

Modifier and Type	Method	Description
static Integer[]	NumberTheory.extendedGCD(Integer a, Integer b)	Extended Euclidean algorithm: finds x, y such that ax + by = gcd(a, b).

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

Modifier and Type	Method	Description
static Integer[]	NumberTheory.extendedGCD(Integer a, Integer b)	Extended Euclidean algorithm: finds x, y such that ax + by = gcd(a, b).

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

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

Modifier and Type	Method	Description
Integer	RandomGenerator.nextInteger(int min, int max)	Returns random Integer in [min, max].

Uses of Integer in org.episteme.core.mathematics.sequences

Classes in org.episteme.core.mathematics.sequences that implement interfaces with type arguments of type Integer

Modifier and Type	Class	Description
class	FibonacciSequence	Represents the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, ...

Methods in org.episteme.core.mathematics.sequences that return Integer

Modifier and Type	Method	Description
Integer	FibonacciSequence.get(int index)
Integer	FibonacciSequence.limit()

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

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

Modifier and Type	Class	Description
final class	Integers	The structure of integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
final class	Integers	The structure of integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).

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

Modifier and Type	Method	Description
Integer	Integers.add(Integer a, Integer b)
Integer	Integers.inverse(Integer element)
Integer	Integers.multiply(Integer a, Integer b)
Integer	Integers.negate(Integer element)
Integer	Integers.one()
Integer	Integers.operate(Integer a, Integer b)
Integer	Integers.zero()

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

Modifier and Type	Method	Description
Integer	Integers.add(Integer a, Integer b)
boolean	Integers.contains(Integer element)
Integer	Integers.inverse(Integer element)
Integer	Integers.multiply(Integer a, Integer b)
Integer	Integers.negate(Integer element)
Integer	Integers.operate(Integer a, Integer b)