Uses of Class
org.episteme.core.mathematics.analysis.functions.Polynomial

Packages that use Polynomial

Package	Description
org.episteme.core.mathematics.algebra.polynomials
org.episteme.core.mathematics.analysis.functions

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

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

Modifier and Type	Field	Description
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.gcd
final Polynomial<R>	PolynomialDivision.DivisionResult.quotient
final Polynomial<R>	PolynomialDivision.DivisionResult.remainder
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.s
final Polynomial<Integer>	PolynomialAlgebra.ExtendedGCDResult.t

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

Modifier and Type	Field	Description
final List<Polynomial<Integer>>	PolynomialFactorization.Factorization.factors

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

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 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

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

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

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 Polynomial

Modifier	Constructor	Description
	DivisionResult(Polynomial<R> quotient, Polynomial<R> remainder)
	ExtendedGCDResult(Polynomial<Integer> gcd, Polynomial<Integer> s, Polynomial<Integer> t)

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

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

Uses of Polynomial in org.episteme.core.mathematics.analysis.functions

Methods in org.episteme.core.mathematics.analysis.functions that return Polynomial

Modifier and Type	Method	Description
Polynomial<R>	Polynomial.add(Polynomial<R> other)	Adds two polynomials.
static <R> Polynomial<R>	Polynomial.constant(R value, Ring<R> ring)	Creates constant polynomial.
Polynomial<R>	Polynomial.derivative()	Returns derivative of polynomial.
static <R> Polynomial<R>	Polynomial.monomial(R coefficient, int degree, Ring<R> ring)	Creates monomial: coefficient * x^degree.
Polynomial<R>	Polynomial.multiply(Polynomial<R> other)	Multiplies two polynomials.
static <R> Polynomial<R>	Polynomial.of(Ring<R> ring, R... coefficients)	Creates a polynomial from coefficients.
Polynomial<R>	Polynomial.subtract(Polynomial<R> other)	Subtracts two polynomials.
static <R> Polynomial<R>	Polynomial.x(Ring<R> ring)	Creates the polynomial x.
static <R> Polynomial<R>	Polynomial.zero(Ring<R> ring)	Creates zero polynomial.

Methods in org.episteme.core.mathematics.analysis.functions with parameters of type Polynomial

Modifier and Type	Method	Description
Polynomial<R>	Polynomial.add(Polynomial<R> other)	Adds two polynomials.
Polynomial<R>	Polynomial.multiply(Polynomial<R> other)	Multiplies two polynomials.
Polynomial<R>	Polynomial.subtract(Polynomial<R> other)	Subtracts two polynomials.