Class Polynomial<R>

java.lang.Object

org.episteme.core.mathematics.analysis.functions.Polynomial<R>

public class Polynomial<R>
extends Object

Polynomial with coefficients in a ring.

Represents polynomials like: a₀ + a₁x + a₂x² + ... + aₙxⁿ Supports arithmetic operations and evaluation.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Polynomial(List<R> coefficients, Ring<R> ring)	Creates a polynomial from coefficients (lowest degree first).

Method Summary

Modifier and Type	Method	Description
Polynomial<R>	add(Polynomial<R> other)	Adds two polynomials.
R	coefficient(int i)	Returns coefficient of x^i (alias for getCoefficient).
static <R> Polynomial<R>	constant(R value, Ring<R> ring)	Creates constant polynomial.
int	degree()	Returns degree of polynomial (highest power with non-zero coefficient).
Polynomial<R>	derivative()	Returns derivative of polynomial.
boolean	equals(Object obj)
R	evaluate(R x)	Evaluates polynomial at given value.
R	getCoefficient(int i)	Returns coefficient of x^i.
int	hashCode()
boolean	isZero()	Returns true if this polynomial is zero.
static <R> Polynomial<R>	monomial(R coefficient, int degree, Ring<R> ring)	Creates monomial: coefficient * x^degree.
Polynomial<R>	multiply(Polynomial<R> other)	Multiplies two polynomials.
static <R> Polynomial<R>	of(Ring<R> ring, R... coefficients)	Creates a polynomial from coefficients.
Polynomial<R>	subtract(Polynomial<R> other)	Subtracts two polynomials.
String	toString()
static <R> Polynomial<R>	x(Ring<R> ring)	Creates the polynomial x.
static <R> Polynomial<R>	zero(Ring<R> ring)	Creates zero polynomial.

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Details

Polynomial

public Polynomial(List<R> coefficients,
 Ring<R> ring)

Creates a polynomial from coefficients (lowest degree first).

Parameters:

coefficients - coefficients [aâ‚€, a₁, aâ‚‚, ...]

ring - the coefficient ring

Method Details

of

@SafeVarargs
public static <R> Polynomial<R> of(Ring<R> ring,
 R... coefficients)

Creates a polynomial from coefficients.

constant

public static <R> Polynomial<R> constant(R value,
 Ring<R> ring)

Creates constant polynomial.

x

public static <R> Polynomial<R> x(Ring<R> ring)

Creates the polynomial x.

zero

public static <R> Polynomial<R> zero(Ring<R> ring)

Creates zero polynomial.

monomial

public static <R> Polynomial<R> monomial(R coefficient,
 int degree,
 Ring<R> ring)

Creates monomial: coefficient * x^degree.

degree

public int degree()

Returns degree of polynomial (highest power with non-zero coefficient).

isZero

public boolean isZero()

Returns true if this polynomial is zero.

coefficient

public R coefficient(int i)

Returns coefficient of x^i (alias for getCoefficient).

getCoefficient

public R getCoefficient(int i)

Returns coefficient of x^i.

add

public Polynomial<R> add(Polynomial<R> other)

Adds two polynomials.

subtract

public Polynomial<R> subtract(Polynomial<R> other)

Subtracts two polynomials.

multiply

public Polynomial<R> multiply(Polynomial<R> other)

Multiplies two polynomials.

evaluate

public R evaluate(R x)

Evaluates polynomial at given value.

derivative

public Polynomial<R> derivative()

Returns derivative of polynomial.

toString

public String toString()

Overrides:

toString in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object