Class Polynomial

Class defining a univarite polynomial.

Inheritance

Object

Polynomial

Bernstein

BSpline

Implements

IGroupAction<Polynomial, Double>

Namespace: BRIDGES.Arithmetic.Polynomials.Univariate

Assembly: BRIDGES.dll

Syntax

public class Polynomial : object, IGroupAction<Polynomial, double>

Remarks

For a multivariate polynomial, refer to Polynomial.

Constructors

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Polynomial(Polynomial)

Initialises a new instance of the Polynomial class from another Polynomial.

Declaration

public Polynomial(Polynomial other)

Parameters

Type	Name	Description
Polynomial	other	Polynomial to deep copy.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Polynomial(Double[])

Initialises a new instance of Polynomial class by defining its coefficients.

Declaration

public Polynomial(params double[] coefficients)

Parameters

Type	Name	Description
Double[]	coefficients	Coefficients of the polynomial, starting from the constant value.

Remarks

For a multivariate polynomial, refer to Polynomial.

Properties

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Degree

Gets the degree of this Polynomial.

Declaration

public int Degree { get; }

Property Value

Type	Description
Int32

Remarks

For a multivariate polynomial, refer to Polynomial.

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Item[Int32]

Gets the value of the coefficient at a given index.

Declaration

public double this[int index] { get; }

Parameters

Type	Name	Description
Int32	index	Index of the coefficient to get.

Property Value

Type	Description
Double	The value of the coefficient at the given index.

Remarks

For a multivariate polynomial, refer to Polynomial.

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One

Gets a new Polynomial, constant equal to one.

Declaration

public static Polynomial One { get; }

Property Value

Type	Description
Polynomial

Remarks

For a multivariate polynomial, refer to Polynomial.

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Zero

Gets a new Polynomial, constant equal to zero.

Declaration

public static Polynomial Zero { get; }

Property Value

Type	Description
Polynomial

Remarks

For a multivariate polynomial, refer to Polynomial.

Methods

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Add(Polynomial, Polynomial)

Computes the addition of two Polynomial.

Declaration

public static Polynomial Add(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial for the addition.
Polynomial	right	Polynomial for the addition.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the addition.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Coefficient(Int32)

Returns the constant coefficient of the term at the given index.

Declaration

public double Coefficient(int index)

Parameters

Type	Name	Description
Int32	index	Index of the term whose coefficient to return.

Returns

Type	Description
Double	The coefficient of the term at the given index.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Derive(Polynomial, Int32)

Computes the Polynomial which is the derivative of the given Polynomial at the given order.

Declaration

public static Polynomial Derive(Polynomial polynomial, int order = 1)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to derive.
Int32	order	Order of the derivative to compute.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the derivation.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Divide(Polynomial, Double)

Computes the scalar division of a Polynomial with a number.

Declaration

public static Polynomial Divide(Polynomial polynomial, double divisor)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to divide.
Double	divisor	number to divide with.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar division.

Remarks

For a multivariate polynomial, refer to Polynomial.

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EvaluateAt(Double)

Computes the current Polynomial at a given value using Horner's method.

Declaration

public virtual double EvaluateAt(double val)

Parameters

Type	Name	Description
Double	val	Value to evaluate at.

Returns

Type	Description
Double	The computed value of the current Polynomial.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Polynomial, Polynomial)

Computes the multiplication of two Polynomial.

Declaration

public static Polynomial Multiply(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial for the multiplication.
Polynomial	right	Polynomial for the multiplication.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Polynomial, Double)

Computes the right scalar multiplication of a Polynomial with a number.

Declaration

public static Polynomial Multiply(Polynomial polynomial, double factor)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to multiply.
Double	factor	number.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Double, Polynomial)

Computes the left scalar multiplication of a Polynomial with a number.

Declaration

public static Polynomial Multiply(double factor, Polynomial polynomial)

Parameters

Type	Name	Description
Double	factor	number.
Polynomial	polynomial	Polynomial to multiply.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Opposite(Polynomial)

Computes the opposite of the given Polynomial.

Declaration

public static Polynomial Opposite(Polynomial operand)

Parameters

Type	Name	Description
Polynomial	operand

Returns

Type	Description
Polynomial	The new Polynomial, opposite of the initial one.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Subtract(Polynomial, Polynomial)

Computes the subtraction of two Polynomial.

Declaration

public static Polynomial Subtract(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial to subtract.
Polynomial	right	Polynomial to subtract with.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the subtraction.

Remarks

For a multivariate polynomial, refer to Polynomial.

Operators

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Addition(Polynomial, Polynomial)

Computes the addition of two Polynomial.

Declaration

public static Polynomial operator +(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial for the addition.
Polynomial	right	Polynomial for the addition.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the addition.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Division(Polynomial, Double)

Computes the scalar division of a Polynomial with a number.

Declaration

public static Polynomial operator /(Polynomial polynomial, double divisor)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to divide.
Double	divisor	number to divide with.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar division.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Polynomial, Polynomial)

Computes the multiplication of two Polynomial.

Declaration

public static Polynomial operator *(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial for the multiplication.
Polynomial	right	Polynomial for the multiplication.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Polynomial, Double)

Computes the right scalar multiplication of a Polynomial with a number.

Declaration

public static Polynomial operator *(Polynomial polynomial, double factor)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to multiply.
Double	factor	number.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Multiply(Double, Polynomial)

Computes the left scalar multiplication of a Polynomial with a number.

Declaration

public static Polynomial operator *(double factor, Polynomial polynomial)

Parameters

Type	Name	Description
Double	factor	number.
Polynomial	polynomial	Polynomial to multiply.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the scalar multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

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Subtraction(Polynomial, Polynomial)

Computes the subtraction of two Polynomial.

Declaration

public static Polynomial operator -(Polynomial left, Polynomial right)

Parameters

Type	Name	Description
Polynomial	left	Polynomial to subtract.
Polynomial	right	Polynomial to subtract with.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the subtraction.

Remarks

For a multivariate polynomial, refer to Polynomial.

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UnaryNegation(Polynomial)

Computes the opposite of the given Polynomial.

Declaration

public static Polynomial operator -(Polynomial polynomial)

Parameters

Type	Name	Description
Polynomial	polynomial	Polynomial to be opposed.

Returns

Type	Description
Polynomial	The new Polynomial, opposite of the initial one.

Remarks

For a multivariate polynomial, refer to Polynomial.

Explicit Interface Implementations

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IGroupAction<Polynomial, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

Polynomial IGroupAction<Polynomial, double>.Divide(double divisor)

Parameters

Type	Name	Description
Double	divisor

Returns

Type	Description
Polynomial	The new element resulting from the scalar dividion.

Remarks

For a multivariate polynomial, refer to Polynomial.

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IGroupAction<Polynomial, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

Polynomial IGroupAction<Polynomial, double>.Multiply(double factor)

Parameters

Type	Name	Description
Double	factor

Returns

Type	Description
Polynomial	The new element resulting from the scalar multiplication.

Remarks

For a multivariate polynomial, refer to Polynomial.

Implements

IGroupAction<TSelf, TValue>