Class Polynomial

Class defining a multivariate polynomial.

Inheritance

Object

Polynomial

Namespace: BRIDGES.Arithmetic.Polynomials.Multivariate

Assembly: BRIDGES.dll

Syntax

public class Polynomial : object

Remarks

For a univarite polynomial, refer to Polynomial.

Constructors

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 univarite polynomial, refer to Polynomial.

Polynomial(Double[], Monomial[])

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

Declaration

public Polynomial(double[] coefficients, Monomial[] monomials)

Parameters

Type	Name	Description
Double[]	coefficients	Coefficients of the multivariate polynomial associated with each monomials.
Monomial[]	monomials	Monomials of the multivariate polynomial.

Remarks

For a univarite polynomial, refer to Polynomial.

Properties

One

Gets a new Polynomial, constant equal to one.

Declaration

public static Polynomial One { get; }

Property Value

Type	Description
Polynomial

Remarks

For a univarite polynomial, refer to Polynomial.

TermCount

Gets the number of terms in this Polynomial.

Declaration

public int TermCount { get; }

Property Value

Type	Description
Int32

Remarks

For a univarite polynomial, refer to Polynomial.

TotalDegree

Gets the maximum Monomial(Int32) total degree.

Declaration

public int TotalDegree { get; }

Property Value

Type	Description
Int32

Remarks

For a univarite polynomial, refer to Polynomial.

Methods

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 univarite polynomial, refer to Polynomial.

EvaluateAt(Double[])

Evaluates this Polynomial at a given point.

Declaration

public double EvaluateAt(double[] point)

Parameters

Type	Name	Description
Double[]	point	Point to evaluate at.

Returns

Type	Description
Double	The value of this Polynomial at the given point.

Remarks

For a univarite polynomial, refer to Polynomial.

Monomial(Int32)

Returns the monomial of the term at the given index.

Declaration

public Monomial Monomial(int index)

Parameters

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

Returns

Type	Description
Monomial	The Monomial of the term at the given index.

Remarks

For a univarite polynomial, refer to Polynomial.

Operators

Implicit(Monomial to Polynomial)

Converts a Monomial(Int32) into a Polynomial.

Declaration

public static implicit operator Polynomial(Monomial monomial)

Parameters

Type	Name	Description
Monomial	monomial	Monomial(Int32) to convert.

Returns

Type	Description
Polynomial	The new Polynomial resulting from the conversion.

Remarks

For a univarite polynomial, refer to Polynomial.