Polynomial Class

Visual Basic (Declaration)
Public Class Polynomial _ Inherits PolynomialBase

C#
public class Polynomial : PolynomialBase

C++
public ref class Polynomial : public PolynomialBase

Icon	Type	Description
	Add(Double, LinearCombination)	Adds a multiple of another LinearCombination to this instance.
	Add(Polynomial, Polynomial)	Adds two polynomials.
	Add(LinearCombination)	Adds another LinearCombination to this instance.
	Addition(Polynomial, Polynomial)	Adds two polynomials.
	Clone()	Constructs an exact copy of this instance.
	ComplexSlopeAt(DoubleComplex)	Evaluates the slope or first derivative of a polynomial for a DoubleComplex argument.
	ComplexValueAt(DoubleComplex)	Evaluates the polynomial for a DoubleComplex argument.
	Deflate(Double)	Deflates a polynomial by dividing out a root.
	Divide(Polynomial, Polynomial, Polynomial)	Divides one Polynomial by another.
	Divide(Polynomial, Polynomial)	Divides one Polynomial by another.
	Division(Polynomial, Polynomial)	Divides one Polynomial by another.
	Equality(Polynomial, Polynomial)	Compares two Polynomial objects for equality.
	Equals(Object)	Overridden. Returns a value indicating whether this instance is equal to a specified object.
	Equals(Polynomial, Polynomial)	Returns a value indicating whether two Polynomial objects represent the same value.
	Finalize()	Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
	FindComplexRoots()	Gets the set of roots of the Polynomial.
	FindRoots()	Gets the set of X-coordinates where the Polynomial crosses the X-axis.
	FromRoots(Double[]())	Constructs a new polynomial that has the specified roots.
	GetCurveFitter()	Returns a CurveFitter object that can be used to fit the curve to data.
	GetDerivative()	Returns a Curve of type Polynomial that represents the derivative of this Polynomial.
	GetHashCode()	Overridden. Returns the hash code for this instance.
	GetInterpolatingPolynomial(Double[](), Double[]())	Constructs the interpolating polynomial through a set of points.
	GetType()	Gets the Type of the current instance.
	Inequality(Polynomial, Polynomial)	Compares two Polynomial objects for inequality.
	Integral(Double, Double)	Gets the definite integral of the curve between the specified X-coordinates.
	LeastSquaresFit(Double[](), Double[](), Int32, Double[]())	Returns the Polynomial that is the best weighted least squares fit through the given set of points.
	LeastSquaresFit(Double[](), Double[](), Int32)	Returns the Polynomial that is the best least squares fit through the given set of points.
	MemberwiseClone()	Creates a shallow copy of the current Object.
	Modulus(Polynomial, Polynomial)	Divides one Polynomial by another and returns the remainder.
	Modulus(Polynomial, Polynomial)	Divides one Polynomial by another and returns the remainder.
	Multiply(Polynomial, Polynomial)	Multiplies two polynomials.
	Multiply(Polynomial, Polynomial)	Multiplies two polynomials.
	OnParameterChanged(Int32, Double)	Called when a coefficient of the polynomial is changed.
	OnParameterChanging(Int32, Double)	Called before the value of a curve parameter is changed.
	Reduce()	Reduces the degree of a polynomial so that the leading coefficient is different from zero.
	Reduce(Double)	Reduces the degree of a polynomial so that the leading coefficient is greater than the specified tolerance.
	SlopeAt(Double)	Evaluates the slope or first derivative of a polynomial for a real argument.
	Subtract(Polynomial, Polynomial)	Subtracts two polynomials.
	Subtract(LinearCombination)	Subtracts another LinearCombination from this instance.
	Subtraction(Polynomial, Polynomial)	Subtracts two polynomials.
	TangentAt(Double)	Gets the tangent Line to the curve at the specified X-coordinate.
	ToString()	Returns a string representation of this instance.
	ValueAt(Double)	Evaluates the polynomial for a real argument.

Icon	Type	Description
	PolynomialNew(Int32)	Constructs a new polynomial of the specified degree.
	PolynomialNew(Double[]())	Constructs a new polynomial with the specified coefficients.
	PolynomialNew(Vector)	Constructs a new polynomial with the specified coefficients.

Icon	Type	Description
	Basis	Gets the function basis for the polynomial.
	Coefficient(Int32)	Gets or sets the coefficient of the function with the specified index.
	Degree	Gets the degree of the polynomial.
	Item(Int32)	Gets or sets the coefficient of the function with the specified index.
	Parameters	Gets the collection of parameters that determine the shape of this Curve.

Use the Polynomial class to represent ordinary polynomials. A polynomial is an algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and a variable raised to an integral exponent. It inherits from Curve and provides specialized implementation for most methods.

The parameters of a Polynomial correspond to the coefficients of the polynomial. The coefficients can be accessed through the indexed Coefficient(Int32) property. In C#, this property is the indexer for this class.

The ValueAt(Double) method returns the value of the polynomial at a specific point. SlopeAt(Double) returns the derivative of the Line. Integral(Double, Double) evaluates the definite integral over a specified interval.

The FindRoots() method attempts to find all real roots of the polynomial. It returns a Double array. The corresponding FindComplexRoots() method attempts to find all complex roots, and returns them as an array of DoubleComplex values. The roots are sorted in order of ascending real part.

Methods for arithmetic operations on polynomials have been defined. Corresponding operator overloads are available for those languages that support them.

System.Object
  Extreme.Mathematics.Curves.Curve
    Extreme.Mathematics.Curves.LinearCombination
      Extreme.Mathematics.Curves.PolynomialBase
        Extreme.Mathematics.Curves.Polynomial

Syntax

Methods

Constructors

Properties

Remarks

Inheritance Hierarchy