Polynomial Class |
A single-variable polynomial with real-valued coefficients and non-negative exponents.
Inheritance HierarchyNamespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)
SyntaxC#
[SerializableAttribute] public class Polynomial : IFormattable, IEquatable<Polynomial>, ICloneable
The Polynomial type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | Polynomial | Create a zero-polynomial |
| Polynomial(Double) | Create a constant polynomial. Example: 3.0 -> "p : x -> 3.0" |
| Polynomial(Double) | Create a polynomial with the provided coefficients (in ascending order, where the index matches the exponent). Example: {5, 0, 2} -> "p : x -> 5 + 0 x^1 + 2 x^2". |
| Polynomial(IEnumerableDouble) | Create a polynomial with the provided coefficients (in ascending order, where the index matches the exponent). Example: {5, 0, 2} -> "p : x -> 5 + 0 x^1 + 2 x^2". |
| Polynomial(Int32) | Create a zero-polynomial with a coefficient array of the given length. An array of length N can support polynomials of a degree of at most N-1. |
Properties| Name | Description | |
|---|---|---|
 | Coefficients | The coefficients of the polynomial in a |
| Degree | Degree of the polynomial, i.e. the largest monomial exponent. For example, the degree of y=x^2+x^5 is 5, for y=3 it is 0. The null-polynomial returns degree -1 because the correct degree, negative infinity, cannot be represented by integers. |
 | Zero | Gets the zero polynomial. |
Methods| Name | Description | |
|---|---|---|
| Add(Polynomial, Polynomial) | Addition of two Polynomials (point-wise). |
| Add(Polynomial, Double) | Addition of a polynomial and a scalar. |
| Clone | Creates a copy of the polynomial. |
| Differentiate | Differentiates the polynomial. |
| Divide | Scales a polynomial by division by a scalar |
| DivideRemainder(Polynomial) | Division of two polynomials returning the quotient-with-remainder of the two polynomials given |
| DivideRemainder(Polynomial, Polynomial) | Euclidean long division of two polynomials, returning the quotient q and remainder r of the two polynomials a and b such that a = q*b + r |
| EigenvalueMatrix | Gets the eigenvalue matrix A of this polynomial such that eig(A) = roots of this polynomial. |
| Equals(Object) |
Determines whether the specified object is equal to the current instance.
(Overrides ObjectEquals(Object)) |
| Equals(Polynomial) | Determines whether the specified polynomial is equal to the current instance. |
| Evaluate(Complex) | Evaluate a polynomial at point x. |
| Evaluate(Double) | Evaluate a polynomial at point x. |
| Evaluate(IEnumerableDouble) | Evaluate a polynomial at points z. |
| Evaluate(IEnumerableComplex) | Evaluate a polynomial at points z. |
| Evaluate(Complex, Double) | Evaluate a polynomial at point x. Coefficients are ordered ascending by power with power k at index k. Example: coefficients [3,-1,2] represent y=2x^2-x+3. |
| Evaluate(Complex, Complex) | Evaluate a polynomial at point x. Coefficients are ordered ascending by power with power k at index k. Example: coefficients [3,-1,2] represent y=2x^2-x+3. |
| Evaluate(Double, Double) | Evaluate a polynomial at point x. Coefficients are ordered ascending by power with power k at index k. Example: coefficients [3,-1,2] represent y=2x^2-x+3. |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| Fit | Least-Squares fitting the points (x,y) to a k-order polynomial y : x -> p0 + p1*x + p2*x^2 + ... + pk*x^k |
| GetHashCode |
Serves as the default hash function.
(Overrides ObjectGetHashCode) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| Integrate | Integrates the polynomial with a zero constant term. |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Multiply(Polynomial, Polynomial) | Multiplies a polynomial by a polynomial (convolution) |
| Multiply(Polynomial, Double) | Scales a polynomial by a scalar |
| Negate | Negation of a polynomial. |
| PointwiseDivide | Point-wise division of two Polynomials |
| PointwiseMultiply | Point-wise multiplication of two Polynomials |
| Roots | Calculates the complex roots of the polynomial by eigenvalue decomposition. |
| Subtract(Double, Polynomial) | Addition of a polynomial from a scalar. |
| Subtract(Polynomial, Polynomial) | Subtraction of two Polynomials (point-wise). |
| Subtract(Polynomial, Double) | Addition of a scalar from a polynomial. |
| ToString |
Format the polynomial in ascending order, e.g. "4.3 + 2.0x^2 - x^3".
(Overrides ObjectToString) |
| ToString(IFormatProvider) | Format the polynomial in ascending order, e.g. "4.3 + 2.0x^2 - x^3". |
| ToString(String) | Format the polynomial in ascending order, e.g. "4.3 + 2.0x^2 - x^3". |
| ToString(String, IFormatProvider) | Format the polynomial in ascending order, e.g. "4.3 + 2.0x^2 - x^3". |
| ToStringDescending | Format the polynomial in descending order, e.g. "x^3 + 2.0x^2 - 4.3". |
| ToStringDescending(IFormatProvider) | Format the polynomial in descending order, e.g. "x^3 + 2.0x^2 - 4.3". |
| ToStringDescending(String) | Format the polynomial in descending order, e.g. "x^3 + 2.0x^2 - 4.3". |
| ToStringDescending(String, IFormatProvider) | Format the polynomial in descending order, e.g. "x^3 + 2.0x^2 - 4.3". |
Operators| Name | Description | |
|---|---|---|
 | Addition(Double, Polynomial) | adds a scalar to a polynomial. |
| Addition(Polynomial, Polynomial) | Addition of two Polynomials (piecewise) |
| Addition(Polynomial, Double) | adds a scalar to a polynomial. |
| Division(Polynomial, Double) | Divides a polynomial by scalar value. |
| Multiply(Double, Polynomial) | Multiplies a polynomial by a scalar. |
| Multiply(Polynomial, Polynomial) | Multiplies a polynomial by a polynomial (convolution). |
| Multiply(Polynomial, Double) | Multiplies a polynomial by a scalar. |
| Subtraction(Double, Polynomial) | Subtracts a polynomial from a scalar. |
| Subtraction(Polynomial, Polynomial) | Subtraction of two polynomial. |
| Subtraction(Polynomial, Double) | Subtracts a scalar from a polynomial. |
| UnaryNegation(Polynomial) | Negates a polynomial. |
Fields| Name | Description | |
|---|---|---|
 | VariableName | Only needed for the ToString method |
See Also