Polynomial (SuanShuExtension API)

java.lang.Object
- com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.UnivariateRealFunction
- - com.numericalmethod.suanshu.analysis.function.polynomial.Polynomial

All Implemented Interfaces:

Function<Vector,java.lang.Double>, RealScalarFunction, AbelianGroup<Polynomial>, Monoid<Polynomial>, Ring<Polynomial>, VectorSpace<Polynomial,Real>, java.io.Serializable

Direct Known Subclasses:

CauchyPolynomial, DPolynomial, QuadraticMonomial, ScaledPolynomial
```
public class Polynomial
extends UnivariateRealFunction
implements Ring<Polynomial>, VectorSpace<Polynomial,Real>
```
A polynomial is a UnivariateRealFunction that represents a finite length expression constructed from variables and constants, using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. Specifically, it has the form \[ p(x) = a_0x^n + a_1x^{n-1} + ... + a_{n-1}x + a_n \] This implementation is immutable.

See Also:

Wikipedia: Polynomial, Serialized Form

Nested Class Summary
- Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function
  Function.EvaluationException

Field Summary

Fields
Modifier and Type Field and Description

static Polynomial ONE
a polynomial representing 1

static Polynomial ZERO
a polynomial representing 0

Fields
Modifier and Type	Field and Description
`static Polynomial`	`ONE` a polynomial representing 1
`static Polynomial`	`ZERO` a polynomial representing 0

Constructor Summary

Constructors
Constructor and Description

Polynomial(double... coefficients)
Construct a polynomial from an array of coefficients.

Polynomial(Polynomial that)
Copy constructor.

Constructors
Constructor and Description
`Polynomial(double... coefficients)` Construct a polynomial from an array of coefficients.
`Polynomial(Polynomial that)` Copy constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Polynomial`	`add(Polynomial that)` + : G × G → G
`int`	`degree()` Get the degree of this polynomial.
`boolean`	`equals(java.lang.Object obj)`
`Complex`	`evaluate(Complex z)` Evaluate this polynomial at x.
`double`	`evaluate(double x)` Evaluate this polynomial at x.
`Complex`	`evaluate(java.lang.Number x)` Evaluate this polynomial at x.
`double`	`getCoefficient(int i)` Get a_n-i, the coefficient of x^n-i.
`double[]`	`getCoefficients()` Get a copy of the polynomial coefficients.
`Polynomial`	`getNormalization()` Get the normalized version of this polynomial so the leading coefficient is 1.
`int`	`hashCode()`
`Polynomial`	`minus(Polynomial that)` - : G × G → G The operation "-" is not in the definition of of an additive group but can be deduced.
`Polynomial`	`multiply(Polynomial that)` × : G × G → G
`Polynomial`	`ONE()` The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.
`Polynomial`	`opposite()` For each a in G, there exists an element b in G such that a + b = b + a = 0.
`Polynomial`	`scaled(double c)`
`Polynomial`	`scaled(Real c)` × : F × V → V The result of applying this function to a scalar, c, in F and v in V is denoted cv.
`java.lang.String`	`toString()`
`Polynomial`	`ZERO()` The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.UnivariateRealFunction
dimensionOfDomain, dimensionOfRange, evaluate

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ZERO
```
public static final Polynomial ZERO
```
    a polynomial representing 0
  - ONE
```
public static final Polynomial ONE
```
    a polynomial representing 1
- Constructor Detail
  - Polynomial
```
public Polynomial(double... coefficients)
```
    Construct a polynomial from an array of coefficients. The first/0-th entry corresponds to the xⁿ term. The last/n-th entry corresponds to the constant term. The degree of the polynomial is n, the array length minus 1.
    For example,
    new Polynomial(1, -2, 3, 2)
    creates an instance of Polynomial representing x³ - 2x² + 3x + 2.
    
    Parameters:
    
    coefficients - the polynomial coefficients
  - Polynomial
```
public Polynomial(Polynomial that)
```
    Copy constructor.
    
    Parameters:
    
    that - a polynomial
- Method Detail
  - degree
```
public int degree()
```
    Get the degree of this polynomial. It is equal to the largest exponent of the variable. For example, x⁴ + 1 has a degree of 4.
    
    Returns:
    
    the polynomial degree
  - getCoefficients
```
public double[] getCoefficients()
```
    Get a copy of the polynomial coefficients. In general, coefficients[i] is the coefficient of x^n-i, where n is the polynomial degree. Specifically, coefficients[0] is the leading coefficient and coefficients[n] the constant term.
    
    Returns:
    
    a copy of the polynomial coefficients
  - getCoefficient
```
public double getCoefficient(int i)
```
    Get a_n-i, the coefficient of x^n-i.
    
    Parameters:
    
    i - the i-th coefficient in this polynomial, counting from 0
    
    Returns:
    
    a_n-i
    
    See Also:
    
    getCoefficients()
  - getNormalization
```
public Polynomial getNormalization()
```
    Get the normalized version of this polynomial so the leading coefficient is 1.
    
    Returns:
    
    a scaled version of the polynomial that has a leading coefficient 1
  - evaluate
```
public Complex evaluate(java.lang.Number x)
```
    Evaluate this polynomial at x.
    
    Parameters:
    
    x - the argument
    
    Returns:
    
    p(x)
  - evaluate
```
public double evaluate(double x)
```
    Evaluate this polynomial at x.
    
    Specified by:
    
    evaluate in class UnivariateRealFunction
    
    Parameters:
    
    x - the argument
    
    Returns:
    
    p(x)
  - evaluate
```
public Complex evaluate(Complex z)
```
    Evaluate this polynomial at x.
    
    Parameters:
    
    z - the argument
    
    Returns:
    
    p(x)
  - add
```
public Polynomial add(Polynomial that)
```
    Description copied from interface: AbelianGroup
    
    + : G × G → G
    
    Specified by:
    
    add in interface AbelianGroup<Polynomial>
    
    Parameters:
    
    that - the object to be added
    
    Returns:
    
    this + that
  - minus
```
public Polynomial minus(Polynomial that)
```
    Description copied from interface: AbelianGroup
    
    - : G × G → G
    The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to
    this.add(that.opposite())
    .
    
    Specified by:
    
    minus in interface AbelianGroup<Polynomial>
    
    Parameters:
    
    that - the object to be subtracted (subtrahend)
    
    Returns:
    
    this - that
  - multiply
```
public Polynomial multiply(Polynomial that)
```
    Description copied from interface: Monoid
    
    × : G × G → G
    
    Specified by:
    
    multiply in interface Monoid<Polynomial>
    
    Parameters:
    
    that - the multiplicand
    
    Returns:
    
    this × that
  - scaled
```
public Polynomial scaled(Real c)
```
    Description copied from interface: VectorSpace
    
    × : F × V → V
    The result of applying this function to a scalar, c, in F and v in V is denoted cv.
    
    Specified by:
    
    scaled in interface VectorSpace<Polynomial,Real>
    
    Parameters:
    
    c - a multiplier
    
    Returns:
    
    c * this
    
    See Also:
    
    Wikipedia: Scalar multiplication
  - scaled
```
public Polynomial scaled(double c)
```
  - opposite
```
public Polynomial opposite()
```
    Description copied from interface: AbelianGroup
    
    For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
    this.add(this.opposite()) == this.ZERO
    
    Specified by:
    
    opposite in interface AbelianGroup<Polynomial>
    
    Returns:
    
    -this, the additive opposite
    
    See Also:
    
    Wikipedia: Additive inverse
  - ZERO
```
public Polynomial ZERO()
```
    Description copied from interface: AbelianGroup
    
    The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
    
    Specified by:
    
    ZERO in interface AbelianGroup<Polynomial>
    
    Returns:
    
    0, the additive identity
  - ONE
```
public Polynomial ONE()
```
    Description copied from interface: Monoid
    
    The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.
    
    Specified by:
    
    ONE in interface Monoid<Polynomial>
    
    Returns:
    
    1
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object

Class Polynomial

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Field Summary

Constructor Summary

Method Summary

Methods inherited from class com.numericalmethod.suanshu.analysis.function.rn2r1.univariate.UnivariateRealFunction

Methods inherited from class java.lang.Object

Field Detail

ZERO

ONE

Constructor Detail

Polynomial

Polynomial

Method Detail

degree

getCoefficients

getCoefficient

getNormalization

evaluate

evaluate

evaluate

add

minus

multiply

scaled

scaled

opposite

ZERO

ONE

toString

equals

hashCode