RealPolynomial (SOCR_JSci API Specification)

java.lang.Object
- JSci.maths.polynomials.RealPolynomial

All Implemented Interfaces:

java.io.Serializable, Ring.Member, AbelianGroup.Member, Member, Polynomial
```
public class RealPolynomial
extends java.lang.Object
implements Polynomial
```
A Polynomial as a Ring.Member over a real Field

Author:

b.dietrich

See Also:
Serialized Form

Field Summary
- Fields inherited from interface JSci.maths.polynomials.Polynomial
  POLYEPS

Constructor Summary

Constructors
Constructor and Description

RealPolynomial(double[] coeff)
Creates a new instance of RealPolynomial

RealPolynomial(Field.Member[] f)
Creates a new RealPolynomial object.

Constructors
Constructor and Description
`RealPolynomial(double[] coeff)` Creates a new instance of RealPolynomial
`RealPolynomial(Field.Member[] f)` Creates a new RealPolynomial object.

Method Summary

Methods
Modifier and Type	Method and Description
`AbelianGroup.Member`	`add(AbelianGroup.Member g)` The group composition law.
`int`	`degree()` The degree
`RealPolynomial`	`differentiate()` Differentiate the real polynomial.
`RealPolynomial`	`divide(double a)` return a new real Polynomial with coefficients divided by a
`Polynomial`	`divide(Field.Member f)` return a new real Polynomial with coefficients divided by f
`boolean`	`equals(java.lang.Object o)` Is this-o == Null ?
`Field.Member`	`getCoefficient(int n)` Get the coefficient of degree k, i.e.
`double`	`getCoefficientAsDouble(int n)` Get the coefficient of degree k, i.e.
`Field.Member[]`	`getCoefficients()` Get the coefficients as an array
`double[]`	`getCoefficientsAsDoubles()` Get the coefficients as an array of doubles
`int`	`hashCode()` Some kind of hashcode...
`RealPolynomial`	`integrate()` "inverse" operation for differentiate
`boolean`	`isNull()` Does this polynomial represent a "NULL".
`boolean`	`isOne()` Does this polynomial represent a "ONE".
`RealPolynomial`	`multiply(double a)` Returns the multiplication of this polynomial by a scalar
`Polynomial`	`multiply(Field.Member f)` Returns the multiplication of this polynomial by a scalar
`Ring.Member`	`multiply(Ring.Member r)` The multiplication law.
`AbelianGroup.Member`	`negate()` Returns the inverse member.
`AbelianGroup.Member`	`subtract(AbelianGroup.Member g)` The group composition law with inverse.
`java.lang.String`	`toString()` String representation P(x) = a_k x^k +...

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

- Constructor Detail
  - RealPolynomial
```
public RealPolynomial(double[] coeff)
```
    Creates a new instance of RealPolynomial
  - RealPolynomial
```
public RealPolynomial(Field.Member[] f)
```
    Creates a new RealPolynomial object.
    
    Parameters:
    f -
- Method Detail
  - getCoefficient
```
public Field.Member getCoefficient(int n)
```
    Get the coefficient of degree k, i.e. a_k if P(x) := sum_{k=0}^n a_k x^k
    
    Specified by:
    
    getCoefficient in interface Polynomial
    
    Parameters:
    k - degree
    
    Returns:
    coefficient as described above
  - getCoefficientAsDouble
```
public double getCoefficientAsDouble(int n)
```
    Get the coefficient of degree k, i.e. a_k if P(x) := sum_{k=0}^n a_k x^k as a real number
    
    Parameters:
    k - degree
    
    Returns:
    coefficient as described above
  - getCoefficients
```
public Field.Member[] getCoefficients()
```
    Get the coefficients as an array
    
    Specified by:
    
    getCoefficients in interface Polynomial
    
    Returns:
    the coefficients as an array
  - getCoefficientsAsDoubles
```
public double[] getCoefficientsAsDoubles()
```
    Get the coefficients as an array of doubles
    
    Returns:
    the coefficients as an array
  - degree
```
public int degree()
```
    The degree
    
    Specified by:
    
    degree in interface Polynomial
    
    Returns:
    the degree
  - isNull
```
public boolean isNull()
```
    Does this polynomial represent a "NULL". This does not coincide with grade==0. All Coefficients are tested for |a_k| < POLYEPS
    
    Returns:
    true if all coefficients < POLYEPS
  - isOne
```
public boolean isOne()
```
    Does this polynomial represent a "ONE". This does not necessarily mean grade==1. It is tested, whether |a_0 -1. | <=POLYEPS and the remaining coefficients are |a_k| < POLYEPS
    
    Returns:
    true if so
  - add
```
public AbelianGroup.Member add(AbelianGroup.Member g)
```
    The group composition law. Returns a new polynom with grade = max( this.grade, g.grade)
    
    Specified by:
    
    add in interface AbelianGroup.Member
    
    Parameters:
    g - a group member
  - differentiate
```
public RealPolynomial differentiate()
```
    Differentiate the real polynomial. Only useful iff the polynomial is built over a banach space and an appropriate multiplication law is provided.
    
    Returns:
    a new polynomial with degree = max(this.degree-1 , 1)
  - divide
```
public Polynomial divide(Field.Member f)
```
    return a new real Polynomial with coefficients divided by f
    
    Specified by:
    
    divide in interface Polynomial
    
    Parameters:
    f - divisor
    
    Returns:
    new Polynomial with coefficients /= f
  - divide
```
public RealPolynomial divide(double a)
```
    return a new real Polynomial with coefficients divided by a
    
    Parameters:
    a - divisor
    
    Returns:
    new Polynomial with coefficients /= a
  - equals
```
public boolean equals(java.lang.Object o)
```
    Is this-o == Null ?
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    o - the other polynomial
    
    Returns:
    true if so
  - hashCode
```
public int hashCode()
```
    Some kind of hashcode... (Since I have an equals)
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    a hashcode
  - integrate
```
public RealPolynomial integrate()
```
    "inverse" operation for differentiate
    
    Returns:
    the integrated polynomial
  - multiply
```
public Polynomial multiply(Field.Member f)
```
    Returns the multiplication of this polynomial by a scalar
    
    Specified by:
    
    multiply in interface Polynomial
    
    Parameters:
    f -
    
    Returns:
    new Polynomial with coefficients *= a
  - multiply
```
public RealPolynomial multiply(double a)
```
    Returns the multiplication of this polynomial by a scalar
    
    Parameters:
    a - factor
    
    Returns:
    new Polynomial with coefficients *= a
  - multiply
```
public Ring.Member multiply(Ring.Member r)
```
    The multiplication law. Multiplies this Polynomial with another
    
    Specified by:
    
    multiply in interface Ring.Member
    
    Parameters:
    r - a ring member
    
    Returns:
    a new Polynomial with grade = max( this.grade, r.grade) + min( this.grade, r.grade) -1
  - negate
```
public AbelianGroup.Member negate()
```
    Returns the inverse member. (That is mult(-1))
    
    Specified by:
    
    negate in interface AbelianGroup.Member
    
    Returns:
    inverse
  - subtract
```
public AbelianGroup.Member subtract(AbelianGroup.Member g)
```
    The group composition law with inverse.
    
    Specified by:
    
    subtract in interface AbelianGroup.Member
    
    Parameters:
    g - a group member
  - toString
```
public java.lang.String toString()
```
    String representation P(x) = a_k x^k +...
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    String

Class RealPolynomial

Field Summary

Fields inherited from interface JSci.maths.polynomials.Polynomial

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

RealPolynomial

RealPolynomial

Method Detail

getCoefficient

getCoefficientAsDouble

getCoefficients

getCoefficientsAsDoubles

degree

isNull

isOne

add

differentiate

divide

divide

equals

hashCode

integrate

multiply

multiply

multiply

negate

subtract

toString