org.jscience.mathematics.analysis.polynomials
Class DoublePolynomial

java.lang.Object
  org.jscience.mathematics.analysis.DoubleFunction
      org.jscience.mathematics.analysis.polynomials.DoublePolynomial

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable, Field.Member, Ring.Member, AbelianGroup.Member, AbstractMapping, C1Function, Polynomial, PrimitiveMapping, Member

public class DoublePolynomial
extends DoubleFunction
implements Polynomial, java.io.Serializable, java.lang.Cloneable

A Polynomial as a Ring.Member over a realField

See Also:

Serialized Form

Field Summary

static DoublePolynomial	ONE The real polynomial representing the multiplicative identity.
static DoublePolynomial	ZERO The real polynomial representing the additive identity.

Constructor Summary

DoublePolynomial(double[] coeff)
Creates a new instance of DoublePolynomial, polynom is always simplified discarding every trailing zeros and array copied.

DoublePolynomial(double d, int degree)
Simple constructor.

DoublePolynomial(DoublePolynomial polynomial)
Creates a new instance of DoublePolynomial, polynom is always simplified discarding every trailing zeros.

DoublePolynomial(Field.Member[] f)
Creates a new RealPolynomial object, polynom is always simplified discarding every trailing zeros and array copied.

Method Summary

DoubleFunction	add(DoubleFunction g) The group composition law.
java.lang.Object	clone()
static Complex[]	cubic(double d, double c, double b, double a)
int	degree() The degree understood as the highest degree
DoubleFunction	differentiate() Differentiate the real polynomial.
boolean	equals(java.lang.Object o) Is this-o == Null ?
DoublePolynomial[]	euclidianDivision(DoublePolynomial divisor) Perform the euclidian division of two polynomials.
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
java.lang.Object	getSet()
int	hashCode() Some kind of hashcode...
DoublePolynomial	integrate() "inverse" operation for differentiate, zero degree constant set to zero
boolean	isOne() Returns true if this polynomial is equal to one.
boolean	isZero() Returns true if this polynomial is equal to zero.
double	map(double x) Evaluates this polynomial.
double	map(float x) Evaluates this polynomial.
double	map(int x) Evaluates this polynomial.
double	map(long x) Evaluates this polynomial.
DoubleFunction	multiply(DoubleFunction r) The multiplication law.
AbelianGroup.Member	negate() Returns the inverse member.
static Complex[]	quadratic(double c, double b, double a)
Complex[]	roots()
static DoublePolynomial	rootsToPolynomial(double[] roots)
DoublePolynomial	scalarDivide(double a) return a new real Polynomial with coefficients divided by a
Polynomial	scalarDivide(Field.Member f) return a new real Polynomial with coefficients divided by f
DoublePolynomial	scalarMultiply(double a) Returns the multiplication of this polynomial by a scalar
Polynomial	scalarMultiply(Field.Member f) Returns the multiplication of this polynomial by a scalar
void	setCoefficient(int n, Field.Member c) DOCUMENT ME!
void	setCoefficientAsDouble(int n, double c) DOCUMENT ME!
DoubleFunction	subtract(DoubleFunction g) The group composition law with inverse.
ComplexPolynomial	toComplexPolynomial()
ExactComplexPolynomial	toExactComplexPolynomial()
ExactRealPolynomial	toExactRealPolynomial()
java.lang.String	toString() String representation P(x) = a_k x^k +...
java.lang.String	toString(java.lang.String unknown) String representation P(x) = a_k x^k +...

Methods inherited from class org.jscience.mathematics.analysis.DoubleFunction

add, compose, cos, divide, divide, exp, getIntervalsList, inverse, log, multiply, power, setIntervalsList, sin, sqrt, subtract, taylorExpand, tensor

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.jscience.mathematics.algebraic.fields.Ring.Member

multiply

Methods inherited from interface org.jscience.mathematics.algebraic.groups.AbelianGroup.Member

add, subtract

Field Detail

ZERO

public static final DoublePolynomial ZERO

The real polynomial representing the additive identity.

ONE

public static final DoublePolynomial ONE

The real polynomial representing the multiplicative identity.

Constructor Detail

DoublePolynomial

public DoublePolynomial(double[] coeff)

Creates a new instance of DoublePolynomial, polynom is always simplified discarding every trailing zeros and array copied.

Parameters:

coeff - DOCUMENT ME!

Throws:

java.lang.NullPointerException - DOCUMENT ME!

DoublePolynomial

public DoublePolynomial(DoublePolynomial polynomial)

Creates a new instance of DoublePolynomial, polynom is always simplified discarding every trailing zeros.

Parameters:

polynomial - DOCUMENT ME!

DoublePolynomial

public DoublePolynomial(Field.Member[] f)

Creates a new RealPolynomial object, polynom is always simplified discarding every trailing zeros and array copied.

Parameters:

f -

DoublePolynomial

public DoublePolynomial(double d,
                        int degree)

Simple constructor. Build a one term polynomial from one coefficient and the corresponding degree.

Parameters:

d - coefficient

degree - degree associated with the coefficient

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:

n - 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:

n - 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

setCoefficient

public void setCoefficient(int n,
                           Field.Member c)

DOCUMENT ME!

Parameters:

n -

setCoefficientAsDouble

public void setCoefficientAsDouble(int n,
                                   double c)

DOCUMENT ME!

Parameters:

n -

map

public double map(double x)

Evaluates this polynomial.

Specified by:

map in interface PrimitiveMapping

Specified by:

map in class DoubleFunction

Parameters:

x - DOCUMENT ME!

Returns:

DOCUMENT ME!

See Also:

org.jscience.mathematics.analysis.IntervalList.

map

public double map(float x)

Evaluates this polynomial.

Specified by:

map in interface PrimitiveMapping

Overrides:

map in class DoubleFunction

Parameters:

x - DOCUMENT ME!

Returns:

DOCUMENT ME!

map

public double map(long x)

Evaluates this polynomial.

Specified by:

map in interface PrimitiveMapping

Overrides:

map in class DoubleFunction

Parameters:

x - DOCUMENT ME!

Returns:

DOCUMENT ME!

map

public double map(int x)

Evaluates this polynomial.

Specified by:

map in interface PrimitiveMapping

Overrides:

map in class DoubleFunction

Parameters:

x - DOCUMENT ME!

Returns:

DOCUMENT ME!

degree

public int degree()

The degree understood as the highest degree

Specified by:

degree in interface Polynomial

Returns:

the degree

getSet

public java.lang.Object getSet()

isZero

public boolean isZero()

Returns true if this polynomial is equal to zero. All coefficients are tested for |a_k| < GlobalSettings.ZERO_TOL.

Returns:

true if all coefficients < GlobalSettings.ZERO_TOL

isOne

public boolean isOne()

Returns true if this polynomial is equal to one. It is tested, whether |a_0 - 1| <= GlobalSettings.ZERO_TOL and the remaining coefficients are |a_k| < GlobalSettings.ZERO_TOL.

Returns:

true if this is equal to one.

add

public DoubleFunction add(DoubleFunction g)

The group composition law. Returns a new polynom with grade = max( this.degree, g.degree)

Overrides:

add in class DoubleFunction

Parameters:

g - a group member

Returns:

DOCUMENT ME!

differentiate

public DoubleFunction differentiate()

Differentiate the real polynomial. Only useful iff the polynomial is built over a banach space and an appropriate multiplication law is provided.

Specified by:

differentiate in interface C1Function

Specified by:

differentiate in class DoubleFunction

Returns:

a new polynomial with degree = max(this.degree-1 , 0)

scalarDivide

public Polynomial scalarDivide(Field.Member f)

return a new real Polynomial with coefficients divided by f

Specified by:

scalarDivide in interface Polynomial

Parameters:

f - divisor

Returns:

new Polynomial with coefficients /= f

Throws:

java.lang.IllegalArgumentException - DOCUMENT ME!

scalarDivide

public DoublePolynomial scalarDivide(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 DoublePolynomial integrate()

"inverse" operation for differentiate, zero degree constant set to zero

Returns:

the integrated polynomial

scalarMultiply

public Polynomial scalarMultiply(Field.Member f)

Returns the multiplication of this polynomial by a scalar

Specified by:

scalarMultiply in interface Polynomial

Parameters:

f -

Returns:

DOCUMENT ME!

Throws:

java.lang.IllegalArgumentException - DOCUMENT ME!

scalarMultiply

public DoublePolynomial scalarMultiply(double a)

Returns the multiplication of this polynomial by a scalar

Parameters:

a - factor

Returns:

new Polynomial with coefficients = a

multiply

public DoubleFunction multiply(DoubleFunction r)

The multiplication law. Multiplies this Polynomial with another

Overrides:

multiply in class DoubleFunction

Parameters:

r - a RealFunction

Returns:

a new Polynomial with grade = max( this.grade, r.grade) + min( this.grade, r.grade) -1

Throws:

java.lang.IllegalArgumentException - DOCUMENT ME!

negate

public AbelianGroup.Member negate()

Returns the inverse member. (That is mult(-1))

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate in class DoubleFunction

Returns:

inverse

subtract

public DoubleFunction subtract(DoubleFunction g)

The group composition law with inverse.

Overrides:

subtract in class DoubleFunction

Parameters:

g - a group member

Returns:

DOCUMENT ME!

toString

public java.lang.String toString()

String representation P(x) = a_k x^k +...

Overrides:

toString in class java.lang.Object

Returns:

String

toString

public java.lang.String toString(java.lang.String unknown)

String representation P(x) = a_k x^k +...

Parameters:

unknown - The name of the unkwown

Returns:

String

euclidianDivision

public DoublePolynomial[] euclidianDivision(DoublePolynomial divisor)

Perform the euclidian division of two polynomials.

Parameters:

divisor - denominator polynomial

Returns:

an array of two elements containing the quotient and the remainder of the division

toComplexPolynomial

public ComplexPolynomial toComplexPolynomial()

toExactRealPolynomial

public ExactRealPolynomial toExactRealPolynomial()

toExactComplexPolynomial

public ExactComplexPolynomial toExactComplexPolynomial()

clone

public java.lang.Object clone()

Overrides:

clone in class java.lang.Object

rootsToPolynomial

public static DoublePolynomial rootsToPolynomial(double[] roots)

roots

public Complex[] roots()

quadratic

public static Complex[] quadratic(double c,
                                  double b,
                                  double a)

cubic

public static Complex[] cubic(double d,
                              double c,
                              double b,
                              double a)