org.jscience.mathematics.analysis.polynomials
Class ExactRealPolynomial

java.lang.Object
  org.jscience.mathematics.analysis.ExactRealFunction
      org.jscience.mathematics.analysis.polynomials.ExactRealPolynomial

All Implemented Interfaces:

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

public class ExactRealPolynomial
extends ExactRealFunction
implements Polynomial, java.io.Serializable, java.lang.Cloneable

A Polynomial as a Ring.Member over a realField

See Also:

Serialized Form

Field Summary

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

Constructor Summary

ExactRealPolynomial(ExactReal[] coeff)
Creates a new instance of ExactRealPolynomial, polynom is always simplified discarding every trailing zeros and array copied (but not contents of elements).

ExactRealPolynomial(ExactReal d, int degree)
Simple constructor.

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

ExactRealPolynomial(Field.Member[] f)
Creates a new ExactRealPolynomial object, polynom is always simplified discarding every trailing zeros and array copied (but not contents of elements).

Method Summary

ExactRealFunction	add(ExactRealFunction g) The group composition law.
java.lang.Object	clone()
int	degree() The degree understood as the number of coeffiecients, and therefore the highest degree is degree()-1
ExactRealFunction	differentiate() Differentiate the real polynomial.
boolean	equals(java.lang.Object o) Is this-o == Null ?
ExactRealPolynomial[]	euclidianDivision(ExactRealPolynomial divisor) Perform the euclidian division of two polynomials.
Field.Member	getCoefficient(int n) Get the coefficient of degree k, i.e.
ExactReal	getCoefficientAsExactReal(int n) Get the coefficient of degree k, i.e.
Field.Member[]	getCoefficients() Get the coefficients as an array
ExactReal[]	getCoefficientsAsExactReals() Get the coefficients as an array of ExactReals
java.lang.Object	getSet()
int	hashCode() Some kind of hashcode...
ExactRealPolynomial	integrate() "inverse" operation for differentiate
boolean	isOne() Returns true if this polynomial is equal to one.
boolean	isZero() Returns true if this polynomial is equal to zero.
ExactReal	map(ExactReal x) Evaluates this polynomial.
ExactRealFunction	multiply(ExactRealFunction r) The multiplication law.
AbelianGroup.Member	negate() Returns the inverse member.
ExactRealPolynomial	scalarDivide(ExactReal 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
ExactRealPolynomial	scalarMultiply(ExactReal 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	setCoefficientAsExactReal(int n, ExactReal c) DOCUMENT ME!
ExactRealFunction	subtract(ExactRealFunction g) The group composition law with inverse.
ExactComplexPolynomial	toExactComplexPolynomial()
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.ExactRealFunction

add, compose, divide, divide, getIntervalsList, inverse, map, multiply, setIntervalsList, 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 ExactRealPolynomial ZERO

The real polynomial representing the additive identity.

ONE

public static final ExactRealPolynomial ONE

The real polynomial representing the multiplicative identity.

Constructor Detail

ExactRealPolynomial

public ExactRealPolynomial(ExactReal[] coeff)

Creates a new instance of ExactRealPolynomial, polynom is always simplified discarding every trailing zeros and array copied (but not contents of elements).

Parameters:

coeff - DOCUMENT ME!

Throws:

java.lang.NullPointerException - DOCUMENT ME!

ExactRealPolynomial

public ExactRealPolynomial(ExactRealPolynomial polynomial)

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

Parameters:

polynomial - DOCUMENT ME!

ExactRealPolynomial

public ExactRealPolynomial(Field.Member[] f)

Creates a new ExactRealPolynomial object, polynom is always simplified discarding every trailing zeros and array copied (but not contents of elements).

Parameters:

f -

Throws:

java.lang.NullPointerException - DOCUMENT ME!

java.lang.IllegalArgumentException - DOCUMENT ME!

ExactRealPolynomial

public ExactRealPolynomial(ExactReal 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

getCoefficientAsExactReal

public ExactReal getCoefficientAsExactReal(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

getCoefficientsAsExactReals

public ExactReal[] getCoefficientsAsExactReals()

Get the coefficients as an array of ExactReals

Returns:

the coefficients as an array

setCoefficient

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

DOCUMENT ME!

Parameters:

n -

setCoefficientAsExactReal

public void setCoefficientAsExactReal(int n,
                                      ExactReal c)

DOCUMENT ME!

Parameters:

n -

map

public ExactReal map(ExactReal x)

Evaluates this polynomial.

Specified by:

map in class ExactRealFunction

Parameters:

x - DOCUMENT ME!

Returns:

DOCUMENT ME!

degree

public int degree()

The degree understood as the number of coeffiecients, and therefore the highest degree is degree()-1

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 ExactRealFunction add(ExactRealFunction g)

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

Overrides:

add in class ExactRealFunction

Parameters:

g - a group member

Returns:

DOCUMENT ME!

differentiate

public ExactRealFunction 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 ExactRealFunction

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 ExactRealPolynomial scalarDivide(ExactReal 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 ExactRealPolynomial integrate()

"inverse" operation for differentiate

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 ExactRealPolynomial scalarMultiply(ExactReal a)

Returns the multiplication of this polynomial by a scalar

Parameters:

a - factor

Returns:

new Polynomial with coefficients = a

multiply

public ExactRealFunction multiply(ExactRealFunction r)

The multiplication law. Multiplies this Polynomial with another

Overrides:

multiply in class ExactRealFunction

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 ExactRealFunction

Returns:

inverse

subtract

public ExactRealFunction subtract(ExactRealFunction g)

The group composition law with inverse.

Overrides:

subtract in class ExactRealFunction

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 ExactRealPolynomial[] euclidianDivision(ExactRealPolynomial 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

toExactComplexPolynomial

public ExactComplexPolynomial toExactComplexPolynomial()

clone

public java.lang.Object clone()

Overrides:

clone in class java.lang.Object