jsci.maths.polynomials

Class RealPolynomial

java.lang.Object

jsci.maths.analysis.RealFunction

jsci.maths.polynomials.RealPolynomial

All Implemented Interfaces:

java.io.Serializable, Ring.Member, AbelianGroup.Member, Mapping, Member, Polynomial

public class RealPolynomial
extends RealFunction
implements Polynomial

A Polynomial as a Ring.Member over a real Field

See Also:

Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
RealFunction	add(RealFunction g) The group composition law.
int	degree() The degree
RealFunction	differentiate() Differentiate the real polynomial.
boolean	equals(java.lang.Object o) Returns true if this polynomial is equal to another.
Field.Member	getCoefficient(int k) Get the coefficient of degree k, i.e.
double	getCoefficientAsDouble(int k) 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...
RealPolynomial	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.
double	map(double x) Evaluates this polynomial.
RealFunction	multiply(RealFunction r) The multiplication law.
AbelianGroup.Member	negate() Returns the inverse member.
RealPolynomial	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
RealPolynomial	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
RealFunction	subtract(RealFunction g) The group composition law with inverse.
java.lang.String	toString() String representation P(x) = a_k x^k +...

Methods inherited from class jsci.maths.analysis.RealFunction

add, compose, constant, dimension, divide, divide, inverse, multiply, subtract, taylorExpand, tensor

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface jsci.maths.fields.Ring.Member

multiply

Methods inherited from interface jsci.maths.groups.AbelianGroup.Member

add, subtract

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 k)

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 k)

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

map

public double map(double x)

Evaluates this polynomial.

Specified by:

map in interface Mapping

degree

public int degree()

The degree

Specified by:

degree in interface Polynomial

Returns:

the degree

getSet

public java.lang.Object getSet()

Specified by:

getSet in interface Member

Overrides:

getSet in class RealFunction

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 RealFunction add(RealFunction g)

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

Overrides:

add in class RealFunction

Parameters:

g - a group member

differentiate

public RealFunction 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 class RealFunction

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

scalarDivide

public RealPolynomial 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)

Returns true if this polynomial is equal to another.

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

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:

new Polynomial with coefficients *= a

scalarMultiply

public RealPolynomial scalarMultiply(double a)

Returns the multiplication of this polynomial by a scalar

Parameters:

a - factor

Returns:

new Polynomial with coefficients *= a

multiply

public RealFunction multiply(RealFunction r)

The multiplication law. Multiplies this Polynomial with another

Overrides:

multiply in class RealFunction

Parameters:

r - a polynomial

Returns:

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

negate

public AbelianGroup.Member negate()

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

Specified by:

negate in interface AbelianGroup.Member

Overrides:

negate in class RealFunction

Returns:

inverse

subtract

public RealFunction subtract(RealFunction g)

The group composition law with inverse.

Overrides:

subtract in class RealFunction

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