JSci.maths.polynomials
Class RealPolynomial

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

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

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

Method Summary

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