org.jscience.mathematics.functions
Class Polynomial<R extends Ring<R>>

java.lang.Object
  javolution.context.RealtimeObject
      org.jscience.mathematics.functions.Function<R,R>
          org.jscience.mathematics.functions.Polynomial<R>

All Implemented Interfaces:

java.io.Serializable, Realtime, Immutable, GroupAdditive<Polynomial<R>>, Ring<Polynomial<R>>, Structure<Polynomial<R>>

Direct Known Subclasses:

Constant

public class Polynomial<R extends Ring<R>>
extends Function<R,R>
implements Ring<Polynomial<R>>

This class represents a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients (such as x² + x·y + 3y²).

Polynomials are characterized by the type of variable they operate upon. For example:

           Variable<Measure<?>> varX = new Variable.Local<Measure<?>>("x");
           Polynomial<Measure<?>> x = Polynomial.valueOf(Measure.valueOf(1, SI.METER), varX);
     and
           Variable<Complex> varX = new Variable.Local<Complex>("x");
           Polynomial<Complex> x = Polynomial.valueOf(Complex.ONE, varX);

are two different polynomials, the first one operates on physical measures, whereas the second operates on complex numbers.

Terms (others than ONE) having zero (additive identity) for coefficient are automatically removed.

Version:

3.1, April 1, 2006

Author:

Jean-Marie Dautelle

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class javolution.context.RealtimeObject

RealtimeObject.Factory<T extends RealtimeObject>

Nested classes/interfaces inherited from interface javolution.context.Realtime

Realtime.ObjectSpace

Method Summary

<Z> Function<Z,R>	compose(Function<Z,R> that) Returns the composition of this function with the one specified.
Polynomial<R>	compose(Polynomial<R> that) Returns the composition of this polynomial with the one specified.
Polynomial<R>	differentiate(Variable<R> v) Returns the first derivative of this function with respect to the specified variable.
boolean	equals(java.lang.Object obj) Indicates if this function is equals to the specified object.
R	evaluate() Evaluates this function using its variables current values.
R	getCoefficient(Term term) Returns the coefficient for the specified term.
int	getOrder(Variable<R> v) Returns the order of this polynomial for the specified variable.
java.util.Set<Term>	getTerms() Returns the terms of this polynomial.
java.util.List<Variable<R>>	getVariables() Returns a lexically ordered list of the variables (or arguments) for this function (empty list for constant functions).
int	hashCode() Returns the hash code for this function (consistent with Function.equals(Object).
Polynomial<R>	integrate(Variable<R> v) Returns an integral of this function with respect to the specified variable.
Function<R,R>	minus(Function<R,R> that) Returns the difference of this function with the one specified.
Polynomial<R>	minus(Polynomial<R> that) Returns the difference of two polynomials.
boolean	move(Realtime.ObjectSpace os) Moves this real-time object to the specified object space.
Polynomial<R>	opposite() Returns the opposite of this polynomial.
Function<R,R>	plus(Function<R,R> that) Returns the sum of this function with the one specified.
Polynomial<R>	plus(Polynomial<R> that) Returns the sum of two polynomials.
Polynomial<R>	plus(R constantValue) Returns the sum of this polynomial with a constant polynomial having the specified value (convenience method).
Polynomial<R>	pow(int n) Returns this function raised at the specified exponent.
Function<R,R>	times(Function<R,R> that) Returns the product of this function with the one specified.
Polynomial<R>	times(Polynomial<R> that) Returns the product of two polynomials.
Polynomial<R>	times(R constantValue) Returns the product of this polynomial with a constant polynomial having the specified value (convenience method).
Text	toText() Returns the textual representation of this real-time object (equivalent to toString except that the returned value can be allocated from the local context space).
static <R extends Ring<R>> Polynomial<R>	valueOf(R coefficient, Term term) Returns a polynomial corresponding to the specified term with the specified coefficient multiplier.
static <R extends Ring<R>> Polynomial<R>	valueOf(R coefficient, Variable<R> variable) Returns an univariate polynomial of degree one with the specified coefficient multiplier.

Methods inherited from class org.jscience.mathematics.functions.Function

divide, evaluate, evaluate, getVariable

Methods inherited from class javolution.context.RealtimeObject

export, isLocal, moveHeap, preserve, toString, unpreserve

Methods inherited from class java.lang.Object

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

Method Detail

valueOf

public static <R extends Ring<R>> Polynomial<R> valueOf(R coefficient,
                                                        Variable<R> variable)

Returns an univariate polynomial of degree one with the specified coefficient multiplier.

Parameters:

coefficient - the coefficient for the variable of degree 1.

variable - the variable for this polynomial.

Returns:

valueOf(coefficient, Term.valueOf(variable, 1))

valueOf

public static <R extends Ring<R>> Polynomial<R> valueOf(R coefficient,
                                                        Term term)

Returns a polynomial corresponding to the specified term with the specified coefficient multiplier.

Parameters:

coefficient - the coefficient multiplier.

term - the term multiplicand.

Returns:

coefficient * term

getTerms

public java.util.Set<Term> getTerms()

Returns the terms of this polynomial.

Returns:

this polynomial's terms.

getCoefficient

public final R getCoefficient(Term term)

Returns the coefficient for the specified term.

Parameters:

term - the term for which the coefficient is returned.

Returns:

the coefficient for the specified term or null if this polynomial does not contain the specified term.

getOrder

public int getOrder(Variable<R> v)

Returns the order of this polynomial for the specified variable.

Returns:

the polynomial order relative to the specified variable.

plus

public Polynomial<R> plus(R constantValue)

Returns the sum of this polynomial with a constant polynomial having the specified value (convenience method).

Parameters:

constantValue - the value of the constant polynomial to add.

Returns:

this + Constant.valueOf(constantValue)

times

public Polynomial<R> times(R constantValue)

Returns the product of this polynomial with a constant polynomial having the specified value (convenience method).

Parameters:

constantValue - the value of the constant polynomial to multiply.

Returns:

this · Constant.valueOf(constantValue)

plus

public Polynomial<R> plus(Polynomial<R> that)

Returns the sum of two polynomials.

Specified by:

plus in interface GroupAdditive<Polynomial<R extends Ring<R>>>

Parameters:

that - the polynomial being added.

Returns:

this + that

opposite

public Polynomial<R> opposite()

Returns the opposite of this polynomial.

Specified by:

opposite in interface GroupAdditive<Polynomial<R extends Ring<R>>>

Returns:

- this

minus

public Polynomial<R> minus(Polynomial<R> that)

Returns the difference of two polynomials.

Parameters:

that - the polynomial being subtracted.

Returns:

this - that

times

public Polynomial<R> times(Polynomial<R> that)

Returns the product of two polynomials.

Specified by:

times in interface Ring<Polynomial<R extends Ring<R>>>

Parameters:

that - the polynomial multiplier.

Returns:

this · that

compose

public Polynomial<R> compose(Polynomial<R> that)

Returns the composition of this polynomial with the one specified.

Parameters:

that - the polynomial for which the return value is passed as argument to this function.

Returns:

the polynomial (this o that)

Throws:

FunctionException - if this function is not univariate.

compose

public <Z> Function<Z,R> compose(Function<Z,R> that)

Description copied from class: Function

Returns the composition of this function with the one specified.

Overrides:

compose in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

that - the function for which the return value is passed as argument to this function.

Returns:

the function (this o that)

differentiate

public Polynomial<R> differentiate(Variable<R> v)

Description copied from class: Function

Returns the first derivative of this function with respect to the specified variable.

Overrides:

differentiate in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

v - the variable for which the derivative is calculated.

Returns:

d[this]/dv

See Also:

Derivative -- from MathWorld

integrate

public Polynomial<R> integrate(Variable<R> v)

Description copied from class: Function

Returns an integral of this function with respect to the specified variable.

Overrides:

integrate in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

v - the variable for which the integral is calculated.

Returns:

S[this·dv]

See Also:

Integral -- from MathWorld

plus

public Function<R,R> plus(Function<R,R> that)

Description copied from class: Function

Returns the sum of this function with the one specified.

Overrides:

plus in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

that - the function to be added.

Returns:

this + that.

minus

public Function<R,R> minus(Function<R,R> that)

Description copied from class: Function

Returns the difference of this function with the one specified.

Overrides:

minus in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

that - the function to be subtracted.

Returns:

this - that.

times

public Function<R,R> times(Function<R,R> that)

Description copied from class: Function

Returns the product of this function with the one specified.

Overrides:

times in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

that - the function multiplier.

Returns:

this · that.

pow

public Polynomial<R> pow(int n)

Description copied from class: Function

Returns this function raised at the specified exponent.

Overrides:

pow in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

n - the exponent.

Returns:

thisn

getVariables

public java.util.List<Variable<R>> getVariables()

Description copied from class: Function

Returns a lexically ordered list of the variables (or arguments) for this function (empty list for constant functions).

Specified by:

getVariables in class Function<R extends Ring<R>,R extends Ring<R>>

Returns:

this function current unset variables (sorted).

evaluate

public R evaluate()

Description copied from class: Function

Evaluates this function using its variables current values.

Specified by:

evaluate in class Function<R extends Ring<R>,R extends Ring<R>>

Returns:

the evaluation of this function.

equals

public boolean equals(java.lang.Object obj)

Description copied from class: Function

Indicates if this function is equals to the specified object.

Overrides:

equals in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

obj - the object to be compared with.

Returns:

true if this function and the specified argument represent the same function; false otherwise.

hashCode

public int hashCode()

Description copied from class: Function

Returns the hash code for this function (consistent with Function.equals(Object).

Overrides:

hashCode in class Function<R extends Ring<R>,R extends Ring<R>>

Returns:

this function hash code.

toText

public Text toText()

Description copied from class: Function

Returns the textual representation of this real-time object (equivalent to toString except that the returned value can be allocated from the local context space).

Specified by:

toText in interface Realtime

Overrides:

toText in class Function<R extends Ring<R>,R extends Ring<R>>

Returns:

this object's textual representation.

move

public boolean move(Realtime.ObjectSpace os)

Description copied from class: Function

Moves this real-time object to the specified object space.

Specified by:

move in interface Realtime

Overrides:

move in class Function<R extends Ring<R>,R extends Ring<R>>

Parameters:

os - the object space to move this real-time object to.

Returns:

true if the move has to be propagated to external real-time references; false otherwise.