com.dautelle.math.functions
Class Polynomial

java.lang.Object
  com.dautelle.realtime.RealtimeObject
      com.dautelle.math.functions.Function
          com.dautelle.math.functions.Polynomial

All Implemented Interfaces:

Operable, Realtime, java.io.Serializable

Direct Known Subclasses:

Constant

public class Polynomial

extends Function

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

   Polynomial x = Polynomial.valueOf(Scalar.ONE, Variable.X);

and

   Polynomial x = Polynomial.valueOf(Complex.ONE, Variable.X);

are two different polynomials, the first operates on dimensionless quantities, whereas the second operates on complex numbers.

Version:

6.0, March 17, 2004

Author:

Jean-Marie Dautelle

See Also:

Polynomial -- from MathWorld, Serialized Form

Nested Class Summary

static class

Polynomial.Term This class represents the term of a polynomial such as x·y².

Nested classes inherited from class com.dautelle.math.functions.Function

Function.Variable

Nested classes inherited from class com.dautelle.realtime.RealtimeObject

RealtimeObject.Factory

Method Summary

java.lang.StringBuffer	appendTo(java.lang.StringBuffer sb) Appends the text representation of this function to the StringBuffer argument.
Function	compose(Function f) Returns the composition of this function with the one specified.
Function	differentiate(Function.Variable v) Returns the first derivative of this function with respect to the specified variable.
boolean	equals(java.lang.Object that) Compares this polynomial against the specified object.
Operable	evaluate() Evaluates this function by replacing its variables by their current (context-local) values.
java.lang.Object	export() Exports this object out of the current pool context.
Operable	getCoefficient(Polynomial.Term term) Returns the coefficient for the specified term.
int	getOrder(Function.Variable v) Returns the order of this polynomial for the specified variable.
java.util.Collection	getTerms() Returns the terms of this polynomial.
java.util.Set	getVariables() Returns a set containing this function variables.
int	hashCode() Returns the hash code for this polynomial.
Function	integrate(Function.Variable v) Returns an integral of this function with respect to the specified variable.
Operable	opposite() Returns the additive inverse of this object.
Operable	plus(Operable o) Returns the sum of this object with the one specified.
Operable	times(Operable o) Returns the product of this object with the one specified.
java.lang.Object	toHeap() Moves this object to the heap.
static Polynomial	valueOf(Operable coefficient, Function.Variable variable) Returns an univariate polynomial of degree one with the specified coefficient multiplier.
static Polynomial	valueOf(Operable coefficient, Polynomial.Term term) Returns a polynomial corresponding to the specified term with the specified coefficient multiplier.

Methods inherited from class com.dautelle.math.functions.Function

pow, reciprocal, toString

Methods inherited from class com.dautelle.realtime.RealtimeObject

clone, isLocalObject, isPoolObject, recycle

Methods inherited from class java.lang.Object

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

Method Detail

valueOf

public static Polynomial valueOf(Operable coefficient,
                                 Function.Variable 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 Polynomial valueOf(Operable coefficient,
                                 Polynomial.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.Collection getTerms()

Returns the terms of this polynomial.

Returns:

this polynomial's terms.

getCoefficient

public Operable getCoefficient(Polynomial.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(Function.Variable v)

Returns the order of this polynomial for the specified variable.

Returns:

the polynomial order relative to the specified variable.

equals

public boolean equals(java.lang.Object that)

Compares this polynomial against the specified object.

Parameters:

that - the object to compare with.

Returns:

true if the objects are the same; false otherwise.

hashCode

public int hashCode()

Returns the hash code for this polynomial.

Returns:

the hash code value.

getVariables

public java.util.Set getVariables()

Description copied from class: Function

Returns a set containing this function variables.

Specified by:

getVariables in class Function

Returns:

the variables for this function.

evaluate

public Operable evaluate()

Description copied from class: Function

Evaluates this function by replacing its variables by their current (context-local) values.

Specified by:

evaluate in class Function

Returns:

the evaluation of this function.

appendTo

public java.lang.StringBuffer appendTo(java.lang.StringBuffer sb)

Description copied from class: Function

Appends the text representation of this function to the StringBuffer argument.

Overrides:

appendTo in class Function

Parameters:

sb - the StringBuffer to append.

Returns:

sb

plus

public Operable plus(Operable o)

Description copied from interface: Operable

Returns the sum of this object with the one specified.

Specified by:

plus in interface Operable

Overrides:

plus in class Function

opposite

public Operable opposite()

Description copied from interface: Operable

Returns the additive inverse of this object. It is the object such as this.plus(this.opposite()) == ZERO, with ZERO being the additive identity.

Specified by:

opposite in interface Operable

Overrides:

opposite in class Function

times

public Operable times(Operable o)

Description copied from interface: Operable

Returns the product of this object with the one specified.

Specified by:

times in interface Operable

Overrides:

times in class Function

compose

public Function compose(Function f)

Description copied from class: Function

Returns the composition of this function with the one specified.

Overrides:

compose in class Function

Parameters:

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

Returns:

the function (this o that)

differentiate

public Function differentiate(Function.Variable v)

Description copied from class: Function

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

Overrides:

differentiate in class Function

Parameters:

v - the variable for which the derivative is calculated.

Returns:

d[this]/dv

See Also:

Derivative -- from MathWorld

integrate

public Function integrate(Function.Variable v)

Description copied from class: Function

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

Overrides:

integrate in class Function

Parameters:

v - the variable for which the integral is calculated.

Returns:

S[this·dv]

See Also:

Integral -- from MathWorld

export

public java.lang.Object export()

Description copied from interface: Realtime

Exports this object out of the current pool context. Realtime members are exported as well (recursion). This method affects only objects belonging to the current pool context. To avoid pool depletion, a "free" object from the outer pool is moved to replace the object being exported.

Specified by:

export in interface Realtime

Overrides:

export in class RealtimeObject

toHeap

public java.lang.Object toHeap()

Description copied from interface: Realtime

Moves this object to the heap. Realtime members are moved to the heap as well (recursion). This method affects only objects belonging to a pool context (current or not).

Specified by:

toHeap in interface Realtime

Overrides:

toHeap in class RealtimeObject