org.spaceroots.mantissa.algebra

Class Polynomial.Rational

java.lang.Object

org.spaceroots.mantissa.algebra.Polynomial

org.spaceroots.mantissa.algebra.Polynomial.Rational

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

OrthogonalPolynomial

Enclosing class:

Polynomial

public static class Polynomial.Rational
extends Polynomial

This class implements polynomials with one unknown and rational coefficients.

In addition to classical algebra operations, euclidian division and remainder are handled.

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class org.spaceroots.mantissa.algebra.Polynomial

Polynomial.DivisionResult, Polynomial.Double, Polynomial.Rational

Field Summary

Fields

Modifier and Type	Field and Description
protected RationalNumber[]	a Coefficients array.

Constructor Summary

Constructors

Constructor and Description
Rational() Simple constructor.
Rational(long value) Simple constructor.
Rational(long a1, long a0) Simple constructor.
Rational(long a2, long a1, long a0) Simple constructor.
Rational(long a3, long a2, long a1, long a0) Simple constructor.
Rational(RationalNumber value) Simple constructor.
Rational(RationalNumber[] a) Simple constructor.
Rational(RationalNumber c, int degree) Simple constructor.
Rational(RationalNumber a1, RationalNumber a0) Simple constructor.
Rational(RationalNumber a2, RationalNumber a1, RationalNumber a0) Simple constructor.
Rational(RationalNumber a3, RationalNumber a2, RationalNumber a1, RationalNumber a0) Simple constructor.

Method Summary

Modifier and Type	Method and Description
Polynomial.Rational	add(Polynomial.Rational p) Add a polynomial to the instance
static Polynomial.DivisionResult	euclidianDivision(Polynomial.Rational dividend, Polynomial.Rational divisor) Perform the euclidian division of two polynomials.
RationalNumber[]	getCoefficients() Get the coefficients of the polynomial.
int	getDegree() Get the polynomial degree.
java.math.BigInteger	getDenominatorsLCM() Get the Least Common Multiple of the coefficients denominators.
Polynomial	getDerivative() Get the derivative of the instance with respect to the unknown.
boolean	isIdentity() Check if the instance is the identity polynomial.
boolean	isOne() Check if the instance is the constant unit polynomial.
boolean	isZero() Check if the instance is the null polynomial.
Polynomial	multiply(long l) Multiply the instance by a constant.
Polynomial.Rational	multiply(Polynomial.Rational p) Multiply the instance by a polynomial.
Polynomial	multiply(RationalNumber r) Multiply the instance by a constant.
Polynomial	negate() Negate the instance.
Polynomial.Rational	subtract(Polynomial.Rational p) Subtract a polynomial from the instance.
java.lang.String	toString() Returns a string representation of the polynomial.
double	valueAt(double x) Get the value of the polynomial for a specified unknown.

Methods inherited from class org.spaceroots.mantissa.algebra.Polynomial

divide, divide, divide, multiply

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

a

protected RationalNumber[] a

Coefficients array.

Constructor Detail

Rational

public Rational()

Simple constructor. Build a null polynomial

Rational

public Rational(long value)

Simple constructor. Build a constant polynomial

Parameters:

value - constant value of the polynomial

Rational

public Rational(RationalNumber value)

Simple constructor. Build a constant polynomial

Parameters:

value - constant value of the polynomial

Rational

public Rational(long a1,
                long a0)

Simple constructor. Build a first degree polynomial

Parameters:

a1 - leeding degree coefficient

a0 - constant term

Rational

public Rational(RationalNumber a1,
                RationalNumber a0)

Simple constructor. Build a first degree polynomial

Parameters:

a1 - leeding degree coefficient

a0 - constant term

Rational

public Rational(long a2,
                long a1,
                long a0)

Simple constructor. Build a second degree polynomial

Parameters:

a2 - leeding degree coefficient

a1 - first degree coefficient

a0 - constant term

Rational

public Rational(RationalNumber a2,
                RationalNumber a1,
                RationalNumber a0)

Simple constructor. Build a second degree polynomial

Parameters:

a2 - leeding degree coefficient

a1 - first degree coefficient

a0 - constant term

Rational

public Rational(long a3,
                long a2,
                long a1,
                long a0)

Simple constructor. Build a third degree polynomial

Parameters:

a3 - leeding degree coefficient

a2 - second degree coefficient

a1 - first degree coefficient

a0 - constant term

Rational

public Rational(RationalNumber a3,
                RationalNumber a2,
                RationalNumber a1,
                RationalNumber a0)

Simple constructor. Build a third degree polynomial

Parameters:

a3 - leeding degree coefficient

a2 - second degree coefficient

a1 - first degree coefficient

a0 - constant term

Rational

public Rational(RationalNumber[] a)

Simple constructor. Build a polynomial from its coefficients

Parameters:

a - coefficients array, the a[0] array element is the constant term while the a[a.length-1] element is the leeding degree coefficient. The array is copied in a new array, so it can be changed once the constructor as returned.

Rational

public Rational(RationalNumber c,
                int degree)

Simple constructor. Build a one term polynomial from one coefficient and the corresponding degree

Parameters:

c - coefficient

degree - degree associated with the coefficient

Method Detail

isZero

public boolean isZero()

Check if the instance is the null polynomial.

Specified by:

isZero in class Polynomial

Returns:

true if the polynomial is null

isOne

public boolean isOne()

Check if the instance is the constant unit polynomial.

Specified by:

isOne in class Polynomial

Returns:

true if the polynomial is the constant unit polynomial

isIdentity

public boolean isIdentity()

Check if the instance is the identity polynomial.

Specified by:

isIdentity in class Polynomial

Returns:

true if the polynomial is the identity polynomial

getDegree

public int getDegree()

Get the polynomial degree.

Specified by:

getDegree in class Polynomial

Returns:

degree

getCoefficients

public RationalNumber[] getCoefficients()

Get the coefficients of the polynomial.

Returns:

a copy of the coefficients array, the array element at index 0 is the constant term while the element at index a.length-1 is the leading degree coefficient

add

public Polynomial.Rational add(Polynomial.Rational p)

Add a polynomial to the instance

Parameters:

p - polynomial to add

Returns:

a new polynomial which is the sum of the instance and p

subtract

public Polynomial.Rational subtract(Polynomial.Rational p)

Subtract a polynomial from the instance.

Parameters:

p - polynomial to subtract

Returns:

a new polynomial which is the difference the instance minus p

negate

public Polynomial negate()

Negate the instance.

Specified by:

negate in class Polynomial

Returns:

a new polynomial

multiply

public Polynomial.Rational multiply(Polynomial.Rational p)

Multiply the instance by a polynomial.

Parameters:

p - polynomial to multiply by

Returns:

a new polynomial

multiply

public Polynomial multiply(long l)

Multiply the instance by a constant.

Specified by:

multiply in class Polynomial

Parameters:

l - constant to multiply by

Returns:

a new polynomial

multiply

public Polynomial multiply(RationalNumber r)

Multiply the instance by a constant.

Specified by:

multiply in class Polynomial

Parameters:

r - constant to multiply by

Returns:

a new polynomial

valueAt

public double valueAt(double x)

Get the value of the polynomial for a specified unknown.

Specified by:

valueAt in class Polynomial

Parameters:

x - value of the unknown

Returns:

value of the polynomial

getDerivative

public Polynomial getDerivative()

Get the derivative of the instance with respect to the unknown. The derivative of a n degree polynomial is a n-1 degree polynomial of the same type.

Specified by:

getDerivative in class Polynomial

Returns:

a new polynomial which is the derivative of the instance

euclidianDivision

public static Polynomial.DivisionResult euclidianDivision(Polynomial.Rational dividend,
                                                          Polynomial.Rational divisor)

Perform the euclidian division of two polynomials.

Parameters:

dividend - numerator polynomial

divisor - denominator polynomial

Returns:

an object containing the quotient and the remainder of the division

getDenominatorsLCM

public java.math.BigInteger getDenominatorsLCM()

Get the Least Common Multiple of the coefficients denominators. This number is the smallest integer by which we should multiply the instance to get a polynomial whose coefficients are all integers.

Returns:

the Least Common Multiple of the coefficients denominators

toString

public java.lang.String toString()

Returns a string representation of the polynomial.

The representation is user oriented. Terms are displayed lowest degrees first. The multiplications signs, coefficients equals to one and null terms are not displayed (except if the polynomial is 0, in which case the 0 constant term is displayed). Addition of terms with negative coefficients are replaced by subtraction of terms with positive coefficients except for the first displayed term (i.e. we display -3 for a constant negative polynomial, but 1 - 3 x + x^2 if the negative coefficient is not the first one displayed).

Overrides:

toString in class java.lang.Object

Returns:

a string representation of the polynomial