Java Reference
In-Depth Information
Java provides data types for integers and floating-point numbers, but not for rational num-
bers. This section shows how to design a class to represent rational numbers.
Since rational numbers share many common features with integers and floating-point
numbers, and
Number
is the root class for numeric wrapper classes, it is appropriate to define
Rational
as a subclass of
Number
. Since rational numbers are comparable, the
Rational
class should also implement the
Comparable
interface. Figure 15.8 illustrates the
Rational
class and its relationship to the
Number
class and the
Comparable
interface.
java.lang.Number
1
Rational
java.lang.Comparable<Rational>
1
Add, Subtract, Multiply, Divide
Rational
The numerator of this rational number.
-numerator: long
-denominator: long
The denominator of this rational number.
+Rational()
Creates a rational number with numerator 0 and denominator 1.
Creates a rational number with a specified numerator and
denominator.
Returns the numerator of this rational number.
Returns the denominator of this rational number.
Returns the addition of this rational number with another.
+Rational(numerator: long,
denominator: long)
+getNumerator(): long
+getDenominator(): long
+add(secondRational: Rational):
Rational
+subtract(secondRational:
Rational): Rational
+multiply(secondRational:
Rational): Rational
+divide(secondRational:
Rational): Rational
+toString(): String
Returns the subtraction of this rational number with another.
Returns the multiplication of this rational number with another.
Returns the division of this rational number with another.
Returns a string in the form “numerator/denominator.” Returns
the numerator if denominator is 1.
Returns the greatest common divisor of n and d.
-gcd(n: long, d: long): long
F
IGURE
15.8
The properties, constructors, and methods of the
Rational
class are illustrated in UML.
A rational number consists of a numerator and a denominator. There are many equivalent
rational numbers—for example,
1/3 = 2/6 = 3/9 = 4/12
. The numerator and the
denominator of
1/3
have no common divisor except
1
, so
1/3
is said to be in
lowest terms
.
To reduce a rational number to its lowest terms, you need to find the greatest common
divisor (GCD) of the absolute values of its numerator and denominator, then divide both the
numerator and denominator by this value. You can use the method for computing the GCD of
two integers
n
and
d
, as suggested in Listing 4.9, GreatestCommonDivisor.java. The numer-
ator and denominator in a
Rational
object are reduced to their lowest terms.
As usual, let us first write a test program to create two
Rational
objects and test its meth-
ods. Listing 15.12 is a test program.
L
ISTING
15.12
TestRationalClass.java
1
public class
TestRationalClass {
2
/** Main method */
3
public static void
main(String[] args) {
4
// Create and initialize two rational numbers r1 and r2
