Package org.jscience.mathematics.algebraic.numbers

Provides common types of numbers.

See:
Description

Class Summary

BigRational	BigRational: dynamically sized immutable arbitrary-precision rational numbers.
Boolean	The Boolean class encapsulates Boolean numbers.
ComparableNumber<T extends ComparableNumber>	This is the superclass for comparable numbers.
Complex	The Complex class encapsulates complex numbers.
Double	The Double class encapsulates double numbers.
ExactComplex	The ExactComplex class encapsulates complex numbers using ExactReals for real and imaginary part.
ExactInteger	The ExactInteger class encapsulates integer numbers with infinite precision but slower speed than Integer or Long.
ExactQuaternion	The ExactQuaternion class encapsulates quaternions.
ExactRational	The ExactRational class encapsulates rational numbers with infinite precision.
ExactReal	The ExactReal class encapsulates real numbers with infinite precision but slower speed than Float or Double.
ExactSupernumber	The ExactSupernumber class encapsulates supernumbers.
Float	The Float class encapsulates float numbers.
Integer	The Integer class encapsulates integer numbers.
Long	The Long class encapsulates 64 bits integer numbers.
Quaternion	The Quaternion class encapsulates quaternions.
RadixConverter	DOCUMENT ME!
Rational	DOCUMENT ME!
Supernumber	The Supernumber class encapsulates supernumbers.

Package org.jscience.mathematics.algebraic.numbers Description

Provides common types of numbers.

Although numbers defined in this package are not as fast as primitives types (e.g. int or double). They have many advantages (such as arbitrary size or precision) which make them irreplaceable in some calculations. This can be illustrated with the following example:

        double x = 10864;
        double y = 18817;
        double z = 9 * Math.pow(x, 4.0)- Math.pow(y, 4.0) + 2 * Math.pow(y, 2.0);
        System.out.println("Result : " + z);

        > Result : 2.0

The mathematically correct value is z=1. However, Java compilers using ANSI/IEEE double precision numbers evaluate z=2. Not even the first digit is correct! This is due to a rounding error occurring when subtracting two nearly equal floating point numbers. Now, lets write the same formula using ExactReal numbers:

        ExactReal x = new ExactReal(10864);
        ExactReal y = new ExactReal(18817);
        ExactReal z = (ExactReal) new ExactReal(9).times(x.pow(4)).plus(y.pow(4).opposite()).plus(new ExactReal(2).times(y.pow(2)));
        System.out.println("Result : " + z);

        > Result   : 1.000

Not only the correct result is returned, but this result is also guaranteed to be 1 ± 0.001 (only exact digits are written out).