com.perisic.ring
Class IntegerRing

java.lang.Object
  |
  +--com.perisic.ring.Ring
        |
        +--com.perisic.ring.IntegerRing

public class IntegerRing

extends Ring

The ring of Integers. In essential this class wraps the java.math.Biginteger class.

Note that this class has no public constructor. The only public instance of this class is Ring.Z.

Example of use:

 import com.perisic.ring.*;
 import java.math.*;
 class IntegerRingExample { 
 public static void main(String [] args) { 
    RingElt a = Ring.Z.map("3");
    RingElt b = Ring.Z.map( new BigInteger("1000000"));
    a = Ring.Z.add(a,b);
    System.out.println("a = "+a); 
    }
}

writes "a = 1000003" to the output.
• Last Change: 13.12.2003: GPL, MC.
• Copyright:(c) Marc Conrad, 2002, 2003
• Email: ring@perisic.com. Please let me know if you use this software.
• WWW: www.ring.perisic.com
• The com.perisic.ring library is distributed under the terms of the GNU Lesser General Public License (LGPL).
• If you require the package under a different licence please contact me.
• disclaimer: The classes are provided "as is". There is no warranty implied by using the com.perisic.ring package.

Fields inherited from class com.perisic.ring.Ring

C, F2, Q, R, Z

Method Summary

RingElt	add(RingElt a, RingElt b) Returns the sum of the parameters.
RingElt	ediv(RingElt a, RingElt b) Euclidian division.
boolean	equalZero(RingElt b) Returns true if b is equals to zero, false otherwise.
RingElt	inv(RingElt b) Returns b for b == 1 and b == -1.
boolean	isEuclidian() Returns true as Z is an Euclidian ring.
RingElt	mod(RingElt a, RingElt b) Remainder of Euclidian division.
RingElt	mult(RingElt a, RingElt b) Returns the product of the parameters.
RingElt	neg(RingElt b) Returns -b as an element of this Ring.
RingElt	one() Returns 1 as an element of this Ring.
RingElt	tdiv(RingElt a, RingElt b) True division.
static java.math.BigInteger	toBigInteger(RingElt b) Returns the value of b as a BigInteger.
java.lang.String	toString() Returns "Z".
RingElt	zero() Returns 0 as an element of this Ring.

Methods inherited from class com.perisic.ring.Ring

div, eltToString, equal, evaluatePolynomial, gcd, isField, isUFD, map, map, map, map, map, pow, pow, sub

Methods inherited from class java.lang.Object

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

Method Detail

toString

public java.lang.String toString()

Returns "Z".

Overrides:

toString in class java.lang.Object

Returns:

"Z".

isEuclidian

public boolean isEuclidian()

Returns true as Z is an Euclidian ring.

Overrides:

isEuclidian in class Ring

Returns:

true.

add

public RingElt add(RingElt a,
                   RingElt b)

Returns the sum of the parameters.

Overrides:

add in class Ring

Parameters:

a - a RingElt which can be mapped to an element of this ring.

b - a RingElt which can be mapped to an element of this ring.

Returns:

a + b.

mult

public RingElt mult(RingElt a,
                    RingElt b)

Returns the product of the parameters.

Overrides:

mult in class Ring

Parameters:

a - a RingElt which can be mapped to an element of this ring.

b - a RingElt which can be mapped to an element of this ring.

Returns:

a * b.

inv

public RingElt inv(RingElt b)
            throws RingException

Returns b for b == 1 and b == -1. Otherwise throws a RingException.

Overrides:

inv in class Ring

Parameters:

b - a RingElt which can be mapped to an element of this ring.

Returns:

b^-1.

Throws:

RingException - if b is neither 1 or -1.

ediv

public RingElt ediv(RingElt a,
                    RingElt b)

Euclidian division. Performs division with remainder.

Overrides:

ediv in class Ring

Parameters:

a - a RingElt which can be mapped to an element of this ring.

b - a RingElt which can be mapped to an element of this ring.

Returns:

a/b (Euclidian division).

See Also:

BigInteger.divide(java.math.BigInteger)

tdiv

public RingElt tdiv(RingElt a,
                    RingElt b)

True division. If the division cannot be performed without remainder a RingException is thrown.

Overrides:

tdiv in class Ring

Parameters:

a - a RingElt which can be mapped to an element of this ring.

b - a RingElt which can be mapped to an element of this ring.

Returns:

a/b if b divides a.

Throws:

RingException - if b divides not a.

mod

public RingElt mod(RingElt a,
                   RingElt b)

Remainder of Euclidian division. True division. If the division cannot be performed without remainder

Overrides:

mod in class Ring

Parameters:

a - a RingElt which can be mapped to an element of this ring.

b - a RingElt which can be mapped to an element of this ring.

Returns:

a%b (remainder of Euclidian division).

one

public RingElt one()

Returns 1 as an element of this Ring.

Overrides:

one in class Ring

Returns:

1.

zero

public RingElt zero()

Returns 0 as an element of this Ring.

Overrides:

zero in class Ring

Returns:

0.

neg

public RingElt neg(RingElt b)

Returns -b as an element of this Ring.

Overrides:

neg in class Ring

Parameters:

b - a RingElt which can be mapped to an element of this ring.

Returns:

-b.

equalZero

public boolean equalZero(RingElt b)

Returns true if b is equals to zero, false otherwise.

Overrides:

equalZero in class Ring

Parameters:

b - a RingElt which can be mapped to an element of this ring.

Returns:

true if and only if b == 0.

toBigInteger

public static java.math.BigInteger toBigInteger(RingElt b)

Returns the value of b as a BigInteger.

Parameters:

b - a RingElt which can be mapped to an element of this ring.

Returns:

b as BigInteger.