IntegerRing

Package

Class

Use

Tree

Deprecated

Index

Help

PREV CLASS NEXT CLASS

FRAMES NO FRAMES

SUMMARY: NESTED | FIELD | CONSTR | METHOD

DETAIL: FIELD | CONSTR | METHOD

com.perisic.ring
Class IntegerRing

java.lang.Object
  com.perisic.ring.Ring
      com.perisic.ring.IntegerRing

public class IntegerRing
extends Ring
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); 
    }
}

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.

Version:: 0.2
Author:: Marc Conrad

Field Summary

Fields inherited from class com.perisic.ring.Ring
`C, F2, Q, R`

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
`equals, 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.

Specified by:: 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.

Specified by:: 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.

Specified by:: zero in class Ring

Returns:: 0.

neg

public RingElt neg(RingElt b)

Returns -b as an element of this Ring.

Specified by:: 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.

Specified by:: 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.