com.perisic.ring
Class ModularIntegerRing

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

Direct Known Subclasses:

FinitePrimeField

public class ModularIntegerRing
extends Ring

The modular integer ring Z/nZ. This ring uses the BigInteger arithmetic of the java.math.* package and is therefore more efficient then a construction via the ModularRing class of this package

• Last Change: 13.12.2003: eltToString(), GPL.
• Last Change: 01.05.2011: fixed error in documentation.
• Copyright: (c) Marc Conrad, 2002-2011.
• 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:

0.3

Author:

Marc Conrad

Field Summary

Fields inherited from class com.perisic.ring.Ring

C, F2, Q, R, Z

Constructor Summary

ModularIntegerRing(int m)

ModularIntegerRing(java.lang.Object modulus)
Construction of Z/mZ with m = modulus.

Method Summary

RingElt	add(RingElt a, RingElt b) Returns a + b mod m.
boolean	equals(java.lang.Object ob) Two ModularIntegerRing objects are equal, if the modulus is the same.
boolean	equalZero(RingElt b) True if b == 0, false otherwise.
java.math.BigInteger	getModulus() Returns m where this ModularIntegerRing is Z/mZ.
RingElt	inv(RingElt b) Returns b^-1 mod m.
RingElt	map(RingElt a) Performs the ususal map as in Ring.map(RingElt).
RingElt	mult(RingElt a, RingElt b) Returns a * b mod m.
RingElt	neg(RingElt b) Returns -b mod m.
RingElt	one() Returns 1.
RingElt	tdiv(RingElt a, RingElt b) The same as div(a,b).
static java.math.BigInteger	toBigInteger(RingElt b) Returns the BigInteger value of b.
RingElt	zero() Returns 0.

Methods inherited from class com.perisic.ring.Ring

div, ediv, eltToString, equal, evaluatePolynomial, gcd, isEuclidian, isField, isUFD, map, map, map, map, mod, pow, pow, sub

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ModularIntegerRing

public ModularIntegerRing(java.lang.Object modulus)

Construction of Z/mZ with m = modulus.

Parameters:

modulus - An instance of a BigInteger or a RingElt which can be mapped to Ring.Z.

ModularIntegerRing

public ModularIntegerRing(int m)

Method Detail

getModulus

public java.math.BigInteger getModulus()

Returns m where this ModularIntegerRing is Z/mZ.

toBigInteger

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

Returns the BigInteger value of b. A value between 0 and m

add

public RingElt add(RingElt a,
                   RingElt b)

Returns a + b mod m.

Specified by:

add in class Ring

mult

public RingElt mult(RingElt a,
                    RingElt b)

Returns a * b mod m.

Specified by:

mult in class Ring

one

public RingElt one()

Returns 1.

Overrides:

one in class Ring

zero

public RingElt zero()

Returns 0.

Specified by:

zero in class Ring

inv

public RingElt inv(RingElt b)

Returns b^-1 mod m. b must be an unit in Z/mZ.

Overrides:

inv in class Ring

Throws:

java.lang.ArithmeticException - if b is not an unit mod m.

tdiv

public RingElt tdiv(RingElt a,
                    RingElt b)

The same as div(a,b). b must be a unit of Z/mZ.

Overrides:

tdiv in class Ring

Throws:

java.lang.ArithmeticException - if b is not a unit mod m.

neg

public RingElt neg(RingElt b)

Returns -b mod m.

Specified by:

neg in class Ring

equalZero

public boolean equalZero(RingElt b)

True if b == 0, false otherwise.

Specified by:

equalZero in class Ring

equals

public boolean equals(java.lang.Object ob)

Two ModularIntegerRing objects are equal, if the modulus is the same.

Overrides:

equals in class java.lang.Object

map

public RingElt map(RingElt a)

Performs the ususal map as in Ring.map(RingElt). In addition an element of another ModularIntegerRing M with M.modulus == this.modulus is mapped to this. (Not yet implemented: Mapping in case that this.modulus is a divisor of M.modulus. Also to do (if this makes sense): Mapping from F2Field if modulus == 2).

Overrides:

map in class Ring