com.perisic.ring
Class UniversalRing

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

Direct Known Subclasses:

UniversalCyclotomicField, UniversalPolynomialRing

public abstract class UniversalRing
extends Ring

An abstract class for an universal ring. It can be used to implement a cyclotomic field of all unit roots (an inifinite algebraic extension) or a polynomial ring over an infinite number of variables. See the abstract method findRing(...) for details.

• Generated January 16, 2003
• 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, Z

Constructor Summary

UniversalRing()
No parameters in the constructor

Method Summary

RingElt	add(RingElt a, RingElt b) Addition.
RingElt	ediv(RingElt a, RingElt b) Euclidian division.
boolean	equalZero(RingElt b) true if b == 0.
abstract Ring	findRing() A suitable ring able to map 0 (and 1).
abstract Ring	findRing(RingElt a) A suitable ring able to map a.
abstract Ring	findRing(RingElt a, RingElt b) A suitable ring able to map a and b.
RingElt	gcd(RingElt a, RingElt b) gcd.
RingElt	inv(RingElt a) Multiplicative Inverse.
RingElt	map(RingElt a) Maps a RingElt using the findRing() method with one parameter.
RingElt	map(java.lang.String str) Maps a string to the ring obtained by findRing() without parameter.
RingElt	mod(RingElt a, RingElt b) Modular computation.
RingElt	mult(RingElt a, RingElt b) Multiplication.
RingElt	neg(RingElt b) The additive inverse of b.
RingElt	one() The 1 of the ring.
RingElt	tdiv(RingElt a, RingElt b) True division.
java.lang.String	toString()
RingElt	zero() The 0 of the ring.

Methods inherited from class com.perisic.ring.Ring

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

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

UniversalRing

public UniversalRing()

No parameters in the constructor

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

Returns:

"(unspecified) Universal Ring"

add

public RingElt add(RingElt a,
                   RingElt b)

Addition.

Specified by:

add in class Ring

Returns:

a + b.

mult

public RingElt mult(RingElt a,
                    RingElt b)

Multiplication.

Specified by:

mult in class Ring

Returns:

a * b

tdiv

public RingElt tdiv(RingElt a,
                    RingElt b)

True division.

Overrides:

tdiv in class Ring

Returns:

a / b

ediv

public RingElt ediv(RingElt a,
                    RingElt b)

Euclidian division.

Overrides:

ediv in class Ring

Returns:

S.ediv(a,b) for a suitable ring S.

mod

public RingElt mod(RingElt a,
                   RingElt b)

Modular computation.

Overrides:

mod in class Ring

Returns:

a % b

gcd

public RingElt gcd(RingElt a,
                   RingElt b)

gcd.

Overrides:

gcd in class Ring

Returns:

gcd(a,b)

inv

public RingElt inv(RingElt a)

Multiplicative Inverse.

Overrides:

inv in class Ring

Returns:

a^-1

neg

public RingElt neg(RingElt b)

The additive inverse of b.

Specified by:

neg in class Ring

Returns:

-b

one

public RingElt one()

The 1 of the ring.

Overrides:

one in class Ring

Returns:

1

zero

public RingElt zero()

The 0 of the ring.

Specified by:

zero in class Ring

Returns:

0

equalZero

public boolean equalZero(RingElt b)

true if b == 0.

Specified by:

equalZero in class Ring

Returns:

b == 0

map

public RingElt map(java.lang.String str)

Maps a string to the ring obtained by findRing() without parameter. It is recommended to override this method in order to get enhanced flexibility.

Overrides:

map in class Ring

map

public RingElt map(RingElt a)

Maps a RingElt using the findRing() method with one parameter.

Overrides:

map in class Ring

findRing

public abstract Ring findRing()

A suitable ring able to map 0 (and 1).

findRing

public abstract Ring findRing(RingElt a)

A suitable ring able to map a.

findRing

public abstract Ring findRing(RingElt a,
                              RingElt b)

A suitable ring able to map a and b.