com.perisic.ring
Class QuotientField

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

public class QuotientField

extends Ring

A field of fractions p/q with p,q in B, where B is any Ring. Usually B is here a PolynomialRing, for example F2[t] or Z[a][b]. B must be at least an UFD.

You can use this class also to constuct a rational field Q with B = Z. For performance reasons it is recommended to use Ring.Q of type RationalField instead.

• Last Change: 16.01.2003
• Last Change: 13.12.2003: GPL.
• 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

Constructor Summary

QuotientField(Ring BaseRing)
Construction.

Method Summary

RingElt	add(RingElt a, RingElt b) Addition a + b.
RingElt	construct(RingElt numerator, RingElt denominator) Constructs numerator/denominator.
RingElt	denominator(RingElt b) Returns the denominator of b as an element of the base ring.
boolean	equalZero(RingElt b) True if b == 0.
Ring	getBaseRing() Returns the denominator and numerator ring B (the base ring).
RingElt	inv(RingElt b) Returns b^-1.
boolean	isField() Returns true.
boolean	isIntegral(RingElt b) true if the denominator is one.
static void	main(java.lang.String[] args)
RingElt	map(RingElt a) If a is an element of another QuotientRing, numerator and denominator are mapped to B.
RingElt	map(java.lang.String a) Maps the String a into this Ring.
RingElt	mult(RingElt a, RingElt b) Multiplication a * b.
RingElt	neg(RingElt b) Returns -b.
RingElt	numerator(RingElt b) Returns the numerator of b as an element of the base ring.
RingElt	one() Returns 1.
java.lang.String	toString() Returns "Quot(str)" where str = B.toString().
RingElt	zero() Returns 0.

Methods inherited from class com.perisic.ring.Ring

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

Methods inherited from class java.lang.Object

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

Constructor Detail

QuotientField

public QuotientField(Ring BaseRing)

Construction.

Method Detail

isField

public boolean isField()

Returns true.

Overrides:

isField in class Ring

getBaseRing

public Ring getBaseRing()

Returns the denominator and numerator ring B (the base ring).

numerator

public RingElt numerator(RingElt b)

Returns the numerator of b as an element of the base ring.

denominator

public RingElt denominator(RingElt b)

Returns the denominator of b as an element of the base ring.

add

public RingElt add(RingElt a,
                   RingElt b)

Addition a + b.

Overrides:

add in class Ring

mult

public RingElt mult(RingElt a,
                    RingElt b)

Multiplication a * b.

Overrides:

mult in class Ring

one

public RingElt one()

Returns 1.

Overrides:

one in class Ring

zero

public RingElt zero()

Returns 0.

Overrides:

zero in class Ring

inv

public RingElt inv(RingElt b)

Returns b^-1.

Overrides:

inv in class Ring

neg

public RingElt neg(RingElt b)

Returns -b.

Overrides:

neg in class Ring

equalZero

public boolean equalZero(RingElt b)

True if b == 0. False otherwise.

Overrides:

equalZero in class Ring

map

public RingElt map(RingElt a)

If a is an element of another QuotientRing, numerator and denominator are mapped to B. Otherwise a is mapped to B and the denominator set to 1.

Overrides:

map in class Ring

toString

public java.lang.String toString()

Returns "Quot(str)" where str = B.toString().

Overrides:

toString in class java.lang.Object

isIntegral

public boolean isIntegral(RingElt b)

true if the denominator is one.

construct

public RingElt construct(RingElt numerator,
                         RingElt denominator)

Constructs numerator/denominator.

map

public RingElt map(java.lang.String a)

Maps the String a into this Ring. This method is similar to the PolynomialRing.map(java.lang.String) method. In addition negative exponents are allowed.

Overrides:

map in class Ring

main

public static void main(java.lang.String[] args)