Package dk.jonaslindstrom.ruffini.common.structures

Class FieldOfFractions<E>

java.lang.Object

dk.jonaslindstrom.ruffini.common.structures.FieldOfFractions<E>

All Implemented Interfaces:

AdditiveGroup<Fraction<E>>, CommutativeMonoid<Fraction<E>>, Field<Fraction<E>>, Group<Fraction<E>>, Monoid<Fraction<E>>, Ring<Fraction<E>>, Semigroup<Fraction<E>>, SemiRing<Fraction<E>>, Set<Fraction<E>>

Direct Known Subclasses:

BigRationals, Rationals

public class FieldOfFractions<E>
extends Object
implements Field<Fraction<E>>

Constructor Summary

Constructors

Constructor	Description
FieldOfFractions(EuclideanDomain<E> ring)

Method Summary

Modifier and Type	Method	Description
Fraction<E>	add(Fraction<E> a, Fraction<E> b)	Return the result of a+b.
boolean	equals(Fraction<E> a, Fraction<E> b)	Returns true if and only if a = b as elements of this set.
Fraction<E>	identity()	Return the identity element of this monoid.
Fraction<E>	invert(Fraction<E> a)	Return the inverse a-1.
Fraction<E>	multiply(Fraction<E> a, Fraction<E> b)	Return the result of the product ab in this group.
Fraction<E>	negate(Fraction<E> a)	Return -a.
Fraction<E>	reduce(E n, E d)
String	toString()
String	toString(Fraction<E> a)	Returns a human-readable string representation of an element in this set.
Fraction<E>	zero()	Return the zero element.

Methods inherited from class java.lang.Object

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

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.AdditiveGroup

doubling, isZero, scale, scale, subtract, sum

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.CommutativeMonoid

add, add

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Field

divideInt

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Group

divide

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Monoid

isIdentity, power

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Semigroup

multiply, multiply

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.SemiRing

integer, multiply, multiply

Constructor Details

FieldOfFractions

public FieldOfFractions(EuclideanDomain<E> ring)

Method Details

reduce

public Fraction<E> reduce(E n,
 E d)

invert

public Fraction<E> invert(Fraction<E> a)

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<E>

multiply

public Fraction<E> multiply(Fraction<E> a,
 Fraction<E> b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<E>

identity

public Fraction<E> identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<E>

toString

public String toString(Fraction<E> a)

Description copied from interface: Set

Returns a human-readable string representation of an element in this set.

Specified by:

toString in interface Set<E>

add

public Fraction<E> add(Fraction<E> a,
 Fraction<E> b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

negate

public Fraction<E> negate(Fraction<E> a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

zero

public Fraction<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

equals

public boolean equals(Fraction<E> a,
 Fraction<E> b)

Description copied from interface: Set

Returns true if and only if a = b as elements of this set.

Specified by:

equals in interface Set<E>

toString

public String toString()

Overrides:

toString in class Object