Package dk.jonaslindstrom.ruffini.integers.structures

Class Integers

java.lang.Object

dk.jonaslindstrom.ruffini.integers.structures.Integers

All Implemented Interfaces:

AdditiveGroup<Integer>, CommutativeMonoid<Integer>, EuclideanDomain<Integer>, Monoid<Integer>, OrderedSet<Integer>, Ring<Integer>, Semigroup<Integer>, SemiRing<Integer>, Set<Integer>

public class Integers
extends Object
implements EuclideanDomain<Integer>, OrderedSet<Integer>

Method Summary

Modifier and Type	Method	Description
Integer	add(Integer a, Integer b)	Return the result of a+b.
Pair<Integer,Integer>	divide(Integer a, Integer b)	Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see EuclideanDomain.norm(E) for this domain.
boolean	equals(Integer a, Integer b)	Returns true if and only if a = b as elements of this set.
static Integers	getInstance()
Comparator<Integer>	getOrdering()
Integer	identity()	Return the identity element of this monoid.
Integer	multiply(Integer a, Integer b)	Return the result of the product ab in this group.
Integer	negate(Integer a)	Return -a.
BigInteger	norm(Integer a)	The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of EuclideanDomain.divide(E, E).
String	toString()
String	toString(Integer a)	Returns a human-readable string representation of an element in this set.
Integer	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.EuclideanDomain

abs, divide, divideExact, divideExact, divides, mod, mod

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

isIdentity, power

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

greaterThan, greaterThanOrEqual, lessThan, lessThanOrEqual

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

Method Details

getInstance

public static Integers getInstance()

multiply

public Integer multiply(Integer a,
 Integer b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<Integer>

identity

public Integer identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<Integer>

toString

public String toString(Integer a)

Description copied from interface: Set

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

Specified by:

toString in interface Set<Integer>

add

public Integer add(Integer a,
 Integer b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<Integer>

negate

public Integer negate(Integer a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<Integer>

zero

public Integer zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<Integer>

equals

public boolean equals(Integer a,
 Integer 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<Integer>

divide

public Pair<Integer,Integer> divide(Integer a,
 Integer b)

Description copied from interface: EuclideanDomain

Returns a pair (q, r) such that a = qb + r and 0 ≤ f(r) < f(b) where f is the Euclidean function (see EuclideanDomain.norm(E) for this domain.

Specified by:

divide in interface EuclideanDomain<Integer>

toString

public String toString()

Overrides:

toString in class Object

norm

public BigInteger norm(Integer a)

Description copied from interface: EuclideanDomain

The euclidean function is a multiplicative map that maps elements of the domain to the integers and is used in the division of EuclideanDomain.divide(E, E).

Specified by:

norm in interface EuclideanDomain<Integer>

getOrdering

public Comparator<Integer> getOrdering()

Specified by:

getOrdering in interface OrderedSet<Integer>