Package dk.jonaslindstrom.ruffini.reals.structures

Class ConstructiveReals

java.lang.Object

dk.jonaslindstrom.ruffini.reals.structures.ConstructiveReals

All Implemented Interfaces:

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

public class ConstructiveReals
extends Object
implements Field<ConstructiveReal>

The real numbers represented as constructive reals, e.g. arbitrary good binary approximations.

Constructor Summary

Constructors

Constructor	Description
ConstructiveReals()

Method Summary

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

Methods inherited from class java.lang.Object

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

ConstructiveReals

public ConstructiveReals()

Method Details

negate

public ConstructiveReal negate(ConstructiveReal a)

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<ConstructiveReal>

add

public ConstructiveReal add(ConstructiveReal a,
 ConstructiveReal b)

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<ConstructiveReal>

zero

public ConstructiveReal zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<ConstructiveReal>

invert

public ConstructiveReal invert(ConstructiveReal a)

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<ConstructiveReal>

identity

public ConstructiveReal identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<ConstructiveReal>

multiply

public ConstructiveReal multiply(ConstructiveReal a,
 ConstructiveReal b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<ConstructiveReal>

toString

public String toString(ConstructiveReal a)

Description copied from interface: Set

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

Specified by:

toString in interface Set<ConstructiveReal>

equals

public boolean equals(ConstructiveReal a,
 ConstructiveReal 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<ConstructiveReal>