Package dk.jonaslindstrom.ruffini.common.matrices.structures

Class MatrixRing<E>

java.lang.Object

dk.jonaslindstrom.ruffini.common.matrices.structures.MatrixRing<E>

All Implemented Interfaces:

AdditiveGroup<Matrix<E>>, CommutativeMonoid<Matrix<E>>, Monoid<Matrix<E>>, Ring<Matrix<E>>, Semigroup<Matrix<E>>, SemiRing<Matrix<E>>, Set<Matrix<E>>

public class MatrixRing<E>
extends Object
implements Ring<Matrix<E>>

This class represents a ring of n × n matrices over a base ring.

Constructor Summary

Constructors

Constructor	Description
MatrixRing(Ring<E> baseRing, int n)

Method Summary

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

MatrixRing

public MatrixRing(Ring<E> baseRing,
 int n)

Method Details

multiply

public Matrix<E> multiply(Matrix<E> a,
 Matrix<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 Matrix<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(Matrix<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>

equals

public boolean equals(Matrix<E> a,
 Matrix<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>

add

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

Description copied from interface: CommutativeMonoid

Return the result of a+b.

Specified by:

add in interface CommutativeMonoid<E>

negate

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

Description copied from interface: AdditiveGroup

Return -a.

Specified by:

negate in interface AdditiveGroup<E>

zero

public Matrix<E> zero()

Description copied from interface: CommutativeMonoid

Return the zero element.

Specified by:

zero in interface CommutativeMonoid<E>

toString

public String toString()

Overrides:

toString in class Object